MODERN - DAY MAGNET SCHOOLS AND MODERN - DAY NEEDS: ARE MAGNET SCHOOLS IMPROVING EDUCATIONAL EQUITY FOR TRADITIONALLY UNDERSERVED STUDENTS ? By Julie Christine Harris A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Educational Policy Doctor of Philosophy 2015 ABSTRACT MODERN - DAY MAGNET SCHOOLS AND MODERN - DAY NEEDS: ARE MAGNET SCHOOLS IMPROVING EDUCATIONAL EQUITY FOR TRADITIONALLY UNDERSERVED STUDENTS ? By Julie Christine Harris As the public - school student population continues to become more diverse, it becomes increasingly important to reevaluate longstanding policies that are targeted at addressing the needs of traditionally underserved students. To address t he needs of such students, many districts have turned to various school choice policies. The public educational marketplace has expanded and diversified, providing families with many different types of school choice; yet magnet schools, one of the oldest f orms of public school choice, continue to serve large numbers of students. T his study seeks to examine the funct ionality of magnet schools in new demographic, legal, and policy context s . To examine magnet schools in their modern - day context , I utilized data from Houston Independent School District (HISD) . HISD is one of the nation's largest districts, and the district has over one - hundred magnet school s and serves a large n umber of traditionally underserved students. Th e dataset from HISD is a r ich, stud ent - level, longitudinal dataset with information for over 400,000 students across seven school years (20 07/08 through 20 13/14 ). The analysis is centered on two major outcomes: integration and student achievement. I assess ed integration from magn et schools on four fronts: racial, socio - economic, linguistic, and achievement . I also used two perspectives to understand how magnet schools change the composition of schools and the district . The micro - level assessment analyzes individual participation i n choice and looks at what student and school characteristics are related to choosing a magnet school . The macro - level assessment aggregates the actions of individuals and looks at how compositions of schools and the districts change as students leave TPSs for magnet schools. I examine student achievement by looking for improvements in math and reading scores on a standardized exam . Multiple strategies are used to address the selection bias that arises from the n onrandom assignment of students, including th e use of student fixed - effects to control for time - invariant unobservable variables as well as value - added modeling to account for prior achievement in addition to time - invariant unobservables. Much of the analysis is broken down by magnet type to better u nderstand how different magnet policies influence the results. The major findings indicate magnet schools have little effect on integration of the district or on student achievement in math and reading . On average, magnet choosers are relatively advantag ed as compared to the students in the district who do not choose a magnet school. T his is reflected in the average composition of magnet schools as compared to that of TPSs. While magnet schools are more integrated than TPSs, there is little change in meas ures of segregation at the district level when looking at how segregation changes when students leave their zoned school for a nonzoned magnet school. Thus, magnet schools are moving advantaged students away from TPSs in the district. At the same time, t he student achievement analysis provides little evidence of student achievement benefits from magnet schools. Most estimates point to a null or negative effect. While the evidence for integration and studen t achievement does not point to strong benefits from magnet schools, these results need to be put into context. A limited range of student outcomes was studied here. There could be other benefits to students from magnet schools. Additionally, magnet schools are most likely reducing the flow of advantaged st udents out of the district to other schools of choice , and these students are then mix ed into schools that serve nonchoosers . Copyright by JULIE CHRISTINE HARRIS 2015 v The conclusions of this research do not necessarily reflect the opinions or official position of the Houston Education Research Consortium , Houston Independent School District , or the Institute of Education Sciences. vi To my biggest fan , my dad ; my biggest supporter , Sammy; and my biggest motivation , Declan. vii ACKNOWLEDGEMENTS This work was completed with a wide range of support, for which I am very thankful. I must first acknowledge my dissertation committee, which includes Madeline Mavrogordato, David Arsen, Joshua Cowen, and BetsAnn Smith. David and BetsAnn helped me improve the connec tion of this research to theory and practice. Joshua was a particularly helpful with designing the analysis. Finally, Madeline served as both the chair of my committee and as a mentor. Over the past few years, she has provided me with invaluable guidance , and I owe her for making it to where I am today . But for her, I would not have gained access to the data used in this study. Additionally, Madeline invested her time and energy in me and helped me transition from student to researcher. I am very grateful f or all she has done for me. I also had several sources of institutional support. The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305B090011 to Michigan State University (MSU). training program in the economics of education. I also received financial support from MSU's College of Education through research grants from the educational policy doctoral program. I would also like to thank the Houst on Education Research Consortium (HERC) and Houston Independent School District (HISD) for granting me access to the HISD dataset. Finally, I w ant to thank HERC researchers Ruth Lopez Turley and Holly Heard for their assistance with using the HISD data. I have also been blessed with a group of individuals that supported me professionally and personally, in ways that cannot be repaid. Margie Tieslau led me to MSU, and served as a mentor to me while I earned my master's degree; I will always be thankful f or this. Sarah Galey has been viii an amazing colleague and friend. I want to thank her for being there for me in ways no one else could be. My dad has always been my biggest fan. His unconditional love, support, and pride in me are very much a part of this wo r k and who I am. My husband Sammy has been the most supportive person, personally, and I would not have been able to get this far without him. From moving across the country to dealing with a very stressed out wife, his patience, love, and encouragement is unparalleled. Finally, Declan, my little boy, you motivated me to be the best version of me that I can be. I hope I make you proud. ix TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ x i i LIST OF FIGURES ................................ ................................ ................................ ..................... xi v KEY TO ABBREVIATIONS ................................ ................................ ................................ ........ x v CHAPTER 1 ................................ ................................ ................................ ................................ .... 1 INTRODUCTION ................................ ................................ ................................ ........................... 1 1.1 Research Questions ................................ ................................ ................................ .............. 4 1.2 Significance of the Study ................................ ................................ ................................ ..... 6 1.3 Overview of the Study ................................ ................................ ................................ ......... 6 CHAPTER 2 ................................ ................................ ................................ ................................ .... 8 BACKGROUND AND CONTEXT OF THE STUDY ................................ ................................ ... 8 2.1 Historical Overview of Magnet Schools ................................ ................................ ............. 8 2.2 HISD and Its Magnet Schools ................................ ................................ ............................ 14 2.3 Dataset ................................ ................................ ................................ ................................ 19 2.4 Summary ................................ ................................ ................................ ............................ 2 1 CHAPTER 3 ................................ ................................ ................................ ................................ .. 23 THEORETICAL UNDERPINNINGS OF MAGNET SCHOOLS ................................ ............... 23 3.1 Theories Supporting Magnet Schools ................................ ................................ ................ 23 3.2 Conflicts Between the Theories Behind Magnet Schools ................................ .................. 2 5 3.2.1 Residential Choice ................................ ................................ ................................ .... 28 3.2.2 Ability to Participate ................................ ................................ ................................ 30 3.2.3 Parental preferences ................................ ................................ ................................ .. 35 3.2.4 School - Level Policies ................................ ................................ ............................... 40 3.3 Controlled Choice ................................ ................................ ................................ .............. 43 3.4 Summary ................................ ................................ ................................ ............................ 45 CHAPTER 4 ................................ ................................ ................................ ................................ .. 47 ANALYSIS OF INTEGRATION FROM MAGNET SCHOOLS ................................ ................ 47 4.1 Literature Review ................................ ................................ ................................ ............... 50 4.1.1 Micro - Level Analysis of Integration from Magnet Schools ................................ ..... 50 4.1.2 Macro - Level Analysis of Integration from Magnet Schools ................................ .... 55 4.2 Contributions ................................ ................................ ................................ ...................... 59 4.3 Methods ................................ ................................ ................................ ............................. 61 4.3.1 Micro - Level Research Design ................................ ................................ ................. 62 4.3.2 Micro - Level Variables ................................ ................................ ............................. 67 x 4.3.2.1 Outcome Variables ................................ ................................ ........................ 67 4.3.2.2 I ndependent and Control Variables ................................ .............................. 68 4.3.3 Micro - Level Sample ................................ ................................ ................................ . 81 4.3.4 Macro - Level Research Design ................................ ................................ .................. 83 4.3.5 Macro - Level Variables ................................ ................................ ............................. 85 4.3.5. 1 Segregation Indices ................................ ................................ ....................... 85 4.3.5.2 School Composition Comparisons ................................ ................................ 87 4.3.6 Macro - Level Sample ................................ ................................ ................................ . 88 4.4 Results ................................ ................................ ................................ ................................ 89 4.4.1 Micro - Level Results ................................ ................................ ................................ .. 90 4.4.2 Macro - Level Results ................................ ................................ ............................... 101 4.5 Limitations ................................ ................................ ................................ ....................... 108 4.6 Discussion and Implications ................................ ................................ ............................ 110 CHAPTER 5 ................................ ................................ ................................ ................................ 1 1 3 STUDENT ACHIVEMENT IN MAGNET SCHOOLS ................................ ............................. 1 13 5.1 Literature Review ................................ ................................ ................................ ............. 115 5.2 Contributions ................................ ................................ ................................ .................... 1 2 0 5.3 Methods ................................ ................................ ................................ ............................ 1 2 2 5.3.1 Modeling Achievement ................................ ................................ ........................... 12 2 5.3.2 Analytical Plan ................................ ................................ ................................ ........ 1 2 5 5.3.3 Sample ................................ ................................ ................................ ..................... 1 2 8 5.3.4 Variables ................................ ................................ ................................ ................. 130 5.3.4.1 Dependent Variable ................................ ................................ ...................... 67 5.3.4.2 I ndependent and Control Variables ................................ .............................. 68 5.4 Results ................................ ................................ ................................ .............................. 142 5.5 Limitations and Potential Sources of Bias ................................ ................................ ....... 155 5.6 Discussion and Implications ................................ ................................ ............................ 160 CHAPTER 6 ................................ ................................ ................................ ................................ 1 64 CONCLUSION ................................ ................................ ................................ ............................ 1 64 6.1 Review of the Study ................................ ................................ ................................ ......... 164 6.1.1 Integration from Magnet Schools ................................ ................................ ........... 166 6.1.2 Student Achievement in Magnet Schools ................................ ............................... 17 2 6.1.3 Major Contribution s ................................ ................................ ................................ 174 6.2 Implications ................................ ................................ ................................ ...................... 178 6.2.1 Contextualizing the Findings ................................ ................................ .................. 179 6.2.2 Policy Implications ................................ ................................ ................................ . 1 80 6.3 Limitations and Directions for Future Work ................................ ................................ ... 183 6.4 Concluding Remarks ................................ ................................ ................................ ........ 185 APPENDIX ................................ ................................ ................................ ................................ .. 1 86 xi BIBLIOGRAPHY ................................ ................................ ................................ ........................ 2 1 3 xii LIST OF TABLES Table 2.1. Magnet Structure Types, Student Types, and Program Themes ................................ ... 1 7 Table 4.1. Description of Micro - Level Variables ................................ ................................ .......... 79 Table 4.2. Sample Construction: Micro - Level Analysis ................................ ................................ 82 Table 4.3. Disadvantaged - Advantaged Student Pairings ................................ ............................... 86 Table 4.4. Description of Macro - Level Outcome Variables ................................ ......................... 88 Table 4.5. Sample Construction: Macro - Level Analysis ................................ ............................... 89 Table 4.6. Summary Statistics by Magnet Chooser Status: Current Magnet - Choosers ................ 90 Table 4.7. Summary Statistics by Magnet Chooser Status: New Magnet - Choosers ..................... 9 1 Table 4.8. Differences in Student Background and Status Across Magnet Structure Type: Curren t Magnet - Choosers ................................ ................................ ................................ ........................... 93 Table 4.9. Differences in Student Background and Status Across Magnet Structure Type: New Magnet - Choosers ................................ ................................ ................................ ........................... 94 Table 4.10. Linear Probability Model Results for Current Magnet - Chooser Models ................... 96 Table 4.11. Linear Probability Model Results for New Magnet - Chooser Models ........................ 98 Table 4.12. Comparison of the Composition of Houston to Broader Geographic Areas ............ 102 Table 4.13. Comparison of Magnet and TPS Compositions ................................ ........................ 1 03 Table 4.1 4 . Comparison of Compositions Across Magnet Structure Type ................................ .. 1 04 Table 4.15. Segregation Indices: Enrolled School Actual vs. Zoned School Counterfactual ..... 1 05 Table 5.1. Sample Construction ................................ ................................ ................................ ... 129 Table 5.2. Exam Versions by Grade and Year ................................ ................................ ............. 1 30 Table 5.3. Description of Independent and Control Variables ................................ .................... 140 Table 5.4. D escribing Magnet Students: Summary Statistics by Magnet Student Type ......................... 1 44 xiii Table 5.5. Baseline Levels Models for Math Z - Scores ................................ ................................ 1 48 Table 5.6. Baseline Levels Models for Reading Z - Scores ................................ ................................ ... 1 48 Table 5.7. Levels Models for Math Z - Scores ................................ ................................ ..................... 151 Table 5.8. Levels Models for Reading Z - Scores ................................ ................................ ................ 1 52 Table 5.9. Value Added Models for Math Z - Scores ................................ ................................ ........... 1 53 Table 5.10. Value Added Models for Reading Z - Scores ................................ ................................ ..... 1 54 Table 5.11. Summary of Findings for Math Scores ................................ ................................ ..... 1 62 Table 5.12. Summary of Findings for Reading Scores ................................ ................................ 1 62 Table A.1. Linear Probability Model Results for Current Magnet - Chooser Outcome , Using New - Chooser Sample ................................ ................................ ................................ ........................... 1 88 Table A.2. Magnet and TPS Compositions: Weighted Averages ................................ ................ 1 90 Table A.3. Describing Magnet Students: Summary Statistics by Magnet Student Type (An alytical Sample) ................................ ................................ ................................ ................................ ........ 1 91 Table A.4. Baseline Levels Models for Math Z - Score (Full Estimates) ................................ ...... 1 93 Table A.5. Baseline Levels Models for Reading Z - Scores (Full Estimates) ................................ 1 95 Table A.6. Levels Models for Math Z - Scores (Full Estimates) ................................ ................... 1 97 Table A.7. Levels Models for Reading Z - Scores (Full Estimates) ................................ .............. 200 Table A.8. Value - Added Models for Math Z - Scores (Full Estimates) ................................ ......... 203 Table A.9. Value - Added Models for Reading Z - Scores (Full Estimates) ................................ .... 206 Table A.10. Levels Models for Math Z - Scores: Restricting Sample to Middle School and High School ................................ ................................ ................................ ................................ ........... 209 Table A.11. Levels Models for Reading Z - Scores: Restricting Sample to Middle School and High School ................................ ................................ ................................ ................................ ........... 2 1 0 Table A.12. Value - Added Models for Math Z - Scores: Restricting Sample to Middle School and High School ................................ ................................ ................................ ................................ .. 21 1 Table A.13. Value - Added Models for Reading Z - Scores: Restricting Sample to Middle School and High School ................................ ................................ ................................ ........................... 2 1 2 xiv LIST OF FIGURES Figure 3.1. The Four Pathways from Public School Choice to Student - Sorting ........................... 27 Figure 5.1. Kernel Density Plots of Math Achievem ent for Magnet Schools and TPSs .............. 1 42 Figure 5.2. Kernel Density Plots of Reading Achievement for Magnet Schools and TPS s ......... 1 43 Figure 5.3. Test Scores Before and After Magnet Entry ................................ .............................. 1 58 Figure 5.4. Test Scores Before and After Magnet Exit ................................ ................................ 1 58 Figure A. 1 . Example of a Magnet School Admissions Matrix: MS Language, 2014/15 ........................ 1 87 xv KEY TO ABBREVIATIONS AYP - Adequate Yearly Progress ELL - English Language Learner ESA - Enrolled School Actual FRPL - Free and Reduced Price Lunch HERC - Houston Education Research Consortium HISD - Houston Independent School District IB - International Baccalaureate MSA - Metropolitan Statistical Area MSAP - Magnet School Assistance Program NA - Native American SES - Socioeconomic Status STAAR - State o f Texas Assessments of Academic Readiness STEM - Science, Technology, Engineering, and Math SUS - Separate and Unique School SWAS - School - Within - A - School SWP - School - Wide Program TAKS - Texas Assessment of Knowledge and Skills TPS - Traditional Public Sc hool ZSC - Zoned School Counterfactual 1 C HAPTER 1 INTRODUCTION The demographic makeup of the United States and its public schools is dramatically changing ; as of the 2014 - 15 school year , f or the first time in U.S. history , White students account for less than half of the student population in public schools (Hussar & Bailey, 2014). In particular, t he Hispanic population in the United States has been rapidly growin g. Over half of the population increase in the United States from 2000 to 2010 was from growth in the Hispanic population (Humes, Jones, & Ramirez, 2011). It is predicted that almost one - third of the population of the United States will be Hispanic by 2050 (Shrestha & Heisler, 2011). Census data also show children are increasingly likely to be from homes that speak a language other than English; from 1980 - 2007 , the number of people who speak Spanish at home in the United States grew by 211% and the Vietname se speaking population grew by 511% (Shin & Kominski, 2010). Our public school population is also becoming poorer (NCES, 2012) ; t he proportion of students who receive free - and reduced - price lunch increased by over 10% from 2001 - 2011(NCES, 2012). Finally, it is important to note that achievement gaps have been identified for each of these growing student subpopulations (OELA, 2008; Reardon, 2011) . Along with this changing population , we have seen a paradigm shift over the last several decades in the laws an d policies that guide school choice. The first official forms of public school choice arose in response to the Brown v. Board of Education (1954) d ecision, in an attempt to address segregated schools. 1 M agnet schools and busing programs became typical 1 Brown and other segregation - related cases are discussed in more detail Chapter 2. 2 policy vehicles for districts that were required to desegregate their schools . The more recent Supreme Court ruling in Parents Involved in Community Schools v. Seattle School District No. 1 (2007) has made it more difficult to consider race when assigning student s to schools if a district is no longer under a court order to desegregate. At the same time, a ccountability has come to the forefront of policy , in the form of both high - stakes testing and school choice policy . W ith this shift in policy motivation, we have seen the rapid expansion of charter schools. When trying to attract students, magnet schools now have to compete with charter schools , and funding is more competitive . As we see shifts in the demographic , legal, and policy context s of public schools , it is unclear how older forms of school choice, such as magnet schools, are behaving in this new environment . F urther, t he demographic shift raises the importance of understanding how various policies impact traditionally underserved st udents . 2 M agnet schools were typically used to address Black - White segregation. This raises questions about how magnet schools are interact ing with the rapidly growing Hispanic population. Additionally, t he changing school - choice laws and policies raise qu estions about the effectiveness of magnet schools in this modern setting with regards to their ability to integrate . For the aforementioned reasons, I seek to examine how modern - day magnet schools are impacting traditionally underserved students . I limite d my analysis to magnet schools because they are different in nature from other typical forms of public school choice in several meaningful ways. First, any student sorting that may arise from school choice is mitigated by the design of magnet schools becau se students who choose into a magnet school are typically moved into a traditional public school (TPS) that has 2 In this study, traditionally underserved students refers to any groups of students outside of what Delpit (1988) refers to as the "culture of power" (p. 141 ). This concept is explained further in Chapter 3. 3 its own zoned student population. Compare this to charter schools where students who choose are moved into a separate school facility that only serves other choosers , thus any differences in usage and selection of charter schools across race or other background factors will necessarily result in increased segregation. Second, magnet schools have a bit of increased autonomy as compared to non magnet TPSs in areas such as curriculum and admissions policies, but they are not as autonomous as charter schools since they are still managed by the local district. Third, unlike busing programs, magnet schools offer specialized curriculum and they do not put the burden of integration on traditionally underserved racial groups . Finally, because magnet schools are still operated by the school district, this analysis will translate into something that districts can directly use to shape policy for addressing the needs of traditionally underserved racial groups. Because of these differences, magnet schools should be assessed separately from other forms of public school choice. My analysis is further limited to modern - day magnet schools because such magnets are sub stantially different in nature from their predecessors . Note I define modern - day to include two main features. First, it only include s magnet schools that do not emphasize race as a factor in student assignment. As court orders to desegregate were lifted, many districts stopped using race as a factor in student assignment. This was accelerated after Parents Involved restricted the ability of districts to use race as a factor if the district is not currently under a court order to desegregate. Thus not using race in magnet school admissions is a relatively recent trend. Magnet schools that rely on race for student assignments are not privy to many of the same student sorting mechanisms that arise from school choice; 3 th erefore , schools not using race as a fac tor in admissions should be examined separate ly from schools that do consider race . Second, 3 Note this is further explained in Section 2.1 . 4 modern - day magnet schools are part of a larger system of school choice, with a purpose that goes beyond integration. Twenty - first - century choice systems have greatl y expanded over the decades in terms of the number of students served and the types of choices available. When magnet schools are but one part of a system of choice, they are subjected to additional, competitive pressures and may not be as effective at dra wing in students from outside of the school zone and district . Additionally, the policy focus of these new forms of choice such as charter schools and online schools is no longer on integration. These demographic, l egal , and policy shifts call for a n exam ination of how modern - day magnet schools are serving traditionally underserved racial groups. 1.1 Research Questions As the composition of our nation and public schools shifts towards a higher number of students who have been traditionally underserved by schools and we continue making changes to the way public schooling is provided, questions arise about the effectivenes s of older policies in this new setting; this is especially true when such policies were designed to serve traditionally underserved students. Magnet schools, though originally designed to integrate schools, have been compromised in their ability to do so because of changing laws and increased competition. Nevertheless, magnet schools may still serve a purpose in a new setting. Magnet schools often provide services to traditionally underserved students, and such services may be associated with improved stud ent outcomes. Thus, to fully assess the effectiveness of magnet schools in addressing the needs of traditionally underserved students in a modern - day context, I designed the following line of analysis , which relies on data from Houston Independent School D istrict (HISD) : 5 1. Examination of integration: A. Micro - level analysis of integration: In a modern context, w ho chooses to participate in magnet program s ? i. A re there systematic differences across race, socio - economic status ( SES ) , English language learner ( ELL ) status, and achievement? ii. Are there differences across the various magnet structures? B. Macro - level analysis of integration: How segregated is the district, and w hat happens to the composition of the district and its schools once the actions of the individu als who participate in magnet school choice are aggregated ? i. How does the composition of Houston compare to the larger geographical are a that surround s Houston ? i. Are compositions of magnet schools different from those of TPSs? ii. Are there differences in the composition of magnet schools across magnet structure type ? iii. Does HISD's magnet program result in more or less segregation at the district level? 2. Examination of student achievement : A. Wh at types of students stand to receive benefits from magnet schools (i.e ., what types of students attend magnet schools, considering both in and out of program students, either by zoning or choice) ? B. Do magnet schools improve student outcomes as measured by math and reading scores , and are there differences across magnet stude nt type, magnet program theme, or magnet structure? 6 1.2 Significance of the Study This study offers many additions to the literature. First, I conduct ed a much needed assessment of modern - day magnet schools , which is needed because of the vastly different context magnet schools now lie within. The context of the district used in this stud y (Houston, Texas) also allows for a contribution to the literature. This study is the first of its kind to be centered in a primarily Hispanic district . The district also has one of the largest ELL population s in the country (Ruiz - Soto, Hooker, & Batalova, 2015) . As th e Hispanic and ELL population s in our public schools continue to rapidly grow, the results and implications of this study become more impo rtant and are relevant to a wider range of locales. Finally, the large size of the magnet program allow me to study details that other researchers were unable to assess. Particularly, the large number of magnet schools allows me to assess school level feat ures and magnet policies . 1.3 Overview of the Study There are five additional chapters in this dissertation. Chapter 2 offers an overview of the background and context of the study. This includes a brief history of the purpose and the laws that guide ma gnet schools and a discussion of how these things have changed over time. I also provide a description of HISD , as well as a description and brief history of its magnet program . In Chapter 3, I discuss the theory behind magnet schools. I first unpack two of the major theories that support the use of magnet schools. I go on to explain how the modern - day use of magnet schools relies on theory that may conflict with the original purpose and goals of magnet schools. Finally, I describe how the two main theori es behind magnet schools can work together even though they have the potential for conflict . 7 I divided the analysis of the two lines of research questions into two separate analysis chapter s . Chapter 4 assesses integration from magnet schools , while Chapt er 5 focuses on student achievement. Both chapters provide a review of similar studies and their shortcomings, a summary of the contributions of the analysis , an explanation of the methods I use, a description of the sample and analytical plan, a presentat ion of results, and a discussion of the implications of the findings . Finally, the dissertation concludes with Chapter 6. The conclusion chapter provides a summary of the dissertation, including a summary of the motivation, theory, methods, results , and contributions . Along with this summary , I weave together the results of the two analysis chapters in a discussion of the study's implications; as part of this, I offer advice to policymakers about how magnet school programs can be designed to be more effec tive . Because of the importance of context in this study, I also provide a summary of the important contextual information from HISD and a discussion about how the context might relate to the findings. Finally, I discuss the limitations of this study and how future work can build off of it. 8 CHAPTER 2 BACKGROUND AND CONTEXT OF THE STUDY I open this study by providing context for the analysis . This chapter begins with an overview of how magnet scho ols came about and how their place in the education system has shifted over time. I follow this with a discussion about the context of this study , HISD ; here, I include information about the district as well as its magnet schools. Finally, I describe the d ataset I use in the analysis . 2.1 Historical Overview of Magnet School s Magnet schools arose from a long line of court cases regarding segregation in public schools , beginning with Brown v. Board of Educ ation (1954) . In Brown , the Supreme Court held segregated schools were inherently unequal and therefore unconstitutional under the Equal Protection Clause of the Fourteenth Amendment. The Brown ruling blocked states and districts from establishing racially segregated schools. By 1965, 94% of Black students in the South were still in all - Black schools (Rossell, 1990). Integration was unsuccessful up to this point because the Brown decision only required the elimination of de jure segregation, and the ruling failed to give specif ic guidance towards appropriate remedies (Rossell, 1990). Because of these shortcomings, districts failed to implement strategies that moved schools towards integration (Rossell, 1990). The ruling in Green v. County School Board of New Kent County (1968) a ttempted to address the lack of 9 integration that followed the Brown decision by requiring districts to take action that actually led to more integrated schools , as opposed to simply ending de jure segregation . The Supreme Court went even further in Swann v. Charlotte - Mecklenburg Board of Educ (1971) by listing the potential remedies that are acceptable , including : racial balancing using quotas , adjusting attendance lines, and transporting (busing) students to other districts. However, t here were seve ral issues with the remedies suggested in Swann . Busing was a very unpopular option because of the inconveniences associated with it and because of remaining racism and prejudices (Rossell, 1990). Further, many of the remedies led to White flight as White parents were fearful of their children attending more integrated schools ( Frankenberg & Siegel - Hawley, 2008; Rossell, 1990). Finally, the Supreme Court determined in Miliken v. Bradley (1974) that courts could not redraw district lines unless one district directly caused the segregation of another district ; specifically, "it must be [ ] shown that there has been a constitutional violation within one district that p roduces a significant segregati ve effect in another district" ( Miliken , 1974, p. 743). Becau se of the problems associated with the use of other remedies, magnet schools gained support from both sides of the court battle, and school choice advocates pushed for their use as well (Frankenberg & Siegel - Hawley, 2008). Rossell (2005) refers to the use of magnet schools as the "nationwide experiment to integrate public schools using market - like incentives instead of court orders" (p. 44). With the assumption that parents are self - interested, magnet schools, were designed to attract White students to racially isolated schools and districts by providing specialized curriculum (Rossell, 1990; Rossell, 2005). Thus, magnet schools aim at breaking the relationship between residential segregation and school segregation (Frankenberg & Siegel - Hawley, 2008). Th e first magnet school opened in Tacoma , Washington in 1968 as a way 10 to address segregation, but the use of magnet schools did not become common until the late 1970s (Rossell, 2005). The Miliken ruling , and the unpopularity of other remedies, as well as the ir links to White flight , led to the increased reliance on magnet schools during the late 1970s ( Frankenberg & Siegel - Hawley, 2008; Rossell, 1990) . The use of magnet schools continued to spread throughout the 1980s the number of magnet schools more tha n doubled during this decade growing from roughly 1,000 to 2400 schools (Rossell, 2000). The federal government showed support for this option as well and began the Magnet School Assistance Program (MSAP) to help fund magnet schools (U.S. Department of Edu cation , 2014). Funding from MSAP peaked in 198 8 at just under $ 120 million a year (Rossell, 2005). Since then, f unding has fallen, as nominal spending has remained between $ 100 and $ 110 million per year over the last couple of decades (Rossell, 2005; U.S. Department of Education, 2013). The specifics of how magnet school programs operate vary across districts . 4 Examples of how magnet school programs may vary include whether or not students must apply to the magnet program , whether or not there is a zoned , nonprogram student population associated with the magnet school, whether or not seats are reserved for out of district students, and whether or not out of district students have to pay tuition. Whether or not the district is still under court orders to des egregate is a dramatically important contextual factor. Districts became increasingly hesitant to use race as a factor in admissions to magnet schools after the Supreme Court determined racial quotas in the college admissions process were unconstitutional in Grutter v. Bollinger (2002). T he Parents Involved ruling directly addressed the applicability of the Grutter ruling to K - 12 public school admissions in districts that are not under a court order to desegregate . Parents 4 The specifications of the HISD magnet program are provided in the next section. 11 Involved held the Grutter ruling d oes not apply to K - 12 public school admissions , but at the same time, denying a student admission to a public school because of their race , violates the Fourteenth Amendment when such a plan is not narrowly tailored in a way that support s a compelling state interest. There are a few important distinctions to make about the Parents Involved decision. First, t he ruling does not extend to districts that are still under court order to desegregate. The district that was sued in Parents Involv ed had already gained unitary status; thus, the question asked to the court was whether or not "a public school that had not operated legally segregated schools or has been found to be unitary may choose to classify students by race and rely upon that clas sification in making school assignments" ( Parents Involved , 2007, p. 701). A second distinction to make is that the ruling did not outright ban the use of race as an admissions factor. Instead, the Supreme Court was dissatisfied with the specific plan used by the district for a few reasons. First, the district had a very limited notion of diversity White versus non - White ( Parents Involved , 2007) . Second, the district did not show they could achieve their goals by using factors other than race ( Parents Inv olved , 2007) . Third, the district said it was relying on race in pursuit of racial di versity, and the Supreme Court did not find this reason compelling enough without further explanation ( Parents Involved , 2007). While Parents Involved did not ban the use of race in admissions to public schools, it made it much more difficult and risky to do so. D istricts seem hesitant to use race - based assignment policies because the ruling gave little guidance with regards to how a plan can be narrowly tailored in a manne r that would be deemed constitutional ( Siegel - Hawley & Frankenberg , 2013 ). A final distinction to make when considering the Parents Involved ruling is that districts that have gained unitary status may still be segregated. For example, HISD gained unitary status because the court determined the district 12 could no longer be blamed for the segregation that existed in the district because it was a functio n of White flight, not district policy; further, the court determined it would be too burdensome for the district to achieve integration ( Ross v. HISD , 1983). Thus, while Parents Involved makes it more difficult and risky for schools that have obtained uni tary status, such districts could still benefit from using race as a factor in student assignment ( Frankenberg & Siegel - Hawley, 2008 ) . Coinciding with this shifting legal context was a shift in the broader educational p olicy context of magnet schools . The push for high - stakes accountability and school choice became increasingly popular policy mechanism across the country during the 1990s and 2000s (Frankenberg & Seigel - Hawley, 2013) . High - stakes accountability gained a lot of momentum with the passing of t he No Child Left Behind Act of 2001 (NCLB) (Linn, 2000). Charter schools were rapidly expanding at this time as well the number of charter schools increased from 1,500 to 5,700 from 2000 - 2012 (NCES, 2014). Both policies have the underlying assumption tha t schools could be improved through accountability. NCLB relies on tests to hold schools accountable, while school choice injects accountability through competitive pressures. While t h e expansion of public school choice likely allowed magnet schools to continue serving a purpose even after the courts changed their views on the use of race in admissions , this shift in policy focus became apparent in magnet school policies (Rossell, 2005) . Frankenberg & Siegel - Hawley (2008) found a decrease in the frequency at which magnet schools reported desegregation as one of its goals. Similarly, the U.S. Department of Education conducted a series of studies on magnet schools from 1983 onward, and as t ime progressed, these studies began showing less of an interest in the integrative effects of magnet schools and more of an emphasis on academic achievement benefits (Frankenberg & Siegel - Hawley, 2008). 13 A final contextual shift to c onsider is how the dem ographic makeup of the United States has changed during the evolution of magnet schools. The Brown case centered on Black - White segregation, as did many of the Jim Crow laws. Further, the Hispanic population only accounted for roughly 2% of the total U.S. population in the 1950s(Gratton & Gutmann, 2000). Often times remedies did not appropriately handle Hispanic s tudents in the integration process. The concept of segregation was often limited in court cases and desegregation plans. Some districts had limite d concepts of integration such as White versus non - White (see e.g., Parents Involved , 2007). In HISD, Hispanics were treated as White for the purpose of integration ( Ross v. HISD , 1983). As districts were overlooking Hispanics in their integration plans, t his population was rapidly growing from 1980 to 2008, the Hispanic population increased from 6% to 15% (Aud, Fox, & KewalRamani, 2010). Trying to account for the needs of an additional group of students complicates the development of integration plans be cause districts and courts have to decide how to appropriately mix all races. Magnet schools have been a part of the U.S. educational system for several decades now, but it is clear their role in the system is changing as their context is changing . Their changing role is in response to three main things. First, the changing legal context the Supreme Court shifted its stance on the use of race in admissions to public schools. Second, policymakers are increasingly relying on various types of school choice to address educational problems of various types. Third, the demographic makeup of the United States has been shifting, adding more layers. As it becomes more difficult to integrate because of these shifts in legal, policy , and demographic co ntext, magnet schools are moving away from their original purpose of integrating TPSs towards other outcomes such as improved student achievement. 14 2. 2 HISD and Its Magnet Schools HISD is the seventh largest district in the U.S. and the largest district in Texas ( HISD Board of Education , 201 5 ). During the 20 1 3 /1 4 school year, the district operated 282 schools and served roughly 211,000 students , where 8% of the students were White, 25% were Black, and 62% were Hispanic (HISD Board of Education , 2014) . Add itionally, 35% of the district's students were ELLs and 38% were living at or below the poverty level (HISD Board of Education , 2014) . Thus, HISD serves high proportions of traditionally underserved students. Finally, t he district's passing rates for the state's assessment in math and reading tend to be below the state average (HISD Board of Education , 2014) . HISD began its magnet school program in 1975 in response to a 1970 court order to desegregate its schools (U.S. Department of Education, 2004). In t he 1950s, Texas' Constitution called for separate schools for White children, which led to the parents of a group of students filing suit against HISD in 1956 ( Ross v. Rogers , 1957). After a court battle that lasted for 25 years, the district was officiall y placed under a desegregation plan in 1970 ( Ross v. HISD , 1983). The court - approved plan included provisions for matching schools as part of a busing program and an equidistance zoning plan, where zones are drawn by using equidistance lines between school s. Several problems occurred as the district struggled to satisfy the court order. First, the district's student population shifted dramatically during the 1970s: the White student population dropped from 53.1% to 26%, the Black population increased from 3 3.5% to 45%, and the Hispanic population grew from 13.4% to 26% ( Ross v. HISD , 1983). The plan only addressed Black - White segregation ( Ross v. HISD , 1983). What is more, Hispanics were treated as White for the purpose of matching schools for busing; thus, busing mostly lead to the integration of Blacks and Hispanics (Ross v. HISD , 1983). Finally, parents were typically dissatisfied with the 15 idea of using a busing program because of the inconveniences associated with sending their children across town. Becau se of little success with integrating schools from using this plan, the magnet program was created five years later ( Ross v. HISD , 1983). The magnet program's original purpose was to "provide quality education, increase the percentage of students attendi ng integrated schools, and decrease the number of one - race schools" ( Ross v. HISD , 1983, p. 221). The district gained unitary status in 1980, but kept using magnet schools in pursuit of "educational enrichment" (U.S. Department of Education, 2006, p.1). No te that the district did not earn unitary status because the court believed it was integrated. Instead, the court found the segregated student composition does not stem from the unconstitutional segregation practiced in the past but from population changes that have occurred since this litigation commenced, and that the geography of the school district, traffic conditions, and population patterns make further efforts to eliminate all one - race schools impractical. ( Ross v. HISD , 1983, p. 218) Even after HISD gained unitary status, the district continued using race as a factor in admissions to magnet schools (Morrison, 1998). The district strived to maintain 65% Black and Hispanic representation in magnet schools (Morrison, 1998). However, in 1997after a coupl e of White students were denied admissions to two of the district's vanguard magnet programs, the district was sued for relying on race (Morrison, 1998) . The district settled with the plaintiffs, and as part of this, abandoned its racial enrollment goals ( Morrison, 1998). Currently, the district has a large number of magnet schools of various types that serve a large number of students in different ways. HISD operated 115 magnet schools during the 2013 / 14 school year. HISD operates three types of magnet school structures. What I am referring to as a magnet structure is how the magnet program is situated with respect to the TPS it is 16 associated with. Table 2.1 summarizes the three types of magnet structures in the district : school - within - a - school (SWAS), school - wide programs (SWP), and separate and unique schools (SUS) . Because of these various magnet structure types, there are also a variety of different magnet student types, which I summarize in Table 2.1. For SWAS magnet s chools, there are students that attend the magnet school, but they are not in the magnet program (nonprogram magnet students). Another type of student emerges from SWPs ; these schools have a subset of students that were zoned for the magnet program (zoned magnet students). All other magnet students had to apply to the program they attend (magnet choosers). SUSs only serve magnet choosers they have no zoned student population. HISD operates a wide variety of magnet program themes. The district breaks the t hemes up into the following categories: vanguard, Montessori, science, technology, engineering, and math (STEM), language, fine arts, college preparation, and career academies (HISD Office of School Choice , 2013). Table 2.1 provides a brief description of these various program themes. According to the data, in 2013/14, half of the students in the district attended a school that had a magnet program, and half of these students were in the magnet program either by choice or by zoning. 17 Table 2.1 . Magnet Structure Types, Student Types, and Program Themes Type Description Structure Types School - within - a - school (71) Magnet program is within a larger school. Only students who apply to the program may enroll in the program. School has a separate zoned - student population that is not part of the magnet program. Separate and unique school (12) All students are in the magnet program. There is no zoned student population for the school; all students must apply to the magnet program. School - wide progr am (32) The magnet program covers the entire school. Zoned students are included in the program, and nonzoned students may apply to the program. Student Types Nonmagnet - TPS student Student attends a TPS, and it does not have a magnet program Nonprogram magnet student Student attends a TPS that has a magnet program, but is not in the magnet program Zoned magnet - student Student is zoned for a TPS that has a magnet program, and is in the magnet program Magnet chooser Student is in a magnet program at a school they are not zoned for or attend their zoned school but are in a SWAS program that requires an application. Program Themes Vanguard ( 21 ) Vanguard programs serve students who have been identified as gifted and talented. They utilize accelerated and enriched curriculum. STEM (3 1 ) STEM programs emphasize instruction in STEM subjects. Laboratories and hands - on activities are often included. Language (7) Language programs provide students with the opportunity to learn an additional language. Table 2.1 . (cont'd) Fine & Performing Arts (27) A rts programs give students special opportunities in art, music, dance, etc. College Preparation (3) College preparation programs give students an early start with college by earning college credits while in high school. Career Academy (9) Career programs emphasize preparing students for the workforce after high school. Other (16) Many of the programs do not fit into one category neatly (e.g., Math and Music) or there are not enough schools in the category to justify having it as a separate group (e.g., Montessori). Such programs are combined into the other category. Where applicable, the number in parentheses is the number of magnet schools using this structure in 20 13/14 . Program theme descriptions were obtained from the HISD magnet catalogue, which can be retrieved for the current year from the HISD website (HISD Office of School Choice , 2013). 18 Admission s to magnet schools is open to all students in the district, as well as to students who reside outside of the district. The only exception to this is that the district does not allow students from outside the district to attend SUS magnet schools, unless the student gets approval from the superintendent ( HISD , 2015). M agnet schools are however allowed to charge tuition to students who reside outside the district (HISD Office of School Choice, 2013), and SUS programs accepting students from outside of the district are required to charge tuition (HISD, 2015) . 5 HISD also u tilizes admissions matrices to determine eligibility for the various magnet school programs ( Holly H., personal communication, July 10, 2015 ) . 6 The matrices vary slightly across magnet program theme and school level , but they all take into account certain characteristics including attendance, behavior, and performance on standardized exams ( Holly H., personal communication, July 10, 2015 ) . 7 An example matrix is provided in Figure A.1 of the Appendix. 8 When applications outnumber open spots, a lottery system is utilized. Applications are due the December before the school year for which the application is for (HISD, 2015). Up until the application process for the 2014/15 school year, all magnet school applications were completed in a hard copy format; the app lication process became available online after this (HISD, 2015) There are some other contextual factors are worth mentioning. The district provides transportation to magnet students (HISD Office of School Choice, 2013). The district also provides inform ation on its magnet schools in both English and Spanish on its website. 5 Note I do not ha ve data on which programs charge tuition. 6 Prior to the fall of 2015, t he district ma de no mention of magnet school matrices on its website or in the magn et school catalogue. This information was obtained from the Associate Director of HERC. 7 Magnet schools relying on matrices all started using the same matrix starting with application period for the 2015/16 school year (HISD, 2015). 8 Example matrix was o btained from HERC (Holly H., personal communication, July 10, 2015). 19 Information is provided regarding the types of magnet programs available, how to apply, and a list of important dates for the magnet school application process. The district also offer s a few school choice open houses every fall, where representatives are available from all magnet schools, as well as tours that are offered on a weekly basis; information regarding these opportunities is also available on the district's website in both En glish and Spanish. Finally, f unding for magnet schools is another important piece of the context to consider. Money follows students choosing a nonzoned school in the sense that all schools receive their funding primarily through per - pupil allocations (HISD Office of School Choice, 2014) . Additionally, m agnet schools receive supplemental funding on top of the per - pupil base funding that all schools receive , where up until 2014/15 the amount varied by school and was based on prior year resources and not on enrollment (HISD Hattie Mae White Educational Support Center, 2011, 2013) . 9 2 .3 Dataset The data I use for this study come from the Houston Education Research Consortium (HERC). HERC is a partnership between HISD and Rice University, and the purpose of this partnership is "to produce rigorous research for the purpose of closing the socioeconomic gaps in educational achievement and attainment in Houston " (Kinder Institute for Urban Research, 2015). 10 HERC has created a secured student - level, lo ngitudinal database that includes data from various sources on students attending an HISD - operated school. Researchers are granted access 9 Starting with the 2014/15 school year, the additional magnet funding was turned into a per - pupil allocation, where the per - pupil amount varies by magnet theme and school level (HISD Off ice of School Choice, 2014). 10 Refer to https://kinder.rice.edu/aboutherc.aspx for more information on HERC and the Kinder Institute. 20 to study the following topics, all of which are important to the district: early learning, teachers, college readiness , English learners, school choice, and over - age or retained students (HERC, 2014). HERC provides researchers access to a variety of longitudinal datasets that include both student and school level variables. The following data sources are provided: zonin g data, tax assessor data, magnet school enrollment, demographic data from the Public Education Information Management System (PEIMS), school level variables from the Common Core of Data (CCD), various testing data, and bilingual data. 11 The datasets includ e information on students who attended HISD - operated schools at some point during the 20 06/07 school year through the 20 13/14 school year; data is included for a total of 478,468 students and 338 schools, 121 of which are magnet schools. A few of the variables are not available every year. When variables I rely on are available in limited years, I make note of this in the analysis chapters when I describe the sample construction . There are several advantages to using this dataset. The large sample siz e makes it appealing for quantitative analysis. Additionally, the access to lagged data especially enhances my ability to analyze the research questions in this study. The magnet program in HISD is also well - suited for my research questions. HISD has over one - hundred magnet schools, which allows me to control for relevant school - level variables in the analysis. Beyond this, the magnet schools in HISD are what I am referring to as modern - day as HISD no longer considers race as part of admissions and the magn et schools in HISD are part of a much larger system of choice that includes charter schools, specialty prog rams, virtual schools, and intra district transfers. The final advantage of the dataset lies in the context of HISD. This study would be the first, ye t much 11 Specific variables are discussed in Chapters 4 and 5. Available testing data is described in Chapter 5. 21 needed magnet school study that is conducted in a primarily Hispanic school district. The only other studies that examine Hispanic participation in magnet schools rely on datasets that have small Hispanic populations, such as the study conducted in Connecticut (Cobb, Bifulco, & Bell, 2011) and the study conducted in Nashville (Haynes, Phillips, & Goldring, 2010). This does not tell us anything about how magnets fare in contexts that have had a longstanding, sizeable Hispanic population. Nor does it g uide us in the future as other districts begin to see larger proportions of Hispanic students. I also include supplemental data from the U.S. Census Bureau. The American Community Survey is implemented by the Census Bureau on an annual basis to collect a variety of data on the population of the United States (U.S. Census Bureau, 2015). I obtained demographic information from 2013 on the populations of Houston, Harris County (the county that houses Houston), and the Houston metropolitan statistical area (M SA). The data I include describe the proportion of the population in each racial group , the proportion of the population that has a high school diploma, the proportion with a college degree, as well as the median household income. 2.4 Summary The poli cy, legal , and demographic context that surrounds magnet schools has changed dramatically since their first use in the late 1960s. While magnet schools were first created to integrate schools, Parents Involved made it more difficult to consider race as an admissions factor , thereby making it harder for magnet schools to integrate. Add itionally, as magnet schools have become part of a larger system of choice, their focus has shifted away from integration, toward s providing options and improving student achievement through school choice and high 22 stakes accountability . Finally, the Hispanic population has been rapidly growing since the 1960s, and integration policy has often overlooked this group. The magnet scho ols in HISD have seen all of these shifts in context . The creation of a magnet school program in HISD followed court ordered desegregation . T he district is no longer under court order to desegregate, and is thus subject to the ruling in Parents Involved . T he district no longer considers race as an admissions factor for its magnet schools. Additionally, the district's Hispanic population has seen dramatic growth. The major shifts in the context of magnet schools call into question the ir effectiveness in a mo dern - day setting. HISD is an appropriate context to study this question in because it has seen all of these major shifts in context. 23 CHAPTER 3 THEORETICAL UNDERPINNINGS OF MAGNET SCHOOLS As explain ed in the previous chapter, magnet schools were originally designed to integrate schools, but their role in the education system is shifting over time. With this shift is a shift in the theory that is relied on to justify the use of magnet schools to improve the education of traditionally underserved students. While both of these theories are used to justify the use of magnet schools , they are based off of quite different assumptions and may not necessarily be compatible with one another. This chapter briefly outlines the two main theories behind magnet schools, how they are at odds with one another, and how they can work together. 3.1 Theories Supporting Magnet Schools What Orfield (2013) refers to collectively as "i ntegration theory " lies behind the use of magnet schools as they were originally envisioned (p. 38) . 12 Integration theory points to the importance of integration for a few main reasons. First, when schools are segregated, certain schools end up with high concentrations of stu dents who are more costly to educate , such as students living in poverty and students with limited English proficiency (Orfield, 2013) . Additionally, h igh concentrations of such students are linked to a variety of negative school attributes such as high teacher turnover and less experienced teachers (Orfield, 2013) . Also , the importance of peer composition with respect to student achievement is also well known ( see e.g., 12 Orfield (2013 ) came up with the term "integration theory" to summarize the body of literature that points towards the use of integration for improving educational and societal outcomes (p. 38). He is referring to theories such as conditions theory (Allport,1958) and pe rpetuation theory (Crain & Wells, 1994). 24 Hanushek, Kain, Markman, & Rivkin, 2003; Hoxby & Wiengarth, 2006). Finally, using a s ocietal perspective, integration theory calls for the integration of schools to combat the structural and institutional racism that is reinforced by our schooling system (Orfield , 2013). I t is believed student sorting , in and across schools , reinforces wha t Delpit (1988) calls, the "culture of power," which she explains as "the culture that maintains power economic power, status power, any of the kinds of power that you can imagine in a society" (p. 141). Integration of schools is therefore needed t o curt ail this reinforced cycle, to widen access to the culture of power , and to build a society that not only tolerates, but embraces multiculturalism, both of which act to end cultural stratification (Orfield, 2013). Thus integration theory views magnet school s as a tool that can be used to combat the stratification of our society across racial , cultural, socio - economic, and linguistic lines and reduce the inequities that are linked to such stratification . Additional justification s for magnet schools comes from economic theory, specifically, the market model. The market model was first applied to the education realm in the form of school choice by Friedman (1962) , who advocated heavily for the use of a voucher system for schooling . Friedman (1962) saw the government run monopoly over public schooling as a n unnecessary restriction on freedom. In a competitive market, the demand side can put pressure on suppliers to innovate and provide more options to choose from, which allows for mor e specialized forms of education and gives parents more control over the education of their children (Brandl, 2010; Friedman, 1962). Other arguments in favor of s chool choice point to getting rid of the monopoly on education to improve schools through the competition - based incentives of a marketplace (see e.g., Brandl, 2010; Chubb & Moe, 1990 ). The thinking here is that i f competition enters the market for public schooling through school choice policies , 25 competition will create pressure on suppliers in the market to behave efficiently and respond to consumer demand (Friedman, 1962) . Others have argued for the application of the market model to schooling because removing the government run monopoly would reduce union power (Chubb & Moe, 1990) and decrease bur eaucracy (Brandl, 2010; Chubb & Moe, 1990) . Finally, Brandl (2010) refers to competition as "the institutionalization of countervailing powers" and points towards the need of competition as a means of checking self - interests (p. 47). When the government op erates a monopoly, there is no check on those who are in control, and they are free to seek their own self - interests , which are often not aligned with the goals of the public (Brandl, 2010) . Importantly, i ntegration theory and the market model can both be used to support the use of magnet schools to attain equitable outcomes for traditionally underserved students. Integration theory aims to reduce inequities by addressing the problems associated with segregated schools (Orfield, 2013) . Magnet schools can w ork towards integration if they can draw in advantaged students, as they were designed to. At the same time, proponents of school choice that rely on the market model for justification also point to school choice as a way to attain equity by providing choi ces to those who have traditionally not had them through other mechanisms such as choosing a private school or exercising residential choice (Friedman, 1962) . 3. 2 Conflicts Between the Theories Behind Magnet Schools Although integration theory and the market model are both relied up on to advocate for the use of magnet schools to improve outcomes for traditionally underserved students, there also seems to be a n inherent conflict between them. This conflict arises because t he goals of and assumptions behi nd the theories are different . Integration theory takes a societal perspective, and 26 pushes for the integration of schools in the name of social justice. Market theory on the other hand is used in an attempt to enhance the freedom of ind ividual s and to corr ect the assumed inefficiencies that arise from not having a free market for education. Friedman (1962) acknowledged how market theory could clash with the goals of integration theory: " [ g ] iven greater freedom about where to send their children, parents of a kind would flock together and so prevent a healthy intermingling of children from decidedly different backgrounds" (p. 92). But he goes on to say, "it is not at all clear that the stated results would follow" (p. 92). T here is now well over a decade of research on the effects of school choice policies on student sorting across race, SES, and achievement, and the results are concerning. Research has identified what I refer to as the four pathways from public school choice to student sorting : residential segregation, different parental preferences , different ability to navigate choice, and school - level , choice - related policies ; t he pathways are summarized in Figure 3.1 . These pathways to student - sorting arise when there are systematic differen ces in the ways individuals participate in choice across race, SES, and achievement; thus, when these deci sions are aggregated, students end up sorted along these lines. T hese sorting pathways can occur before, during, and after participating in official p ublic school choice. 13 13 Here, official public school choice means some form of public school choice that involves selecting a public school by means other than selecting a residency. Figure 1 shows the point at which these different path ways occur during the choice process. 27 Note that I am discuss ing sorting from public school choice as opposed to simply sorting from magnet schools. I do this for a couple of reasons. A lot of this literature is based off of charter school studies, and the theories used to explain what is happening often apply to the magnet school setting as well. Second, there is a lack of studies on the pathways to student sorting using magnet schools. I believe attention shifted towards studying charter schools once they began rapidly expanding. Additionally, magnet schools were created to address the first pathway to student sorting, so decades ago it may have seemed out of place to study how magnet schools might lead to student sorting as opposed to integration. How ever, as the policy and legal context s have shift ed towards magnet schools operating as part of a system of public school choice as opposed to part of an integration plan , the sorting effects from magnet schools become more of a concern. This section sum marizes the research on these four pathways and their corresponding student sorting. Note that there are two articles that accomplish similar tasks with older studies . Residential Ability to Parental School - level choice participate preferences policies Concern: Who has access to this type of choice? Result: Inter district and intra - district segregation of public schools. Concern: Can parents use public school choice equally well? Result: Across school segregation (TPS versus school of choice). Concern: Do preferences differ across parents in a systematic way? Result: Across school segregation (across schools of choice). Concern: Do certain magnet program designs fail to integrate schools? Result: Within school segregation. Figure 3.1. The Four Pathways from Public School Choice to Student - Sorting Before official During official choice During & after choice official choice 28 Smrekar (2011) reviews the literature on parental preferences and ability to navigate ch oice. 14 This review also includes some of the research on private forms of choice. Teske and Schneider (2001) conducted a far more broad review of older research on school choice, including discussions on student outcomes from schools of choice, parental sa tisfaction and parental involvement. 15 3. 2 .1 Residential Choice The first pathway to student sorting is through unequal access to choice of school through unequal access to choice of residency. 16 Choice of residency is linked to segregation in public schools because location of residency is immediately tied to public school assignment. Further, w ith residential choice, we see the ability to choose is directly related to income as income increases, so does the choice set . What is more, as differences in income arise across race , choice sets are then also different on average across race. Barrow (2002) found evidence of this when examining school choices of Black families; in this study, the examination first pointed towards Black families placing a low er valuation on school quality, but in actuality, this result was found to be an artifact of White communities being unavailable to Black families because of income disparities. When those who have a larger choice set also base their decisions, at least in part, on racial and/or SES composition of the school, school choice through selection of residency will result in segregated schools. Holme (2002) studied what she refers to as the "unofficial" market for public schools school choice via residential cho ice (p. 177). Through interviews with 14 Note, Smrekar(2011) does not use the pathway setup I have created, instead she divides the literature into how and why parents choose schools. 15 Part of their work overlaps with the current discussion. They included research regarding parent values and use of information, which overlaps with the second and third pathways. 16 See Denton (1995) for theoretical perspectives on the links between residential and school segregation. 29 mostly white, upper - middle - class parents who used residential choice to select a school for their child, Holme (2002) found that because these parents relied on race and class as proxies for school quality, they chose schools in a manner that resulted in sorting by race and class. 17 Research has found a strong link between residential segregation and school segregation , and the link seems to be growing over time (Frankenberg, 2013a) . Using nationally representative data from 2000 - 2010, Frankenberg (2013a) examined the link between residential segregation and school segregation and found it increased over this decade. Reardon and Yun (2005) found the same results when studying schools in the South during 1990 - 2000. The ac countability movement is partially to blame for this, as evidence suggests accountability measures are linked to housing prices thereby making it more difficult for low - income families to attend high - performing schools (Figlio & Luca s , 2004). W hile residen tial segregation is still an issue and its link to school segregation is strengthening , it seems to be declining over time (Frankenberg, 2013a). It is also worth mentioning Frankenberg (2013a) concluded Black - White residential segregation has been and cont inues to be worse than Hispanic - White residential segregation (Frankenberg, 2013a). S everal authors have raised concerns about both racial and SES , inter district segregation when assessing the segregating effects of schools of choice and when considering how to effectively integrate schools. Using Common Core Data from states in the South, Reard on and Yun (2005) found inter district segregation in the South could e xplain almost 75% of the variation in school segregation during the years of their study (1990 - 2000). Frankenberg, Lee, and Orfield (2003) analyzed over three decades worth of data (late 1960s to 2000) to follow segregation in schools over time and emphasi zed in their conclusion the importance of 17 Additional evidence of preferences for c ertain racial and/or SES compositions is provided in the section on parental preferences, section 3.1.3. 30 addressing inter district segregation if we hope to integrate our schools. Similar conclusions were reached by examining dat a from Cleveland (Greene, 2005) and Philadelphia and Houston (Yancey & Saporito, 1995). 3. 2 .2 Ability to Participate The second source of student sorting through public school choice mechanisms stems from differing ability levels of pare nts when it comes to participating in school choice systems. Utilizing school choice in a manner other than simply choosing where to live takes resources such as time and information sources. Access to resources traditionally differs across different demographics, and such differences could lead to sorting in schools of choice. Research has analyzed the import ance of information in the choice process. Dougherty et al. (2013) examined the decision - making process for parents choosing a school by holding informational workshops and conducting interviews with some of the parents. They found roughly two - thirds of pa rents change their mind when given additional information. Marschall (2000) assessed the importance of information by surveying both choosers and non - choosers. Using regression techniques to control for other relevant variables, Marschall (2000) found p are nts were more likely to choose if they identified themselves as having "enough information" or if they had lived in the district for a longer period of time (p. 345). 18 Schneider, Teske, Marshall, and Roch (1998) wanted to see whether or not school choice c an operate effectively even without high levels of information available to parents. The ir theory behind this is that so 18 Here, the author relied on a survey question that asked parents whether or not they felt they had "enough information" about the schools in the distr ict when they enrolled their child. It is not clear where the parents got their information from or which information they relied on. The districts under analysis both had outreach and advertising programs in place. Two separate variables were utilized to try to capture other sources of information: church attendance was used as a proxy for the extent of the social network within the community and length of residency in the district was used as a proxy for familiarity with the district's schooling options. 31 long as there is at least an informed sub - group of parents, this could be enough to drive the demands of the rest of the parents and th us effectively shape the competitive market of schooling (Schneider et al., 1998) . The authors compared what parents said they wanted, using survey data, to what they actually chose (Schneider et al., 1998). They did in fact find a connection between what less - informed parents wanted from a school and what they chose, but this connection was weaker than it was for the more informed parents (Schneider et al., 1998) . Studies have also examined how access to information varies across demographic factors. Schn eider and Buckley (2002) used an internet search system to examine how parents navigate the choice process, and what their preferences are. They found there was generally a higher level of education associated with the ability to use the internet site (Sch neider & Buckley, 2002) . Neild (2005) interviewed low - income parents who were attempting to navigate the choice system in Philadelphia and concluded parents want information, but they often do not have essential information such as program quality data . Hi gh - income parents on the other hand, were found to use more information, and they use more formal sources such as test scores and school visits as compared to low - income parents (Smrekar & Goldring, 1999). Teske, Fitzpatrick, and Kaplan (2006) moved beyond whether or not there is an information gap to examining how large the information gap is by using survey data, and they found the gap not to be very large , as low - income parents reported feeling well - informed; h owever, these findings did not hold for pare nts who were extremely low - income. Note that because these are self - reported information - levels, this does not necessarily describe what the actual information gap looks like. While access to information is important on its own, how information is used m atters too. Interview data shows parents are not able to use district materials on schools of choice in the same way, and such diverging uses lead to inequities (Andre - Bechely, 2004; 2005). Specifically, 32 Andre - Bechely (2004) found minorities and immigrants had greater difficulty navigating magnet school brochures and application procedures. He concluded that as choice processes have become more textually based, such processes "further [privilege] the material, social, cultural, and linguistic capital of som e families over others" (Andre - Bechely, 2004, p. 314). This could partially explain why low - income parents and Black parents more frequently report ed having access to a counselor or information center would benefit them as compared to higher - income and Whi te parents, respectively (Teske, Fitzpatrick, & Kaplan, 2007). 19 Additionally, Dougherty et al . (2013) found the prior educational context of the parent's child was related to how data on schools is used . 20 Such contextual importance could easily result in s tudent sorting by race or other demographic factors that are also related to race. In addition to knowing information is important in the choice process, researchers have examined how choosers get their information , and many studies have pointed to the im portance of social networks (see e.g., Bell, 2009a; Smrekar & Goldring, 1999). By interviewing upper - middle - class parents who chose a school through buying a home, Holme (2002) found heavy reliance on social networks for information related to schools ; ver y little of the information parents had came from firsthand sources . Additionally, the parents in this study mostly used the opinions of people they viewed as being of "high - status," and opinions regarding quality typically came in the form of a school bei ng considered "good or bad" as opposed to more substantial information about a particular school (p. 189). Similarly, Smrekar and Goldring (1999) found social networks to be the most important source of information . D ifferences in the 19 This study only sampled low - and moderate - income parents, so it is not clear what high - income parents would report on this question. 20 The authors do not give any more detailed information on what differences emerge, but the existence of such difference s is enough to cause concern since such differences could lead to student sorting. 33 importance of social networks appear when looking at extremely low - income parents however (Teske et al., 2007). Teske et al. (2007) found that for those who were surveyed and reported a family income of $20,000 or less per year, social networks became less important; instead, parents from this group relied more on teachers than they did on friends , family or other parents. The authors posit this is because these parents believe they can get better information from teachers who have college degrees than they can from their social network (Teske et al., 2007). Bell (2009a) also found differences when comparing the types of schools different types of parents were referred to by their social networks, and middle - class parents received better referrals in the for m of schools that were more frequently non - failing or selective. Social networks have been linked to the choice set of parents , and there are important differences in social networks when looking across demographic factors . T hrough interviews with parent s, Bell (2007) describes how the social network of the parents in her study was important for making certain choice options available. The social network becomes more impo rtant for parents who are concerned about transportation (Bell, 2007). Additionally, low - income parents reported attempting to fill in gaps in their information with their social network (Neild, 2005). At the same time, there are differences in what information is available through a person's social network. Haynes et al. (2010) note that Hispanics in particular had very limited access to people with information on magnet schools. Smrekar (2011) points to how the network makeup is changing and how this results in inequities a s parents are spending rel atively more time at work, the portion of their social network from the workplace becomes increasingly important for gathering information regarding schools (Smrekar, 2011) . As employees are segregated in the workforce by factors such as place of residence and education level, social networks and information pools are also segregated (Smrekar, 2011). Smrekar and Goldring 34 (1999) point to the importance of information being distributed by the district because of the limited social networks of low - SES parents. Several studies have looked for evid ence of differences in ability to participate by examining which factors are related to participation in choice. By estimating the probability of choosing a school, researchers have found a higher probability of attending a charter school was associated wi th being Black (Bifulco, Ladd, & Ross, 2009a), having a college educated parent (Bifulco, Ladd, & Ross, 2009a; 2009b), and higher income (Saporito, 1998), as compared to Whites, parents with no college experience, and lower income parents. Instead of compa ring choosers to non - choosers, Haynes and colleagues (2010) looked at magnet school applicants and compared background factors across race to see if Hispanic magnet school applicants in Nashville were somehow different from Black and White applicants. Hisp anics were on average more highly educated than their Black and White applicant peers. This is perhaps evidence of additional hurdles for Hispanics in the choice process that education is somehow able to help with. It is important to notice how ELLs in pa rticular are at a major disadvantage with regards to the ability to participate in school choice. As ELLs are typically non - White and tend to come from poor and uneducated homes (Capps, Fix, Murray, Ost, Passel, & Herwantoro, 2005), all of the sorting by r ace and SES affects the ELL community disproportionately. For example, just from the tendency of this group to be low - SES, we see things like reduced access to information and a higher need for schools that provide transportation. Also, parents of ELLs typ ically do not speak fluent English either; thus, navigating the choice system can be especially difficult and isolating for them. Their ability to use common information sources such as websites and their access to social network resources can be severely limited, especially with regards to gathering 35 information on schools (Haynes et al, 2010; Valdés, 1996). We also see immigrant ELLs tending to live in segregated communities (Iceland &Scopilliti, 2008; Jacobs, 2013a), which limits the diversity of their so cial networks. Lastly, it seems reasonable to believe parents who are undocumented immigrants may be fearful of participating in school choice. 3. 2 .3 Parental preferences The third pathway to student sorting arises from preferences differing across demographics. If parents make choices based on preferences, and preferences differ across race or SES, school choice will result in student sorting . The research on this topic ca n be divided into two types. The first group of studies is based off of interviews and surveys. The results of this ty pe of study tell us about the stated preferences of parents, which may or may not align with their actual behavior. The second group of st udies look at what or how parents actually choose, using statistical methods to work backwards to show us their revealed preferences. This latter group is based off of purely quantitative studies, while the former is a mix of qualitative and quantitative r esearch. I will also discuss a couple papers that combine these two types of studies by looking at whether or not stated preferences match reveled preferences (Stein, Goldring, & Cravens, 2011; Weiher & Tedin, 2002). Th e rest of this section is devoted to discussing the findings of the literature on parental preferences as it relates to student sorting. Researchers have found proximity of the school to be important to parents, though the relative importance level of proximity varies across demographics (se e e.g., Kleitz, Weiher, Tedin , & Matland, 2000). Bell (2007; 2009a; 2009b) points towards the importance of context with regards to what schools a parent considers and what geographical preferences a parent has. For example, preferences for proximity were dependent on factors such as access to carpools, flexible work schedules, and the number of siblings that also have to be taken to school as well 36 as where those schools are located (Bell, 2007; 200 9b ). What is more, the importance of proximity may mean fac ing tradeoffs between distance and quality, and the likelihood of facing such a tradeoff varies by demographic factors (Bell, 2007; Hastings et al., 2008). Hastings et al. (2008) found evidence of this when comparing Black and White families; because of di fferences in what schools were near the home, Black families faced a tradeoff between proximity and academic quality that their White counterparts did not face (Hastings et al., 2008). Finally, it is important to point out that the preference for proximity leads to student sorting because of residential segregation (Jacobs, 2013b). Closely related to proximity, transportation is also important to parents . Further, schools of choice do not always provide transportation, yet low - income parents are more reliant on it. Even if transportation is provided, it may be overly burdensome to use. When transportation is a concern or issue for a parent, the choice set of that parent is limited (Bell, 2007). Andre - Bechely (2007) highlights some of these concerns in interviews with low - income mothers. Safety of the area becomes a concern when a child has to wait at bus stops, or when using public transportation, both of which impact low - SES parents more heavily (Andre - Bechely, 2007). Findings from survey and interview data suggest transportation is more of a concern for low - SES parents and minorities (Goldring & Smrekar, 1999; Hastings, Kane, & Staigner, 2008). When parents have preferences for proximity and transportation, their choice sets are limited accordingly. This limitation is reinforced by the high costs associated with moving, which is the only way to open up more options without sacrificing proximity. Parents might prefer certain schools but lack access to them .Bifulco and Ladd (2006) found evidence of this when using charter school, student - level , longitudinal data from North Carolina. They found Whites and Blacks moving to schools that are comprised of more students of their own race as 37 compared to the TPS they moved from. However, preferences were the cau se of this only for Whites Blacks would prefer more integrated schools (40 - 60% Black), they are just not readily available. 21 Using data from charter schools in Washington D.C., Jacobs (2013b) explicitly examined the relationship between preferences for p roximity and segregation in schools and found de facto residential segregation and the strong preference for proximity resulted in segregated charter schools. Many researchers have asked whether or not race itself is a consideration for parents in the cho ice process. If preferences for race vary by race, choice would result in segregated schools of choice and TPSs. A concern arises when examining racial preferences, as honesty becomes an issue. Weiher and Tedin (2002) compared the revealed and stated prefe rences of parents regarding racial composition and found Whites had a same race preference, but this preference only appeared once they examined the revealed preferences, it was not a stated preference (Weiher & Tedin, 2002). Because of concerns regarding ho nesty on this topic, the majority of studies addressing this issue examined this topic by looking at revealed preferences instead of stated preferences (see e.g., Bifulco & Ladd, 200 6 ; Henig, 1990; Lankford& Wyckoff, 2000; Saporito, 2003) . These s tudies have found minority families preferred schools that were predominately minority (Hastings, Kane, & Staiger, 2008; Henig, 1990), while White families avoided such schools even when controlling for other relevant factors ( Bifulco, Ladd & Ross, 2007 ; Bifulco, Ladd & Ross, 2009 b ; Lankford & Wyckoff, 2000; Saporito, 1998; Saporito, 21 In other words, Black parents are often faced with a tradeoff if they wanted to use a school of choice, it will typically end up being more segregated than their assigne d public school, as more integrated schools of choice are not located nearby because of residential segregation. 38 2003 ). 22 The specific findings of Saporito and Lareau (1999) are alarming they found White families picking schools that are inferior on measures such as safety and test scores in favor of schools that are more White. However, this study did not account for choice sets in any way . Holme (2002), who relied on stated preferences, found upper - middle - class parents had race preferences because they used race as a proxy for school quality. There are different explanations for same - race preferences. 23 It is believed Whites use racial composition of schools as a p roxy for school quality (Hamilton & Guin, 2005; Holme, 2002; Saporito, 1998). Additionally, cultural values were found to be more important than test scores to Blacks and Hispanics, which results in them seeking out schools that have students who are cultu rally similar to their child (Weiher & Tedin, 2002). This means racial minorities must face a tradeoff research has found minorities often have to choose between being part of the ethnic majority and academic quality (Hastings, Kane, & Staiger, 2008). To put it differently, they often have to choose between having a school environment that accepts and reflects their own culture and attending an integrated school, which often have more resources (e.g., lower teacher turnover, more qualified teachers, etc.) . The importance of cultural values to minority groups is a direct source of student sorting (Bulman, 2004). P references about academic characteristics of schools are another potential source of student sorting . Using regression techniques to l ook at rev ealed preferences using data from Washington D.C. , Jacobs (2013b) found parents do not pick a school based on test scores , instead proximity and language homogeneity was important . Stated preferences tell a different story Smrekar and Goldring (1999) con cluded academic reputation is more important to high - 22 These studies controlled for a variety of variables including peer composition of the students' zoned school, students' achievement, distance to zoned school, distance to other types of schools to capture the choice set, etc. 23 Theories behind racial preferences are more formally discussed in Chapter 4. 39 SES parents than it is to low - SES parents. Stein, et al. (2011) examined both stated and revealed preferences of parents who enrolled their child in an Indianapolis charter school. They found parents who said academics were important to them were not making decisions that matched this stated preference (Stein et al., 2011) . Less than a third of the parents in the study moved their child to a school that was meeting AYP , and many parents even sent their ch ild to a school that was performing worse than their current school (Stein et al., 2011) . Weiher and Tedin (2002) found similar results when comparing stated and revealed preferences of parents in Texas , however they did not control for the choice set in a ny way . Note that the reason behind the discrepancy between revealed and stated preferences is unclear parents could be using different measures for academic quality, or it may not truly be a top priority to them. Finally , researchers have found parents having preferences for other things such as safety and discipline, and again these preferences differ across demographic factors. Hispanics actually rated discipline as the most important factor in one study (Weiher & Tedin, 2002), and Blacks have been found doing the same (Haynes et al. 2010). Similarly, i nterviews found minori ties and low - SES parents valued safety more than their corresponding counterparts (Kleitz, et al., 2000). We see these patterns bec ause of residential segregation Whites a nd high - SES families tend to live in better areas that have less crime and thus do not need to prioritize safety . To summarize the empirical findings of work on parental preferences, most preferences differ across demographic characteristic s. First and foremost, (same) race appears to be a preference for all races, though the evidence on non - Whites is more mixed. Additionally, because of residential segregation, and the importance of proximity, there are differences in choice sets across demographics. Fi nally, c ulture, safety, discipline, proximity and transportation are less important to White and high - SES families . All of this translates into different types of 40 families facing different decisions from different choice sets, which results in student sort ing by race and SES. 3. 2 .4 School - Level Policies The fourth and final pathway to student sorting arises from school - level policies. For magnet schools, the type of magnet program structure employed is an important school - level policy . Some magnet programs enroll all choosers, while others enroll a mix of choosers and non choosers. Those that mix choosers and non choosers may mix them at the school level , like SWPs do, where every student who attends the school is in the magnet program. Alternatively, SWAS program s may isolate magnet students from the general student population because only part of the student population is in the magnet program . Some researchers have raised concerns about SWAS programs. Bush, Burley, and Causey - Bush (200 1) examined a SWAS program and found that while the school appeared integrated, looking within the school told a different story ; the classes were racially segregated, and segregation kept students from better classes, better faculty, and college preparati on. Additionally, students not in the magnet program had teachers with lowered expectations who sometimes voiced their frustration with having to teach non magnet students. In a similar ethnographic study, Staiger (2004) examined a gifted magnet school prog ram in California. The author found the magnet program limited interactions between magnet and non - magnet students, and it worked to exclude non - White students from the gifted and talented program (Staiger, 2004) . In doing so, the magnet program created th e idea of "whiteness as giftedness" ( Staiger, 2004, p. 161). In contrast to these two studies, a nationally - representative, quantitative study found more positive results for Hispanic students , as advanced classes became more accessible to them in magnet s chools than they were in TPSs (Davis, 2012). It appears some magnet school programs may be more cap able of integrating than others. 41 Additional research in this area is needed so we can better understand how magnet schools result in student sorting within s chools. Schools can create admissions policies that are more favorable for certain students. For example, certain magnet schools may require things of their applicants such as a minimum grade point average, or they may have multiple dimensions to the admis sions decision such as recommendations or interviews. Such requirements are often linked to different resources that may be more easily accessed by certain demographics than others (Siegel - Hawley & Frankenberg, 2013; Smrekar & Goldring, 1999). Similarly, c harter schools have been found using admission policies to prune their student - body compositions, and such pruning leads to student sorting (see e.g., Arsen, Plank, & Sykes, 1999). The evidence on cream - skimming is mixed. Bifulco, Ladd, and Ross (2009a; 20 09b) used data from one district and found high achievers were more likely to opt out for a magnet school or transfer to another TPS, providing evidence of creaming. Schools of choice can avoid certain groups of students by failing to provide services they want or need, and there is an incentive to do this when such students are more costly to educate. 24 This higher cost becomes a major concern in today's high - stakes educational accountability context . The difficulty of educating ELLs is particularly worrisome to schools because NCLB requires schools to track the progress of ELLs separately from the general student population (NCLB, 2002). Further, ELLs traditionally perform worse on standardized 24 While I only discuss ELLs here, a lot of this discussion of high - need students applies equally well to the special education student population. However, I do not include special education students as a group of interest for the purposes of analysis. I ex clude them because of the lack of achievement data for much of this student group and because the integration literature that I rely on does not speak to the integration of special education students; such a discussion is quite different from the discussio ns surrounding the integration of students by race, SES, achievement, and ELL status. For this reason, I do not emphasize the previous literature on sorting by special education status. 42 exams for a wide variety of reasons. 25 More troubling is the fact that many schools use reclassification policies that rely on proficient test scores of some kind (Abedi, 2004) . 26 Thus by definition, the ELL subgroup is comprised of students who are performing po orly on standardized tests (Abedi, 2004). Schools may fear educating these students, as they will be held accountable for their failure. It is also possible that choice programs were simply not designed with high - need students in mind. In fact, magnet schools were designed to attract typically White, high - SES students. M agnet school curriculum may not be designed in a way that is easily taught to ELLs . Or, there could be conflicts that arise from trying to provide ELL services and the specialized curric ulum of the magnet program. The result here would be that these schools are relatively less appealing to ELLs than they are to non - ELL s. T he limited supply of schools for these students results in more concentrated populations of them in TPSs . What is more , t here are additional concerns that are raised when ELLs are segregated, and even more troubling is the fact that all four pathways lead to the segregation of ELLs. When ELLs are segregated residentially and through the inequities of the choice process, t he schools that have to educate these consolidated groups of ELLs are left with a large burden because of the low - SES associated with these students as well as the generally higher degree of difficulty that goes along with educating students who are not fl uent in English (Jacobs, 2013a). DeCohen (2005) found almost 70% of ELL students were served by 10% of the nation's schools. Linguistic isolation adds another layer of complexity it becomes harder to learn English when there is little opportunity to have informal interactions with native English speakers (Jacobs, 25 For an explanation of the various reasons that lead to an achieveme nt gap on performance exams between ELLs and non - ELLs, refer to Abedi and Gandara (2006). 26 It is hard to speak more generally about the reclassification of ELLs because such policies are determined at the state, and district level. 43 2013a). The net consequences are not clear however since there could actually be benefits associated with the grouping of ELLs. For example, there is evidence such schools may have better resourc es, training, and infrastructure to educate ELLs (De Cohen, 2005). There is evidence of the sorting of ELLs across schools. ELLs were found to be significantly underrepresented in the charter schools of New York City (Buckley & Sattin - Bajaj, 2011), Texas ( Fusarelli, 2000), Massachusetts (META, 2009), and Washington D.C. (Jacobs, 2013a). Additionally, the ELLs who were enrolled in Massachusetts charter schools tended to be further along in their English proficiency than those in TPSs (META, 2009). Studies on magnet schools and other public choice options found similar results. Moore and Davenport (1990) looked at enrollment rates across the different high school types in New York City, Philadelphia, Chicago, and Boston. They found ELLs were overly represented in the non - selective low - income high schools. Nationally, ELLs were present in magnet schools at two - thirds of the district average rate (Blank et al.,1996) . As a final note on the pathways to student sorting, it is possible that these pathways can interact with one another, or create feedback. For example, if school officials know preferences vary by demographics, they may adjust school - level policies to attract certain types of students. Such manipulations then worsen the segregation caused by diff erent preferences. 3. 3 Controlled Choice Sorting from public school choice arises from both supply - and demand - side issues. T he market model relies on informed consumers to drive the demand side that then puts pressure on schools to act efficiently and i nnovatively. On the supply side t he market - model does not consider what happens when some students go un - served by schools of choice ; the emphasis 44 seems to be more on creating competitive pressures than equitably serving students . There is nothing in the m arket model that says there will be a supplier for every consumer, as some business ventures are simply unprofitable. In the previous section, I discuss ed the negative incentives suppliers have when it comes to educating high - need students in some policy e nvironments . While laws may prevent public schools from turning high - need students away, schools of choice have not put effort i n to attracting these students. For ELLs in particular, schools of choice can easily avoid them by hiding behind the language bar rier. Markets tend to leave high - need students with few options, which leaves them congested in overburdened TPSs. This supply issue can be extended to situations where residential segregation has consolidated students living in poverty such students are more costly to educate, which limits the supply to this group of students. There are a couple of things happening on the demand side as well. In the previous section, I detailed the many ways there are restrictions on the flow of information and how such restrictions vary across demographic factors. These differences limit the effectiveness of the demand side and result in sorting of students across demographic factors. The individualistic nature of the market model also fails to consider how preferences a nd choice sets of parents will result in sorting across demographic factors and why such sorting is harmful. In the previous section, I noted how preferences differ across race and SES. Different preferences often arise out of different needs, and racial a nd ethnical minorities often face tradeoffs White parents do not have to face. Because such students tend to be have higher needs and are thus more costly to educate, the market for schooling that is available to them is limited. Schools that may be profit able in well - to - do neighborhoods may not be profitable in the inner city. Further, the tradeoffs these parents face lead to academic quality not always being the first p riority when 45 choosing a school. The limitations on supply from higher costs to educate, coupled with t hese differences in preferences lead to sorting, and such sorting reinforces the system that led to sorting in the first place. Both the supply - and demand - side issues can be addressed thro ugh controlled choice policies. Integration theory posits there is room for school choice in the integrati on process, but it must be controlled thro ugh policy (Orfield, 2013). The specifics of how school choice policy should be implemented in a manner that integrates schools rely heavily on the local context. Berkeley Unified School District offers a good example of how a voluntary, controlled choice plan can both work to integrate and provide good options to residents as to not cause White - flight ( Frankenb erg, 2013b). 27 Importantly, Berkeley 's voluntary plan was held up as constitutional after the Parents Involved ruling (Frankenberg, 2013b). 3 . 4 Summary To summarize, integration theory and market theory can both be used to justify the use of magnet schools to serve traditionally underserved students , but a t the same time, the two theories have different assumptions and focuses. Integration theory focuses on the importance of diversity in schools, while market theory accentuates reducing government co ntrol on education. Because the foci are different, they may not necessarily be working towards the same goals. Market theory relies on individuals who are acting in their own self - interest. What is more, self - interests do not always align with what is bes t for society. Researchers have uncovered ample evidence of how self - interests in the market for education result in student sorting, and these sorting processes can be grouped into four categories: differences in access to residential choice, 27 I do not discuss the specifics of the plan, as BUSD is not used in this study and the design and effectiveness of its plan are highly contextual. 46 differing ab ilities to participate in choice, different preferences, and differences in school - level policies. While magnet schools were created to address the first pathway to student sorting, they are now part of the larger system of public school choice that lead t o the other three pathways to student sorting. It is clear from this literature that a pplying the market model in an uncontrolled manner results in a series of inequities thrust upon students who are already disadvantaged. Such inequities can be seen in the unequal ability to participate in school choice, the differing choice sets of parents, and the resulting student sorting by race, SES, and high - need status. ELLs seem to be particularly at risk of facing obstacles when it comes to utilizing a system of choice. School choice policies that address the supply - and demand - side issues with uncontrolled choice c an howev er work towards goals of diversity. Importantly, magnet schools have more school - level policies they can manipulate that are directly related to the ability to integrate than other types of public schools. For example, as previously mentioned, the magnet school structure is quite important with respect to the ability to integrate. With this in mind, magnet schools can still be a viable policy to ol for integrating schools in a modern - day context. 47 CHAPTER 4 ANALYSIS OF INTEGRATION FROM MAGNET SCHOOLS This chapter examines integration from the magnet school program in HISD. Segregation is still a relevant problem in today's schools. White students are still the most likely to attend schools where they are part of the majority , leaving Black students to be more integrated with the increasing Hispanic population (Aud , et al., 2010). Integration theory supports integration across race, SES, a nd achievement on two fronts (Orfield, 2013). 28 For traditionally underserved students, integration can allow them to have access to the better teachers and better resources that are found in schools they do not typically have access to (Orfield, 2013). The benefits go beyond this however, otherwise we could simply focus on equalizing resources across schools. Researchers have linked student performance to that of the students ' peers, even af ter controlling for the student s ' individual characteristics (see e .g., Hanushek et al. , 2003). 29 Additionally, segregated schools block underserved racial groups from the benefits that go along with being in the culture of power (Delpit, 1988). More privileged students stand to benefit from integration as well as it expos es them to and familiarizes them with other cultures, and such exposure is needed to succeed in an increasingly multicultural world as exposure lessens ignorance and prejudice and increases tolerance (Allport, 1958; Killen, Crystal, & Ruck, 2007; Orfield, 2013). Magnet schools were originally created to address segregation in public schools, but their policy and legal context has changed dramatically since their inception. The Parents Involved 28 Orfield (2013) uses integration theory to refer to theories that relate to how integration improves educational and social outcom es (see e.g., Allport, 1958). 29 Peer effects are discussed more in Chapter 5. 48 ruling made it harder to address segregation in schools in dist ricts that are not under a court order to desegregate. Additionally, magnet schools are part of a larger system of choice that has moved away from being concerned with integration towards holding schools accountable and providing parents with options outsi de of their zoned traditional public school. Along with this shifting paradigm there has been a shift in the student population to one that is more diverse, and it is no longer clear how magnet schools are impacting traditionally underserved students. Int erdistrict residential segregation also lower s the effectiveness of magnet schools when it comes to their ability to integrate schools. R esidential segregation by race and SES is often quite severe, especially in metropolitan areas. For example, in HISD du ring 20 13/14 , 87 % of the students were Hispanic or Black and 38 % were living at or below the poverty line . Unless HISD is able to draw in substantial numbers of students from outside the district, it may be hard for the district to integrate along certain racial and SES lines. Drawing in students from outside the district can be difficult when the district has to compete with high performing suburban schools and a growing number of schools of choice. Cur rent HISD policy allows magnet schools to charge tuiti on to students who live outside the district (HISD Office of School Choice, 2013) ; this policy may need to be reassessed if the district wants to better address segregation. Additionally, as detailed in Chapter 3, there is ample evidence that systems of pu blic school choice often result in student sorting (see e.g., Smrekar, 2011; Teske & Schneider, 2001). Integration efforts can be thwarted when magnet schools rely on the choices of parents instead of on student assignment based on race or SES . To explore integration in HISD from magnet school s, I utilize two perspectives. I use a micro - level perspective to understand individual behavior and a macro - level perspective to see what happens in the aggregate when there are patterns in who participates in the mag net school 49 program. More specifically , my research questions use two perspectives to answer the following questions: 1. Micro - level analysis of integration: In a modern context, who chooses to participate in magnet programs? A. Are there systematic differences across race, SES, ELL status, and achievement? B. Are there differences across the various magnet structures? 2. Macro - level analysis of integration: How segregated is the district, and w hat happens to the composition of the district and its schools once the ac tions of the individuals who participate in magnet school choice are aggregated ? A. How does the composition of Houston compare to the larger geographical are a that surround s Houston? B. Are compositions of magnet schools different from those of TPSs? C. Are there differences in the composition of magnet schools across magnet structure type? D. Does HISD's magnet program result in more or less segregation at the district level? I begin this chapter by review ing studies o n integration from magnet schools . I then point out the many gaps in this body of literature, and I provide a summary of the contributions of this work . Next, I explain how I assess integration from both a micro - and macro - level . Finally, I present the results of my analysis and discuss their implications and limitations. 50 4 . 1 Literature Review Chapter 3 provided a review of the literature on the pathways to student sorting from public school choice , whereas this section focuses on , and provides more details for, the studies that examine integration or sorting from magnet schools. The analyses from these studies can be divided into two types: micro - and macro - level analyses. I use the term micro - level analysi s to describe the group of studies that focus es on indivi dual behavior and looks for patterns in behavior . These studies typically look for differences in who chooses a magnet school , differences in who chooses different types of magnet schools, and differences in what types of schools lose students to magnet schools. Such studies are looking for patterns that lead to student sorting. As opposed to looking for signs of the pathways th at lead to student sorting, m acro - level studies focus on the aggregate of individual behaviors and go straight to evaluating whether or not student sorting occurs . This is typically accomplished by comparing various segregation indices. This section provid es a review of previous studies that have utilized micro - and macro - analyses that to examine integration from magnet schools. 4.1.1 Micro - Level Analysis of Integration from Magnet Schools Several studies have looked for evidence of the pathways to stude nt sorting in districts that utilize magnet schools. However, research on outcomes from magnet schools seemed to peak in the 1990s. After this, attention shifted towards the rapidly growing charter school sector. Because of this , most magnet school outcome studies rely on data from the 1980s and 1990s, which makes these studies less relevant in the current policy, legal, and demographic context. I will limit my discussion to the handful of studies that analyze contexts that have at least one 51 modern feature (e.g., race is not considered as a factor in admissions to magnet schools ). 30 The methods for these studies vary as do the types of data they rely on. Further, the contexts of the magnet schools in these studies are quite different . Because of the importance of context with respect to magnet school outcomes, when able to, I describe the magnet school policies of the studies along with their methods and results. Bifulco et al. (2007) relied on data from Durham , North Carolina from the 2002 - 03 school year to examine what factors are related to the likelihood of choosing a nonzoned public school. The district had a variety of public school choice options available including magnet schools, open enrollment, year - round schools, and charter schools. Thus the analysis wa s not limited to magnet school choosers. Specifically, the authors looked for differences between the types of students who opt out of their zoned school and those who do not. The dependent variable was a binary in nature and indicated wheth er or not the student chose a magnet school. The authors included several independent variables in their analysis including whether or not the parent had a college education , the student's own achievement, the zoned school 's percentage of Black students and students with college educated parents, and the average distance to the three nearest schools. They also included measures of distance to the nearest schools that have substantially different compositions than the student's zoned school. 31 The authors r an separate models for each B lack - White and college/no - college combination because they had different hypotheses regarding preferences for racial composition of the school. 32 The models were 30 Refer to Chapter 1 for a discussion on how modern - day magnet school is defined. 31 One variable was included for distance to nearest school with a racial composition that has mor e students of the same race as the student, and a separate variable was included to capture difference in SES composition. The authors considered substantially different to mean a 15% increase in same race composition and a 10% difference in percent of stu dents with college educated parents. 32 Racial preference hypotheses are explained more formally in Section 4.3.7. 52 estimated separately for elementary and middle school because in D urham, there were a lot of differences in context across school level that influence the likelihood of choosing. 33 The total sample of students included in the various models was 14,919 students. The results i ndicated higher performing students were more li kely to enroll in magnet schools at the middle school level, though the authors did not rely on lagged achievement, so it is possible the scores are higher because of the magnet schools. Distance to zoned school was positively related to choosing a magnet school as expected. Similarly, as the average distance to the nearest schools increases, the likelihood of choosing decreases. As for racial preferenc es, except for Black and White , college - educated parents at the elementary school level, as the proportion of Black students in the zoned school increases, the likelihood of choosing increases. There also seemed to be a preference for schools with higher SES levels as the likelihood of choosing went down when the proportion of students with college educated parents at a student's zoned school went up. Finally, the variables that measured the distance to the nearest school with a substantially different composition had null effects. There are several limitatio ns to the Bifu l co et al. (2007) study . Because the authors grouped together the various forms of public school choice that were available in the district, it is not fully clear what magnet choosers look like. It is possible this group of choosers looks dif ferent from the other types of choosers in the study. Also, t he magnet school program in Durham was quite small, there were only eight magnet schools. There were no magnet high schools, so the study is limited to elementary and middle school. Additionally, t he generalizability of the findings is limited by the policy context of the magnet schools. In Durham, r ace was not considered in admissions , enr ollment was by application only , and only 33 For example, the student body compositions of elementary schools had a much wider variance because they drew from smaller attendance zones than the middle schools did. 53 one of the magnet schools followed a SWAS format the rest of the programs were SUSs . Because the models were estimated separately by race and SES, there are no direct estimates of the effects of these variables on the likelihood of choosing a magnet school. Finally , Hispanic s tudents were excluded from the analysis. Bi fulco et al. (2009 b ) relie s on the same data from Durham , but the authors used different methods to evaluate outcomes from magnet schools . They again compare students who opt out to those who do not. However, they changed their models. Since the previous study failed to find a relationship between the distance to the nearest school with a substantially different racial and SES composition, these variables were excluded; instead, the authors included a similar variable to capture access to a school with hig her achievement. Finally, instead of including variables that captured the students' zoned school student racial and SES composition, the authors included a zone disadvantage index , which averages the percent of students in the school zone that are not pro ficient in reading and the percent of students in the school zone that do not have parents with a college degree. Instead of running separate models by race and SES, race and SES were included as predictor variables. Models were still separately run for el ementary and middle schools. The final sample of students was 14,366. T he results indicate d that even when controlling for other factors, Black students are most likely to opt out of their zoned school as compared to other racial groups . The zoned school di sadvantage index was positively related to the likelihood of opting out of the zoned school. Additionally, having a college - educated parent was associated with an increased likelihood of opting out, and this effect was stronger as the zoned school's disadv antage index increased. There was no difference in the likelihood of opting out between students who were proficient and not proficient in reading, but students who earned a superior score were more likely to opt out at the middle school level. D istance to the student's 54 zoned school was negatively related to the likelihood of opting out , as was the distance to the nearest high - achieving school. College educated parents were not found to be more or less sensitive to the distance to the nearest high achieving school. The authors dealt with some of the limitations of the ir earlier study , but the contextual limitations still remain . They included Hispanic students, and they only used one model that included race and SES as predictor variables , instead of estima ting separate models by race and SES . The authors excluded racial composition of the students' zoned school even though this was found to be an important predictor in their earlier study because the sample of zoned schools was too small (twenty - six) . 34 Also note that Black students were the base group in the model , so there is no direct comparison between White and Hispanic students. H aynes et al. (2010) placed a much needed emphasis on the Hispanic student population in their assessment of student sorting from magnet schools . The authors relied on survey and interview data from Nashville from the 2002 - 03 school year. The authors looked for differences in background attributes and school characteristic preferences of magnet school applicants between Hispani cs and other races. They found Hispanics who applied to magnet schools typically had a higher level of education than other races. This indicates there are perhaps additional hurdles Hispanics have to make it past to participate in choice, and only the mor e educated parents are able to clear these hurdles. Another interesting finding from this study was that education and income were not correlated for the Hispanics in this study as they were for other races. The authors at tribute this to language differenc es lowering their wages to no longer align with their education level. Importantly, this could explain why Hispanics utilize magnet 34 Although they are no longer estimating separate models, if the sample of schools was large enough, they could have utilized interaction terms to capture differences in these estimates across race as they did with SES. 55 schools at rates higher than private schools; they value education, but cannot afford tuition. With respect to preferences, Hispanics prioritized academics and safety; they also preferred convenience more than any other race. Finally, Hispanics were less likely to report having a close friend or family member that uses a magnet school. As such, these parents were less reliant o n their social networks for information on magnet schools. While this study made many important contributions with its focus on Hispanics, it of course has limitations. The sample used for this study was rather small (less than two hundred) , as was the Hi spanic population in Nashville . Only one percent of the magnet students were Hispanic. The generalizability is also limited by the magnet school policy context: race was not considered in admissions, ma gnet school admissions were via application only , and no transportation was provided. 35 Ad ditionally, the authors had to rely on stated preferences, which do not always align with actual choices (see e.g., Stein et al., 2011). 4.1.2 Macro - Level Analysis of Integration from Magnet Schools Instead of looking for evidence of the pathways to student sorting, o ther researchers look directly for student sorting . Several studies have looked at the aggregate effect of individual decisions by asking how student - body compositions change across schools and districts fr om various public school choice options. Such studies rely on a variety of comparisons and measures of segregation to answer this question. This section reviews studies that utilize district, state, and national datasets to look at the effects of magnet sc hools on student sorting by race , SES , English language proficiency, and achievement . Rossell (2003) conducted what is perhaps the most comprehensive study on integration from magnet schools. R ossell (2003) utilized a national dataset to examine the racial integration 35 It is unclear what magnet program structures were available. 56 effects from different types of desegregation plans over time . The dataset included information for six - hundred school districts from 1968 - 1991 . Using regression techniques, Rossell (2003) predicted segregation indices using district le vel demographic variables as we ll as variables that indicated whether the district used a voluntary or mandatory integration plan . In districts using voluntary plans (i.e., plans that rely on students voluntarily changing schools) magnet schools were link ed to higher levels of integration, but this is only when compared to districts with no plan at all. The benefits of magnet schools were no different from benefits associated with voluntary majority - to - minority programs. Mandatory plans (i.e., plans that r eassign students to different schools) that included magnet programs that had smaller affects associated with them when compared to the voluntary programs, but again the effect on integration was positive. Rossell (2003) also looked for differences in leve l of integration based on the amount of magnet schools used. As the percent of schools that are magnets increased, the level of integration decreased; however, when looked at closer, it appears integration is only impacted when the percent of schools that are magnet schools is above 50%. 36 A major limitation of this study is that the author only examined magnet schools that used "racial controls or targets" in admissions (p. 4). Archbald (2004) assessed SES integration from magnet schools us ing a similar strategy with district level data for 355 districts from the 1991 - 92 school year . He utilized various segregation indices as the dependent variable and neighborhood block demographics, district 36 Rossell (2003) included a percentage of schools that are m agnet schools variable, and the estimate was significant. However, when this variable is transformed into a series of categorical variables instead of a continuous variable, the only category that was significant was the "greater than 50% of schools are ma gnets" category. 57 size, and a series of dummy variables that indicate how much m agnet choice is available . 37 The results provided no evidence of a relationship between the measure of magnet choice availability and the level of SES integration . Using school - level data from 1990 - 91, Yancey and Saporito (1995) assessed whether or not mag net schools increased within district SES segregation in Philadelphia and Houston (Yancey & Saporito, 1995). They ran four separate regression models to predict the percentage of White, Black, Hispanic, and low - SES students in a school. For each model, the authors included a variable that captured the percentage of the respective students in the neighborhood and the percentage of students in the neighborhood who are attending private schools. A magnet school dummy variable was included to capture difference s in composition across magnet school status. Note the authors excluded high schools from the analysis. The authors concluded magnet schools decrease d racial segregation but increase d SES segregation. Since this study was conducted in HISD before the distr ict quit using race as an admissions factor for magnet schools, when the population of Hispanic students was much smaller (30.3%) , and before charter schools entered the district , it is unclear what the results would be in a modern - day context . Using the same data fr om Philadelphia as Yancey and Saporito (1995), Saporito (1998; 2003) concluded the magnet schools in Philadelphia led to higher concentrations of Black students in vocational programs, as well as more low - income students in TPSs and vocational schools. Racial segregation levels in the schools that housed the magnet programs were lower, but they increased in the feeder and vocational schools (Saporito, 1998; 2003). The conclusion of all of these 37 The dummy variables were included for "some choice" and "much choice" (p. 295). To be in the much choice category, districts had to have more than 20% of its schools as magnet schools, provide transportation, and disseminate information on the magnet program in at least 3 ways. The districts were coded as some choice if they had magnet schools but did not meet one of the requirements of the much choice category. 58 studies was that while the magnet schools were able to integrate, it was at the cost of further segregating the TPSs that lost students to the magnet schools. Most previous studies that examined integration from magnet schools grouped magnet schools in with other forms of school choice. Two consideration s should be made here, and both considerations point towards assessing magnet schools separately from other types of public school choice. First, certain types of magnet schools move choosers into other TPSs that primarily serve traditionally underserved r acial groups, as opposed to some separate facility like many other forms of school choice, any segregation effects from magnet schools are necessarily lessened. Second, magnet schools are under the control of the district, thus their individual effects wou ld have implications for district policy. Information on the sorting effects of school choice is lost when the various types of choice are grouped together in the analysis. For example, magnet schools may be integrating schools while charter schools are se gregating them; if examined together, it is not clear what is happening. Nonetheless, we can still learn from such studies. The results from studies that utilize school - level data to exam student sorting from school choice more broadly provide mixed evid ence . For instance, the public choice system in San Diego, which included busing, magnet schools, open enrollment, and charter schools, led to integration across schools by race and SES but segregation across achievement and ELL status (Betts, Rice, Zau, T ang, & Koedel, 2006). In Durham however, a system with similar options led to sorting across schools by race, SES, and achievement (Bifulco et al., 2009a; 2009b). Similar evidence emerged from a series of studies that relied on a data set compiled of school - level data from over twenty of the largest metropolitan areas in the country (Saporito & Sohoni, 2006; Saporito & Sohoni, 2007; Sohoni & Saporito, 2009) . The authors compared the demograph ic 59 composition of a school zone to the actual school; thus , all (pu blic and private) forms of choice other than residential are grouped as one. The results indicate public schools would be more racially (Saporito & Sohoni, 2006; Sohoni & Saporito, 2009) and economically (Saporito & Sohoni, 2007) integrated if everyone att ended the ir zoned school. These results were the strongest for Hispanics (Saporito & Sohoni, 2006), and attendance zones that had a majority of racial minorities (Saporito & Sohoni, 2007). The results of the various macro - level studies are mixed . Context could explain such differences , and many other researchers have pointed to the need to consider such contexts when assessing the outcomes of school choice options (see e.g., Arsen et al., 1999; Scott, 2005; Siegel - Hawley & Frankenberg, 2013). The research discussed in the previous section assessed different forms of choice and examined different locations; importantly, different locations come with different populations as well as policy and case - law contexts. Future research should move toward a better un derstanding of what contextual factors are important with respect to the sorting effects of different public choice options. More studies in this area are needed for two reasons . Much of the evidence on magnet schools is outdated given the changed c ontext modern - day magnet schools lie within. The positive effects found in older studies may no longer be present. Second, more studies are needed to better understand how context relates to integration from magnet schools. 4. 2 Contributions The analysis in this chapter offers ma n y contributions to the magnet school and broader school choice literature. First, the large number of magnet schools in HISD allows me to answer more school - level questions that prior studies have been unable to ask . For example, I c an 60 include more school composition variables and interaction terms. Additionally, magnet schools exist at all levels of schooling in HISD, which has not been the case in many of the previous studies. The longitudinal nature of the dataset allows me to add ress some of the shortcomings of previous work. When looking at how student achievement is related to the likelihood of enrolling in a magnet school via choice, pre - magnet test scores should be utilized as to not create an endogeneity issue. In other words , r esearchers are typically looking for evidence of cream - skimming . If current scores are relied on instead of lagged scores, it is unclear whether higher achievement is caused by enrolling in a magnet school or if instead high - achievers are attracted to magnet schools. To avoid this, pre - magnet test scores should be used in the analysis , and I have access to these data . This chapter also makes contributions to the literature because of t he demographic context of HISD . HISD has a majority Hispanic student population and a substantial ELL student population, which allows f or a better understanding of how different , typically ignored, student populations are impacted by magnet schools. Prior studies tend to focus on Black and White students, and but for the study out of San Diego, the contexts of the studies have all had sma ll Hispanic and ELL student population. The magnet policy context of the data allows for additional contributions. The available magnet school structures vary from district to district, and the structures in HISD allow me to examine different types of ma gnet schools that have not been addressed in a modern - day context. Specifically, HISD allows students who do not apply to a magnet school to have access to benefits of magnet schools , as many students are zoned for a magnet school . This policy can combat t he sorting effects that are typically associated with school choice because choosers join 61 nonchoosers in magnets that are structured as a SWP or a SWAS instead of becoming isolated in a separate school of choice. I also look for differences in student sort ing across the different magnet structure types to see if certain structures are perhaps better at integrating or more likely to segregate. Finally, I designed the analysis in ways that lead to a dditional contributions. First, a t the macro - level, I use s egregation indices to consider a variety of types of segregation including Hispanic - White, Black - White, SES, ELL status, and achievement. Prior studies typically limit the analysis to one or two types, and ELL integration from magnet schools has only been included in one other study (Betts et al., 2006) . Second , most studies group magnet schools with other forms of public school choice in their analysis . This strategy hides details about how various forms of school choice lead to student sorting or integration. For this reason, I separate magnet schools from the other forms of public school choice that are available in HISD. 4 . 3 Methods To analyze integration from magnet schools in HISD, I use both a micro - and macro - level perspective. With magnet schools, it is particularly important to consider bot h perspectives. The micro - level analysis describes the group of choosers as well as what types of schools they are leaving b ehind to look for evidence of the typical pathways to student sorting . However, b ecause certain magnet school structures mix choosers with nonchoosers, differences that emerge from the micro - level analysis may not tell the entire story. In other words, m ag net schools were designed to attract advantaged students , and finding patterns in who chooses a magnet school might not necessarily be problematic. The composition of the schools they leave behind and the schools they join are also important determinants o f whether or not integration is 62 achieved. It is possible that parents make decisions in ways that lead to sorting when aggregated. Thus, it is important to look at the macro - level as well. This section describes my analytical plan for both the micro - and m acro - level analyses, which build off of the research that was discussed in Section 4.1. This section also offers a summary of the sample and variables I rely on for each level of the analysis. 4.3.1 Micro - Level Research Design I begin the micro - level analysis with descriptive statistics that summarize who participates in magnet schools via choice. Specifically, I look at participation rates in magnet schools across racial groups, SES, ELL status , and I look for differences in the composition of school s that students leave. I also assess differences in sorting related to school - level policies . I do this by looking for systematic differences in the types of students that choose the different types of magnet school structures. Some structures are better a t integrating than others; for example, SUSs only have choosers in them, so they are typically less able to integrate. SWPs have the highest potential for integrating because they do not face classroom level segregation like SWPs , and they mix choosers wit h nonchoosers. I believe the descriptive analysis is particularly valuable because regression analysis controls away any effects that are correlative. Since I am examining integration, these correlative effects are important to consider as it allows for se eing the compound effects that certain student subgroups are subjected to. Beyond the descriptive analysis, I utilize regression models to see which student background factors (e.g., race, SES, etc.) and school factors (e.g., composition of student body at zoned school) are most related to choosing into a magnet school, because these are the types of differences that lead to student sorting. Additionally, because of their tendency to be correlated 63 with one another, it is valuable to assess which of the va riables are more directly related to magnet school enrollment. Similar to Bifulco (2007; 2009b) I model the decision to choose a magnet school a s a bi - variate response , where t he outcome of interest , which I refer to as current magnet - chooser status ( Y it ) , takes on two possible outcome s as shown in Equation 4.1. 38 (4.1) Based on the research discussed in Section 4.1, I model Y 1it as a function of four groups of variables, including: student background, special student statuses, zoned school composition, and other control variables. 39 The model for Y 1it is shown in Equation 4.2. Y 1it = ( Student Background ) it + ( Special Stud ent Statuses ) it + ( Zoned - School Composition ) it + ( Other Control Variables ) it it (4.2) , , , and represent the vectors of parameters I estimate for the four sets of right - hand - side variables. it is the error term for student "i" at time "t," and it is assumed to have an expected value of zero conditional on the values of the regressors (Wooldridge, 2010). Because my study centers on how TPS student populations change in the presence of magnet schools, it is important to see what the estimates of are without controlling away for things that are highly correlated with background factors. For this reason, I begin by excluding , , and from the model, and then I build in the vectors of independent and control variable s, to see how the estimates for student background factors. 38 Y it can equal zero when students are not in a magnet school via choice or when they are not in a magnet school. 39 The specifics on which variables are included, the reasoning for their inclusion, and their hypothesized relationship to the dependent variable are included in the next section. 64 Due to the binary nature of the dependent variable, I use a linear probability model and ordinary least squares to estimate Y 1 i t . Thus, I estimate the conditional probability of observing Y 1 it = 1 for student "i" in year "t . " The standard errors of a linear probability model will be heteroskedastic ; however, this can be fixed by implementing heteroskedasticity - robust standard errors (Wooldridge, 2010). Linear probability models are sometimes criticized for allowing the predicted values to fall outside zero and one, but this is less of an issue when the probabilities are rarely zero and one and when the predictor variables are mostly discrete in nature (Wooldridge, 2010). At the same time, ther e are benefits a ssociated with using a linear probability model including producing estimates that have a direct interpretation and having the ability to add fixed effects thr ough the use of dummy variables , which introduces bias to probit and logit models (Schmidheiny, 2014). For these reasons, I use a linear probability model instead of a logit or probit model. A shortcoming of the model in section 4.2 is that it does not include lagged achievement , which is needed to determine if magnet schools are attr acting high - achievers (i.e., whether or not they are cream - skimming) . Lagged achievement is specifically needed to avoid the endogeneity that is introduced by including current year achievement for magnet students. If magnet schools improve student achieve ment, using scores that came from magnet schools could make it look like high - achievers choose magnet schools when this is not the case. T he micro - level studies discussed in Section 4.1 do not include lagged achievement, because these studies all used one year of data. Since I have access to longitudinal data, I am able to include lagged achievement. At the same time, lagged test scores cannot be included in Equation 4.2 when the dependent variable is based off of the specification in Equation 4.1. Studen ts who became a magnet chooser in a prior year would not have a lagged test score that aligns with their choice; 65 endogeneity reenters as the lagged scores become magnet scores for non - new magnet choosers. The inclusion of pre - magnet test scores means I can only assess who switches to a magnet school via choice in each year. As such, I estimate a second set of model s where the outcome variable , which I refer to as new magnet - chooser status (Y 2it ), is specified as shown in Equation 4.3. 40 (4.3) The right hand side of the model is specified as shown in Eq uation 4.4 . Y 2 it = ( Student Background ) i(t - 1) + ( Test Data ) i(t - 1) + ( Special Student Statuses ) i t + ( Zoned - School 's Lagged Composition ) i t + ( Other Control Variables ) it i t (4. 4 ) I again rely on a linear probability model using OLS to estimate a series of models that build in the vectors of independent and control variables. Notice some of the vectors contain data from time "t - 1" while others contain data from time "t." Because the dependent variable emph asizes switching to magnet schools, I align the regressors to match up with what the student's background was at the time of the choice, and what information was available at that time of the decision - making . So for example, if the concern is low - income families are less able to participate in choice, income should be examined at the time the choice is made, which could be different from the income that is reported the year the student starts attending the sch ool of choice. On the other hand, some variables should align with the current time period. 41 For example, at the time of the decision, the parents typically know what grade their child will be in the next year, so using a lagged school level would not be 40 Y it can equal zero when students are not in a magnet school via choice or are not in a magnet school at all. Students who were new magnet - choosers in t - 1 are dropped from the sample in time t. 41 I have the zoned school's lagged composition as "t" instead of "t - 1" because it is the lagged com position of the zoned school in the current year, not the lag of the students' zoned school composition. 66 a ppropriate. F or the special student status variables , I use current year data (t) because it is more interesting to consider how often students with some sort of special status are served by schools of choice, and using a lagged special status could contor t the relationship between special student statuses and enrollment in schools of choice. For example, if the parent does not expect their child to be classified as gifted and talented in the upcoming year, they will probably not apply to vanguard programs. Similarly, if their child is going to need special education or English language services in the upcoming year, this will likely inform the parents' decision about which school to send their child to and what services their child will need . Additionally , I believe parents can accurately forecast these statuses for the school year for which they are applying , and attempting to forecast is needed for the decision - making and application processes. I use this pair of models for a couple of reasons. The way t hey are designed leads to estimates that tell a slightly different story. Equation 4.2 describe s the group of students that are typically served by magnet schools via the school choice system. Equation 4.4 leads to a better understanding of who participate s in magnet school choice. The estimates from both equation s are important for understanding who is served by magnet schools and whether they are able to integrate. There could be differences between the two groups for two reasons. Magnet schools could att ract ELLs who are closer to reclassification than the average ELL . This might happen because by the nature of the reclassification process, students who have been in school longer will have parents that are on average more familiar with schooling in the U. S., perhaps making them more able to participate in a system of choice. If this is the case, Equation 4.4 would make it appear as though more ELLs are being served than Equation 4.2 would show. Additionally, groups of students that switch schools more freq uently could be overrepresented by the estimates from Equation 4.4. The other reason for using two sets of models is that I am unable to include 67 interdistrict transfer students in Equation 4.4 because of the reliance on lagged data, especially the reliance on lagged achievement data. I do not have data for students until they enter the district. Thus I have to exclude this group of students from the second model. 42 4.3. 2 Micro - Level Variables This section offers descriptions of the variables I rely on for the analysis of integration from magnet schools. I describe all of the outcome variables, as well as their uses. I also include an explanation of why each of the independent and control variables are included. For the independent variables included in the analysis of the first research question, I provide hypotheses about each variable's relationship to the outcome of interest, magnet chooser status. 4.3.2.1 Outcome Variables Current Magnet - Chooser : For the current - chooser models, I created a dummy var iable that indicates the student is attend ing a magnet school via choice in the current year. This variable is used as the dependent variable for the model from Equation 4.2. A student is a magnet chooser only if they had to apply to the magnet program. Th us, students who are zoned for a SWP are not considered magnet choosers. Students who are zoned for a SWAS program are considered choosers so long as they are actually in the magnet program as opposed to being a nonprogram magnet student. New Magnet - Choos er : For the new magnet - chooser models, I rely on a dummy variable that captures whether or not a student switched to a new magnet school by choice in the current year. In other words, in the previous year, the student did not attend the magnet school they are currently attending. Additionally, such students are part of the magnet school program through 42 Note that I rerun the first model using the sample from the second model for comparison purposes. 68 choice, not zoning. This could mean the student had to apply to a SWAS program that is housed within the TPS they are zoned for, or they are attending a scho ol they are not zoned for. A final note on the construction of this variable is that students who are magnet choosers but are not new to the magnet school in the current year are coded as missing. This is done so that the data being used a lign with the cho ice. Thus, new magnet - choosers are compared to students who are attending a TPS, or zoned magnet students. 4.3.2.2 Independent and Control Variables The independent and control variables that are used to answer the first research question are separated i nto three groups: family and student background characteristics, special student statuses, and school composition variables. These variables are included based off of the work discussed in Chapter 3 as well as in Section 4.1. Student Background Characteri stics : As I explained in Chapter 3, many student background characteristics are linked to differences in participation in school choice and in preferences for school characteristics. I include several variables that capture important facets of a student's background. Race : Research evidence points towards differences that emerge across race in the ability to participate in choice as well as in preferences for schools. These differences can then turn into differences in the rates of participation in magnet school choice . The research evidence presented in Chapter 3 points toward differences across race in access to important information in social networks (Haynes et al., 2010) , which seems to at least partially arise from residential and workplace segregatio n that limits access to information from social networks (Smrkear, 2011) . Additionally, many studies found differences in preferences that arose across race ( see e.g., Bulman, 2004; Hastings et al., 2008) . Differences in preferences then translate into dif ferences in 69 who chooses a magnet school. For example, if proximity is more important to racial minorities, their option set will be smaller. Finally, racial minorities may find it harder to satisfy admissions requirements such as recommendation letters or certain attendance rates. Hypothesis: White students will be more l ikely to choose a magnet school as compared to Hispanic and Black students . I include a series of dummy variables to capture differences in participation in magnet school choice across race, where White students are the reference group. Gender : Gender is included because females are known to have better noncognitive skills than males, and such skills translate into higher grades in classes (Voyer & Voyer, 2014). Additionally, part of th e magnet program admissions process includes some minimum standards for GPA, attendance, and discipline. It could be easier for females to gain admissions to magnet schools because of better noncognitive skills, making the parents of females more likely to apply. Hypothesis: Females are more likely to choose a magnet school. To understand how gender relates to the likelihood of choosing, I include a dummy variable that indicates the students' gender, with males being the references group. Free - and - R educed - P rice - L unc h : I use free - and - reduced - price lunch (FR PL) status as a measure of SES. In Chapter 3, I provided evidence of how differences in rates of participation in school choice differ along SES lines. This happens because of differences in access to information (Neild, 2 005; Schneider & Buckley, 2002), differences in social networks (Neild, 2005; Teske et al., 2007 ; Smrkear, 2011), and because of the higher importance of proximity and reliance on transportation that effectively makes the choice set sm aller for low - income families (see e.g., Bell, 2007; Kleitz, Weiher, Tedin, & Matland, 2000) . 70 Hypothesis: As a student reaches higher percentages of the poverty level , the ir likelihood of choosing a magnet school will increase . I utilize a set of dummy var iables to capture the various levels of poverty. I have access to a more finely grained breakdown of FRPL status that includes four groups: students ineligible for FRPL (<185% of the poverty line ), students eligible for reduced lunch (131 - 185% of the pover ty line ), students eligible for free lunch, but who are living above the poverty line (101 - 130% of the poverty line ). The reference group is students who are not qualified for FRPL because they live at more than 185% of the poverty line . Home Language S ta tus : Haynes et al. (2010) found parents who did not speak English had l imited social network resources for school choice (Haynes et al, 2010; Valdés, 1996 ). Additionally, there are language barriers to participating in school choice ( Sattin - Bajaj, 2014 ) . Hypothesis: When a student's home language is not English, the student is less likely to enroll in a magnet school via choice . I include a dummy variable indicating whether or not the students' home language is English, where English speaking homes are the reference group. Immigrant S tatus : Immigrant status is important in this context because this group often has less of the various types of capital that are linked to participation in choice. While some of this is captured by other variables such as the F RPL and home language indicators, there are still other important differences between immigrants and nonimmigrants. Immigrants have more difficulty navigating school choice systems (Andre - Bechely, 2004). It also seems reasonable to believe t hey may be fear ful of participating if they are undocumented. Hypothesis: When the student is a recent immigrant, the student will be less likely to choose a magnet school. 71 I include a dummy variable to capture the students' immigrant status, where nonimmigrants are the reference group. Student Achievement : A typical concern with schools of choice is that such schools cream - skim the best performing students from TPSs (see e.g., Arsen, et al., 1999). Additionally, admissions requirements typically favor high - achievers, leaving parents of low achievers less likely to apply. Hypothesis: As the students' test scores in reading and math increase, the likelihood of choosing a magnet school increases. I include standardized math and reading scores to look for differences in the likelihood of choosing a magnet school across student achievement levels. 43 I standardized the scores by grade and year . Note that I am unsure of whether or not math and reading scores have the s ame relationship to the outcome. It is possible for one sc ore to be more strongly related to the likelihood of choosing a magnet school. For this reason, I include math and reading scores separately, as opposed to averaging the two , to allow for different marginal effects of math and reading scores. Special Stud ent Statuses : There are several student statuses that are related to student achievement, either directly or indirectly. Such statuses also impact what special services students are eligible for, and such services act as inputs in achievement. Because thes e statuses can vary over time, they will not be absorbed by a student fixed effect. I will include a series of dummy indicators for the following student statuses: gifted and talented, special education, limited English proficiency, and parent denial. 43 Note I chose to use Stanford scores. I discuss wh ich test scores are available by grade and year as well as why I chose to use Stanford scores over other types of scores in Chapter 5, where achievement is the focus of the chapter. 72 Gifted and Talented : Many of the magnet programs are vanguard programs that require the student to be identified as gifted and talented. Additionally, higher performing students are expected to be more likely to enroll in a school of choice, and gifted and talented students are high performing by definition. Hypothesis: Gifted and talented students are more likely to choose a magnet school. I include a dummy variable that indicates whether or not the student is classified a s gifted and talented, with non - gi fted - and - talented students as the reference group. Special Education : There are a couple of reasons to suspect differences in the likelihood of choosing a magnet school across special education status. Special education students, by definition, have an im pediment to learning, and these students are legally entitled to receive specialized instruction (Texas Project First, 2015 ). 44 Because many magnet schools have admissions criteri a , including all vanguard programs, the likelihood of special education stude nts qualifying for admissions is reduced . There is also evidence of public school choice leading to sorting by special education status because of the higher cost that is associated with educating these students. Ahearn, Lange, Rhim, and McLaughlin (2001) assessed this issue by examining the enrollment of special education students in charter schools across 15 states. They found evidence of both discouraging students from enrolling in the first place and counseling students out once they enrolled, though so me locales did not fit this general trend. 45 Other studies out of Michigan (Arsen et al., 1999), Texas (Fusarelli, 2000), Colorado (McLaughlin, Henderson, & Ullah, 1996), and Arizona (Garn & Braden, 2000) all found charter schools were serving 44 There are many laws that govern special education services and eligibili ty. For HISD, the applicable laws are summarized here: http://www.texasprojectfirst.org/FedRulesLaws.html . 45 See Welner & Howe (2005) for a discussion on the different ways in which charter schools steer and counsel special education students away. 73 disproportion ately low amounts of students with special needs and less severe disabilities. However, it is less clear if this applies to magnet schools that are still operated by the district. Hypothesis: Special education students are less likely to choose a magnet s chool. I include a dummy variable that indicates whether or not the student is eligible for special education services, with non - special - education students as the reference group. English Language Learner : As discussed in Chapter 3, there are a few reasons to believe ELLs will be underrepresented in schools of choice even after controlling for background factors that ELLs tend to have in common like race and SES. ELLs tend to live in segregated communities ( Iceland &Scopilliti, 2008; Jacobs, 2013a), which limits the information they can gather from their social network. Additionally, magnet schools may not try to attract ELLs because it is more costly to educate them . Magnet schools could also be unintentiona lly less attractive to ELLs. For example, if the specialized curriculum of a magnet school is not designed for students who are learning English, language services may not be available in the same ways they would be in a TPS. Hypothesis: ELLs will be less likely to enroll in a magnet school via choice . To analyze this hypothesis, I include a dummy variable that indicates whether or not the student is an ELL, where non - ELL s are the reference group. School Composition Variables and Interaction Terms : I incl ude variables capturing the composition of a student's zoned school for two main reasons. First, evidence and theory point towards parents having preferences about the composition of the school their child attends. If the zoned school does not fit these pr eferences, the parents will be more likely to choose a different school. Second, differences that emerge along these dimensions are especially likely to lead to student sorting. For these reasons, I include a series of variables that describe the compositi on of 74 the students' zoned school. In the current magnet - chooser analysis, I used the students' current year zoned school composition, as this set of models does not use lagged data so it better speaks to the result of students moving via school choice. In the new magnet - chooser analysis, I use the students' current zoned school's lagged composition. The new magnet - chooser model emphasizes switching to a magnet school, and what variables are related to this switch. This being the case, it makes more sense to consider what school's looked like when they were deciding to switch away from them by choosing a magnet school. Racial C omposition : Various theories point towards the existence of preferences regarding t he racial composition of a school. What Saporito (2003) refers to as "out - group avoidance theory," suggests parents who belong to higher - status groups will try to avoid lower - status groups "to maintain their superior social position" (p. 184). Alternatively, parents could simply be using race as a proxy for school quality (Saporito, 2003). "Neutral ethnocentrism" suggests parents want their children to interact with students who are similar to them (Bifulco et al., 2007, p. 6). Finally, "liberation theory" suggests disadvantaged groups will utilize choic e to gain access to more integrated schools (Bifulco et al., 2007, p. 7). The various theories point towa rds the avoidance of schools with higher proportions of racial minorit ie s, except for perhaps same - race preferences of Blacks and Hispanics. The resear ch evidence presented in Chapter 3 supports this conclusion . White parents typically avoid higher minority schools (see e.g., Bifulco, Ladd & Ross, 2009b; Saporito & Lareau, 1999). There is some evidence of racial minorities having same race preferences (s ee e.g., Hastings, et al., 2008; Henig, 1990). Researchers found racial minorities have preferences regarding cultural values which prompt s them seek out schools that are high minority (Weiher & Tedin, 2002). Other evidence points 75 towards same race prefere nces merely being a reflection of their limited choice sets (Bifulco & Ladd, 2006). The theories lead me to several hypotheses. To test for evidence of outgroup avoidance and liberation theory, I test the following hypotheses. Hypothesis: As the percentag e of racial minority students in a student's zoned school increases, the student's likelihood of choosing a magnet school increases . Hypothesis: As the percentage of White students in a student's zoned school increases, the student's likeliho od of choosing a magnet school de creases. To test for evidence of neutral ethnocentrism, I test the following hypotheses Hypothesis: For Black students, as the percentage of Black students increases in their zoned school, their likelihood of choosing a magnet school decreases. Hypothesis: For Hispanic students, a s the percentage of Hispanic students increases in their zoned school , their likelihood of choosing a magnet school decreases . To test th ese various hypotheses I include a series of variables that indicate the racial composition of a student's zoned school in terms of percentage White, percentage Black, and percentage Hispanic students. I then allow for differences to emerge in preferences for these compositions when it is a same - race preference. Thus, I include interaction terms that interact race and same - race racial composition of the zoned school. SES C omposition : Out - group avoidance theory and liberation theory can be applied to preferences for SES compositi on as well. Both theories point towards the avoidance of low - SES schools. Research evidence supports these theories as well (see e.g., Holme, 2002). Hypothesis: As a the proportion of low - SES students at a student's zoned school increases, the likelihood of that student choosing a magnet school increases. 76 To test this hypothesis, I include a measure of the students' zoned s chool SES - composition. Note that both theories point towards h igh - SES students avoiding low - SES schools. Hypothesis: High - SES parents will be more likely to avoid low - SES schools than low - SES parents are. I test this hypothesis by includi ng an interaction term between SES and zoned school SES - composition. ELL C omposition : The various preference theories can be applied to the ELL subgrou p as well. Out - group avoidance theory and liberation theory suggest schools with higher proportions of ELLs will be less appealing to parents. Jacobs (2013b) provides evidence of this as his research uncovered the importance of language composition to parents, though he did not allow for differences in preferences to emerge by ELL status. Hypothesis: Students who are zoned for schools with high er proportions of ELLs will be more likely to choose a magnet school. To test this hypothesis, I include a variable that accounts for the proportion of ELLs at each student's zoned school. Neutral ethnocentrism can also be applied in this setting . In this case it would mean ELLs would prefer schools that serve more ELLs. Hypothesis: For ELL students, as the proportion of ELLs in their zoned school increases, their likelihood of choosing a magnet school decreases . To allow for differences in preferences fo r ELL composition of schools by ELL status, I include an interaction term between ELL status and zoned school ELL - composition. Achievement Composition : Out - group avoidance theory and liberation theory can be applied to preferences for SES composition as w ell. Both theories point towards the avoidance of low - achievement schools. 77 Hypothesis: As the proportion of low - performing students at a student's zoned school increases, the likelihood of that student choosing a magnet school increases. To test this hypo thesis, I include a measure of the average achievement in reading and math at a students' zoned school . Control Variables : I include several variables that relate to the likelihood of choosing a magnet school, but are not related to student sorting like student background characteristics and school composition variables. Such variables are merely included as controls. As such, I am not particularly interested in the estimates for these variables or designing testable hypotheses about their relationship to the dependent variable. School L evel S hift : I utilize a dummy variable to capture years in which a student is changing schools regardless of whether or not the y participate in school choice. Thus, I include dummy variables to indicate the student is star ting 6th or 9th grade. I hypothesize a student transitioning to middle or high school is more likely to participate in school choice because during this natural transition, any choice is less disruptive to educational trajectories. School L evel : I include a set of dummy variables to indicate which school level the student is in. There are differences in the number and types of options available at different school levels, which could impact the likelihood of choosing. Distance to Z oned S choo l: Because of the importance of proximity and transportation, I hypothesize parents will be more likely to participate in school choice if they are further from their zoned school. For this reason, I include distance, in miles, from the student's home to their zoned sch ool. Year : I include a series of year dummy variables to capture any differences in the participation in choice that might occur across years. Differences could emerge from year to year 78 due to things such as school closures and openings. I do not have any hypotheses regarding outcomes for individual years, I just hypothesize there will be differences across years. Zip C ode : I include a series of dummy variables for the five - digit zip code to roughly capture the choice set. The dataset includes over sixty zip codes that at least partially fall within the district boundaries. It is important to consider in some way what options are available when considering whether or not a parent will choose a school for their child. Because of the importance of proximity, zip code can act as a proxy for the choice set. In other words, because parents do not want to have to travel far from their home, the parents in each zip code should roughly have the same schools available to them within a given distance. Therefore, the inclusion of zip code will act as a proxy for the choice set that is available to those living in the area. I do not have any hypotheses regarding outcomes for individual zip codes. I simply hypothesize there will be differences across zip code. Zoned Mag net Student : The district has many students who attend a magnet program via zoning. I hypothesize these students will be less likely to choose a magnet school because the increased utility associated with choosing a magnet school should be smaller on avera ge for the group of students who are zoned for a (different) magnet program as compared to students who attend a TPS, because these students are already receiving magnet school benefits. Table 4. 1 provides details for each of the variables used in the mic ro - level analysis . Along with this is a description of how the variable is defined, what values it takes on, and any data cleaning that affected the variables. 79 Table 4. 1 . Description of Micro - Level Variables Variable Name Description Outcome Variables Magnet - Chooser Switcher A binary outcome variable that indicates whether or not the student newly switched to a magnet school via choice in the current year, where Yes=1, No=0. Note that students who have switched to a magnet school in a prior year and are coded as missing as long as they remain in the same magnet school. Magnet Chooser A binary outcome variable that indicates whether or not the student attended a magnet school via choice in the current year, where Yes=1, No=0. Student Background Race or Ethnicity A series of dummy variables describing the race or ethnicity of a student that includes the following categories: White, Black or Native American , Hispanic , and Asian or Pacific Islander , where Yes=1, No=0 and White is the base group. The ethnicity variable switched to include multi - racial midway through the dataset. Previous year data was used to identify a single race for multi - racial students when possible; if not possible, the student was dropped from the dataset. Female A dummy variable indicating the student is a female, where Yes=1, No=0. The gender variable was cleaned to be time - invariant. The gender that was reported most frequently across time was used for all time periods; if there was a tie, the student was dropped. Poverty Status A series of dummy variables for various poverty levels that includes the following categories: at or b elow p overty l ine (free lunch), 101 - 130% p overty line (free lunch) , 131 - 185% p overty line (reduced lunch), a bove 185% p overty line (non - FRPL ), where Yes=1, No=0 and a bove 185% poverty l ine is the base group. The poverty level used here is set by the U.S. Department of Agriculture, and this variable is tracked by HISD for the purposes of determining FRPL status. Home Language Not English English, where Yes=1, No=0. Immigrant Status A dummy variable indicating the student was born outside the U.S. and has n ot been enrolled in U.S. schools at any point in the last three years, where Yes=1, No=0. Note that by this definition, all pre - K through 1st graders are flagged as immigrants if born outside the U.S. Student Achievement Math Score Student's Stanford math score, standardized across the district by grade and year. Reading Score Student's Stanford reading score, sta ndardized across the district by grade and year. Special Student Statuses Gifted and Talented A dummy variable that indicates the student has been identified as gifted and talented, where Yes=1, No=0. Special Education A dummy variable that indicates the student has an individualized education plan because of a cognitive, physical or emotional disability and consequently receives special education services, where Yes=1, No=0. 80 Table 4.1. (cont'd) Variable Name Description ELL Status A dummy variable that indicates the student is an English language learner, where Yes=1, No=0 . In other words, they have been categorized as having limited English proficiency and are therefore eligible for English language services School - Level Variables Zoned School Composition Includes a series of school - level variables that constructs the percentage of certain student subgroups at each school. This set of variables is referred to when wanting to know what the composition of each student's zoned school is. Variables included are: % White, % Hispanic, % Black, % ELL, and % At or Below Poverty. School level average scores in reading and math are also included (I rely on Stanford scores that have been standardized at the district level by grade and year). Note here that for the purpose of calculating peer composition, SWAS magnets are treated as part of the TPS that houses it. Zoned School's Lagged Composition Includes a series of school - level variables that constructs the percentage of certain student subgroups for each student's zoned school (i.e., the student's current year's zoned school's lagged composition). This set of variables is referred to when wanting to know what the composition of each student's zoned school wa s in the previous year when the decision to choose a magnet school was made. Variables included are: % White, % Hispanic, % Black, % ELL, and % At or Below Poverty. School level average scores in reading and math are also included (I rely on Stanford score s that have been standardized at the district level by grade and year). Note here that for the purpose of calculating peer composition, SWAS magnets are treated as part of the TPS that houses it. Interaction Terms Black x % Black Zoned School Hispanic x % Hispanic Zoned School ELL x % ELL Zoned School Poverty x % Poverty Control Variables School Level Shift A dummy variable indicating whether or not the student is shifting school level (i.e., the student is starting 6th or 9th grade), where Yes=1, No=0. School Level A series of dummy variables that indicate which school level the student is in, including elementary, middle, and high school levels, where Yes=1, No=0 and elementary school is the reference group. Distance to Zoned School Measures the distance from a student's home to their zoned school to the nearest one - hundredth of a mile. Year A series of dummy variables that indicate the year the data are from. Year 2006/07 is the base year. Zip Code A series of dummy variables indi cating which five digit zip - code the student lives in. Zoned magnet student A dummy variable indicating the student is zoned for a magnet program (i.e., they are zoned for a SWP), where Yes=1, No=0. 81 4.3. 3 Micro - Level Sample Data for the micro - level analysis of integration includes students who attended either a traditional public school or a magnet school at some point between 20 07/08 and 20 11/12 . The time span for this analysis is shorter because the zip code and distance to zoned school data I rely on for the model portion of the analysis are only available in these years. 46 Alternative school and district - run charter - school students were dropped from the analysis because I am interested in how the populations of TPSs change when students attend magn et schools. Additionally, the sample was narrowed in a few ways due to data anomalies. The coding for ethnicity changed half - way through the years beginning in 20 10/11 , multiracial became an option. When possible, I used data from prior years to identify a single race for these students. When a single race could not be identified, the student was dropped from the sample. The gender variable also had to be cleaned as it was not time - invariant for all students. When gender varied, the most frequently report ed gender is used in all years, and in the case of a tie, the student was dropped from the sample. Finally, Native American (NA) students were dropped from the sample because there were too few of them to include as a group on their own. 47 Beyond the afo rementioned data - cleaning that resulted in sample reduction, I constructed two separate samples for the micro - level analysis. I use one sample for the current magnet - chooser analysis and another sample for the new magnet - chooser analysis. The sample varies across models for a couple of reasons. First, the new - magnet - chooser models rely on lagged data, which requires students to be in the dataset for more than one year. A side - effect of this is that 46 The n umber of students dropped from having missing zip code and distance to zoned school variables is so high because of the limited time frame of availability for these variables. 47 In Chapter 5, I keep Native Americans students in the sample by including them with Black students. It was not appropriate to use the same strategy in this chapter because I am examining same - race preferences. 82 the new - chooser models exclude interdistrict transfer stude nts because this data is not available for them. Second, only students who have lagged testing data are in the new magnet - chooser models, so students who were not in a tested grade in the previous year are excluded from the sample. 48 Additionally, because a lot of Spanish speaking ELLs take a different version exam, such students are dropped from the sample when test scores are brought in. 49 Finally, the dependent variable of the new magnet - chooser models drops students who are at a magnet school they started attending by choice in a prior year. The sample construction for the current and new magnet - chooser analyses are shown in Table 4. 2 . Table 4. 2 . Sample Construction: Micro - Level Analysis Current Magnet Chooser New Magnet - Chooser Reason for D ropping Number D ropped Number R emaining Number Dropped Number R emaining Starting s ample s ize (student - year) - 1,757,893 Charter 123,961 1,633,932 123,961 1,633,932 Alternative 24,020 1,609,912 24,020 1,609,912 Pre - K or e arly e d uc 109,972 1,499,940 109,972 1,499,940 No PEIMS data 123,237 1,376,703 123,237 1,376,703 Native American 2,835 1,373,868 2,835 1,373,868 Multiracial 2,048 1,371,820 2,048 1,371,820 Time - varying gender 962 1,370,858 962 1,370,858 Missing zip code and distance to zoned school 542,398 828,460 542,398 828,460 Not in dataset in t - 1 - - 169,976 658,484 No lagged Stanford data ( Aprenda or non - tested grade ) - - 140,833 517,651 Other missing data 42,468 785,992 72,223 445,428 Final Sample 785,992 445,428 48 As is further explained in Chapter 5, stude nts are tested in grades K through 11 up until 2009/10, and then they are tested in grades K through 8 thereafter. 49 The different language versions of the standardized exams do not directly equate to the English versions of the exams and are therefore no t comparable. Standardizing the scores is not appropriate either because different subsamples of the population take the different language versions. This issue is discussed in more detail in Chapter 5 when I discuss the various exams and versions. 83 4.3. 4 Macro - Level Research Design The macro - level portion of the analysis seeks to uncover the aggregate effects of individual actions. This analysis is especially important if the micro - level analysis uncovers evidence of the pathways to student sorting. Because interdist rict residential segregation can limit the ability of magnet schools to integrate across the district, I beg i n th e macro - level portion of the analysis by examining the level of residential segregation that HISD is subjected to. This information explains th e importance of drawing in students from outside of the district; if the greater metropolitan area is similarly segregated, interdistrict transfers would be limited in effectiveness as well. Using Census data, I compare the racial , linguistic, and SES comp osition of HISD to that of the school - aged population in the greater Houston metropolitan area to get a picture of how segregated HISD is from the surrounding community. Next, I hypothesize magnet schools are more integrated than TPSs in the district bec ause they attract choosers and in most cases mix these students with zoned, non - choosers. To see if magnet schools are relatively more integrated than TPSs, I compare the mean composition of magnet schools to that of TPSs . I use this strategy to compare ra cial, SES, and ELL compositions . 50 I also hypothesize there will be differences in school compositions across magnet structure type. In particular, I believe the compositions of SWAS and SUS magnet schools will have more advantaged students than SWP magnet schools. To test this hypothesis, I breakdown the mean magnet school composition by magnet structure type. To assess integration across the district , I use methods similar to those utilized by Bifulco et al. (200 9 b ) and Saporito (1998). I compare the student body composition of what scho ols 50 I do not look at segregation by achievement because such an analysis would only be appropriate when looking at pre - magnet scores since magnet schools could be causing higher achievement. I do this in the micro - analysis, but it does not fit in with the analysis I conduct here. 84 would be like if all magnet students attended their zoned school , which I refer to as the zoned school c ounterfactual (ZSC) composition , to what to the enrolled school actual (ESA) composition is. For this I will rely on the student level data that cap tures the students' zoned school and enrolled school. This is an imperfect measure as I cannot truly know what the without - magnet - school compositions would look like, 51 but it is still useful for determining whether or not magnet schools are moving students in an integrative manner. To compare the ZSC and ESA compositions, I rely on three indices: dissimilarity, exposure, and isolation . 52 I use the indices to consider racial (Black - White and Hispanic - White), SES, and ELL segregation in magnet schools and TPSs . The three indices each provide different, but useful information. The dissimilarity index conveys how segregated the schools are compared to the district population. For districts that are highly segregated from other districts, this index can fail t o adequately represent the amount of segregation students in the distric t are facing. The exposure and isolation indices do a better job of describing how segregated students in the district really feel. The isolation index is similar to the exposure index , but becomes increasingly valuable when the number of groups is greater than two. While the exposure index describes the level of contact between two groups, the isolation index is able to describe how segregated a group is from all other groups. Note how ever that for policy purposes, looking at the exposure and isolation indices can be misleading if the district does not have a diverse student population to draw from. In other words, the schools could seem really segregated when looking at the exposure an d isolation indices, but this could be mostly due to interdistrict 51 If magnet schools were nonexistent, students may use some other form of choice instead of their zoned school. 52 Descriptions of the indices are provided in Section 4.3.6. 85 segregation. The three indices are best used together because of the different information they provide. 4.3. 5 Macro - Level Variables The macro - level analysis I conduct relies on the comparison of different outcome variables to measure the level of segregation or integration from magnet schools. This section describes the various outcomes I examine, including a series of segregation indices and composition comparisons. I also ex plain why I rely on these various measures. 4.3.5.1 Segregation Indices I created two sets of variables that represent each student's zoned school counterfactual - composition and their enrolled school composition. To create the counterfactual zoned school composition I rely on data that tells me which school a student is zoned for. I create a series of variables that reflect what the composition of a school would look like if all magnet school students attended their zoned school. Using student level data, for each school, I calculated the proportions of students in the following groups: White, Hispanic, Black, ELL, and at or below the poverty level. I calculated the same set of compositions for each student's enrolled school. I utilize a variety of indice s for my analysis, as the different indices are able to provide different information about the segregation levels of schools. Such indices are calculated for a number of disadvantaged - advantaged pairings, which I have summarized in Table 4. 3 . I calculate each of the indices for the set of magnet schools in HISD and the set of TPSs in HISD, and then compare the two sets of results. 86 Table 4. 3 . Disadvantaged - Advantaged Student Pairings Disadvantaged Group (D) Advantaged Group (A) Black White Hispanic White At or below poverty Ineligible for FRPL ELL N on - ELL Dissimilarity Index : The dissimilarity index, which is the most used measure of segregation , measures the amount of students that would have to change schools to achieve a distribution that reflects the composition of the district (Massey & Denton, 1998). The equation for this index is shown in Equation 4.5. I use "D" and "A" to denote the number of disadvantaged and advantaged students in the district , respectively. "d s " and "a s " represent the number of disadvantaged and advantaged students in school "s," respectively. The index is calculated for the set of schools s=(1, 2, ..., S ) . The index ranges from 0 - 100 , where 0 indicates no students need to move , or each school's composition perfectly reflects the composition of the district. Exposure Index : The exposure index conveys how much students from a particular disadvantaged group are exposed to memb ers of the corresponding advantaged group (Massey & Denton, 1998). The calculation of this index is shown in Equation 4.6. "D" denotes the number of disadvantaged students in the district . "d s " and "a s " represent the number of disadvantaged and advantaged students in school "s," respectively. "Ts" is equal to the total student population of school "s." The index is calculated for the set of schools s=(1, 2, ..., 87 S). The index ranges from 0 - 100, where 0 indicates the disadvantaged group has 0 contact with the advantaged group . Isolation Index : As opposed to measuring exposure to other groups, the isolation index measures how much exposure a group has to other members of their group (Massey & Denton, 1998). It is measured as the typical percentage of the students of this group in each school, as shown in Equation 4.7. "D" again denotes the number of disadvantaged students in the district, and "d s " represents the number of disadvantaged students in school "s." "Ts" is the total student population of school "s." The index is calculated for the set of schools s=(1, 2, ..., S). The index ranges from 0 - 100 where 100 indicates the group is totally isolated. 4.3.5.2 School Composition Comparisons To compare magnet and TPS compositions, I compare the ESA compositions of magnet schools to those of TPSs. I also compare ESA compositions ac ross magnet structure types. I include race, SES, and ELL compositions in th is portion of the analysis . The various outcome variables that I rely on for the macro - level analysis are summarized in Table 4.4. 88 Table 4. 4 . Description of Macro - Level Outcome Variables Outcome Description Dissimilarity Index This index measures the amount of students that would have to change schools to achieve a distribution that reflects the composition of the district. The index ranges from 0 - 100, where 0 indicates 0% of the students need to relocate. Indices are created for Black - White, Hispanic - White, Poverty/ Non - FRPL, and ELL/ non - ELL pairings. Exposure Index This index measures the exposure of Group A to Group B, where such exposure is measured by the typical percentag e of Group B. The index ranges from 0 - 100 where 0% indicates Group A is totally isolated from Group B. Isolation Index This index measures the concentration of students of a certain group. It is measured as the typical percentage of the students of this g roup in each school. The index ranges from 0 - 100 where 100% indicates the group is totally isolated. Enrolled School Actual (ESA) Composition Includes a series of school - level variables that constructs the percentage of certain student subgroups at each s chool. This set of variables is referred to when wanting to know what the composition of each student's enrolled school is. The following v ariables are included: % White, % Hispanic, % Black, % ELL, and % a t or b elow p overty. Note here that for the purpose of calculating peer composition, SWAS magnets are treated as part of the TPS that houses it. Zoned School Counterfactual (ZSC) Composition Includes a series of school - level variables that constructs the percentage of certain student subgroups at each school. This set of variables is referred to when wanting to know what school compositions would look like if each magnet student attended their zoned school. Variables included are: % White, % Hispanic, % Black, % ELL, and % at or b elow p overty. Note here that for the purpose of calculating peer composition, SWAS magnets are treated as part of the TPS that houses it. 4.3. 6 Macro - Level Sample I am able to use a much larger group of students for the macro - level analysis because I rely on fewer variables and I do not use test data or lagged data. Because I am not using zip code or distance from zoned school, I can include data from all years of the dataset as well. Data for this analysis includes students who attended either a traditional public school or a magnet school at some point between 20 06/07 and 20 13/14 . I again dropped charter and alternative school students since I am only considering magnet schools and TPSs. I also dropped early education and pre - K students because I my analysis focuses on K - 12. Additionally, the sample was narrowed in a few ways due to data anomalies. As mentioned earlier, the coding for ethnicity changed half - way through the years beginning in 20 10/11 , multiracial became an option. 89 When a single race could not be identified f rom prior data, the student was dropped from the sample. I also had to drop the group of students who have no PEIMS data, as these students have no demographic data available. Beyond this, I do not drop any other students before creating composition variab les so that these variables contain as much information as possible. The summary of the sample construction for the macro - level analysis is provided in Table 4. 5 . Table 4. 5 . Sample Construction : Macro - Level Analysis Reason for D ropping Number D ropped Number Remaining Starting s ample s ize (student - year) - 1,757,893 Charter 123,961 1,633,932 Alternative 24,020 1,609,912 Pre - K or e arly e d uc ation 109,972 1,499,940 No PEIMS data 123,237 1,376,703 Ambiguous r ace 2,048 1,374,655 Final Sample 1,374,655 4.4 Results This section presents the results of both the micro - and macro - level analys e s. This begins with the micro - level analysis, which takes a descriptive look at the types of students who choose a magnet school and what types of schools are left behind. Regression techniques are used to help untangle the correlations between many of the i ndependent variables to better understand which variables are more directly related to choosing a magnet school. The results from the micro - level analysis need to be aggregated to tell the whole story however. Since magnet schools mix choosers with nonchoo sers, the macro - level results are important for determining the overall impact of magnet schools on integration. The micro - level results may point towards pathways to student sorting, but sorting may not occur when choosers are mixed into schools with nonc hoosers. The composition of the school students enter and leave behind are important in the 90 magnet school context. The macro - level results help understand whether magnet schools are more integrated than TPSs. It also shows whether or not magnet schools int egrate at the cost of segregating TPSs and what the net effect is (i.e., whether or not the district is more or less integrated). 4.4.1 Micro - Level Results I began the analysis with summa ry statistics that describe current and new magnet - choosers as compared to non magnet - choosers, as shown in Tables 4. 6 and 4. 7 , respectively . I provide the mean, standard deviation, and the results of a test for mean differences across magnet chooser status. As explained in Section 4.3.3, the samples for the two diffe rent magnet chooser outcomes , current and new magnet - choosers, are examining slightly different group of students, so the results could differ. Table 4. 6 . Summary Statistics by Magnet Chooser Status : Current Magnet - Choosers Non Magnet - Chooser Magnet Chooser Non Ma gnet - Chooser Magnet Chooser Variable Variable Female 0.48 ***0.54 Gifted & Talented 0.1 0 ***0.39 (0.50) (0.50) (0.30) (0.49) White 0.07 ***0.14 Special Ed 0.1 0 ***0.04 (0.26) (0.35) (0.30) (0.20) Black 0.26 ***0.3 ELL 0.31 ***0.11 (0.44) (0.46) (0.46) (0.32) Hispanic 0.64 ***0.5 % White Zoned School 0.06 ***0.06 (0.48) (0.50) (0.12) (0.11) Asian 0.03 ***0.07 % Hisp Zoned School 0.63 ***0.57 (0.17) (0.25) (0.29) (0.28) Poverty 0.27 ***0.16 % Black Zoned School 0.27 ***0.35 (0.44) (0.37) (0.27) (0.28) Free Lunch 0.48 ***0.35 % Poverty Zoned School 0.25 ***0.27 (0.50) (0.48) (0.14) (0.13) Reduced Lunch 0.08 ***0.12 % ELL Zoned School 0.28 ***0.22 (0.27) (0.33) (0.20) (0.17) Home Lang uage not English 0.51 ***0.36 Zoned Sch ool's Avg Reading Z - Score - 0.12 *** - 0.14 (0.50) (0.48) (0.36) (0.35) 91 Table 4.6. (cont'd) Variable Non Magnet - Chooser Magnet Chooser Variable Non Magnet - Chooser Magnet Chooser Immigrant 0.03 ***0.01 Zoned Sch ool's Avg Math Z - Score - 0.1 *** - 0.14 (0.18) (0.09) (0.34) (0.33) For each variable, the mean is shown and the standard deviation is below in parentheses. T - tests for differences in means across magnet chooser status were conducted where *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 785,992 includes data for 287,912 students . Table 4. 7 . Summary Statistics by Magnet Chooser Status: New Magnet - Choosers Non Magnet Chooser Magnet Chooser Non Magnet Chooser Magnet Chooser Variable Variable Female 0.48 ***0.55 Special Ed 0.11 ***0.03 (0.50) (0.50) (0.31) (0.18) White 0.09 ***0.11 ELL 0.12 ***0.05 (0.28) (0.31) (0.33) (0.21) Black 0.30 *0.31 Reading Z - Score (lag /pre - magnet ) - 0.14 ***0.61 (0.46) (0.46) (0.95) (0.92) Hispanic 0.58 ***0.51 Math Z - Score (lag /pre - magnet ) - 0.12 ***0.60 (0.49) (0.50) (0.94) (0.99) Asian 0.03 ***0.07 Zoned School's lag of %White 0.10 ***0.07 (0.18) (0.26) (0.15) (0.11) Poverty (lag) 0.24 ***0.16 Zoned School's Lagged %Hispanic 0.58 ***0.55 (0.43) (0.36) (0.28) (0.25) Free Lunch (lag) 0.46 ***0.41 Zoned School's Lagged %Black 0.28 ***0.34 (0.50) (0.49) (0.26) (0.26) Reduced Lunch (lag) 0.09 ***0.13 Zoned School's Lagged %Poverty 0.20 ***0.21 (0.29) (0.33) (0.10) (0.09) Home Lang uage not English 0.41 **0.40 Zoned School's Lagged %ELL 0.20 ***0.14 (0.49) (0.49) (0.17) (0.11) Immigrant (lag) 0.03 ***0.01 Zoned Sch ools Lagged Avg Reading Z - S core 0.01 *** - 0.02 (0.16) (0.10) (0.33) (0.25) Gifted & Talented 0.12 ***0.38 Zoned Sch ools Lagged Avg Math Z - S core 0.02 *** - 0.03 (0.32) (0.49) (0.32) (0.25) For each variable, the mean is shown and the standard deviation is below in parentheses. T - tests for differences in means between magnet schools and TPSs were conducted. When variances of the two groups were not equal, the Welch's option was employed. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0. 01 levels, respectively. The sample size of 445,428 includes data for 180,479 students. 92 The results of the descriptive statistics for the two samples are quite similar. The results show magnet choosers are more often female. White and Asian students make up a larger proportion of students in the magnet chooser group, and for Whites, the difference is larger when comparing the current and non magnet - chooser groups. Black students also make up a larger proportion in the two magnet chooser group s, though the difference is almost nonexistent when looking at new magnet - choosers. 53 Hispanics are less likely to be in a magnet school by choice; the difference is smaller when looking at new magnet - choosers however. Students living at or below the povert y or qualified for free lunch have less of a presence in the magnet chooser groups. For reduced lunch students, a relatively advantaged group considering most students in the district are qualified for FRPL, have a higher presence in the magnet chooser gro ups. Immigrants have a relatively much larger representation in the non magnet - chooser group, as the proportion is three times that of the magnet chooser groups. The student status results all matched my hypotheses: gifted and talented students have a high er proportion of students in the magnet chooser groups, while special education and ELL students have lower proportions in the magnet chooser groups. The school composition variables point towards students being more likely to choose when their zoned schoo l has fewer White, Hispanic, or ELL students and more Black, lower performing, or poverty students. T he new magnet - chooser model includes lagged achievement and provides evidence of cream - skimming, as the z - scores in reading and math are substantially high er in the magnet chooser group. The only statistics that really look different from one another across the two sets of results are the variables related to ELLs (e.g., home language and ELL status). This can be explained by the difference in samples. Apren da test - 53 This points toward Black students changing schools more frequentl y than other students. 93 takers , students who tend to be further away from English proficiency and newer to schools, were dropped from the new magnet - chooser sample. 54 I ran another set of descriptive statistics that break s down magnet choosers across the three types of m agnet school structures. Because SWPs are better at integrating, I am interested in seeing what types of students choose these magnet schools. Additionally, SUSs are least able to integrate as these schools do not have a zoned student population. I again i nclude the results for both the current and new magnet - chooser samples, and the results are shown in Tables 4. 8 and 4. 9 , respectively. Table 4. 8 . Differences in Student Background and Status Across Magnet Structure Type : Current Magnet - Choosers Non Magnet - Chooser SWP Chooser SUS Chooser SWAS Chooser Variable Female 0.48 0.51 0.56 0.55 (0.50) (0.50) (0.50) (0.50) {10.36} {4.98} {4.12} White 0.07 0.12 0.14 0.15 (0.26) (0.32) (0.35) (0.35) {3.80} {1.48} {2.18} Black 0.26 0.34 0.32 0.28 (0.44) (0.47) (0.47) (0.45) {0.89} {1.11} {0.44} Hispanic 0.64 0.50 0.39 0.53 (0.48) (0.50) (0.49) (0.50) {4.14} {4.96} {2.53} Asian 0.03 0.04 0.15 0.05 (0.17) (0.20) (0.35) (0.21) {2.75} {2.12} {1.76} Poverty 0.27 0.19 0.10 0.17 (0.44) (0.39) (0.31) (0.38) {7.25} {6.01} {1.75} Free Lunch 0.48 0.35 0.30 0.37 (0.50) (0.48) (0.46) (0.48) {6.04} {4.17} {3.29} 54 Refer to section 4.3.3 for why these students are dropped from the sample. 94 Table 4.8. (cont'd) Variable Non Magnet - Chooser SWP Chooser SUS Chooser SWAS Chooser Reduced Lunch 0.08 0.12 0.12 0.12 (0.27) (0.33) (0.32) (0.33) {7.75} {2.45} {0.76} Home Lang not Eng 0.51 0.33 0.32 0.38 (0.50) (0.47) (0.47) (0.49) {5.70} {6.15} {3.76} Immigrant 0.03 0.01 0.00 0.01 (0.18) (0.11) (0.06) (0.09) {9.15} {10.01} {0.78} Gifted and Talented 0.10 0.23 0.45 0.42 (0.30) (0.42) (0.50) (0.49) {8.03} {3.16} {3.46} Special Ed uc 0.10 0.06 0.09 0.03 (0.30) (0.24) (0.28) (0.17) {14.63} {0.36} {6.47} ELL 0.31 0.22 0.04 0.10 (0.46) (0.41) (0.20) (0.30) {10.02} {9.85} {1.35} For each variable, the mean is shown and the standard deviation is below in parentheses. For each type of magnet student, the absolute T - statistic from a regression of each individual variable on magnet student status is shown in brackets. The sample size of 785,992 includes data for 287,912 students. Table 4. 9 . Differences in Student Background and Status Across Magnet Structure Type: New Magnet - Choosers Non Magnet - Chooser SWP Chooser SUS Chooser SWAS Chooser Variable Female 0.48 0.50 0.56 0.55 (0.50) (0.50) (0.50) (0.50) {7.24} {3.73} {1.66} White 0.09 0.06 0.14 0.10 (0.28) (0.24) (0.35) (0.29) {1.39} {1.23} {2.23} Black 0.30 0.48 0.30 0.30 (0.46) (0.50) (0.46) (0.46) {0.07} {0.21} {0.43} Hispanic 0.58 0.43 0.39 0.56 (0.49) (0.49) (0.49) (0.50) {1.19} {3.35} {3.63} 95 Table 4. 9 . (cont'd) Variable Non Magnet - Chooser SWP Chooser SUS Chooser SWAS Chooser Asian 0.03 0.03 0.16 0.04 (0.18) (0.16) (0.37) (0.20) {1.91} {1.93} {1.82} Poverty 0.24 0.24 0.11 0.17 (lag) (0.43) (0.43) (0.31) (0.37) {5.32} {3.80} {0.93} Free Lunch 0.46 0.39 0.33 0.44 (lag) (0.50) (0.49) (0.47) (0.50) {1.88} {2.72} {3.32} Reduced Lunch 0.09 0.14 0.12 0.13 (lag) (0.29) (0.34) (0.32) (0.34) {8.29} {2.07} {0.78} Home Lang uage not English 0.41 0.21 0.35 0.44 (0.49) (0.40) (0.48) (0.50) {0.02} {2.37} {8.22} Immigrant 0.03 0.01 0.01 0.01 (0.16) (0.08) (0.10) (0.10) {4.66} {3.78} {0.54} Gifted and Talented 0.12 0.16 0.47 0.37 (0.32) (0.37) (0.50) (0.48) {6.70} {2.94} {2.72} Special Ed ucation 0.11 0.07 0.04 0.03 (0.31) (0.26) (0.20) (0.16) {17.51} {4.54} {5.75} ELL 0.12 0.09 0.02 0.05 (0.33) (0.28) (0.15) (0.23) {8.39} {8.47} {3.78} For each variable, the mean is shown and the standard deviation is below in parentheses. For each type of magnet student, the absolute T - statistic from a regression of each individual variable on magnet student status is shown in brackets. The sample size of 445,428 includes data for 180,479 students. The results are not very promising with regards to the integrative capacity of magnet schools . Ideally, the results would show more advantaged students choosing SWPs as opposed to SWAS and SUS programs this is the opposite of what I found. White and Asian students make up a larger proportion of the students in the SUS and SWAS magnet chooser groups . Asians are 96 particularly overrepresented in the SUS group. On the other hand, Blacks, Hispanics, ELLs, and students living at or below the poverty line are more represented in SWPs. Gifted and talented students are heavily represented in the SWAS and SUS programs, which is not surprising considering students have to have gifted and talented status to attend a vanguard program (i.e., vanguard programs cannot be SW Ps). Finally, the reduced lunch group and immigrants have an even spread amongst the groups. Beyond descriptive statistics, I also utilized regression analysis to further examine patterns in who participates in magnet school choice to see which variables are more directly tied to choosing a magnet school . The results are divided into two sets of models, one for the current magnet - chooser analysis and another for the new magnet - chooser analysis; the results are shown in Tables 4. 10 and 4.1 1 , respectively. Table 4. 10 . Linear Probability Model Results for Current Magnet - Chooser Models Variable (1) (2) (3) (4) Controls Zoned Magnet Student - 0.217*** - 0.208*** - 0.214*** - 0.214*** (0.034) (0.032) (0.032) (0.032) School Level Shift 0.013* 0.017*** 0.018*** 0.018*** (0.007) (0.006) (0.006) (0.006) Middle School 0.027 0.017 - 0.017 - 0.020 (0.029) (0.028) (0.038) (0.038) High School - 0.015 - 0.021 - 0.080 - 0.081* (0.038) (0.037) (0.049) (0.048) Dist ance t o Zoned Sch ool 0.017*** 0.017*** 0.016*** 0.015*** (0.005) (0.005) (0.004) (0.004) Student Background Female 0.034*** 0.023*** 0.023*** 0.023*** (0.004) (0.003) (0.003) (0.003) Black - 0.094*** - 0.030* - 0.055*** - 0.067*** (0.022) (0.018) (0.016) (0.021) Hisp anic - 0.090*** - 0.036** - 0.046*** 0.057** (0.019) (0.015) (0.014) (0.026) Asian 0.077** 0.054 0.058* 0.059* (0.038) (0.034) (0.032) (0.032) Poverty - 0.196*** - 0.150*** - 0.157*** - 0.113*** (0.018) (0.015) (0.015) (0.015) Free Lunch - 0.156*** - 0.119*** - 0.127*** - 0.129*** (0.016) (0.013) (0.013) (0.013) 97 Table 4.10. (cont'd) Variable (1) (2) (3) (4) Reduced Lunch - 0.068*** - 0.049*** - 0.055*** - 0.057*** (0.013) (0.011) (0.011) (0.011) Home Lang uage n ot Eng lish - 0.033*** - 0.008 - 0.011 - 0.013 (0.007) (0.008) (0.008) (0.008) Immigrant - 0.096*** - 0.041*** - 0.042*** - 0.042*** (0.011) (0.009) (0.009) (0.009) Special Student Statuses Gifted a nd Talented 0.282*** 0.282*** 0.283*** (0.028) (0.028) (0.028) Special Education - 0.065*** - 0.065*** - 0.065*** (0.009) (0.009) (0.008) E LL - 0.063*** - 0.061*** - 0.063*** (0.011) (0.010) (0.017) Composition o f Zoned School Zoned School's % White 0.204 0.231 (0.287) (0.288) Zoned School's % Hisp anic 0.279 0.402* (0.234) (0.239) Zoned School's % Black 0.426* 0.413 (0.252) (0.258) Zoned School's % Poverty - 0.225* - 0.163 (0.128) (0.131) Zoned School's % ELL - 0.100 - 0.119 (0.109) (0.111) Avg Reading Zoned School - 0.172*** - 0.175*** (0.064) (0.064) Avg Math Zoned School 0.064 0.067 (0.049) (0.049) Interaction Terms Hisp anic x Zoned School's % Hispanic - 0.179*** (0.040) Black x Zoned School's % Black 0.041 (0.044) Poverty x Zoned School's % Poverty - 0.151*** (0.035) ELL x Zoned School's % ELL 0.015 (0.046) R - squared 0.082 0.159 0.170 0.172 All models include a zip - code fixed effect and set of year dummies. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 785,992 includes data for 287,912 students. 98 Table 4. 1 1 . Linear Probability Model Results for New Magnet - Chooser Models Variable (1) (2) (3) (4) (5) Controls Zoned Magnet Student - 0.033*** - 0.034*** - 0.031*** - 0.031*** - 0.031*** (0.011) (0.011) (0.011) (0.011) (0.011) School Level Shift 0.220*** 0.213*** 0.212*** 0.213*** 0.209*** (0.022) (0.021) (0.021) (0.021) (0.020) Middle School - 0.011 - 0.006 - 0.004 - 0.010 - 0.010 (0.010) (0.010) (0.013) (0.013) (0.013) High School - 0.023** - 0.019* - 0.020 - 0.027* - 0.029* (0.011) (0.011) (0.016) (0.015) (0.015) Dist ance t o Zoned Sch ool 0.006** 0.006*** 0.007*** 0.006*** 0.006*** (0.002) (0.002) (0.002) (0.002) (0.002) Student Background Female 0.013*** 0.009*** 0.009*** 0.009*** 0.009*** (0.002) (0.002) (0.002) (0.002) (0.002) Black - 0.023*** 0.003 - 0.010 - 0.001 0.011 (0.008) (0.006) (0.007) (0.009) (0.009) Hisp anic - 0.025*** - 0.005 - 0.010 0.011 0.022** (0.007) (0.006) (0.006) (0.010) (0.010) Asian 0.052** 0.040* 0.040* 0.040* 0.033 (0.024) (0.023) (0.023) (0.023) (0.022) Poverty - 0.061*** - 0.045*** - 0.050*** - 0.038*** - 0.033*** ( l ag) (0.009) (0.008) (0.008) (0.007) (0.006) Free Lunch - 0.044*** - 0.031*** - 0.036*** - 0.034*** - 0.029*** ( l ag) (0.007) (0.006) (0.006) (0.006) (0.006) Reduced Lunch - 0.017*** - 0.010** - 0.013*** - 0.014*** - 0.012** ( l ag) (0.005) (0.005) (0.005) (0.005) (0.005) Home Lang uage n ot Eng lish - 0.010*** - 0.005 - 0.007** - 0.010*** - 0.011*** (0.003) (0.003) (0.003) (0.003) (0.003) Immigrant - 0.029*** - 0.008* - 0.008** - 0.004 0.007* (0.005) (0.004) (0.004) (0.004) (0.004) Student Statuses Gifted a nd Talented 0.118*** 0.119*** 0.119*** 0.084*** (0.018) (0.018) (0.018) (0.018) Special Education - 0.031*** - 0.031*** - 0.031*** - 0.001 (0.003) (0.003) (0.003) (0.003) ELL - 0.028*** - 0.029*** - 0.064*** - 0.040*** (0.005) (0.005) (0.008) (0.007) Composition of Zoned School Zoned School's Lagged % White - 0.071 - 0.075 - 0.062 (0.105) (0.106) (0.106) Zoned School's Lagged % Hispanic - 0.022 - 0.002 - 0.012 (0.097) (0.096) (0.096) Zoned School's Lagged % Black 0.044 0.045 0.029 (0.101) (0.103) (0.102) Zoned School's Lagged % Poverty - 0.045 0.001 - 0.021 (0.065) (0.066) (0.065) Zoned School's Lagged % ELL 0.008 - 0.033 - 0.035 (0.044) (0.043) (0.042) 99 Table 4.11. (cont'd) Variable (1) (2) (3) (4) (5) Zoned Sch ools Lagged Avg Math (z - score) - 0.039 - 0.042 - 0.054 (0.036) (0.036) (0.036) Zoned Sch ools Lagged Avg Reading (z - score) - 0.017 - 0.014 - 0.029 (0.032) (0.031) (0.031) Interaction Terms Hisp anic x Zoned School's Lagged % Hispanic - 0.037** - 0.040** (0.017) (0.017) Black x Zoned School's Lagged % Black - 0.026 - 0.022 (0.018) (0.018) Poverty x Zoned School's Lagged % Poverty - 0.077*** - 0.069*** (0.016) (0.015) ELL x Zoned School's Lagged % ELL 0.135*** 0.117*** (0.019) (0.018) Test Data Reading Score 0.018*** (0.002) Math Score 0.018*** (0.003) R - Squared 0.155 0.185 0.189 0.191 0.201 All models include a zip - code fixed effect and set of year dummies. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 445,428 includes data for 180,479 students. Most of the results are similar across the two model specifications . 55 The differences that emerge between the two sets of results can be explained by the different model specifications that result in different samples, dependent variable s, and the use of lagged regressors in one model . For example, if certain types of students change schools more often, such students have the potential to be counted as a chooser more often than students who choose a school and stay at that school. The results for Hispanic and Black students provide a good example of thi s happening. For the most part, the results indicate Hispanic and Black students have a lower likelihood of choosing a m agnet school than White students, but the difference is larger in the current magnet - chooser model . Before introducing other control var iables, the difference is almost 10% in the current magnet - chooser model. The magnitude is reduced as additional 55 Because the samples of the two sets of models have so many differences, I reran the current magnet - chooser models using the new magnet - chooser sample. The results are provided in Table A.1 of the Appendix. 100 variables are accounted for, but there is still a noticeable difference. In the new magnet - chooser models however , the difference is small even before other variables are introduced, and the differences disappear once the other variables enter the model . This can be explained by the se groups of students changing schools more often than White students. After all control and independent variables are brought into the model, the association with Hispanic becomes positive and significant , though the magnitude is rather small . Asian students are roughly 5% mo re likely than White students to enroll in a school of choice, but the summary statistics point towards this group choosing SUSs, which are the least capable of integrating. The estimates for the rest of the student background characteristics and special student statuses are as expected for the most part. For the series of FRPL variables, as the percentage of the poverty level decreases, the likelihood of choosing a magnet school also decreases. The student statu s estimates are all as expected. G ifted and talented students are more likely to be a magnet chooser, while special education and ELL students are less likely to be a magnet chooser. Finally, the students' lagged (pre - magnet) test scores in the new magnet - chooser model provide evidence of cream - ski mming from TPSs. Estimates for both reading and math are significant even when all other independent and control variables are in the model. One surprising result is that the home language estimate is not significantly different from zero in many of the mo dels, and in the cases of significance, the magnitude is rather small. This could be due to correlations between the home language variable and some of the other regressors such as ELL status or poverty stats. Alternatively, p erhaps a district like HISD is better capable of including parents who do not speak English in school choice programs. As a whole, the zoned school composition variables, whether current or lagged seem to have little relationship with the likelihood of being a chooser; the standard er rors for these 101 estimates are quite large, and the model fit only marginally improves when bringing in this group of regressors. 56 Average reading of the students' zoned school in the current year is the only estimate that is strongly related to being a curr ent magnet - chooser. The interaction terms for composition show that Hispanics and students living below the poverty line are less likely to choose when their zoned school has more students that are similar to them , supporting the neutral ethnocentrism hypo thesis . At the same time, the estimate for the interaction between ELL and percentage of ELLs in the student's zoned school from the new magnet - chooser model points towards liberation theory. ELLs seem to avoid schools with larger proportions of ELLs. Al though the regression results point towards more advantaged students choosing magnet schools, such results might not necessarily mean magnet schools are unable to integrate. In fact, magnet schools purposefully attempt to draw in advantaged students so the y can integrate. This works when the schools that students are leaving do not become more segregated, and when advantaged students do not all congregate in SUS magnet programs. However, some of the descriptive results point ed towards more advantaged studen ts using SUS and SWPs more frequently than SWAS programs and schools with higher compositions of underserved students. The macro - level analysis is needed to see what school compositions look like after students move from TPSs to magnet schools via choice. 4.4.2 Macro - Level Results Before examining the district's integration from magnet schools, I compared the composition of the city of Houston to the county it resides in as well as the Houston MSA. I 56 Note I stay away from discussing the marginal effect of these estimates because of their continuous nature. For continuous variables, the estimates are calculated as the instantaneous rate of change (i. e., the marginal effect as the change is approaching zero) and may not extrapolate out linearly to larger changes such as a one unit increase, or in this case a one percentage point change (Cameron & Trivedi, 2010). 102 believe it is important to provide context for the res t of the macro - level analysis. If the district does not have a diverse population to draw from, it may be unreasonable to expect much integration along certain lines. Table 4. 1 2 presents the results of this analysis. Table 4. 1 2 . Comparison of the Composition of Houston to Broader Geographic Area s MSA Harris County Houston MSA - Houston Harris County - Houston Total Population 2,195,914 6,313,158 4,117,244 4,352,752 2,156,838 White (%) 25.6 38.3 45.0 31.9 39.6 Hispanic (%) 43.8 36.1 32.0 41.6 41.1 Black (%) 23.7 16.8 13.2 19.5 16.0 At or Below Poverty (%) 22.9 16.4 12.9 18.5 14.0 Home Lang not Eng lish (%) 46.3 37.5 32.8 42.5 38.6 Numbers are based on ACS data for 2013 . Data is for the entire population, not just the school - aged population. White and Black students are only counted as White or Black if they did not report being Hispanic. For the MSA and Harris County compositions, compositions are provided for the corresponding area bot h with and without the Houston population included; the compositions are reported in the first and second columns of the respective geographic area. The composition of Houston, as compared to the Houston MSA and Harris county, is quite different. As the geographic area expands from Harris County to the MSA, the differences grow. The difference s are especially noticeable once the population of the city of Houston is differenced out. There is a much larger proportion of Whites in the larger geographi c areas and lower proportions of Blacks and Hispanics. Similarly, there are smaller proportions of home languages other than English and children living at or below the poverty - level outside the city of Houston. The results of this analysis point towards t he potential of integration if students are drawn in from outside of the district. The next portion of the macro - level analysis compares the compositions of magnet schools to that of TPSs to see if magnet schools are more or less integrated. While this do es not convey how integrated the district is, it points to whether or not magnet programs are at least helping to integrate the schools they are housed in. The results of this analysis are shown in 103 Table 4.1 3 . Note that here the percentage variables were calculated for each school, and then averaged separately for magnet schools and TPSs . 57 Table 4.1 3 . Comparison of Magnet and TPS C ompositions Perc W hite Perc Black Perc Hispanic Perc Poverty Perc ELL Year Magnet TPS Magnet TPS Magnet TPS Magnet TPS Magnet TPS 0 6/0 7 *** 0.11 0.04 0.33 0.32 *** 0.51 0.63 *** 0.17 0.25 *** 0.18 0.38 07/ 08 *** 0.11 0.04 0.33 0.29 *** 0.52 0.65 *** 0.16 0.22 *** 0.17 0.35 0 8/ 09 *** 0.10 0.04 0.32 0.29 *** 0.53 0.66 *** 0.16 0.22 *** 0.19 0.38 09/ 10 *** 0.10 0.04 0.31 0.28 *** 0.54 0.66 *** 0.18 0.26 *** 0.18 0.36 10/ 11 *** 0.10 0.04 0.31 0.28 *** 0.54 0.66 *** 0.27 0.38 *** 0.18 0.37 11/ 12 *** 0.10 0.04 0.31 0.25 *** 0.54 0.68 *** 0.33 0.44 *** 0.18 0.40 12/ 13 *** 0.11 0.03 0.30 0.26 *** 0.54 0.68 *** 0.36 0.47 *** 0.18 0.39 13/ 14 *** 0.11 0.03 0.29 0.27 *** 0.54 0.67 *** 0.35 0.47 *** 0.19 0.42 Numbers shown reflect the (unweighted) average composition of magnet schools versus that of TPSs. T - tests for differences in means between magnet schools and TPSs were conducted. When variances of the two groups were not equal, the Welch's option was employed. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size is 1,929 campus - year observations. Asi de from the percentage of Black students, magnet schools have quite different compositions than TPSs. They tend to have more advantaged students, pointing towards more integrated populations in these schools. Traditionally underserved students attending ma gnet schools encounter more White students and fewer Hispanics, students living at or below the poverty level, and ELLs. A shortcoming of this analysis however is that it does not speak to the overall integration of the district. In particular, magnet scho ols could be integrating magnet schools at the cost of leaving TPSs more segregated. I also examined how school compositions varied across magnet structure type. Their different designs may attract different types of students. Additionally, SWP and SWAS m agnet schools mix zoned and nonzoned students, which will most likely lead to differences in the compositions of these schools when compared to SUS magnet schools that only serve choosers. 57 I also compared means that are weighte d by the number of students at each school. Because the results are so similar, I present the results of this additional analysis in Table A.2 of the Appendix. 104 If the compositions for the various magnet structures are not broken down, these differences are hidden and valuable, policy - guiding information is lost. Table 4.14 shows the results of a breakdown of school compositions across magnet structure type. Table 4.1 4 . Comparison of Compositions Across Magnet Structure Type Perc White Perc Black Perc Hispanic Year SWP SUS SWAS SWP SUS SWAS SWP SUS SWAS 0 6/0 7 0.14 0.19 0.10 0.36 0.29 0.33 0.45 0.39 0.54 07/ 08 0.14 0.19 0.09 0.34 0.29 0.32 0.46 0.38 0.56 0 8/ 09 0.14 0.18 0.08 0.33 0.28 0.32 0.49 0.38 0.57 09/ 10 0.14 0.17 0.08 0.31 0.28 0.32 0.50 0.38 0.57 10/ 11 0.14 0.17 0.08 0.31 0.28 0.31 0.50 0.38 0.57 11/ 12 0.14 0.15 0.08 0.31 0.32 0.31 0.49 0.40 0.58 12/ 13 0.14 0.16 0.08 0.31 0.29 0.30 0.48 0.40 0.58 13/ 14 0.14 0.15 0.08 0.33 0.28 0.29 0.47 0.42 0.59 Perc Poverty Perc ELL Year SWP SUS SWAS SWP SUS SWAS 0 6/0 7 0.19 0.07 0.17 0.24 0.03 0.17 07/ 08 0.16 0.06 0.17 0.23 0.02 0.17 0 8/ 09 0.16 0.06 0.17 0.25 0.03 0.18 09/ 10 0.18 0.08 0.20 0.24 0.03 0.17 10/ 11 0.27 0.12 0.29 0.26 0.04 0.17 11/ 12 0.33 0.20 0.36 0.25 0.03 0.18 12/ 13 0.35 0.21 0.38 0.24 0.06 0.18 13/ 14 0.35 0.20 0.38 0.24 0.05 0.19 Numbers shown reflect the (unweighted) average composition of magnet schools across magnet structure type. The sample size is 874 campus - year observations. There are a lot of differences in composition across magnet structure type. The only steady composition across structure type is the percentage of Black students. Otherwise, t he results indicate SUS magnet schools typically have the smallest proportion of dis advantaged students. This however is not surprising since these schools do not have a zoned student population. The differences are rather dramatic when looking at the percentage of ELL students across magnet structure type. ELLs have very low presence in SUS magnet schools , especially when compared to SWP magnet schools . The larger proportion of White students and lower 105 proportion of Hispanic students in SWP mag net schools as compared to SWAS magnet schools is consistent with the findings in Chapter 5 that show White students are overrepresented in the zoned magnet student group. The comparisons of compositions up to this point have not spoken to whether or not the district is more integrated as a whole. While magnet schools appear more integrated than TPSs, they could be causing segregation at the district level. To understand how magnet schools affect the integration of the district, I used a variety of segre gation indices , and compared what the composition of schools looks like with students attending magnet schools to what it would look like if these students attended their zoned school . The different indices tell slightly different stories regarding integra tion, and as such, the results vary by index. Indices are calculated across different disadvantaged - advantaged pairings, and the results are pr esente d in Table 4.1 5 . Table 4.1 5 . Segregation Indices: Enrolled School Actual vs. Zoned School Counterfactual Dissimilarity Index (Higher=more segregated) Exposure Index (Lower=more segregated) Isolation Index (Higher=more segregated) Year ESA ZSC Difference ESA ZSC Difference ESA ZSC Difference Black - White 07 81.6 77.5 4.1 13.2 12.5 0.7 54.1 51.8 2.3 08 82.3 78.3 4.1 15.1 13.7 1.4 53.7 51.7 2.0 09 86.1 83.1 3.0 13.6 13.2 0.4 53.0 51.3 1.8 10 82.0 78.0 3.9 13.6 13.1 0.5 50.9 49.1 1.8 11 77.8 73.5 4.3 11.8 11.3 0.5 51.2 49.1 2.1 12 80.4 74.9 5.4 12.9 11.4 1.5 50.7 47.5 3.2 13 69.5 64.6 4.8 7.7 7.0 0.7 49.3 46.1 3.2 14 77.7 71.1 6.6 10.7 9.3 1.4 50.2 46.6 3.6 Hispanic - White 07 86.0 82.4 3.6 7.5 7.0 0.5 73.4 72.7 0.8 08 89.6 86.2 3.4 6.8 6.7 0.1 74.4 77.8 - 3.4 09 90.9 88.3 2.5 8.3 8.1 0.1 74.8 75.6 - 0.8 10 88.1 85.2 2.9 7.4 7.2 0.2 75.0 76.3 - 1.3 11 82.7 79.4 3.3 6.9 6.6 0.2 74.9 75.6 - 0.7 12 85.7 80.6 5.0 7.5 7.3 0.2 74.8 75.2 - 0.3 13 72.3 68.6 3.7 5.5 5.3 0.3 74.5 74.2 0.3 14 81.2 75.6 5.6 7.0 6.5 0.5 74.4 74.1 0.3 106 One thing to point out is that the district is quite segregated when students attend their zoned school instead of a nonzoned magnet school. Both in terms of inter - and intra - distr ict segregation. The dissimilarity index shows that White - Black and Hispanic - Black segregation is quite severe a majority of students would have to change schools to reach a composition that reflects that of the district. Hispanics are more segregated than Black students, a finding that holds for all three indices. Segregation along the lines of income and ELL status does not seem to be as much of a problem as racial segregation. The isolation and exposure indices When comparing the ESA and ZSC indices , the results vary by index. The dissimilarity index points to the district being more segregated when students are enrolled in magnet schools instead of their zoned school . On the other hand, e xcept for the ELL /non - ELL pairing , the Table 4.15. (cont'd) Dissimilarity Index (Higher=more segregated) Exposure Index (Lower=more segregated) Isolation Index (Higher=more segregated) Year ESA ZSC Difference ESA ZSC Difference ESA ZSC Difference Poverty/Non - FRPL 07 56.3 52.9 3.4 14.5 13.7 0.8 25.5 25.2 0.3 08 56. 9 54.5 2.4 13.1 13.1 0.0 23.3 23.2 0.0 09 56. 8 53.8 2.9 15.2 15.1 0.1 27.7 27.4 0.3 10 56.5 53.1 3.4 13.3 13.0 0.3 26.8 26.8 0.0 11 57. 8 54.2 3.6 12.6 12.2 0.4 37.0 37.2 - 0.2 12 56. 9 53.8 3.1 12.2 12.0 0.2 43.9 43.8 0.1 13 56.6 52.6 4.0 12.7 12.1 0.5 46.7 46.1 0.6 14 58. 0 53.3 4.7 12.2 11.7 0.5 46.5 45.5 1.0 ELL/non - ELL 07 50.5 47.2 3.3 54.8 54.6 0.2 47.5 44.4 3.1 08 49. 7 47.2 2.6 55.3 57.0 - 1.7 48.4 44.8 3.6 09 49. 9 46.6 3.2 55.3 56.0 - 0.7 48.5 44.0 4.5 10 49.5 46.5 3.0 55.6 56.6 - 1.0 49.5 46.0 3.6 11 49. 5 46.4 3.1 57.4 58.4 - 1.0 48.2 44.0 4.2 12 48. 3 45.5 2.8 57.5 58.0 - 0.6 45.6 42.3 3.3 13 47.2 44.1 3.1 58.7 58.5 0.2 44.2 40.9 3.3 14 47. 0 43.3 3.7 55.5 55.0 0.5 47.1 43.6 3.6 Indices are calculated for both enrolled school actual (ESA) and zoned school counterfactual (ZSC) compositions. The difference is calculated by subtracting the ZSC index from the ESA index. The difference is bold if it shows ESA compositions are less segregated than ZSC compositions. 107 exposure index provides evidence of integration. Finally, t he isolation index shows Hispanic - White integration, but all other comparisons are slightly more segregated. The differences that emerge across the various indices can be explai ned by differences in what the indices meas ure. In this context , Black - Hispanic segregation can also explain the differences that emerge. To be more integrated, t he dissimilarity index requires the school compositions to be more reflective of the district's composition . If Black - Hispanic segregatio n is a problem, changing the proportion of White students in the school will have less of an impact on the dissimilarity index than it would on the other two indices that simply look at how exposed one group is to another or how isolated they are . In fact, increasing the proportion of White students in a school could be shifting its composition further away from what the district composition looks like , leading to a dissimilarity index that points towards increased segregation . Compare this to the isolation and exposure indices, which will always improve when the proportion of White students in a school increases , all else equal . As a whole, segregation of the district from students moving from TPSs to magnet schools does not seem to be a big problem , whic h is a concern when the micro - level results point towards more advantaged students leaving their zoned school . The results that indicate the district is more segregat ed are small in magnitude , and at the same time, some of the results point towards a more integrated district . Further, the way the ZSC compositions are calculated most likely leads to an overstate ment of segregation from students attending magnet schools and an understatement of the integration that occurs from students attendi ng magnet schools . Because some students might opt for some other nonzoned school in lieu of a magnet school if magnet schools were not an option, the ZSC is not truly reflective of what school compositions would be without magnet schools. 108 4. 5 Limitations There are several shortcomings and limitations of the analysis in this chapter due to data constraints and methodological design . This study only uses data from one district. While i t is a large district that is able to provide a large sample of students , it is unclear how far outside the HISD context these results extend. It can however provide more information about how large districts are able to serve students that are typically overlooked in other studies, primarily Hispanics and ELLs. The sample of students for the second set of models , the new magnet - chooser models, is limited in many ways because of the reliance on test scores and lagged data. A large proportion of ELLs are dropped, no Kindergarteners are included, and interdistrict transfer stude nts are left out as well. However, the sample for the first set of models is able to include all of these groups, and the results were not very different from one another. The same general trends emerged in the two sets of models. This s tudy is mostly descriptive (non causal) in nature . In particular, I do not account for the matrices the district uses in the application process. I do not do so for a few reasons. I am interested in seeing how magnet schools integrate across racial, SES, and achievement l ines, and this is hidden in the analysis when I control for variables that tend to be related to race, SES, and achievement. It would be beneficial to include such variables to better understand the causal relationship between race, SES, and achievement, b ut there are several problems with trying to connect the HISD matrices to my models. I only have access to the matrices used in the most recent application round. I have been unable to ascertain whether similar matrices have been used in other years. Addit ionally, the matrices that are available are quite complex in their 109 nature, and they vary across magnet program theme and school level . 58 For these reasons, I leave the inclusion of such variables for future research. While I cannot exactly say why the patterns emerge, as they could be from difficulties participating or not meeting admissions requirements, the results are still informative . The results allow the district to understand more about who is benefiting from magnet schools and how school compositions are changed as students leave TPSs to attend magnet schools. Another problem with trying to get at causation with the data I have is that I do not have access to application data. Because I use enrollment data as opposed to application data, differences between choosers and nonchoosers could be understated due to caps on enrollment. This also speaks to the importance of policy schools might be even more segregated if limits are not placed on enrollment in certai n schools (Betts et al., 2006). More parents might choose a magnet school without the caps in place. Thus, my analysis still guides policy. The enrollment caps placed on magnet schools is within the districts control, and if there is evidence of TPSs being drained of the relatively more advantaged students, then perhaps the caps should not be raised. Finally, the with - and without - magnet school compositions are an imperfect measure of the magnet school effect on integration. It is unclear what composition s would truly be without magnet schools. It is unclear what compositions would truly be without magnet schools. Students may still opt out of their zoned school for a different TPS, a charter school, or they may leave the public school system all together. Thus, the segregation linked to magnet schools in the macro - level analysis is most likely overstated. 58 The matrices are initially discussed in Chapter 2, and an example of one of the matrices is pr ovided in the Appendix. 110 4.6 Discussion and Implications The results of the micro - and macro - level analyses provide different information. The micro - level analysis informs as to who chooses a magnet school and how this group is different from non magnet school choosers. This information can tell the district whether or not magnet schools are attracting advantaged students as they were designed to do, and whether these students are leaving schools that are relatively disadvantaged. While magnet schools are designed to attract advantaged students, enrollment patterns can lead to student sorting. The macro - level analysis goes beyond examining individual behavior to look for sorting from individual behavior. This is accomplished by looking at compositions of magnet schools and TPSs as well as the district overall. This information tells the district whether magnet schools are more integrated than TPSs, and whether or not the net effe ct for the district is segregation or integration. The micro - level analysis points towards advantaged students choosing a magnet school more often than traditionally underserved students. White, Asian, non - ELL , higher income, and higher performing student s are all more likely to choose than Black, Hispanic, ELL, lower income, and lower performing students. This is not necessarily a problem in the magnet school setting however, because magnet schools were created to do this. It becomes a problem when studen ts are more likely to leave schools that serve higher numbers of traditionally underserved students as this leads to student sorting. This appears to be the case in HISD where students leave schools that have fewer White students and more Black, lower perf orming, or students living at or below the poverty level , providing evidence of outgroup avoidance theory. At the same time, schools with higher proportions of Hispanics and ELLs were associated with fewer students 111 leaving for magnet schools. Because of the high proportions of Hispanics and ELLs in the district, neutral ethnocentrism could explain this. The results from the micro - level analysis that broke down magnet choosers across magnet structure should be highlighted. SWPs are the best at integrating schools for two reasons. First, they serve nonchoosers, who differ on average from choosers. Second, the nonchoosers are in the magnet program, so the integration is at the classroom level. Ideally, the district would want advantaged students choosing the se programs. The results pointed towards advantaged students choosing SWAS and SUS programs more often, however. The macro - level analysis explores the compositions of magnet schools, TPSs, and the district as a whole to better understand how the micro - lev el analysis plays out in the aggregate. The district does seem to be quite segregated when its composition is compared to that of the larger county and MSA geographical areas. This brings hope for integration if the district is able to attract students fro m outside the district. By comparing magnet school compositions to that of TPSs, I found magnet schools served higher proportions of advantaged students , especially SUS magnet schools . This does not however equate to integration. If advantaged magnet choo sers are leaving schools with higher proportions of traditionally un derserved students, the district could end up more segregated than it would be if these students attended their zoned school. When I looked at district - level integration from magnet school s, I found mixed evidence when comparing different segregation indices calculated for the ZSC and ESA compositions of the district. One of the indices pointed towards increased segregation, one pointed towards integration, and the third pointed towards b ot h, depending on the specific disadvantaged - advantaged comparison group . All in all, the district does not appear to be much different in composition than it would be if all magnet 112 choosers in the district attended their zoned school. However, if the magnet schools are more integrated, this means the TPSs are at least somewhat more segregated. I conclude by saying magnet schools are more integrated, but at the cost of segregating TPSs. The net effect s eems to be little change to district level integration or segregation. With this in mind, the results of the student achievement chapter become more important. If magnet schools are not integrating at the district level, there really needs to be evidence of student achievement benefits to consider magnet schoo ls beneficial to traditionally underserved students. 113 CHAPTER 5 STUDENT ACHIVEMENT IN MAGNET SCHOOLS While magnet schools were originally designed to integrate schools, their modern - day context has compromised their ability to do so. However, even if magnet schools fail to integrate, they could still be beneficial ; t his is especially true if traditionally underserved groups are the recipients of the special features of magnet schools. Various peer effect models lead to different hypotheses regarding student achieve ment gains from magnet schools, and the directionality of some of these hypotheses depend on whether or not the magnet schools are able to integrate. When magnet schools draw in higher achieving or more advantage students, one might expect h igher student achievement for a variety of reasons. These types of students require less inputs, leaving relatively more inputs for their peers. Additionally, models like the bad apple model and the shining light model predict positive correlations between own and peer achievement because students can either be a distraction or an encouragement, respectively (Hoxby & Weingarth, 2006). Alternatively, some peer effect models point towards better outcomes for students who attend school with similar peers. For example, the boutique model hypothesizes students will do better when the school specializes to serve students like them (Hoxby & Weingarth, 2006). 59 Thus, based on peer effect models, it is unclear whether or not magnet schools should be expected to lead to higher achievement. The answer most likely depends on whether or not they integrate and what type of magnet program it is. 59 See Hoxby and Wiengarth (2006) for a brief summary of the various peer effect models. 114 There are several reasons one might expect to see improved student achievement from magnet schools, regardless of their ability to integrate . Market theory posits we should see improved student outcomes from competitive pressures (Friedman, 1962) and reduced bureaucracy (Chubb & Moe, 1992). Additionally, magnet schools have specialized curricula and often have additional resources su ch as specially trained teachers and additional funding for special programs through grants and donations (U.S. Department of Education, 2006). Certain programs such as college preparation programs may improve achievement as measured by test scores, while other programs like performing arts might lead to other types of positive outcomes that are not measured by test scores (e.g., lower discipline rates). There could also be indirect curricular and instructional benefits research has shown how prejudices o f teachers and counselors can lead to low tracking and reduced expectations of racial minorities (see e.g. Oakes, 1985). Magnet schools could potentially reduce such tracking since scheduling and curriculum decisions are made at the program level. This ch apter examines the student achievement effects from the magnet school program in HISD. In particular, my research question asks two things: 1. What types of students stand to receive benefits from magnet schools (i.e., what types of students attend magnet sc hools, considering both in and out of program students, either by zoning or choice)? 2. Do magnet schools improve student outcomes as measured by math and reading scores, and are there differences across magnet student type, magnet program theme, or magnet s tructure? 115 Note the analysis considers all types of magnet students: nonprogram , zoned, and chooser magnet students. 60 This chapter begin s with a review of the literature that looks for student achievement effects from magnet schools . I go on to point out the many gaps in this body of literature, and I provide a summary of the contributions this work provides. Next, I explain how I model and analyze student achievement effects from magnet schools. Then I present the results of my analysis along with a disc uss ion of the ir implications and limitations. 5.1 Literature Review There are several recent studies that have examined the effects of magnet schools on student achievement. 61 Ballou, Goldring, and Liu (2006) studied a mid - size district in Tennessee that had a relatively even mix of Black and White students and a low proportion of Hispanics. Because magnet school attendance is endogenously determined, the authors use lottery outcomes as a source of random assignment. 62 They relied on lottery data from and standardized reading and math test scores from 1998 - 99 through 2002 - 03 for five magnet middle schools, with a final sample of 2,747 students. They found little evidence supporting gains in math or reading from magnet schools once student background charact eristics were accounted for, as the standard errors of the estimates were too large to rule out null or even negative effects. 63 60 Refer back to Table 2.1 for a summary of the various magnet student types. 61 I am only considering more recent (post - 2006) magnet achievement studies; studies prior to this time period are methodologically weak (Ballou et al., 2006). Additionally, older studies will have less of a connection to the modern - day context I am interested in studying. 62 Notice lottery outcomes are used, where the outcome refers to the result of the lottery drawing, not where the student actually ended up attending school. Selection bias and attrition issues enter in when the latter is used; thus, the lottery outcome is used in an instrumental v ariable approach. 63 Background characteristics were included in the model because by chance, random assignment from the lottery led to differences in these characteristics across lottery outcome. 116 Bifulco, Cobb, and Bell (2009) examined magnet school achievement using lottery data from Connecticut. They relied on lottery data from 2003 - 04 and student achievement data from 2001 - 02 through 20 06/07 . They conducted their analysis on a final sample of 553 students from two magnet schools. 64 The authors found the magnet schools were associated with higher scores in both reading a nd math by 0.14 and 0.28 standard deviations, respectively. 65 It is unclear why these results differ from the results in Tennessee , as there are many differences between the contexts of the studies . It is important to note that studies that rely on lottery data are limited in nature with regards to their generalizability. While lottery studies allow the researcher to use the lottery as a source of random assignment to the treatment, such studies are limited in their generalizability because they can only ex amine schools that are oversubscribed and thus rely on lotteries. It is highly plausible that oversubscribed schools lead to higher than average treatment effects, and researchers have fou nd evidence of this in both charter and magnet school setting s (Angr ist, Pathak, & Walters, 2012; Bifulco et al., 2009 a ). For this reason, quasi - experimental methods have been relied on more recently; such studies have the advantage of being generalizable across a larger subset of schools because they do not rely on lotter y data. Another shortcoming of the lottery data is that these studies tell us nothing about students who attend a magnet school they are zoned for. Depending on district policy, magnet schools may have students who are zoned for the school but are not in the magnet program; this would be the case for SWAS magnet programs that are housed within a larger TPS. 66 These students may 64 One of the magnet schools served 6th through 8th grade, an d the other served 6th through 12th grade. 65 The outcome variable was the student's standardized test score, where the score was standardized using the year - specific mean and standard deviation of the population. 66 Refer back to Chapter 2 for descriptions of different magnet program types. 117 receive spillover benefits from the magnet program in their school in a variety of ways, especially if the schools are able to int egrate. If the school has less underserved students because it is able to attract advantaged students, it is likely the learning environment for all of the students at the school is enhanced as there are relatively more resources and less distractions. Mag net schools may attract higher quality teachers as they are needed to teach specialized curriculum or because they have more advantaged students, and these teachers could end up teaching nonmagnet students as well. Additionally, some magnet schools have st udents who are zoned for a magnet school and are in the magnet program, but not by choice; this would be the case in certain SWPs that absorb all students who attend the TPS that houses the magnet school. In both cases, it would be interesting to understan d how these students are impacted by the magnet program that is at the school they are zoned to attend. In fact, as explained in Chapter 3, these non - choosing students are often relatively more underserved by the education system than students who choose i nto a magnet school, so it would be interesting to see whether or not they receive any benefits from magnet schools. Finally, because lottery studies rely on using different students as controls for other students, such studies have to be concerned with b alances in the data. More specifically, the group of students that are in the treatment group need to have control students that are similar to them. This balanced data issue becomes more of a problem in the later grades when there are fewer students enter ing into schools of choice from TPSs. When this is the case, unbalanced grades must be dropped. This is why Hoxby and Rockoff (2004) limited their analysis to students who enter charter schools in kindergarten through fifth grade. 118 To address one of the s ources of limited generalizability, Bifulco et al. (2009 a ) did a few other important things with their study. 67 First, they compared the results of the lottery analysis to results obtained using non - experimental methods on the same sample to see if we shoul d be concerned with the potential biases that arise when using such methods. They looked at two models, what they refer to as value - added and fixed - effect regressions. 68 The value - added model used student - level variables including age, gender, ethnicity, sp ecial education status in fourth grade, FRPL eligibility in fourth grade, and pre - treatment math and reading test scores from fourth and sixth grade to predict the student's score in eighth grade. The student fixed - effect model estimates student performanc e in time "t" and utilizes student fixed - effects to contr ol for time - invariant, unobservable heterogeneity at the student level. Thus, the non - random selection into schools of choice is controlled for by using the student as their own control and then diff erencing out these unobserved traits. The authors found small differences when comparing the estimates of these models to those of the lottery analysis; all differences were found to be statistically insignificant. Estimates from the value - added and fixed - effect regressions were 4% larger and 6% smaller than the lottery estimates for the math score and 22% larger and 10% larger than the lottery estimates for the reading score, respectively. Even the largest percentage difference, the difference between valu e - added reading and lottery reading estimates, is operationally small when looking at the actual difference in estimated effect size: 0.34 versus 0.28 standard deviations, respectively. The take away from this portion of the analysis is that 67 Their study does not address the limitations associated with excluding zoned magnet students from the study, because the magnet schools in this study had no zoned students. 68 They also did the analysis with propensity score matching, but the results were so similar to those obtained from the value - added analysis, they were excluded from the discussion. 119 lottery result s can be closely replicated using non - experimental regression techniques. 69 Thus, the sources of bias that Hoxby and Murarka (2006) worry about with regards to utilizing quasi - experimental methods in place of lottery data may not be much of an issue. Afte r Bifulco et al. (2009 a ) found non - experimental methods could closely replicate the results of the lottery analysis, they extended these non - experimental methods to a larger sample of magnet schools since they were no longer relying on lottery data. This p ortion of the analysis included twelve magnet high schools and seven magnet middle schools. The final sample included an analysis of 1,922 magnet school students. Both value - added and fixed - effect regressions found magnet schools at both the middle and hig h school level led to higher scores in reading and math. Finally, Bifulco et al. (2009 a ) utilized this larger sample to see if lotteried magnet schools are associated with larger gains than nonlotteried magnet schools, the primary concern about lottery stu dies. The authors found this pattern to hold in the data. There is evidence of this being the case when examining charter schools as well; schools that utilized lottery systems for admissions were associated with higher gains in student achievement (Angris t et al., 2012). There are some issues with the Bifulco et al. (2009 a ) study however. Their regression methods include relying on the assumption that previous years' educational inputs have no impact on the current year's test score. 70 Beyond methods, the context of the study is important to discuss. The magnet schools under study were part of an interdistrict choice program, and as part of this program, they had access to, and reserved seats for, a diverse set of students from across the districts that wer e part of this interdistrict choice program. Additionally, the magnet schools 69 Using the same dataset, Bifulco (2012) confirms these results after a more detailed analysis. He concludes "using pre treatment test scores reduces bias in nonexperimental methods between 64 and 96 percent" (p. 731). 70 This assumption and the alternatives will be explained in more detail in the methods section. 120 did not have any students that were zoned for them (neither in the program, nor outside of the program); thus the entire sample of students were choosers, which limits the genera lizability of the findings in three ways. 71 First, we are left with no input on how non - choosers are affected by magnet schools, the group of students magnet schools were originally designed to benefit (Orfield, 2013). Second, it is unclear how these result s would differ when magnet schools are educating a more diverse set of students as opposed to only choosers. Finally, in the theoretical framework, the authors hypothesize desegregation is the source of student achievement effects; the students who attende d the lotteried magnet programs ended up at schools that were more integrated. 72 Thus, it is not clear whether or not similar effects would be found when integration does not occur. 5.2 Contributions There are several gaps in the research literature that I seek to address. The magnet school achievement studies have had several contextual limitations that the data from HISD can address. 73 Elementary school students have been excluded from analysis in previous studies because of constraints with testing data ; no such restraint exists with the HISD dataset. The previous studies have all taken place in a school district or set of districts that have a relatively even mix of Black and White students and a low proportion of Hispanic students. It is unclear how re sults will change when magnet schools do not have access to a diverse set of students and are less able to integrate effectively. It is also unclear how magnet schools perform in districts 71 While fixed effects can control for time - invariant, unobse rved differences, there may still be differences in achievement growth trajectories across chooser status. Bifulco et al. (2009) found evidence against this in their analysis however. 72 Note that the authors are not able to confirm this hypothesis in the a nalysis because the sample of magnet schools is too small. 73 Refer back to Chapter 2 for a description of the dataset in use. 121 that serve large proportions of Hispanic students. HISD allows for the examination of these differences. Another major benefit of the HISD context is that a lot of the magnet schools have zoned students, both in and out of the magnet program. With this policy - induced source of variation, I am able to see how a much wider variety of students are affected by magnet schools. Additionally, I can confirm whether or not students whose parents formally participate in school choice via applying to a magnet school are different from students whose parents do not pick a school in th is way. This is the main source of bias that quasi - experimental methods are trying to address, so I am interested in seeing what the difference in achievement is between these groups of students. The large magnet system in HISD allows me to make addition al contributions to the literature. The largest magnet achievement study, Bifulco et al. (2009 a ) included 19 magnet schools, whereas HISD has over 100 magnet schools. This large sample of magnet schools will allow me to examine school level variables. Spec ifically, I can include indicators for different magnet program themes and structures to see if there are differences in their ability to influence student achievement. 74 I can also include peer composition of the school as a factor, something other authors have not been able to do with magnet schools because of the need for a large sample of schools (Bifulco & Ladd, 2006). Another benefit of this large sample of magnet schools is that I can look at the distribution of achievement levels from magnet schools, something that has been done in the charter school literature (Hanushek, Kain, Rivkin, & Branch, 2007), but has yet to be applied to magnet schools. Finally, Cullen, Jacobs, and Levitt (2005) say that the typically small sample size of magnet school stude nts is "an aspect that limits what can 74 Magnet program theme refers to the type of curriculum being offered; for example, fine arts or vanguard. Magnet structure refers to the setup of the magnet school; for example it is housed within a TPS (SWAS) or it absorbs the student population of the TP S that houses it (SWP). Refer to Chapter 2 for a detailed explanation of these topics. 122 be learned from studies of [magnet schools]," making it hard to learn about their benefits and spillover effects (p. 773). Because there are so many magnet schools in HISD, there is a large proportion of students bein g served by these schools, which allows me to better study these things. 5.3 Methods The methods I rely on build off of a growing body of literature that seeks to understand how various schools of choice impact student achievement. I begin this section by explaining how previous studies have modeled achievement. I then go on to describe my analytical plan for assessing the student achievement effects from magnet schools in HISD . I a lso include a description of the sample construction. Finally, I discuss the variables included in the analysis and provide justifications for their inclusion. 5.3.1 Modeling Achievement Many researchers have turned their attention towards student achievement effects from charter schools, and the methods from this line of research offer improvements over the non - experimental methods utilized by Bifulco et al. (2009 a ). As such, I relied on this research to design my analysis, with adaptations made for studying magnet schools as needed. This section details the formation of the empirical model and the various assumptions behind it . The modeling of this pr oblem relies substantially on work conducted by Bifulco and Ladd (2006), Hanushek, et al. (2007), Imberman (2011), and Sass (2006). 75 75 Mills (2013) uses the same strategies as these other authors for charter schools in a different location, but since this author directly borrows from Sass (2006) and H anushek et al. (2007), I will only be referring to the direct sources. 123 Educational achievement can be modeled through the use of a production function, where various inputs go into producing t he academic achievement of a student. Equation 5.1 shows a typical educational production function (5.1) where student achievement (A) is a function of school inputs (S), time - varying, observable student and fami lial characteristics (X), time - invariant, unobservable student and familial characteristics ( The production function for education should be viewed as cumulative in nature, meaning prior inputs have impacts on current pro duction. For this reason, the production function is really a function of "input histories" for S, X, and (Sass, 2006, p. 8). If we further assume the production function is additive in nature, does not vary with age, and the effects of the control vari ables do not vary by grade it can be written as: (5.2) where student achievement for student "i" at time "T" is a function of all inputs from previous time periods. 76 It is assumed the impact of previous inputs declines exponentially as a function of time at a rate of 1 - , where 0 . 77 The researchers go a few different directions from here, as more assumptions have to be introduced before estimation is possible. Bifulco and Ladd (2006) and Bifulco et al. (2009 a ) use similar strategies they use a value - added model to estimate the growth in achievement. 78 After taking the first - difference of Equation 5.2 and assuming = 1, Equation 5.2 becomes: 76 Bifulco and Ladd (2006), Sass (2006), and Hanushek et al. (2007) all begin with these assumptions and work with a variant of this model. 77 Note that the equation also shows the rate o f depreciation as being the same for all inputs, but this does not have to be an assumption of the model. This is merely done for ease of discussion. 78 Alternatively, this is referred to as a growth model. 124 (5.3) This assumption regarding implies the value of educational inputs never depreciates; in other words, inputs received in the second grade have as much of an im pact on eighth grade scores as they do on second grade scores. Bifulco and Ladd (2006) try an alternative specification by utilizing a levels model, which models the achievement level, not the growth in achievement. They further assume = 0, which in thi s case, transforms Equation 5.2 into the following: (5.4) The assumption that = 0 implies the value of educational inputs has a onetime benefit; so for example, fourth grade i nputs have no effect on fifth grade scores. Bifuclo and Ladd (2006) do not include a student fixed effect in this portion of the analysis, leaving time - invariant unobservables accounted for. Additionally, prior achievement is also excluded and thus absorbe d by the error term, leading to an upward bias of the estimates (Imberman, 2011). Finally, the assumptions regarding seem unrealistic, and thus the estimates from both 5.3 and 5.4 are likely biased. Sass (2006) and Hanushek et al. (2007) both utilize d a strategy that does not impose a specific value on . Instead of estimating the growth in achievement as in Equation 5.3, the lagged achievement becomes a regressor, as shown in Equation 5.5. (5.5) However, the inclusion of fixed effects in a dynamic panel data model leads to bias, and the problem is more severe for datasets with short panels (Nickell, 1981). Sass (2006) and Hanushek et al. (2007) use estimatio n techniques that rely on scores that are lagged twice or more as an instrument for once - lagged achievement. While no restrictions are placed on the value of , the 125 estimates are likely biased because it is unlikely higher order lags are exogenous (Imberm an, 2011; Todd & Wolpin, 2007). Imberman (2011), who studie d achievement from charter schools in a large urban district in the South, recognizes the bias that is introduced by these other methodologies. He goes on to prove that one can obtain the boundaries for the true parameters by estimating a value - added model and a levels model, each with a student fixed effect. 79 This is the strategy I will employ, because it acknowledges the biases that arise in quasi - experimental methods but utilizes this knowledge in a constructive way a way that allows the researcher to c lose in on the true estimates. Thus I will be estimating a value - added model similar to that shown in Equation 5.3 and a levels model like that shown in Equation 5.4 except with a student fixed effect also included. 5.3. 2 Analytical Plan As a preliminar y look at the achievement effects of magnet schools, I look at the kernel density plot for achievement in reading and math and compare magnet schools to TPSs. Hanushek et al. (2007) use this strategy with charter schools. They found charter schools had a w ider achievement distribution than TPSs; this information adds detail that the regression models leave out. At the same time, selection bias is not addressed by this method, so it is insufficient on its own. I also include descriptive statistics and t - tes ts to summarize the entire group of students who attend magnet schools. 80 I am interested in seeing what types of students are potentially receiving benefits from magnet schools. I especially want to know about the zoned magnet 79 Imberman (2011) provided a mathematical proof of this in the Appendix. 80 Similar analyses were included in Chapter 4, but that portion only considered nonzoned magnet students; here, zoned magnet students are also included. 126 students because nonchoosers in urban districts tend to be amongst the most underserved students, and this is typically the group of students researchers are concerned about when they are looking for student sorting from school choice. Thus, I also include a sub - analysis that describe s zoned magnet - students. Finally, I describe the sample of students who are considered nonprogram magnet students, as there could potentially be spillover effects related to integration or peer effects. I begin the model portion of my analysis by estimat ing the simple levels model Bifulco and Ladd (2006) utilize as a baseline analysis (Equation 5.4). Normally there is a concern regarding nonrandom selection into schools of choice when trying to identify achievement effects. When all students are in a scho ol by choice, you are unable to distinguish whether any benefits are due to the school or due to some unobservable background characteristics that the students have in common. In HISD however, there are students who are zoned into magnet programs. This giv es me the opportunity to make a first - attempt at estimating a proxy for parental involvement. If the thought is that parents who participate in school choice in a formal manner are somehow more motivated or involved in the education of their children, this should emerge in differences in student achievement. Because of this source of variation, I estimate the difference in achievement scores between zoned and non - zoned magnet students by including a series of dummy variables that indicate the students' magn et status. Additionally, because of this unique characteristic, I can see how different the OLS estimates are from a more sophisticated model that is designed to handle the typical nonrandom assignment into schools of choice. During this process, I build i n the vectors of control variables to see how the estimates for the independent variables change. 127 Beyond the baseline analysis, I estimate two other sets of models. As explained in Section 5.3.1, these two sets of models are used because they bind the tru e parameters, and the value - added models in particular have the least restrictive assumptions of those discussed. Additionally, because quasi - experimental methods have been found to closely replicate lottery findings, I am less concerned about the potentia l biases that are discussed in the limitations section. For both sets of models, I estimate one model for each set of independent variables (magnet student type, magnet program theme, and magnet structure). 81 First I estimate a series of levels models (Equa tion 5.4), but I also include a student fixed effect to capture time - invariant background characteristics, similar to the levels model used by Imberman (2011). These estimates provide the upper limit when the true parameter is positive and the lower limit otherwise (Imberman, 2011). To obtain the other boundary for the true parameters, I also estimate a series of value - added models that include a student fixed - effect (Equation 5.3). For both the levels models with student fixed effects and value - added mod els with student fixed - effect, each set of models is run twice. Once without peer composition variables included and once with them included. I do this for a couple of reasons. Magnet schools were originally created to integrate schools, thus if I control for peer composition, I am in effect taking away part of what is supposed to make magnet schools effective. Additionally, with respect to the magnet structure variables, a lot of what makes these structures different from one another relates to the peer co mposition; so again, controlling for peer composition could make magnets look less effective. At the same time, it is unfair to give magnet schools credit for achievement gains that are simply a reflection of the makeup of the school. Finally, this work ce nters on modern - day magnet schools magnet schools that are less able to integrate; therefore, I want to 81 Section 5.3.4 and Table 5.3 detail the three sets of control variables. 128 see how effective magnet schools are outside of any benefits related to changing the peer composition of schools. 5.3.3 Sample Data for this analys is includes students who attended either a traditional public school or a magnet school at some point between 20 07/08 and 20 13/14 . Students attending charter schools or alternative schools have been dropped from the sample so that magnet outcome s are compa red to TPS outcomes. Because the analysis is centered on student achievement, o nly students who are in tested grades are in the sample. Additionally, students taking the Spanish version of the exam (Aprenda) are dropped from the sample beca use of different scaling used for the different language versions . 82 For the descriptive portion of the analysis, the sample was further narrowed as I had to drop students who are missing various background data. The dataset was missing PEIMS data for roughly 40,000 stud ents, so these students are excluded from the analysis. 83 Additionally, the sample was reduced due to data anomalies. The coding for ethnicity changed half - way through the years beginning in 20 10/11 , multiracial became an option. When possible, I used dat a from prior years to identify a single race for these students. When a single race could not be identified, the student was dropped from the sample. For some students, gender was not time - invariant. When gender varied, the most frequently reported gender is used in all years, and in the case of a tie, the student was dropped from the sample. Finally, students are only included in the descriptive and regression analysis if they have both reading and math scores. 84 82 Thi s issue is discussed in more detail in Section 5.3.4 83 There is no indication of why PEIMS data was not collected for this group of students. 84 As is detailed in section 5.3, students are tested in grades K through 11 through 2009/10 and grades K through 8 thereafter 129 For the model portion of the analysis, I c reated an analytical sample; thus, all of the regression models utilize the same set of students. The sample varied across models for a couple of reasons. First, some models rely on lagged data; specifically, those models that include the structural and no nstructural move variables and the value - added models require students to have at least two years of data. Students without lagged data are dropped from the sample. Second, the models build in vectors of variables, and some variables did not have as many o bservations because they came from a dataset that was merged with the main dataset provided by HERC . 85 The sample construction for the various portions of the analysis is summarized in Table 5.1. Table 5.1 . Sample Construction Reason for Dropping Number Dropped Number Remaining Sample Use Starting s ample (student - year) 1,757,893 Charter 123,961 1,633,932 Alternative 24,020 1,609,912 Nontested grade 281,633 1,328,279 Aprenda 203,860 1,124,419 Kernel density plots No PEIMS data 119,355 1,005,064 Multiracial 1,846 1,003,218 Time - varying gender 726 1,002,492 Missing reading or math score 81,645 920,847 Describing magnet students No lagged data 331,232 589,615 Other missing data 26,760 562,855 Analytical sample 85 As explained in Chapter 2, variables in the dataset were merged in from a few different datasets provided by HERC. 130 5.3.4 Variables 5.3.4.1 Dependent Variable I estimated models for two separate dependent variables: reading and math scores on standardized exams. 86 There are several different types of scores available for modeling. The specific exam used by the district varies by year, grade, and language version. Table 5.2 summarizes the various exams utilized by HISD. Table 5.2. Exam Versions by Grade and Year Year TAKS STAAR Stanford Aprenda English Spanish English Spanish English Spanish 06/07 3 - 11 3 - 6 None None K - 11 K - 8 07/08 3 - 11 3 - 6 None None K - 11 K - 8 08/0 9 3 - 11 3 - 6 None None K - 11 K - 8 09/10 3 - 11 3 - 5 None None K - 11 K - 8 10/11 3 - 11 3 - 5 None None K - 11 K - 8 11/12 10 - 11 None 3 - 8, some 9* 3 - 5 K - 8 K - 8 12/13 11 None 3 - 8, some 9 and 10* 3 - 5 K - 8 K - 8 13/14 None None 3 - 8; some 9 - 11* 3 - 5 K - 8 K - 8 Unless marked with a *, grades listed are the same for both reading and math exams. *Because the STAAR exam shifts to end of course exams in high school as opposed to end of grade exams, timing for the English I and II, Algebra, and Geometry exams varies. Some students will not have high school math scores at all because they took Algebra prior to high school. The Texas Assessment o f Knowledge and Skills (TAKS) exam was the main state assessment from 2002 - 03 through 2010/11, and was given to all students in grades 3 - 11. TAKS was designed by the state of Texas and was aligned with the Texas Essential Knowledge and Skills (TEKS), the s tate designed standards for content area mastery. During this time period, 86 Note that reading scores become English language arts scores in 10th and 11th grade for the TAKS and STAAR exams. 131 TAKS was the sole source of the student performance measure that is required for tracking adequate yearly p rogress (AYP) as required by NCLB . 87 TAKS was also used as part of what de termines promotion to the next grade in certain grades (HERC, 2014). Different versions of the exam are available for students who need accommodations, modifications, alterations, or language accommodations (TEA Student Assessment Division, 2010). The st ate of Texas designed a new test, the State of Texas Assessments of Academic Readiness (STAAR), to replace TAKS. STAAR was phased in starting in 20 11/12 and fully replaced TAKS by 20 13/14 . This exam is given to all students in grades 3 - 8. A major differenc e with the STAAR exam was a shift towards end of course exams in place of end of grade exams in high school. Thus, instead of taking a math and an English exam at the end of every grade in high school, students take particular exams, such as Algebra and Ge ometry, at the end of the corresponding course. While this may be better for tracking student learning because the tests are better aligned with the courses a student has taken in high school, it leads to missing occurrences in high school at higher rates. Additionally, this missingness is nonrandom students who take math courses earlier will have more missing scores, and this selection problem worsens as the grade level increases. An alternative to the TAKS and STAAR data, are the Stanford and Aprenda s cores. Scores from these exams are used as a part of each of the following: the school's measure of accountability, the passing criterion for moving on through grades 1 - 8, and determining gifted and talented status (HISD Department of Research and Accounta bility , 2015 b ). Additionally, these tests were designed to allow for norm - referencing to a national sample. Finally, the district uses these tests so they can track student progress both in grades and subjects that are not tested 87 For more information on how AYP is determined in HISD, refer to HISD Department of Research and Accountability (2012). 132 by TAKS or STAAR. The Stan ford exam was given to students in HISD in grades K - 11 until 20 10/11 ; beyond this, it continues to be offered in grades K - 8. In all years of the dataset, Spanish speaking ELLs in grades K - 8 often take the Aprenda exam instead of the Stanford exam. The Apre nda exam is designed specifically for Spanish speaking students . T he exams are similar in content but not identical , and the scores are not scaled in the same way (HISD Department of Research and Accountability, 2015 a ). Because of the inconsistencies in the implementation of exams across years and grades throughout the dataset, I had to face some tradeoffs in determining which scores to rely on. Although TAKS and STAAR are the official exams required by the state to measure AYP, the gradual transition fro m TAKS to STAAR and the new end of course scheme, make it difficult to use these scores at the high school level past 20 10/11 . A similar problem emerges with the Stanford and Aprenda scores when these exams are no longer given to high school students after 20 10/11 . However, the Stanford and Aprenda scores have the advantage of being offered in more grades , and they are offered across all years of the dataset . Additionally, for the testing grades that align with those of TAKS and STAAR, the Stanford and Apre nda exams account for more students. 88 For these reasons, I chose to utilize the Stanford exams for my analysis. Unfortunately, because of the differences in scoring and in the group of students taking the Stanford and Aprenda exams, I cannot compare scores from different language versions. Therefore, I have to drop students taking the Spanish version of the exam, a problem that would have arisen using TAKS and STAAR as well. I converted the Stanford scaled scores into z - scores so that tests from different grades and years can be compared to one another; raw scores are not comparable because of differences in 88 There are roughly 3,000 additional students with Stanford and Aprenda test scores each year. 133 testing across grade and year (Hanushek et al., 2003). For example, raw scores may have different scales or exams may have a different amount of questi ons across grades or years. To standardize the dependent variable, I relied on testing data for all students taking the Stanford exam in the district, and I standardized the scores by grade, and year. 89 5.3.4.2 Independent and Control Variables The indepen dent and control variables are separated into three groups: family and student background characteristics, special student statuses, school - level variables, and test controls. The school - level variable group includes magnet school indicators as a new addit ion to this type of study. As detailed below, the rest of the variables are included based on similar work conducted by other researchers. Student Background Characteristics : A student's family provides many inputs into their education (e.g., helping wit h homework, books, etc.). Such inputs typically vary with access to various resources, and thus proxies for family inputs into education are derived from information regarding the family background (e.g., poverty status). Characteristics about the students themselves are also important predictors of student achievement. There are several student characteristics that I can account for with the data, but many characteristics are unobservable in nature (e.g., grit). Additionally, many of the family background characteristics are unobservable or I do not have access to them in the HISD dataset. Fortunately, so long as these characteristics do not vary over time, they can be controlled for using other methods such as student fixed effects or difference - in - differe nce methods. Free - and - reduced - price - lunch : I use free - and - reduced - price lunch (FRPL) status as a measure of SES. It has long been recognized that SES is positively related to student 89 Note that I will also include a dummy variable t o indicate which exam version the student took. 134 achievement (see e.g., Coleman et al., 1966). There are numerous explan ations for this link between SES and achievement, such as access to more resources, and the link is getting stronger with time (Reardon, 2011). I have access to a more finely grained breakdown of FRPL status that includes four groups: students ineligible f or FRPL, students eligible for reduced lunch, students eligible for free lunch, but who are living above the poverty line , and students who for are eligible for free lunch and live at or below the poverty line . I include a series of dummy indicators for st udents who are living at 131 - 185% of the poverty line , 101 - 130% of the poverty line , and at or below the poverty line , with the reference group being students who are living above 185% of the poverty line (students who are not eligible for FRPL). Immigrant status : Immigrant status is important in this context because this group often has less of the various types of capital that are linked to higher student achievement. While some of this is captured by other variables such as the FRPL and home lan guage indicators, there are still other important differences between immigrants and nonimmigrants. Immigrants are less familiar with U.S. schools and often lack the cultural capital that is beneficial in U.S. schools (Mavrogordato, 2012). I include a dumm y indicator for the students' immigrant status. Students are considered an immigrant if they were born outside of the United States and they have not attended U.S. schools for at least three years. Such an indicator is meant to capture any negative impacts on achievement that are associated with being new to the United States and its schools. Student moves : I utilize a set of indicator dummies to capture different types of student moves. The first indicator is for structural moves. Structural moves occur i n two ways, school level shifts and school closures and openings. The former refers to when students change school levels (e.g., go from elementary to middle school). In the charter literature, many of the authors also consider it a structural move if a st udent moved to a new school in the current year with 135 more than 10% of their previous year's class (see e.g., Bifulco & Ladd, 2006; Imberman, 2011), which typically occurs in the case of school closures and openings; this is how I defined the variable as we ll. When structural moves occur, students are changing schools, and at the same time, so did some or many of their classmates. This can be disruptive to achievement trajectories and should be included as an indicator (Bifulco & Ladd, 2006). The second indi cator is for students who made a non - structural move; in other words, students who made any other type of school move. When students move and change schools, this may be disruptive to their educational trajectory in ways that are different from the effects associated with structural moves (Bifulco & Ladd, 2006). I include a dummy indicator that includes students who moved to the district or changed addresses within the district during the school year. Special Student Statuses : There are several student sta tuses that are related to student achievement, either directly or indirectly. Such statuses also impact what special services students are eligible for, and such services act as inputs in achievement. Because these statuses can vary over time, they will no t be absorbed by a student fixed effect. I will include a series of dummy indicators for the following student statuses: gifted and talented, special education, limited English proficiency, and parent denial. Gifted and Talented : These students are highe r performing students by their nature. They are defined as a student "who performs at or shows the potential for performing at a remarkably high level of accomplishment when compared to others of the same age, experience, or environment. . . ." (Texas Educ ation Code, 2013). 136 Special Education : Special education students, by definition, have an impediment to learning, and these students are legally entitled to receive specialized instruction (Texas Project First, 2015 ). 90 Thus, this groups of students is more difficult and costly to educate. English Language Learner : I control for ELL status because ELLs face additional struggles when taking achievement exams. These students are tasked with learning English on top of lear ning subject material (Abedi & Gandara, 2006). Further, some of these students are tested in English; for these students, English comprehension then becomes part of what is being tested in addition to the subject material of the exam (Abedi, 2005). Finally , exams are often unnecessarily, linguistically complex or make cultural references that lead to unfair assessment of ELLs (Abedi, 2005). Parent Denia l: Students who are found to have limited English proficiency have a legal right to English language ser vices (Lau v. Nichols, 1974). Parents may however deny such services ; such students are then flagged as parent denials. Parent denials could be linked to student achievement in multiple ways. First, a lot of research points towards the importance of langu age services with respect to fostering the learning of ELLs (see e.g., Collier & Thomas, 2004; Greene, 1997). Students who do not utilize such services may have a harder time learning English and thus also have a harder time learning subject material. At t he same time, being classified as an ELL may lead to negative consequences such as tracking ELLs into classes that provide them with limited opportunities (Callahan, 2005; Callahan, Wilkinson, Muller, & Firsco, 2009). As a final possibility, because denyin g services takes effort on the part of the parent, parents who deny services may be more involved in their child's education; thus, a parent denial 90 There are many laws that govern special education services and eligibility. For HISD, the applicable laws are summarized here: http://www.texasprojectfirst.org/FedRulesLaws.html . 137 could be linked to higher achievement as it is some proxy for parental involvement (Harris & Mavrogordato, 2 015). Time - invariant, observable student characteristics : This set of variables includes traditional dummy indicators for gender and race, as well as an indicator for home language status, where male, White, and English are the reference groups, respectiv ely. Note that this group of variables will drop out of the analysis when student fixed - effects are included. Gender is included because of known differences across gender in performance on standardized exams. Females tend to do better on reading achieveme nt exams while males tend to have the higher math achievement scores (Voyer & Voyer, 2014). Race is included because of the known achievement gaps that appear when looking at achievement across race; Black - White achievement gaps (Reardon, 2011) and Hispani c - White achievement gaps (Reardon & Galindo, 2008) are well documented. Finally, home language status is included because students whose parents speak a language other than English will have a harder time participating in their child's schooling because of language barriers (Oakes & Lipton, 2003). Additionally, similar to the immigrant subgroup, this group of students most likely have parents that have less capital that is found to be useful in the U.S. schooling system (Mavrogordato, 2012). School - Level V ariables : This group of variables consists of the relevant school - level variables. Included are peer composition variables, an indicator for International Baccalaureate ( IB ) programs, as well as the independent variables of interest, magnet school enrollme nt, which is broken down in three different ways, each is detailed further below. Independent variable group A (IVGA) is a set of dummies indicating the students' magnet student status. Independent variable group B (IVGB) is a set of dummies indicating the magnet program theme the student is in. Finally, independent variable group C (IVGC) is a set of dummies indicating the magnet 138 structure the student is in. These different groups cannot be used in conjunction with one another because this would result in perfect multicollinearity. 91 I estimate different versions of the model; one for each independent variable group. Magnet student status : I am including a set of indicator variables for non - zoned magnet students, zoned magnet students, and magnet TPS - studen ts. Non - magnet TPS students will be the reference group for most of the analysis. For a portion of the analysis however, I will include a dummy variable for non - magnet TPS students and have zoned magnet students as the reference group; this is further expl ained in the analytical plan section. 92 The estimates of these parameters will show whether or not the various types of magnet school students benefit from student achievement gains. Magnet program theme : The program theme of a magnet school refers to the type of curriculum that is in place. There are various magnet themes available in HISD, including: vanguard (gifted and talented), Montessori, STEM , language, fine arts, college prep, and career academies (HISD Office of School Choice, 2013). Because of the differences in curriculum by program theme, achievement effects are likely to vary by program theme. A group of dummy indicators will be included for the various program themes. Only students who are in the magnet program are flagged as having a program theme . N on program magnet students do not have any magnet theme indicated. Students not in a magnet program form the reference group. Magnet program structure : In addition to the various magnet program t hemes, there are multiple structural setups. SWPs include the entire student population in the magnet program, 91 When a group of regressor s is a perfect linear combination of another group of regressors, including all of these regressors will result in perfect multicollinearity and estimates cannot be calculated. Here, the base group for all three independent variable groups is nonmagnet stu dents. Thus, the different independent variable groups each sum to one, and including them with one another will result in perfect multicollinearity. 92 Refer to Table 2.# for a summary of the various magnet student types. 139 and there are both zoned and non - zoned students in the school. SUSs also provide the magnet program to the entire school, but no students are zon ed for the school. Finally, SWAS magnet schools have a zoned student population, but they are not a part of the magnet program; only students who apply for the magnet program are in the magnet program. I will include a series of program structure indicator s. Again, only students who are in a magnet program are flagged for having a magnet structure , and students who are not in a magnet program form the reference group. Peer composition : Besides the set of magnet school variables, Hanushek, Kain, Markman, an d Rivkin (2003) show that the achievement of peers is positively related to a student's achievement trajectory. Hanushek et al. (2007) and Bifulco and Ladd (2006) recommend the inclusion peer achievement if the sample of schools is large enough to allow fo r this. As such, the peer composition of the school, as measured by the average achievement of peers will be included. Additionally, like Hanushek et al. (2007), I will include a set of school - level demographic composition variables because the student com position of a school is related to a wide variety of school quality indicators (Hanushek, Kain, & Rivkin, 2002; Orfield, 2013). International Baccalaureate : Many of the schools in HISD, both TPS and magnet, offer an IB program. This program provides speci alized curriculum and instruction. Schools must be authorized to call themselves an IB world school. 93 This special programming could lead to improved student outcomes, and such effects should be separated from those of magnet schools; thus, I include an in dicator for schools offering this programming. Test Controls : A series of dummy variables are included to control for differences that arise in testing. Grade, year, and grade - by - year dummies are typically included to capture any 93 For more information on IB progr amming and authorization, see http://www.ibo.org/ . 140 differences that may aris e in tests that could impact student scores (see e.g., Hanushek et al., 2003; Imberman, 2011). For example, a test may be unusually hard in one year or in one grade. Table 5.3 provides a summary of both the independent and control variables. Along with t his is a description of any data cleaning that affected the variables. Table 5.3 . Description of Independent and Control Variables Variable Name Description Student Background Race or Ethnicity A series of dummy variables describing the race or ethnicity of a student that includes the following categories: White, Black or Native American , Hispanic , and Asian or Pacific Islander , where Yes=1, No=0 and White is the base group. The ethnicity variable switched to include multi - racial midway through t he dataset. Previous year data was used to identify a single race for multi - racial students when possible; if not possible, the student was dropped from the dataset. Female A dummy variable indicating the student is a female, where Yes=1, No=0. The gender variable was cleaned to be time - invariant. The gender that was reported most frequently across time was used for all time periods; if there was a tie, the student was dropped. Poverty Status A series of dummy variables for various poverty levels that inc ludes the following categories: At or b elow p overty l ine (free lunch), 101 - 130% p overty line (free lunch) , 131 - 185% p overty line (reduced lunch), a bove 185% p overty line (no n - FRPL ), where Yes=1, No=0 and a bove 185% p overty line is the base group. The poverty level used here is set by the U.S. Department of Agriculture, and this variable is tracked by HISD for the purposes of determining FRPL status. Home Language Not English home language is not English, where Yes=1, No=0. Immigrant Status A dummy variable indicating the student was born outside the U.S. and has not been enrolled in U.S. schools at any point in the last three years, where Yes=1, No=0. Note that by this defini tion, all pre - K through 1st graders are flagged as immigrants if born outside the U.S. Student Move A series of dummy variables that indicates the student is changing schools. The categories included are : n o m ove, s tructural m ove, n onstructural m ove , wher e Yes=1, No=0 and n o Move is the base group. Special Student Statuses Gifted and Talented A dummy variable that indicates the student has been identified as gifted and talented, where, Yes=1, No=0. Special Education A dummy variable that indicates the student has an individualized education plan because of a cognitive, physical or emotional disability and consequently receives special education services, where Yes=1, No=0. 141 Table 5.3. (cont'd) Variable Name Description ELL Status A dummy variable that indicates the student is an English language learner, where . Yes=1, No=0 . In other words, they have been categorized as having limited English proficiency and are therefore eligible for English language services Parent Denied ELL Services A dummy variable that indicates the parent chose to deny or waive English language services, where Yes=1, No=0. School - Level Variables Magnet Student Status (Independent Variable Group A) A series of dummy variables that indicate the students' magnet program and chooser status. The following categories are included: student is in a magnet program by choice, in a magnet program by zoning, in a magnet school but not in the program, or in a nonmagnet school , where Yes=1, No=0 and n onmagnet school student is the base group. Magnet Structure ( Independent Variable Group B) A series of dummy variables indicating the magnet structure type where the following categories are included: SWAS, SWP, and SUS , where Yes=1 and No=0, and SWP is the base group. Magnet Program Theme ( Independent Variable Group C) A series of dummy v ariables indicating the magnet program type where the following categories are included: vanguard, STEM, language and humanities, performing and fine arts, college prep, career academies, and other , where Yes=1 and No=0, and no - program is the base group. T he other category includes themes that did not have enough schools to include them as their own category; these themes had three or fewer schools. A couple of the themes did not fall into one category (e.g., math and foreign language); these themes are als o included in the other category. The following types of magnets were included in the other category: academy, architecture and graphic design, communications, flexible learning, integrated technology, international studies center, leadership, math and for eign language, medical health science, technology and fine arts, and Montessori. Peer Composition Includes a series of school - level variables that constructs the percentage of certain student subgroups at each student's enrolled school. The following vari ables are included: % White, % Hispanic, % Black, % ELL, % special education, % gifted and talented, % at or below poverty, and % chooser. Note here that for the purpose of calculating peer composition, SWAS magnets are treated as part of the TPS that hous es it. IB Status A dummy variable that indicates the student attends a school that has an International Baccalaureate (IB) program, where, Yes=1, No=0. Many magnet schools also have IB programs, but when this is the case, they always have a separate magne t theme; the theme is not IB. Such schools would thus have both an IB flag and a theme flag. Test Controls Grade, year, and grade - by - year dummies A series of dummy and interaction terms that cover each grade, year, and grade - year combination. 142 5.4 Results As a first glance at average achievement in magnet schools as compared to TPSs, Figures 5.1 and 5.2 provide kernel density plots of math and reading achievement, respectively. Similar to the results of Hanushek et al. (2007), magnet schools seem to have a wider distribution of scores than TPSs. An important difference emerges however; when compared to the distribution of TPSs, the charter schools in Hanushek et al. (2007) had a higher density of scores on the lo wer end of the distribution, whereas the magnet schools in this study have a higher density of scores on the upper end of the distribution. This is true for both reading and math scores. However, no background factors are accounted for in this portion of t he analysis; thus, it is unclear whether or not higher scores in magnet schools are a result of non - random selection into magnet schools. Figure 5 .1. Kernel Density Plots of Math Achievement for Magnet Schools and TPSs 143 Figure 5 . 2 . Kernel Density Plots of Reading Achievement for Magnet Schools and TPSs In Table 5.4, I show the mean and standard deviation for family and student characteristics and outcome variables, by magnet student status. 94 Looking at the outcome variables, higher reading and math scores are related to being a magnet program student, regardless of whether the student is there by choice or by zoning. The scores are dramatically higher for the group that attends magnet schools by choice, which is likely an indication of a selection bias problem. The nonprogram magnet students appear to perform worse than nonmagnet school students; it may however be the case that magnet programs are included in typically lower performing TPSs by design. 94 I include a larger sample of students for this portion of the analysis to get a better picture of which students are served by magnet schools in HISD. As detailed in section 5.3.3, the analytical sample includes fewer students because lagged data are relied on. Summary statistics for the analytical sample are provided in Table A.3 of the appendix. Refer to Table 2.1 for a description of the various magnet student types. 144 Table 5.4 . Describing Magnet Students: Summary Statistics by Magnet Student Type Magnet Student Type Nonm agnet - TPS Student Nonprogram Magnet - Student Zoned Magnet - Student Magnet Chooser Variable Female 0.48 0.48 0.49 0.54 (0.50) (0.50) (0.50) (0.50) {3.02} {0.89} {10.14} White 0.06 0.08 0.26 0.15 (0.23) (0.28) (0.44) (0.36) {1.15} {2.63} {3.84} Black or N ative A merican 0.33 0.28 0.29 0.32 (0.47) (0.45) (0.46) (0.47) {1.19} {0.47} {0.32} Hispanic 0.58 0.60 0.36 0.46 (0.49) (0.49) (0.48) (0.50) {0.56} {3.03} {2.98} Asian 0.03 0.03 0.08 0.07 (0.18) (0.17) (0.27) (0.25) {0.52} {1.93} {2.53} Poverty 0.35 0.24 0.23 0.18 (0.48) (0.43) (0.42) (0.38) {5.64} {2.62} {9.21} Free Lunch 0.43 0.45 0.27 0.32 (0.49) (0.50) (0.45) (0.46) {0.81} {3.28} {5.60} Reduced Lunch 0.08 0.09 0.07 0.12 (0.28) (0.28) (0.26) (0.32) {1.20} {0.85} {6.55} Home Lang not Eng 0.38 0.45 0.23 0.31 (0.49) (0.50) (0.42) (0.46) {2.24} {4.53} {2.62} Immigrant 0.03 0.03 0.03 0.01 (0.16) (0.17) (0.17) (0.08) {0.66} {0.30} {4.87} Gifted & Talented 0.11 0.08 0.23 0.41 (0.31) (0.27) (0.42) (0.49) {1.83} {2.59} {8.41} Special Ed uc 0.08 0.11 0.07 0.04 (0.27) (0.32) (0.25) (0.19) {5.50} {3.01} {8.66} 145 Table 5.4. (cont'd) Magnet Student Type Variable Nonm agnet - TPS Student Nonprogram Magnet - Student Zoned Magnet - Student Magnet Chooser Parent Denial (0.21) (0.11) (0.18) (0.13) {9.11} {1.76} {7.40} ELL 0.20 0.15 0.11 0.06 (0.40) (0.36) (0.32) (0.24) {3.06} {4.12} {12.15} For each variable, the mean is shown and the standard deviation is below in parentheses. For each type of magnet student, the absolute T - statistic from a regression of each individual variable on magnet student status is shown in brackets. The sample size of 920,847 includes data for 307,189 students, and 241,450 of these students attended a school with a magnet program at some point in the dataset. I specifically want ed to examine what the zoned magnet students and nonpr ogram magnet students look like to see what types of students are served by magnet schools outside of the choice mechanism. The composition variables show students in magnet schools are exposed to higher proportions of white students, lower proportions of students in poverty, and lower proportions of Hispanics and ELLs. The higher proportion of White students seems to stem from a large proportion of White students being zoned for a magnet school program. Integration should be more successful when underserve d students are zoned for magnet schools (regardless of program status) and advantaged students are in a magnet program by choice. This is not the pattern that emerges however. The highest proportions of White students and Asian students actually fall withi n the zoned for program group. At the same time, Hispanics are underrepresented in this group; they make up a much larger proportion of the nonmagnet and nonprogram groups as compared to the two groups that are in magnet programs. The nonmagnet and nonprog ram magnet student group s ha ve over 10% more Hispanic students than the magnet chooser group and over 20% more than the zoned magnet student grou p. Poverty rates are lower 146 for all three of the magnet student groups as compared to the nonmagnet student grou p . These enrollment patterns are concerning if the goal is to use magnet schools to integrate schools. Some more promising results emerge when looking at enrollment across ELL, home language , and immigrant status. While ELLs are underrepresented in the program chooser group, t here are almost twice as many ELLs in a magnet program via zoning and almost triple the number in the nonprogram magnet group ; however, the rates are still noticeably lower than the proportion of ELLs who are not in a magnet school. The home language status indicator shows students with non - English speaking parents are in magnet schools by choice at rates similar to those in the nonmagnet school group, and the rate for the nonprogram magnet group is even higher. As explained in Chapt er 2, this group of students faces many hurdles when it comes to participating in choice (see e.g., Haynes et al., 2010), so it is good to see a large representation of these students in magnet schools, though they are underrepresented in the zoned for pro gram group . Finally, immigrant students are evenly distributed across all groups except the program chooser group. It is encouraging to see this group of students gaining access to magnet schools via zoning, and this pattern conforms to the pattern that is the most conducive to integration from magnet schools. Additionally shown in Table 5.4, for each type of magnet student, I regressed each variable on each magnet student type, and the absolute value of the T - statistic is provided in brackets. This shows which variables are related to the various magnet student statuses. Most variables are related to whether or not a student is in the group of students who are in a magnet program by choice; thus selection bias is likely a problem. Fewer variables are relat ed to the other two groups of magnet students, but there are still relationships between many of the 147 variables and students who attend a magnet school via zoning. This could be explained by the schools drawing students from segregated neighborhoods. Beca use of the nonrandom assignment to magnet schools, I turned to regression techniques to further examine student achievement in magnet schools. I began with a series of baseline levels models for math and reading (refer to Equation 5.4). At this point, no s tudent fixed - effect is included. I start with a baseline model and build in vectors of independent variables; this is done so I can see how the estimates change as variables that are related to enrolling in a magnet school are controlled for and to see if selection bias is a problem . Each model includes IVGA so I can examine differences across magnet student type, because I am interested in how achievement varies across magnet student type. Each model also includes the test control variables because such va riables are not related to the probability of receiving treatment like background characteristics and student statuses are. Additionally, the IB indicator is included in all version s of the model because I do not want the effects of IB programs to be confu sed with magnet effects. The results for math and reading z - scores are shown in Tables 5.5 and Table 5.6, respectively. 95 95 I include the estimates for the control variables (other than test controls) in Tables A. 4 and A.5 of the Appendix. 148 Table 5.5 . Baseline Levels Models for Math Z - Scores (1) (2) (3) (4) Magnet Student Type Baseline Student Background Special Student Status Peer Composition Zoned magnet - student 0.307* 0.109* 0.051 0.046 (0.159) (0.062) (0.045) (0.032) Nonprogram magnet - student - 0.048 - 0.078** - 0.011 - 0.024 (0.063) (0.038) (0.027) (0.033) Magnet chooser 0.595*** 0.452*** 0.181*** 0.192*** (0.071) (0.047) (0.031) (0.034) Observations 562,855 562,855 562,855 562,855 R - squared 0.100 0.225 0.412 0.418 All models include grade, year, and grade - year dummies, as well as an IB indicator. Each model builds in an additional vector of independent variables; the column heading states which vector of variables is added. Standard errors are clustered by school and are shown in parentheses. *, **, and *** denote statistical signi ficance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. Table 5.6 . Baseline Levels Models for Reading Z - Scores (1) (2) (3) (4) VARIABLES Baseline Student Background Special Student Status Peer Composition Zoned magnet - student 0.372** 0.131* 0.074 0.029 (0.175) (0.068) (0.051) (0.031) Nonprogram magnet - student - 0.028 - 0.067* 0.003 - 0.036 (0.074) (0.040) (0.027) (0.027) Magnet chooser 0.677*** 0.481*** 0.215*** 0.183*** (0.074) (0.044) (0.028) (0.028) Observations 562,855 562,855 562,855 562,855 R - squared 0.123 0.263 0.470 0.479 All models include grade, year, and grade - year dummies, as well as an IB indicator. Each model builds in an additional vector of independent variables; the column heading states which vector of variables is added. Standard errors are clustered by school an d shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. 149 The results for math and reading scores are quite similar. The results indicate zoned magnet program students and nonprogram magnet students have scores that cannot be distinguished from nonmagnet students once control var iables are introduced to the model. The only estimates that are significant, are no longer significant once additional vectors of control variables are introduced. Magnet choosers however, have higher scores, even after controlling for observable student a nd family characteristics, student statuses, and peer composition. However, prior test scores and unobservable background characteristics are not controlled for at this point, meaning selection bias is still a concern. These results could simply be an arti fact of the magnet chooser variable acting as a proxy for parental involvement. Alternatively, parents could be choosing the better magnet programs. The next set of models I estimated are the levels models that include a student fixed - effect. I estimated six separate models for both math and reading achievement models were run separately for each set of independent variables (IVGA, IVGB, and IVGC) with and without peer composition control variables. The levels models provide an upper boundary for the true estimates in the case of positive estimates and a lower boundary when the estimates are negative (Imberman, 2011) . The results of the levels models for math and reading z - scores are presented in Tables 5.7 and 5.8, respectively. 96 Most of t he results indicate that magnet schools have a result that is either statistically indistinguishable from zero or negative as compared to students attending a nonmagnet TPS . There are only three estimates from the math models this does not hold true for, the estimate for other magnet programs when peer composition variables are 96 The Appendix includes the estimates for the non - test - related control variables in Tables A. 6 and A.7. 150 included and the SWAS estimate s with and without peer composition variables . 97 The results from the reading models were similar. Only the estimates for SWAS were positive . The final s et of models I estimate d are the value - added models (Equation 5.3). I again estimated six separate models for both math and reading. These models provide the lower boundary when the estimates are positive and the upper boundary when the estimates are negat ive (Imberman, 2011). The results for math and reading z - scores are presented in Tables 5. 9 and 5.10, respectively. 98 The estimates from the value - added models are all either statistically indistinguishable from zero or negative. Importantly, the estimat es for magnet choosers are negative once prior achievement is accounted for. 97 Refer to Table 2.1 for a summary of the types of magnet themes included in the other category. 98 Again, estimates for the control variables are included in Tables A. 8 and A.9 of the Appendix. 151 Table 5.7 . Levels Models for Math Z - Scores (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned magnet student - 0.058*** - 0.041** (0.022) (0.018) Nonprogram magnet student - 0.003 - 0.006 (0.014) (0.014) Magnet chooser 0.003 0.010 (0.013) (0.013) Career prep - 0.130** - 0.149*** (0.053) (0.047) College prep - 0.147*** - 0.177*** (0.047) (0.039) Vanguard - 0.017 - 0.062* (0.039) (0.034) Humanities or Literature - 0.133** - 0.058 (0.059) (0.040) STEM 0.010 0.027 (0.018) (0.017) Language 0.016 - 0.004 (0.018) (0.025) Performing or Fine Arts - 0.034** - 0.031** (0.014) (0.013) Other 0.039 0.090*** (0.027) (0.025) SWP - 0.083*** - 0.059*** (0.021) (0.020) SUS - 0.014 - 0.109*** (0.041) (0.034) SWAS 0.021* 0.029*** (0.011) (0.010) All models include a student fixed effect, observable student and family characteristics, student statuses, grade, year, and grade - year dummies, as well as an IB indicator. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 o f these students attended a school with a magnet program at some point in the dataset. 152 Table 5.8 . Levels Models for Reading Z - Scores (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned magnet student - 0.038*** - 0.040*** (0.015) (0.013) Nonprogram magnet student - 0.004 - 0.011 (0.009) (0.009) Magnet chooser 0.001 0.002 (0.010) (0.009) Career prep - 0.049 - 0.064** (0.036) (0.032) College prep - 0.070*** - 0.121*** (0.020) (0.024) Vanguard - 0.003 - 0.010 (0.014) (0.013) Humanities or Literature - 0.139*** - 0.090*** (0.038) (0.025) STEM 0.004 0.011 (0.008) (0.009) Language - 0.013 - 0.026 (0.016) (0.019) Performing or Fine Arts 0.006 - 0.003 (0.013) (0.011) Other - 0.008 0.025 (0.018) (0.018) SWP - 0.046*** - 0.041*** (0.012) (0.011) SUS - 0.024 - 0.066*** (0.019) (0.022) SWAS 0.019** 0.024*** (0.008) (0.007) All models include a student fixed effect, observable student and family characteristics, student statuses, grade, year, and grade - year dummies, as well as an IB indicator. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. 153 Table 5.9 . Value Added Models for Math Z - Scores ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned magnet student - 0.032* - 0.017 (0.017) (0.018) Nonprogram magnet student - 0.010 - 0.001 (0.012) (0.013) Magnet chooser - 0.03 5 *** - 0.022* (0.01 2 ) (0.012) Career prep - 0.081** - 0.084** (0.040) (0.041) College prep - 0.111*** - 0.108*** (0.029) (0.031) Vanguard - 0.046** - 0.045** (0.020) (0.022) Humanities or Literature - 0.025 - 0.002 (0.034) (0.028) STEM - 0.024** - 0.016 (0.012) (0.013) Language - 0.050*** - 0.045*** (0.011) (0.014) Performing or Fine Arts - 0.043*** - 0.035*** (0.012) (0.011) Other 0.007 0.023 (0.026) (0.028) SWP - 0.053*** - 0.040** (0.017) (0.018) SUS - 0.052** - 0.044 (0.023) (0.031) SWAS - 0.020** - 0.015* (0.008) (0.008) All models include a student fixed effect, observable student and family characteristics, student statuses, grade, year, and grade - year dummies, as well as an IB indicator. Standard errors are clustered by school and shown in parentheses. *, **, and *** de note statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. 154 Table 5.10 . Value Added Models for Reading Z - Scores (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned magnet student - 0.027** - 0.019* (0.011) (0.012) Nonprogram magnet student - 0.011 - 0.003 (0.007) (0.008) Magnet chooser - 0.022*** - 0.009 (0.007) (0.009) Career prep - 0.046 - 0.040 (0.033) (0.032) College prep - 0.045*** - 0.044*** (0.012) (0.016) Vanguard - 0.010 0.005 (0.013) (0.017) Humanities or Literature - 0.062*** - 0.049*** (0.015) (0.017) STEM - 0.008 - 0.001 (0.008) (0.009) Language - 0.037*** - 0.024* (0.012) (0.013) Performing or Fine Arts - 0.018** - 0.013* (0.008) (0.007) Other - 0.014 - 0.001 (0.016) (0.018) SWP - 0.027*** - 0.018* (0.010) (0.010) SUS - 0.045*** - 0.021 (0.016) (0.023) SWAS - 0.009 - 0.002 (0.006) (0.007) All models include a student fixed effect, observable student and family characteristics, student statuses, grade, year, and grade - year dummies , as well as an IB indicator. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0. 01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. 155 5.5 Limitations and Potential Sources of Bias As with most studies, there are limitations to this work. By the study's design, I am unable to speak about how kindergarten students are affected by magnet schools because of the reliance on lagged test scores. The exclusion of such students introduces a pot ential source of bias because there are concerns that students who choose midstream are different in nature from students who choose during a natural school transition (Hoxby & Murarka, 2006). There is nothing I can do to address this bias, but it simply l imits the generalizability to students who enter magnet schools in later grades. I conducted a sensitivity analysis that reruns the models while excluding schools where the lowest grade offered is high enough to have pre - treatment test scores (i.e., only m iddle school and high school students are included) (Zimmer et al., 2012; Zimmer et al 2009). If results substantially differ from the results presented in the previous section, then th is source of bias is a concern. The estimates for this portion of the a nalysis are provided in Tables A. 10 through A.1 3 of the Appendix. As a whole, the differences in estimates do not indicate an overarching problem with bias from excluding kindergarten students from the full sample. Except for the math levels model, m ost of the results are similar , having less than a 0.02 difference between estimates . The math levels models have several estimates that differ by more than 0.05, though there is no clear pattern in the differences (i.e., some estimates become smaller while ot hers become larger). Outside of the math levels model, t here are only three estimates that differ by more than 0.05. The reading score levels model estimate for humanities and literature programs, which had a large negative estimate with the full sample, b ec a me indistinguishable from zero once the sample was restricted. The estimate from the reading score value added model for SWPs , while negative for both samples, became substantially larger in magnitude for the restricted sample. Finally, t he 156 math score v alue - added estimates for zoned magnet students are the most different. The estimate from the larger sample of students is indistinguishable from zero, while the limited sample estimate is negative and has a large magnitude. Importantly, across all of the m odels, none of the estimates become statistically different from zero and positive once the sample is restricted. In other words, the selection bias is not hiding positive achievement effects. The reliance on lagged scores raises another issue. The datase t only includes information for students while they attend an HISD - operated school, thus I am unable to include students who transfer from outside of the district to a magnet school. Therefore, my findings may not generalize to this group of students. Ano ther shortcoming of my research design is that it is still possible for bias to arise from time - varying unobserved heterogeneity because I rely on student fixed - effects to account for unobserved heterogeneity. A specific issue that arises in this setting i s the fac t that information parents have a bout schools and their children is most likely growing over time (Hoxby & Murarka, 2006). Because this effect is not absorbed by the student fixed - effect, I am not able to account for the selection bias that arises from this. However, no study on this topic has been able to address this source of bias, lottery studies are subject to it as well. There are also many other potential sources of selection bias with this type of study. First, a concern in this setting is that there is some sort of negative shock in a student's education that causes them to change schools. 99 This leads to a dip in achievement prior to entering a magnet school; such a dip could cause the student to gain more than expected in the next time pe riod, which would give the new school overdue credit for improved achievement (Hanushek, 2007, p. 99 Hoxby and Murarka (2006) refer to this as a "negative - in - trajectory" or "negative - in - level" de pending on whether the shock affects the growth trajectory or is just a onetime shock (p.5). They also provide a nice set of examples of these types of shocks. 157 14). There may also be positive shocks that lead to a change in school that is followed by growth that is not solely attributable to the new school (Hoxby & M urarka, 2006). Imberman (2011) designed an effective way to detect pre - magnet - entry and post - magnet - exit dips in achievement. Any shocks in student achievement trajectories that are not accounted for by the control variables or a student fixed - effect, will be picked up by the residual term. By graphing the residuals from a regression model that includes the independent variables and student fixed effects, across time, such shocks will be visible; they will appear as a dip in the achievement trajectory in th e year prior to entry or exit from a magnet school. I implemented this technique, and the results of this analysis are shown in Figures 5.3 and 5.4, respectively. A vertical line is drawn in each graph at the pre - magnet - entry and pre - magnet - exit year ( - 1) ; this is the year of interest with respect to searching for a negative shock. The concern is finding a dip in achievement at t= - 1.There do not appear to be any dips prior to entering or exiting magnet schools. Thus, negative shocks prior to entry or exit do not appear to be an issue. 158 Figure 5 . 3 . Test Scores Before and After Magnet Entry Figure 5 . 4 . Test Scores Before and After Magnet Exit 159 It is worth mentioning that the aforementioned potential sources of bias are limited in this study by the nature of the magnet school program. Because the magnet school program includes students who do not choose into a magnet school, selection bias effects are dulled by this group of students as compared to studies that look at schools of choice that o nly serve choosers . When it comes to identifying different types of magnet students, I cannot perfectly identify the group of nonchoosing magnet students. I cannot identify those who choose a magnet school by choosing to live within the boundary of the sc hool zone; thus, these students are grouped in with students who just happen to live within the zoning of a SWP , the true nonchooser magnet students. However, when comparing zoned and nonzoned magnet students, this source of bias causes the differences tha t emerge to be understated , thus providing a lower bound for the true estimate. 100 This study only uses data from one district, thus the generalizability is limited to districts similarly situated to HISD. HISD is a large district that serves a large number of ELLs. Additionally, its magnet program features should also be considered when extending the findings. The magnet program includes both choosers and nonchoosers, and it does not emphasize drawing in students from outside of the district. It also is lim ited in its ability to integrate because of the low proportion of white and high - income students in the district combined with the small representation of out - of - district users. Finally, the analysis is limited to only considering outcomes as measured by test scores. There may be other benefits from magnet schools that are not uncovered by this type of analysis; 100 For this portion of the analysis I used zoned magnet - students as the reference group. I would expect students whose parents chose a school for them to outperform their counterparts, as this participation is a proxy for many things such as access to resources and involvement in education. If some choosers are left grouped in with the true nonchoose r group, the difference between choosers and nonchoosers will be understated. 160 this is probably more likely to be the case with programs that do not emphasize academic curriculum (e.g., career preparation programs). Future wo rk can expand upon this work by increasing the range of outcomes that are assessed. 5.6 Discussion and Implications This chapter assessed the student achievement effects in math and reading that are associated with attending a magnet school. The finding s are mixed. With respect to the composition of the nonprogram and zoned magnet student groups, I had hoped these groups would have similar compositions to that of the nonmagnet student group. This would mean magnet schools are serving underserved students at a rate that closely reflects their presence in the district. Even better would be seeing this group comprised of a higher proportion of underserved students; for example, it would be good to see the highest poverty rates in these categories of magnet s tudents. This would mean magnet schools are serving a lot of students in poverty students who are less likely to attend these schools by choice. 101 Instead, the nonprogram and zoned magnet student groups are made up of a disproportionately high amount of W hite and Asian students and a lower representation of Hispanic and students in poverty as compared to nonmagnet students. For a district serving such a large number of Hispanic students, it is unfortunate to see these students underrepresented in magnet sc hools. On the other hand, a large number of ELLs are receiving the benefits of magnet programs via zoning; there are twice as many ELLs in a magnet program by zoning as compared to by choice. This finding indicates that some of the district's most underser ved students are eligible for the special programming of 101 Refer back to Chapter 3 for a detailed discussion of why such students are less likely to attend magnet schools by choice. 161 magnet schools at rates much higher than they would be if only choosers were in the magnet programs. A first glance at achievement in magnet schools shows magnet students performing better than TPS students on average. Kernel density plots showed magnet schools are represented in the upper end of the achievement distribution more often than TPSs. Descriptive statistics also point towards higher average achievement for students in a magnet program, e specially those in a program by choice as opposed to zoning. Once control variables are used however, most of the positive student achievement effects disappear and many estimates become negative. I have summarized the findings of the levels and value - add ed models for math and reading, both with student fixed - effects, in Tables 5.11 and 5.12. Using the boundaries provided by the two sets of models, I show the best - and worst - case estimates for each of the independent variables. 102 What is troubling is that m any of the effects are clearly negative, as the best - case estimate is often negative (i.e., the upper boundary of the estimate is negative). For career preparation, college preparation, and performing or fine arts programs, all estimates for math are negative, regardless of the model specification; the same can be said for reading scores when looking at college preparation and language programs. Overall, the estimates for reading scores are more promising. There are several estimates that are positive, though it is unclear if the true parameters are positive since the worst - case estimates are either zero or negative. 102 When estimates are insignificant, they are treated as the equivalent of zero. Estimates that are statistically significant are labeled correspondingly as either positive or negative. 162 Table 5.11 . Summary of Findings for Math Scores Without Peer Compositio n With Peer Composition Variable Worst - Case Best - Case Worst - Case Best - Case Zoned Magnet Student Negative Negative Negative 0 Nonprogram Magnet Student 0 0 0 0 Magnet Ch ooser Negative 0 Negative 0 Career Prep Negative Negative Negative Negative College Prep Negative Negative Negative Negative Vanguard Negative 0 Negative Negative Humanities or Literature Negative 0 0 0 STEM Negative 0 0 0 Language Negative 0 Negative 0 Performing or Fine Arts Negative Negative Negative Negative Other 0 0 0 Positive SWP Negative Negative Negative Negative SUS Negative 0 Negative 0 SWAS Negative Negative Positive Positive Table 5.12 . Summary of Findings for Reading Scores Without Peer Compositio n With Peer Composition Variable Worst - Case Best - Case Worst - Case Best - Case Zoned Magnet Student Negative Negative Negative Negative Nonprogram Magnet Student 0 0 0 0 Magnet Chooser Negative 0 0 0 Career Prep 0 0 Negative 0 College Prep Negative Negative Negative Negative Vanguard 0 0 0 0 Humanities or Literature Negative Negative Negative Negative STEM 0 0 0 0 Language Negative 0 Negative 0 Performing or Fine Arts Negative 0 Negative 0 Other 0 0 0 0 SWP Negative Negative Negative Negative SUS Negative 0 Negative 0 SWAS 0 Positive 0 Positive 163 One interesting pattern that emerges is the lack of importance of the inclusion of peer composition. I hypothesized its inclusion might make magnet schools look less effective because part of the believed benefit of magnet schools is related to the composi tion of the school. Instead, some estimates actually became positive once peer composition was accounted for. This indicates that perhaps these schools are better at teaching certain peer compositions that TPSs are less successful at teaching; this is enco uraging. When considering the implications of this study, it is important to reiterate that this study is limited with regards to the scope of student outcomes under examination. Because magnet schools fail to improve math and reading scores does not mea n they are wholly unbeneficial. As previously mentioned, I would expect some magnet programs to have little effect on these outcomes. For example, the specialized programming of performing arts programs most likely has little to do with math and reading. H owever, the programs that one might expect to lead to higher scores, do not appear to do so. For example, STEM magnet schools have no impact on math scores, and humanities and literature programs have no effect on reading scores , using best - case estimates. While the scope here is limited, it is still important to understand these effects. If such schools are associated with negative achievement in reading and math, such costs should be considered along with any potential benefits. 164 CHAPTER 6 CONCLUSION This chapter concludes the dissertation by provid ing several things. First, I offer a review of th e study including a summary of the motivation for study , contributing research , research design and methods , major contributions, and main results of the s eparate integration and student achievement portions of the analysis . Because of the importance of context in this type of study, I also review the context of HISD and discuss how the context might relate to the results. With the context in mind, I then sy nthesize the results of the study in a discussion of the implications . Next I discuss the limitations of this study and offer direction for future research . In closing, I provide concluding remarks. 6.1 Review of the S tudy This study is motivated by the changing landscape of our nation's public schooling system. There have been dramatic shifts in the demographic, legal, and policy context s of schools, and it is unclear how older policy tools, such as the use of magnet schools, are operating in this new co ntext. Magnet schools were originally created to help address the segregation of public schools, but the modern - day context leads to concerns about how viable of a policy - tool magnet schools remain in this regard. At the same time, the demographic shift sc hools are facing increases the importance of understanding the policy effectiveness of various policies that are aimed at meeting the needs of traditionally underserved students. With this in mind, I examined what types of students magnet schools serve and what benefits they are con ferring to these 165 students in a modern - day context . Additionally, I placed an emphasis on understanding how traditionally underserved students are affected by magnet schools . To assess the benefits of magnet schools, I focused o n two major outcomes, integration and student achievement. Integration is examined because schools are often still segregated, and the potential benefits of integration still remain. While magnet schools were designed to integrate schools, their modern - day context may limit their ability to do so. At the same time, if magnet schools are unable to integrate, then the next set of questions becomes, who are they serving and are these students receiving any other benefits? This is where the student achievement portion of the analysis comes in. More specifically, this dissertation is built on the following line of analysis : 1. Examination of integration: A. Micro - level analysis of integration: In a modern context, who chooses to participate in magnet programs? i. Are there systematic differences across race, SES, ELL status, and achievement? ii. Are there differences across the various magnet structures? B. Macro - level analysis of integration: What happens to various school compositions when aggregating the actions of th e individuals who participate in magnet school choice? i. How does the composition of Houston compare to the larger geographical area surrounding Houston? ii. Are compositions of magnet schools different from those of TPSs? 166 iii. Are there differences in the composit ion of magnet schools across magnet structure? iv. Does HISD's magnet program result in less segregation at the district level? 2. Examination of student achievement: A. What types of students stand to receive benefits from magnet schools (i.e., what types of students attend magnet schools, considering both in and out of program students, either by zoning or choice)? B. Do magnet schools improve student outcomes as measured by math and reading scores, and are there differences across magnet student type, magnet program theme, or magnet structure? 6.1.1 Integration from Magnet Schools While magnet schools were created as a tool to address segregation, their modern - day context makes it more difficult to do so. Additionally, there is a large body of research that connects public school choice to student sorting. Researchers have identified what I refer to as the four pathways to student sorting: residential segregation, differen t parental preferences, different ability to navigate choice, and school - level, choice - related policies. The main findings of these studies point towards differences in resources of parents and differences in their preferences for schools and how these dif ferences result in student sorting in public schools across race, SES, linguistic, and achievement (see e.g. Bell, 2007; Holme, 2002; Schneider et al., 1998; Smrekar & Goldring, 1999; Teske et al., 2006). As magnet schools are part of the modern - day system of public school choice, such findings are relevant. However, magnet schools are different in nature from charter schools in that magnet schools do not necessarily isolate choosers from nonchoosers. In fact, magnet schools were designed to attract advanta ged students to 167 schools that serve larger proportions of traditionally underserved students. Thus, finding more advantaged parents able to participate in choosing a magnet school does not necessarily translate into more segregated schools. Because of this important distinction , student sorting from magnet schools should be assessed separately from other forms of public school choice. There are two perspectives typically relied on for studying student sorting from school choice . The micro - level perspective focuses on individual behaviors by looking at differences in participation in schools of choice. Such studies typically look for the pathways to student sorting that arise from particular patterns in individual behavior. Other researchers have taken a macro - level view by looking at the results of aggregating the choices of individuals. Such studies typically compare compositions of choice schools to TPSs, or they compare districts with certain choice options to those without su ch options. Because the micro - level analysis is unable to speak to the aggregate effects of students leaving TPSs for magnet schools, the macro - level analysis is important . When it comes to magnet schools, the macro - level analysis is even more important be cause chooser students are mixed with nonchooser students; in other words, evidence of micro - level student sorting does not necessarily mean there is student sorting that leads to segregation in the aggregate. The two perspectives work well together as the y uncover different pieces of the picture. The macro - level analysis shows net effects of individual behaviors, while the micro - level analysis helps explain what we see in the aggregate . Some studies have examined the ability of magnet schools to integrate, separately from other forms of choice, using a micro - level perspective. However, the context of these studies is typically not modern - day. I define modern - day to include two key features. First, modern - day magnet school do not consider race as a factor in admissions. Second, modern - day magnet schools are part of a wider system of school choice that no longer emphasizes integration. Most 168 studies on integration from magnet schools were conducted in the 1980s and 1990s, when race was typically considered in t he admissions process. More recent studies on integration from magnet schools are limited by their policy context. Haynes et al. (2010) and Bifulco et al. (2007 & 2009b) used data from districts that only enrolled students in magnet schools via application s. Further, all but one of the magnet schools in the Bifulco et al. (2007 & 2009b) studies were a n SUS , and such a policy context has a direct link to the integration outcome. Districts that utilize SWP and SWAS magnet structures may see quite different in tegration results, as these structures mix choosers and nonchoosers. Finally, Haynes et al. (2010) relied on stated preferences, which could differ from actual preferences. Several studies have used a macro - level perspective to examine integration from var ious forms of school choice. However, this body of literature suffers from two shortcomings. First, some studies lump multiple types of school choice into one group. For example, Betts et al. (2006) grouped the results from students attending open - enrollme nt, charter, and magnet schools. It is possible, and likely that different types of choice to have different affects on integration. Charter schools, by their design, isolate choosers from nonchoosers. Depending on district policy, this may not be the case for magnet schools. When results are not separated out for magnet and charter schools, the net effect could be hiding important differences. Second, the studies that only looked at magnet schools all rely on data from the 1960s through 1990s. It is likely results would differ in a modern - day context, a context that makes it more difficult to integrate. I am able to address the limitations of these previous studies utilizing data from HISD. HISD meets the definition of modern - day, allowing me to understand how magnets function in a new context. Specifically, the district no longer considers race in admissions and has a variety of 169 public school choice options. Additionally, the district incorporates nonchoosers into most of its magnet schools, as the district has very few SUS magnet schools but a large number of SWP and SWAS magnet schools. This allows me to extend the literature base to include a micro - level analysis of a different magnet policy context. A final major contribution of the present study is its use of data from a district that has a Hispanic student majority. Not only is this study the first to do this, this population of students is rapidly growing throughout the U.S., increasing the importance and relevance of such a study . To assess integrati on at the micro - level, I relied on student - and school - level data to uncover evidence of the pathways to student sorting. Prior research points to a host of student background characteristics and special student statuses that are related to participation i n school choice. Additionally, I incorporated achievement scores of students to see if magnet schools cream - skim higher performing students from TPSs. Finally, school compositions of each student's zoned school were included in this analysis because it is important to consider what types of schools students leave behind. If there are patterns indicating students avoid their zoned school when it is comprised of more traditionally underserved students, magnet schools can worsen segregation in TPSs. The micr o - level analysis I conducted provides evidence of advantaged students choosing a magnet school more often than traditionally underserved students. White, Asian, non - ELL , higher income, and higher performing students are all more likely to choose than their respective comparison groups. At the same time, students are more likely to leave their zoned school when they have fewer White students and more Black, lower performing, or students living at or below the poverty level. S chools with higher proportions of Hispanics and ELLs were associated with fewer students leaving for magnet schools, which could be explained by the high proportions of 170 Hispanics and ELLs in the district, if parents prefer sending their children to schools with students who are similar to them. I also broke down the micro - level analysis by magnet structure type. I do this because SWAS and SWP magnet schools are more able to integrate than SUS magnet schools because they mix choosers with nonchoosers. Further, SWPs may lead to more meaning ful integration because nonchoosers are included in the magnet program; thus, students are not segregated by program status within the school as they are in SWAS magnet schools. To achieve the most integration, the district would want advantaged students c hoosing SWPs over other types of magnet schools and SWAS magnet schools over SUSs. However, the results pointed towards advantaged students choosing SWAS and SUS programs more often than SWPs. While there is evidence of the pathways to student sorting at the micro - level, it is unclear what the net effect is when students leave their zoned TPS for a magnet school. For this reason, I also conducted a macro - level analysis , which was broken into three parts. First, I examined the level of segregation in the ci ty of Houston, by comparing its school - aged population composition to that of Harris County and the Houston MSA. If the surrounding areas have similar compositions to HISD , it would be very difficult to integrate HISD. However, I found the composition of H ouston to be quite different from the larger geographical areas. There is a much larger representation Blacks and Hispanics in the city of Houston as compared to the larger geographical areas. Additionally, there are more students with a home language othe r than English and children living at or below the poverty - level in the city of Houston as compared to the larger geographical areas. Thus, t he district has access to a more diverse set of students outside the district. 171 The second portion of the macro - le vel analysis compared the composition of magnet schools to that of TPSs to see if magnet schools are more integrated than TPSs. I also broke these results down across magnet stru cture type to see if certain structures attract more advantaged students. I looked at racial, SES, and ELL compositions. I found magnet schools are more integrated than TPSs in the sense that they serve higher pro portions of advantaged students . While all of the different structures reflected a more advantaged student populati on on average when compared to TPSs, SUS magnet schools had the highest proportion of advantaged students. The third portion of the macro - level analysis looks at district - level integration because t he difference in magnet and TPS compositions could refle ct the siphoning of advantaged students from the district's TPSs, which could result in district - level segregation . To assess the net effect , I looked at the movement of students from TPSs to magnet schools by comparing the counterfactual of what school co mpositions would look like if magnet choosers attended their zoned school to what school compositions actually look like. I noted this is an imper fect counterfactual, as some students still might not attend their zoned school if magnet schools were not ava ilable. Therefore, any segregation from magnet schools is most likely overstated. To compare integration at the district level, I relied on a series of indices to see if the district is more or less segregated across racial, SES, and ELL status lines when students leave their zone school to attend a magnet school. I found mixed evidence from the different indices. The results varied across index as well as across the different disadvantaged - advantaged pairings (e.g., ELL versus non - ELL ). One of the indices pointed to segregation, while the other two varied depending on the composition pairing. Many of the differences were close to zero. Considering the mixed results and the fact that segregation would be overstated because of the imperfect counterfactual, th e district does not appear to be much different in composition than it would be if all magnet 172 choosers in the district attended their zoned school. If magnet schools are more diverse than TPSs, and the net effect is around zero, magnet schools must be inte grated at the cost of segregating TPSs. 6.1.2 Student Achievement in Magnet Schools If magnet schools are unable to effectively integrate at the district level, it becomes even more important to see if there are any other benefits of these s chools. While there are many potential benefits of magnet schools, I focused on student achievement effects because there are many theories that point towards magnet schools improving student achievement. I n a district like HISD, where nonchooser students attend magnet schools, it is relevant to inquire about the entire group of students that could be receiving benefits from magnet schools . The integration analysis centered on examining what types of students choose a magnet school and how this impacts the composition of schools and the district, leaving what the nonchooser magnet student group looks like unclear. For this reason, I start the student achievement analysis with a look at what types of students are zoned for magnet schools. Such students, whether in the ma gnet program or outside of the program, stand to benefit from potential achievement effects of magnet schools. Prior studies on magnet student achievement have not addressed this group of students, and importantly, this is the group of students magnet scho ols were created to assist . Ideally, traditionally underserved students would be zoned for magnet schools, as magnet schools attract advantaged students. This is not what I found however. White and Asian students were overly represented in the zoned magnet student group, while Hispanics in particular were underrepresented in this group. Students living below the poverty line are also underrepresented in the zoned for magnet program group. The most promising results indicate the under representation of ELLs, students with a home language other 173 than English, and immigrants in the magnet chooser group, is improved upon when looking at the nonprogram magnet student and zoned magnet program groups ; these groups are closer to reflecting the presence of these group s in the district. After exploring what nonchooser magnet students look like , I assessed the student achievement effects of magnet schools as reflected standardized exam scores in math and reading . Examining achievement benefits from magnet schools is dif ficult because of the nonrandom assignment to treatment. Some studies have relied on lotteries as a source of random assignment (see e.g. Bifulco et al . , 2009 a ). This however limits the results to oversubscribed magnet schools which could be different in nature from the broader set of magnet schools. Additionally, such studies do not tell us anything about zoned magnet students and nonprogram magnet students. An alternative is to rely on quasi - experimental methods such as value - added and fixed - effect models, though these methods are imperfect and have biases that need to be addressed. Bifulco et al. (2009 a ) used quasi - experimental methods, but this study has seve ral contextual limitations. The magnet schools in this study were part of an interdistrict choice program that reserved seats for a diverse set of students from across the districts that were part of the program. Additionally, the magnet schools were SUSs and thus only served choosers. This raises questions about the extension of these findings to other policy contexts, and again, there are no nonchoosers in the analysis. Finally, the sample of magnet schools was rather small, and no school level variables could be used in the analysis. I used quasi - experimental methods to assess achievement e ffects from magnet schools in HISD. This extends the literature to a context that is substantially different from that of Bifulco et al. (2009 a ). Importantly, I wa s abl e to assess if nonchoosers, whether in a magnet program or outside the program, experiences gains in achievement. I also addressed the bias that is 174 introduced by the model assumptions used in Bifulco et al. (2009 a ). By estimating both value - added and level s models with a student fixed - effect, boundaries are provided for the true estimates (Imberman, 2012). Finally, I had access to a sample of magnet schools that was large enough to incorporate school - level variables. This allowed me to breakdown the results by magnet program and structure, something that has not been done in previous studies. After accounting for student background factors (observable and time - invariant unobservables), special statuses, pre - treatment achievement, and peer composition, there is little evidence of student achievement benefits in math and reading from magnet schools. In fact, many of the effects are clearly negative, as the upper boundary of the estimate was negative. For career preparation, college preparation, and performing or fine arts programs, all estimates for math are negative, regardless of the model specification; the same can be said for reading scores when looking at college preparation and language programs. However, several of the upper boundary estimates for readi ng were positive, though it is unclear if the true parameters are positive since the lower boundaries were either zero or negative. 6.1. 3 Major Contributions This dissertation provides several major contributions to the literature on magnet schools. First, the methods I employ offer improvements to previous research in a few ways. First, I study magnet schools separately from other forms of school choice. This is especially important in a context like HISD, where magnet schools have a zoned student po pulation. When magnet schools mix choosers with nonchoosers, the student sorting effects will differ from schools that isolate choosers. Second, I use both a micro - and macro - perspective to assess integration from magnet schools for a wider range of disadv antaged - advantaged student pairings. Third, I rely on pre - magnet test scores to assess whether or not magnet schools cream - skim better performing 175 students from magnet schools. Previous studies that try to look at this do not use pre - magnet scores, introdu cing endogeneity. Finally, the methods I use to assess student achievement benefits improve upon previous non - lottery - based studies. I recognize the biases that result from the models that are typically used to estimate student achievement effects, and I i nstead use two sets of models in conjunction to bind the true estimates. Beyond methodological improvements, the study is the first to look at the effectiveness of magnet schools in a modern - day setting. The legal, policy, and demographic context of magn et schools has shifted rather dramatically since magnet schools first came about. primarily , leaving questions about how magnet schools fit into the larger school choice system where the emphasis has turned away from integration towards accountability . Fur ther, the student demographics have shifted. Schools are more diverse and larger proportions of Hispanics are served by public schools. This study updates the literature base by providing an analysis of both integration and student achievement effects from magnet schools in this new context. Importantly, I found HISD was not more integrated at the district level when students choose a magnet school, conflicting with the results of Rossell (2003). However, Rossell (2003) only considered districts that used r ace as a factor in admissions. Perhaps when the district cannot consider race , integration efforts suffer. Similarly, Bifulco et al. (2009 a ) found magnet schools had a positive effect on student achievement. However, the district under study brought in a r ather diverse set of students and the authors believed the improvements could have been the result of integration. This leaves questions about what the effects would be if there was no integration. In HISD, the only student achievement impact estimates tha t were positive were for SWAS magnet schools. All other estimates were negative or indistinguishable from zero. 176 The context of HISD allows for several other contributions. First, the district is primarily Hispanic and has a large number of ELLs. No other magnet study ha s examined such a context. The findings as they relate to Hispanics and ELLs become increasingly important as these student populations continue to grow. I found a few differences in results for the Hispanic and ELL subgroups. Hispanic stud ents were the only ethnic group in the district that was underrepresented in the magnet chooser group. Most of the gap in participation can be explained by features Hispanic students tend to have in common such as poverty status or ELL status. I would like to point out that one might expect the gaps between Hispanics/non - Hispanics and ELLs/non - ELLs to to be smaller in a district like HISD, where these populations have long been served and they make up a large proportion of the district. Thus, these findings could be a sort of best - case scenario. I also found Hispanics tended to have a stronger same - race preference when it comes to the composition of their school , which partially explained the difference in the rates at which they choose a magnet school . The largest difference in magnet and TPS compositions was in the percentage of ELLs , where ELLs had a much larger presence in TPSs. The difference was especially large when comparing SUS magnet schools to other types of magnet schools and TPSs. SUS magnet sch ools had less than one - tenth of the proportion of ELLs in the district as a whole. Hispanics and ELLs had the largest magnet presence in the nonprogram magnet student group. Thus, of the different magnet structures, SWAS magnet programs served the most His panic and ELLs, though these students were often not in the magnet program. At the district level, the strongest evidence for integration occurred for the Hispanic - White pairing. At the same time, the strongest evidence of district - level segregation occurr ed for the ELL/non - ELL pairing. In other words, for Hispanics, the net effect of students leaving their zoned TPS for a magnet school was increased integration, but the opposite was true for ELLs. 177 Second, using data from HISD allowed me to examine magnet policies in new ways because of the large number of magnet schools and the variation in magnet type . More specifically, I was able to look for differences in the results across different magnet structures a nd program themes , and I was able to include magnet schools at all school levels . This analysis allows for additional insights on magnet schools , as it uncovered important differences across magnet school type. SUS magnet schools have the most advantaged c ompositions , however b ecause SUS magnet schools only serve choosers, integration is limited because more advantaged students are being mixed with other relatively advantaged students. For example, as previously mentioned, ELLs are almost nonexistent in SUS programs, so while the composition is more advantaged, ELL/non - ELL segregation worsens. SWAS and SWP magnet schools had lower proportions of advantaged students than SUS magnet schools , but they also served higher proportions of disadvantaged, nonchoosing students , making them more effective at integrating . At the same time, SWAS magnet schools were the only magnet type (structure or program) associated with positive student achievement effects. Third, HISD has a large number of students in magnet schools via zoning. This allow ed me to explore how the achievement of nonchooser magnet students is affected by magnet schools. This also weakens the typical selection bias issue that arises in studies of achievement benefits from schools of choice. The student a chievement portion of the analysis failed to show achievement benefits for nonchooser magnet students for either students in or out of the magnet program. Finally, the results of this research add to the broader magnet school literature base in a few way s. A large body of research has uncovered several pathways from public school choice to student sorting (see e.g., Bifulco et al., 2009b; Jacobs, 2013b; Goldring & Smrekar, 1999; 178 Schneider et al., 1998) . This study provides more evidence of this, as I fou nd magnet choosers were relatively advantaged as compared to TPS students . However, there is an important distinction to make. Although magnet choosers were relatively advantaged , because these students mostly attended schools with a zoned student populati on, the effects of student sorting are felt differently . Magnet schools end up more integrated but at the cost of segregating TPSs further. The net effect was little change to the district level segregation. These results also bolster the research that poi nts to the importance of context in the effectiveness of school choice policies as an equity tool ( e.g., Arsen et al., 1999; Scott, 2005; Siegel - Hawley & Frankenberg, 2013 ). Here, HISD would probably see net segregation if they only had SUS magnet schools. These findings also support the argument that school choice can only be used in the integration process if it is controlled through policy (Orfield, 2013). 6.2 Implications The findings of this study have several important policy implications. Howeve r, these implications should be contextualized, and the findings should only be generalized to similar contexts. Thus, I begin this section by reviewing the context of HISD. I then discuss how different pieces of the context could relate to the results and how the results might differ in another context. With these contextual factors in mind, I provide a discussion of the policy implications that flow from my analysis and provide guidance for policymakers. I base this discussion on a synthesis of the result s from both the integration and student achievement portions of the analysis. 179 6. 2 . 1 Contextualizing the Findings While magnet schools were created to integrate schools, their ability to do so has been compromised in several ways by their new context . For HISD, a major obstacle to integration seems to be interdistrict segregation. HISD serves very few advantaged students , making i t hard for the district to integrate without drawing in students from outside the district. When the district is segregate d at the district level as opposed to at the school level, the district is at risk of the pathways to student sorting resulting i n magnet schools cream - skimming advantaged students from the TPSs in the district . This is what I found in HISD , and such crea m - skimming limits district - level integration from magnet schools. It is also important to consider the fact that HISD has long served ELLs and students with a home language other than English. Such students have different needs, and HISD is more familiar with and better prepared to address these needs. In the school choice setting, HISD provides information on magnet schools in Spanish. In fact, the entire HISD website can be viewed in Spanish. These resources may not be provided in districts that do not serve a large number of ELLs or students with a h ome language other than English . These students may end up more isolated due to student sorting from school choice as they are less able to participate in school cho ice when they do not have information that is disseminated by the district. Beyond the demographic context of the district, the policy context is also important to consider. The policies that shape a magnet school system are directly related to the outcomes of such a system. There are several magnet school policies that should be considered when generalizing the findings. First, most of the magnet schools in HISD mix choosers with nonchoosers. Such a policy weakens the link between school choice and student sorting. Districts with magnet schools that only serve choosers will likely see different results when it comes to 180 integration I would expect such districts to be more segregated as a whole as a result of magnet schools. Second, the district provides tra nsportation to magnet students, making magnet schools a viable option for more students, students that tend to be more disadvantaged and more reliant on transportation being provided. This policy should also weaken the connection between school choice and student sorting. Third, the district allows magnet schools to charge tuition to out - of - district students. This policy limits the demand for HISD magnet schools from students residing outside the district. In this setting, such a policy probably limits the integrative effects of magnet schools considering how segregated HISD is at the district level , it becomes more important for the district to bring in students from outside the district . 6. 2 .2 Policy Implications There are several policy insights gai ned from this study , which flow from both the integration and achievement portions of the analysis. The integration results pointed towards magnet schools being more integrated at the cost of TPSs being more segregated; the net effect is little change to t he district level segregation. With evidence of magnet schools drawing the more advantaged students away from TPSs, I would also make a funding suggestion. As money follows students when they leave their zoned school, equity can be sabotaged as TPSs are le ft with a group of students that are on average more costly to educate. When these schools also lose funding and do not see their costs go down proportionally, the students in these schools are harmed both directly and indirectly as a result of increased s egregation. To address this, the district could reduce the money it takes from TPSs losing students to magnet schools. While the magnet schools in the district seem to be contributing to the segregation of the district's TPSs, this finding should be contextualized in the larger school choice context of the district. Specifically, although magnet schools are moving advantag ed students away from the 181 dsitrict's TPSs, not only are these students remaining in the district, they are moving these students to schools with a zoned student population, a student population that tends to be relatively disadvantaged. If magnet schools w ere the only choice option, this flow of advantaged students could result in a null net effect or even a net effect that is associated with more costs than benefits. However, the magnet schools in HISD are part of a portfolio of choice options. If magnet s chools were not offered, it is reasonable to assume some proportion of the students who choose a magnet school would be lost to other forms of school choice like charter schools or private schools. Thus, magnet schools are most likely preventing the flow o f advantaged students from TPSs to schools that are not operated by the district. Because the macro - level analysis pointed toward the district having little segregation or integration from magnet schools, with this consideration in mind, the net effect is most likely positive when compared to what the district would look like without magnet schools. Magnet schools seem to be a good way for the district to compete with nondistrict run schooling options. I f HISD wants to better address segregation, I woul d recommend that the district work on drawin g in more students from outside of the district because of a lack of diversity within the district . The larger geographical area surrounding the district has a much more diverse population from which the distric t can draw students. Currently however, the district has a policy of allowing magnet schools to charge tuition to students who reside outside of the district. The district may need to reconsider this policy if it wants to integrate its schools at the distr ict level. Additionally, b ecause it is hard for districts to address problems that extend outside of their borders, state and federal policies could provide better tools for addressing segregation. I would also advise the district to work on the placement of SWP and SWAS magnet schools if it wishes to reduce segregation . Ideally, traditionally underserved students would be 182 zoned for magnet schools at rates that are similar to or higher than their rates in TPSs. In othe r words, to maximize integration, magnet schools should be housed within schools that serve higher proportions of traditionally underserved students, then magnet schools would attract advantaged students to these schools, leading to integration. Additional ly, when this happens, any benefits associated with magnet school programming outside of integration are provided to traditionally underserved students, thereby potentially improving equity in other ways . While it would be ideal to see a larger proportion of traditionally underserved students in magnet schools, I found advantaged students were disproportionately represented in the zoned for magnet school groups. I t is possible that parents are moving to live within the boundaries of SWPs because of the prog ramming. This is something I cannot untangle with the data I have. If data is available, the district could perhaps look at compositions of residents in the school zone before a magnet school is introduced to a TPS and see if the composition changes after a magnet school opens in the school zone. This issue should be examined because if the magnet schools are located in schools that have a more advantaged student population, the proportion of traditionally underserved students who are served by magnet schoo ls is limited, which weakens the potential for integration . I would add to this discussion that the district should work on ensuring ELLs are not more isolated as a result of magnet schools. ELLs are some of the most underserved students, and HISD in par ticular has a rather large ELL population, making the results as they apply to ELLs more important. The results indicated ELLs are vastly underrepresented in the magnet chooser group and that they tend to end up more segregated when students leave their zo ned school for a magnet school, I would recommend placing magnet schools in schools that serve a lot of ELLs. 183 There are also insights to be gained from the student achievement portion of the analysis. First, the evidence for achievement effects from SWP s was negative, even using best - case estimates, and SUS magnet schools have negative or at best null effects. Although SWP magnet schools are beneficial in the sense that they extend magnet programming to nonchoosers, if there are not benefits associated w ith the magnet program, it would be more cost effective to focus on SWAS programs. I would however expand the analysis of student outcomes before making such a dramatic policy change. Second, more generally speaking, most of the estimated achievement effec ts were null or negative. The district should ensure students are receiving adequate instruction in core courses. It may not be in the best interest of students to introduce special programming if it comes at the cost of lowering performance in core subjec ts. Considering the results of both the integration and student achievement portions of the analysis. SWAS magnet programs appear to be the most effective magnet structure type. They were the only type of magnet school that had positive achievement effect estimates. Additionally, because they are located in a school that has a zoned student population, they are not associated with segregation in the ways SUS magnet schools are. They may drain more advantaged students from TPSs, but they are not isolating c hoosers from nonchoosers. I would recommend the district focus on SWAS magnet structures. 6. 3 Limitations and Direction for Future Work This section discusses the larger limitations of this study and gives guidance for fu ture work that can address these limitations and continue to move the literature on this subject forward . While t here are many minor limitations that are discussed in the two analysis chapters , 184 this section focuses on the limitations that have broad consequences on the implications and generalizability of the results of the dissertation. First and foremost, it is not clear how far the results extend outside of contexts that are dissimilar to that of HISD. In particular, magnet school policy is quite important with respect to magnet school outcomes. A multi - district study that examines integration and district policy would be extremely beneficial as it could help tease out which policies are important determinants of integration and student achievement from magnet schools. The micro - level analysis I conducted is non - causal in nature. The choice patterns that emerge could be the result of differences in the ability to participate, differences in preferences, or differences in eligibility for admissions. Additionally, I do not have acce ss to application data, so the results of the micro - level analysis could understate differences. Further, t he results could look quite different if caps on enrollment of certain magnet schools were changed or removed. Qualitative work similar to that of Ha ynes et al. (2010) could add to this discussion by helping to untangle why certain groups are less likely to participate in magnet school choice . Additionally, trying to better control for admissions criterion of magnet schools could help understand the ro le such criterion play in who chooses a magnet school. Finally, my assessment of student outcome benefits is quite limited. I only examine d math and reading scores on a standardized exam. There could be other benefits associated with magnet programs. In f act, many of the programs place no emphasis on math or reading, so it might be inappropriate to expect such benefits from these schools. Future work should examine a broader array of student outcomes, including both short - and long - term benefits. For examp le, short - term benefits could include higher attendance and lower discipline rates, and long - term benefits could include graduation, dropout, or college - going rates . 185 6. 4 Concluding Remarks This study provided a much needed update t o the magnet school lit erature by examining magnet school outcomes in a modern - day setting. This new setting is quite different from the original con text magnet schools operated in, as the policy, legal, and demographic context of magnet schools has dramatically changed over the last few decades . These changes lead to questions about how magnet schools function in this new context. This update to the literature found magnet schools still have a place in a modern - day setting, but the policies that shape magnet schools are highly related to their effectiveness. As far as the capacity to integrate, this research points to the importance of magnet structure type and location in particular. SWAS magnet schools appear to be the most effective magnet structure option, as they are the o nly structure linked to positive student achievement effects, and they are better at integrating than SUS magnet school. Additional research should examine other student outcomes to confirm. 186 APPENDIX 187 Figure A. 1 . Example of a Magnet School Admissions Matrix: MS Language , 2014/ 15 188 Table A. 1 . Linear Probability Model Results for Current Magnet - Chooser Outcome , Using New - Chooser Sample Variable (1) (2) (3) (4) Controls Zoned Magnet Student - 0.062*** - 0.064*** - 0.067*** - 0.067*** (0.014) (0.014) (0.015) (0.015) School Level Shift 0.205*** 0.196*** 0.192*** 0.192*** (0.022) (0.020) (0.020) (0.020) Middle School - 0.012 - 0.006 - 0.010 - 0.014 (0.012) (0.012) (0.018) (0.018) High S chool - 0.038*** - 0.032** - 0.044** - 0.048** (0.013) (0.013) (0.021) (0.021) Dist ance t o Zoned Sch ool 0.006** 0.007*** 0.007*** 0.006*** (0.002) (0.002) (0.002) (0.002) Student Background Female 0.017*** 0.011*** 0.011*** 0.011*** (0.002) (0.002) (0.002) (0.002) Black - 0.029*** 0.002 - 0.009 - 0.010 (0.010) (0.008) (0.008) (0.011) Hisp anic - 0.033*** - 0.008 - 0.011 0.026* (0.009) (0.007) (0.007) (0.013) Asian 0.051** 0.037 0.039* 0.038 (0.024) (0.024) (0.023) (0.023) Poverty - 0.069*** - 0.050*** - 0.057*** - 0.032*** (0.010) (0.008) (0.009) (0.008) Free Lunch - 0.046*** - 0.032*** - 0.040*** - 0.041*** (0.007) (0.006) (0.007) (0.007) Reduced Lunch - 0.016*** - 0.008 - 0.015*** - 0.016*** (0.006) (0.005) (0.006) (0.006) Home Lang n ot Eng lish - 0.012*** - 0.005 - 0.006* - 0.009** (0.004) (0.004) (0.004) (0.004) Immigrant - 0.036*** - 0.006 - 0.006 - 0.002 (0.007) (0.006) (0.005) (0.005) Special Student Statuses Gifted and T alented 0.145*** 0.142*** 0.143*** (0.021) (0.021) (0.021) Special Ed ucation - 0.036*** - 0.034*** - 0.034*** (0.004) (0.004) (0.004) ELL - 0.032*** - 0.031*** - 0.062*** (0.005) (0.005) (0.008) Composition o f Zoned School Zoned Sch ool 's % White 0.062 0.060 (0.153) (0.154) Zoned Sch ool 's % Hisp anic 0.046 0.082 (0.128) (0.128) Zoned Sch ool 's % Black 0.130 0.116 (0.140) (0.143) Zoned Sch ool's % Poverty - 0.045 0.004 (0.078) (0.086) 189 Table A.1. (cont'd) Variable (1) (2) (3) (4) Zoned Sch ool's % ELL 0.007 - 0.031 (0.055) (0.055) Zoned Sch ools Lagged Avg Math (z - score) - 0.089** - 0.092** (0.036) (0.036) Zoned Sch ools Lagged Avg Reading (z - score) 0.037 0.039 (0.029) (0.029) Interaction Terms Hisp anic x Zoned Sch ool's % Hisp anic - 0.064*** (0.023) Black x Zoned Sch ool's % Black 0.002 (0.024) Poverty x Zoned Sch ool's % Poverty - 0.091*** (0.029) ELL x Zoned Sch ool's % ELL 0.114*** (0.019) R - Squared 0.118 0.154 0.155 0.156 All models include a zip - code fixed effect and set of year dummies. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 445,428 includes data for 1 80,479 students. 190 Table A.2 . Magnet and TPS Compositions: Weighted Averages Perc white Perc Black Perc Hispanic Perc Poverty Perc ELL Year Magnet TPS Magnet TPS Magnet TPS Magnet TPS Magnet TPS 06/ 07 *** 0.12 0.04 0.30 0.27 *** 0.53 0.66 *** 0.15 0.23 *** 0.15 0.38 07/ 08 *** 0.11 0.04 0.30 0.25 *** 0.55 0.68 *** 0.14 0.20 *** 0.15 0.36 08/ 09 *** 0.11 0.04 0.29 0.25 *** 0.56 0.69 *** 0.14 0.21 *** 0.16 0.39 09/ 10 *** 0.11 0.04 0.28 0.23 *** 0.56 0.70 *** 0.17 0.24 *** 0.15 0.37 10/ 11 *** 0.11 0.04 0.28 0.23 *** 0.56 0.70 *** 0.25 0.36 *** 0.15 0.39 11/ 12 *** 0.11 0.04 0.27 0.22 *** 0.57 0.71 *** 0.31 0.44 *** 0.16 0.40 12/ 13 *** 0.11 0.04 0.26 0.23 *** 0.57 0.70 *** 0.33 0.47 *** 0.16 0.40 13/ 14 *** 0.11 0.04 0.26 0.24 *** 0.57 0.69 *** 0.33 0.46 *** 0.17 0.42 T - tests for differences in means between magnet schools and TPSs were conducted. When variances of the two groups were not equal, the Welch's option was employed. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sampl e size is 1,374,655 student - year observations. 191 Table A.3 . Describing Magnet Students: Summary Statistics by Magnet Student Type ( Analytical Sample ) Magnet Student Type Nonm agnet - TPS Student Nonprogram Magnet - Student Zoned Magnet - Student Magnet Chooser Variable Female 0.49 0.48 0.49 0.54 (0.50) (0.50) (0.50) (0.50) {2.83} {0.76} {9.07} White 0.07 0.08 0.28 0.15 (0.25) (0.27) (0.45) (0.35) {0.51} {2.68} {3.11} Black or NA 0.31 0.26 0.28 0.30 (0.46) (0.44) (0.45) (0.46) {1.32} {0.34} {0.10} Hispanic 0.59 0.64 0.36 0.48 (0.49) (0.48) (0.48) (0.50) {1.05} {3.25} {2.44} Asian 0.04 0.03 0.08 0.06 (0.19) (0.16) (0.27) (0.25) {1.10} {1.81} {1.88} Poverty 0.41 0.28 0.26 0.20 (0.49) (0.45) (0.44) (0.40) {5.21} {2.62} {9.09} Free Lunch 0.36 0.42 0.22 0.31 (0.48) (0.49) (0.42) (0.46) {2.69} {3.34} {2.25} Reduced Lunch 0.09 0.09 0.07 0.12 (0.28) (0.28) (0.26) (0.32) {0.54} {1.11} {5.48} Home Lang uage not English 0.37 0.49 0.20 0.32 (0.48) (0.50) (0.40) (0.47) {3.30} {5.15} {1.41} Immigrant 0.02 0.02 0.02 0.01 (0.12) (0.14) (0.14) (0.07) {0.78} {0.44} {4.30} Gifted and Talented 0.14 0.09 0.30 0.44 (0.34) (0.28) (0.46) (0.50) {2.41} {2.69} {7.70} Special Ed ucation 0.09 0.12 0.07 0.04 (0.28) (0.32) (0.26) (0.20) {4.42} {2.74} {9.49} 192 Table A.3. (cont'd) Magnet Student Type Variable Nonm agnet - TPS Student Nonprogram Magnet - Student Zoned Magnet - Student Magnet Chooser Parent Denial 0.05 0.01 0.03 0.02 (0.21) (0.11) (0.18) (0.13) {8.68} {1.63} {7.47} LEP 0.15 0.14 0.08 0.05 (0.35) (0.35) (0.27) (0.22) {0.17} {4.32} {9.47} Zoned School 's % White 5.31 8.30 22.39 13.24 (10.43) (11.94) (24.41) (15.49) {1.35} {2.41} {3.49} Zoned School 's % Hisp anic 59.90 56.14 38.83 50.03 (27.80) (24.47) (27.29) (23.69) {0.86} {3.08} {2.60} Zoned School 's % Black 22.80 24.05 23.64 25.20 (24.47) (20.32) (25.14) (20.24) {0.38} {0.14} {0.78} Zoned School 's % Poverty 30.51 20.99 19.14 20.74 (15.40) (12.46) (16.49) (13.63) {5.28} {2.95} {5.63} Zoned School's % G ifted and T alented 9.94 14.91 21.94 23.02 (7.58) (12.71) (15.68) (19.65) {2.64} {2.68} {5.09} Zoned School's % Special Ed ucation 7.49 9.36 6.15 7.86 (3.70) (4.01) (2.14) (4.62) {3.26} {2.19} {0.62} Zoned School 's % ELL 33.77 14.42 21.40 15.73 (19.26) (10.87) (16.19) (12.67) {8.21} {3.00} {7.75} Reading (z - score) - 0.11 - 0.14 0.36 0.60 (0.93) (0.91) (1.10) (0.94) {0.48} {2.68} {9.63} Math (z - score) - 0.11 - 0.13 0.28 0.53 (0.94) (0.89) (1.09) (1.00) {0.43} {2.44} {8.56} For each variable, the mean is shown and the standard deviation is below in parentheses. For each type of magnet student, the absolute T - statistic from a regression of each individual variable on magnet student status is shown in brackets. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. 193 Table A. 4 . Baseline Levels Models for Math Z - Score (Full Estimates) Variable (1) (2) (3) (4) Magnet Student Type Zoned Magnet - Student 0.307* 0.109* 0.051 0.046 (0.159) (0.062) (0.045) (0.032) Nonprogram Magnet Student - 0.048 - 0.078** - 0.011 - 0.024 (0.063) (0.038) (0.027) (0.033) Magnet Chooser 0.595*** 0.452*** 0.181*** 0.192*** (0.071) (0.047) (0.031) (0.034) Student Background Female 0.007 - 0.054*** - 0.055*** (0.007) (0.006) (0.006) Black or Native American - 0.714*** - 0.454*** - 0.365*** (0.034) (0.024) (0.018) Hisp anic - 0.510*** - 0.313*** - 0.258*** (0.032) (0.023) (0.016) Asian 0.460*** 0.376*** 0.363*** (0.054) (0.040) (0.030) Poverty - 0.421*** - 0.239*** - 0.183*** (0.029) (0.017) (0.012) Free L unch - 0.292*** - 0.156*** - 0.112*** (0.027) (0.016) (0.012) Reduced L unch - 0.186*** - 0.100*** - 0.066*** (0.024) (0.016) (0.012) Home L ang uage not Eng lish 0.037*** 0.111*** 0.109*** (0.014) (0.013) (0.014) Immigrant - 0.296*** - 0.049 - 0.069* (0.045) (0.036) (0.036) Special Student Statuses Gifted and Talented 0.917*** 0.874*** (0.018) (0.019) Special Education - 0.745*** - 0.736*** (0.015) (0.014) Parent Denial 0.133*** 0.125*** (0.020) (0.020) ELL - 0.420*** - 0.415*** (0.014) (0.013) Structural Move - 0.040** - 0.023 (0.019) (0.020) N onstructural Move - 0.069*** - 0.065*** (0.010) (0.010) School - Level Variables Zoned School 's % Chooser - 0.001* (0.001) Zoned School 's % White - 0.005* (0.003) Zoned School 's % Hisp anic - 0.005** (0.002) 194 Table A.4. (cont'd) Variable (1) (2) (3) (4) Zoned School 's % Black - 0.005** (0.002) Zoned School 's % Poverty - 0.001 (0.002) Zoned School's % G ifted and T alented 0.005*** (0.002) Zoned School 's % Special Education - 0.010*** (0.004) Zoned School 's % ELL 0.001 (0.001) IB 0.662*** 0.260** 0.188* 0.041 (0.133) (0.103) (0.095) (0.092) Observations 562,855 562,855 562,855 562,855 R - squared 0.100 0.225 0.412 0.418 All models include grade, year, and grade - year dummies, as well as an IB indicator. Each model builds in an additional vector of independent variables; the column heading states which vector of variables is added. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school wit h a magnet program at some point in the dataset. 195 Table A. 5 . Baseline Levels Models for Reading Z - Score (Full Estimates) Variable (1) (2) (3) (4) Magnet Student Type Zoned Magnet - Student 0.372** 0.131* 0.074 0.029 (0.175) (0.068) (0.051) (0.031) Nonprogram Magnet Student - 0.028 - 0.067* 0.003 - 0.036 (0.074) (0.040) (0.027) (0.027) Magnet Chooser 0.677*** 0.481*** 0.215*** 0.183*** (0.074) (0.044) (0.028) (0.028) Student Background Female 0.140*** 0.070*** 0.068*** (0.006) (0.005) (0.005) Black or NA - 0.705*** - 0.470*** - 0.359*** (0.029) (0.021) (0.015) Hisp anic - 0.569*** - 0.395*** - 0.303*** (0.025) (0.018) (0.015) Asian 0.182*** 0.090*** 0.105*** (0.035) (0.024) (0.018) Poverty - 0.526*** - 0.348*** - 0.261*** (0.030) (0.019) (0.012) Free L unch - 0.385*** - 0.252*** - 0.184*** (0.026) (0.016) (0.011) Reduced L unch - 0.229*** - 0.154*** - 0.101*** (0.023) (0.015) (0.011) Home L ang uage not Eng lish - 0.139*** - 0.015 - 0.017 (0.014) (0.013) (0.013) Immigrant - 0.540*** - 0.208*** - 0.231*** (0.056) (0.043) (0.041) Special Student Statuses Gifted and Talented 0.832*** 0.791*** (0.015) (0.015) Special Education - 0.875*** - 0.866*** (0.012) (0.011) Parent Denial 0.346*** 0.326*** (0.020) (0.019) ELL - 0.656*** - 0.646*** (0.014) (0.013) Structural Move - 0.061*** - 0.039** (0.015) (0.015) N onstructural Move - 0.065*** - 0.060*** (0.009) (0.009) School - Level Variables Zoned School's % Chooser - 0.000 (0.001) Zoned School's % White 0.001 (0.002) Zoned School's % Hisp anic - 0.002 (0.002) 196 Table A.5. (cont'd) Variable (1) (2) (3) (4) Zoned School's % Black - 0.001 (0.002) Zoned School's % Poverty - 0.004*** (0.001) Zoned School's % G ifted and T alented 0.003* (0.002) Zoned School's % Special Education - 0.009*** (0.003) Zoned School's % ELL 0.002 (0.001) IB 0.687*** 0.254*** 0.182*** 0.021 (0.101) (0.079) (0.069) (0.072) Observations 562,855 562,855 562,855 562,855 R - squared 0.123 0.263 0.470 0.479 All models include grade, year, and grade - year dummies, as well as an IB indicator. Each model builds in an additional vector of independent variables; the column heading states which vector of variables is added. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sampl e size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset. 197 Table A. 6 . Levels Models for Math Z - Scores (Full Estimates) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Poverty 0.002 0.002 0.006 0.002 0.005 0.003 (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) Free L unch 0.016*** 0.016*** 0.013*** 0.016*** 0.013*** 0.016*** (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) Reduced L unch 0.017*** 0.017*** 0.015*** 0.016*** 0.014*** 0.017*** (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) Home Language not Eng lish 0.032 0.033 0.035* 0.033 0.035* 0.035 (0.021) (0.021) (0.021) (0.021) (0.021) (0.022) Immigrant - 0.157*** - 0.157*** - 0.151*** - 0.156*** - 0.150*** - 0.159*** (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) Gifted and Talented 0.041*** 0.039*** 0.025*** 0.043*** 0.035*** 0.035*** (0.008) (0.008) (0.007) (0.008) (0.007) (0.008) Special Education - 0.090*** - 0.090*** - 0.079*** - 0.090*** - 0.079*** - 0.082*** (0.010) (0.010) (0.010) (0.010) (0.010) (0.010) Parent Denial - 0.020 - 0.021 - 0.020 - 0.021 - 0.020 - 0.021 (0.014) (0.014) (0.014) (0.014) (0.014) (0.014) ELL - 0.083*** - 0.084*** - 0.092*** - 0.083*** - 0.091*** - 0.085*** (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) Structural Move 0.008 0.007 0.007 0.004 0.005 0.007 (0.009) (0.009) (0.009) (0.009) (0.008) (0.011) N onstructural Move - 0.003 - 0.003 - 0.004 - 0.002 - 0.002 - 0.003 (0.005) (0.005) (0.005) (0.005) (0.005) (0.006) IB - 0.031 - 0.028 - 0.015 - 0.013 0.004 - 0.021 (0.036) (0.034) (0.028) (0.031) (0.025) (0.033) Zoned Magnet - Student - 0.058*** - 0.041** (0.022) (0.018) Nonprogram Magnet Student - 0.003 - 0.006 (0.014) (0.014) Magnet Chooser 0.003 0.010 (0.013) (0.013) 198 Table A.6. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Career prep - 0.130** - 0.149*** (0.053) (0.047) College prep - 0.147*** - 0.177*** (0.047) (0.039) Vanguard - 0.017 - 0.062* (0.039) (0.034) Humanities or Literature - 0.133** - 0.058 (0.059) (0.040) STEM 0.010 0.027 (0.018) (0.017) Language 0.016 - 0.004 (0.018) (0.025) Performing or Fine Arts - 0.034** - 0.031** (0.014) (0.013) Other 0.039 0.090*** (0.027) (0.025) SWP - 0.083*** - 0.059*** (0.021) (0.020) SUS - 0.014 - 0.109*** (0.041) (0.034) SWAS 0.021* 0.029*** (0.011) (0.010) Zoned School's % Chooser - 0.001** - 0.001 - 0.000 (0.000) (0.000) (0.000) Zoned School's % White - 0.008*** - 0.008*** - 0.008*** (0.001) (0.001) (0.002) Zoned School's % Hisp anic - 0.001 - 0.001 - 0.001 (0.001) (0.001) (0.001) Zoned School's % Black 0.000 0.001 - 0.000 (0.001) (0.001) (0.001) Zoned School's % Poverty - 0.004*** - 0.004*** - 0.004*** (0.001) (0.001) (0.001) 199 Table A.6. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned School's % G ifted and T alented 0.003*** 0.004*** 0.004*** (0.001) (0.001) (0.001) Zoned School's % Special Education - 0.005** - 0.005*** - 0.004** (0.002) (0.002) (0.002) Zoned School's % ELL 0.000 0.001 0.000 (0.001) (0.001) (0.001) All models include a student fixed effect as well as grade, year, and grade - year dummies . Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students a ttended a school with a magnet program at some point in the dataset. 200 Table A. 7 . Levels Models for Reading Z - Scores (Full Estimates) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Poverty - 0.005 - 0.002 - 0.005 - 0.002 - 0.005 - 0.002 (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) Free L unch 0.005 0.003 0.005 0.003 0.004 0.003 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Reduced L unch 0.002 0.001 0.002 0.001 0.002 0.001 (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) Home Language not Eng lish 0.024 0.027 0.024 0.027 0.026 0.029 (0.017) (0.018) (0.017) (0.017) (0.017) (0.018) Immigrant - 0.188*** - 0.183*** - 0.188*** - 0.183*** - 0.189*** - 0.184*** (0.016) (0.017) (0.016) (0.017) (0.016) (0.017) Gifted and Talented 0.028*** 0.020*** 0.030*** 0.024*** 0.027*** 0.019*** (0.007) (0.006) (0.006) (0.006) (0.007) (0.006) Special Education - 0.091*** - 0.081*** - 0.091*** - 0.081*** - 0.090*** - 0.080*** (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) Parent Denial 0.024** 0.024** 0.024** 0.025** 0.023** 0.024** (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) ELL - 0.139*** - 0.143*** - 0.138*** - 0.143*** - 0.139*** - 0.143*** (0.007) (0.007) (0.008) (0.007) (0.008) (0.007) Structural Move - 0.001 - 0.004 - 0.003 - 0.006 - 0.002 - 0.006 (0.008) (0.007) (0.008) (0.007) (0.008) (0.007) N onstructural Move - 0.007 - 0.008** - 0.007 - 0.007* - 0.007 - 0.008* (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) IB - 0.015 - 0.001 - 0.000 0.014 - 0.016 - 0.006 (0.022) (0.020) (0.019) (0.018) (0.021) (0.020) Zoned Magnet - Student - 0.038*** - 0.040*** (0.015) (0.013) Nonprogram Magnet Student - 0.004 - 0.011 (0.009) (0.009) Magnet Chooser 0.001 0.002 (0.010) (0.009) 201 Table A.7. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Career prep - 0.049 - 0.064** (0.036) (0.032) College prep - 0.070*** - 0.121*** (0.020) (0.024) Vanguard - 0.003 - 0.010 (0.014) (0.013) Humanities or Literature - 0.139*** - 0.090*** (0.038) (0.025) STEM 0.004 0.011 (0.008) (0.009) Language - 0.013 - 0.026 (0.016) (0.019) Performing or Fine Arts 0.006 - 0.003 (0.013) (0.011) Other - 0.008 0.025 (0.018) (0.018) SWP - 0.046*** - 0.041*** (0.012) (0.011) SUS - 0.024 - 0.066*** (0.019) (0.022) SWAS 0.019** 0.024*** (0.008) (0.007) Zoned School's % Chooser - 0.001*** - 0.001** - 0.001*** (0.000) (0.000) (0.000) Zoned School's % White - 0.004*** - 0.004*** - 0.005*** (0.001) (0.001) (0.001) Zoned School's % Hisp anic 0.001 0.001 0.000 (0.001) (0.001) (0.001) Zoned School's % Black 0.002*** 0.002*** 0.002** (0.001) (0.001) (0.001) Zoned School's % Poverty - 0.004*** - 0.004*** - 0.004*** (0.001) (0.001) (0.001) 202 Table A.7. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned School's % G ifted and T alented 0.002*** 0.002*** 0.002*** (0.001) (0.001) (0.001) Zoned School's % Special Education - 0.006*** - 0.006*** - 0.005*** (0.001) (0.001) (0.001) Zoned School's % ELL - 0.001 - 0.000 - 0.001 (0.000) (0.000) (0.000) All models include a student fixed effect as well as grade, year, and grade - year dummies. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset . 203 Table A. 8 . Value - Added Models for Math Z - Scores (Full Estimates) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Poverty 0.003 0.003 0.003 0.003 0.003 0.003 (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) Free L unch 0.005 0.004 0.005 0.004 0.005 0.004 (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Reduced L unch 0.006 0.005 0.006 0.005 0.006 0.005 (0.006) (0.006) (0.006) (0.006) (0.006) (0.006) Home Language not Eng lish 0.048* 0.048* 0.048* 0.048* 0.049* 0.049* (0.025) (0.025) (0.025) (0.025) (0.025) (0.025) Immigrant 0.071*** 0.071*** 0.072*** 0.072*** 0.071*** 0.071*** (0.018) (0.018) (0.018) (0.018) (0.018) (0.017) Gifted and Talented - 0.127*** - 0.129*** - 0.123*** - 0.126*** - 0.127*** - 0.129*** (0.011) (0.010) (0.011) (0.011) (0.011) (0.010) Special Education 0.015 0.016 0.014 0.015 0.015 0.016 (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) Parent Denial - 0.036** - 0.036** - 0.036** - 0.036** - 0.036** - 0.036** (0.014) (0.014) (0.014) (0.014) (0.014) (0.014) ELL 0.050*** 0.048*** 0.051*** 0.048*** 0.050*** 0.048*** (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) Structural Move 0.009 0.010 0.007 0.010 0.008 0.010 (0.017) (0.016) (0.017) (0.016) (0.017) (0.016) N onstructural Move 0.011 0.013 0.012 0.014 0.012 0.013 (0.011) (0.010) (0.010) (0.010) (0.010) (0.010) IB 0.042* 0.049** 0.044* 0.052** 0.041* 0.047* (0.023) (0.024) (0.023) (0.025) (0.023) (0.025) Zoned Magnet - Student - 0.032* - 0.017 (0.017) (0.018) Nonprogram Magnet Student - 0.010 - 0.001 (0.012) (0.013) Magnet Chooser - 0.035*** - 0.022* (0.012) (0.012) 204 Table A.8. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Career prep - 0.081** - 0.084** (0.040) (0.041) College prep - 0.111*** - 0.108*** (0.029) (0.031) Vanguard - 0.046** - 0.045** (0.020) (0.022) Humanities or Literature - 0.025 - 0.002 (0.034) (0.028) STEM - 0.024** - 0.016 (0.012) (0.013) Language - 0.050*** - 0.045*** (0.011) (0.014) Performing or Fine Arts - 0.043*** - 0.035*** (0.012) (0.011) Other 0.007 0.023 (0.026) (0.028) SWP - 0.053*** - 0.040** (0.017) (0.018) SUS - 0.052** - 0.044 (0.023) (0.031) SWAS - 0.020** - 0.015* (0.008) (0.008) Zoned School's % Chooser - 0.000 - 0.000 - 0.000 (0.000) (0.000) (0.000) Zoned School's % White - 0.001 - 0.001 - 0.001 (0.001) (0.001) (0.001) Zoned School's % Hisp anic 0.000 0.000 0.000 (0.001) (0.001) (0.001) Zoned School's % Black 0.000 0.000 - 0.000 (0.001) (0.001) (0.001) Zoned School's % Poverty 0.000 0.000 0.000 (0.001) (0.001) (0.001) 205 Table A.8. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned School's % G ifted and T alented 0.001 0.001 0.001 (0.001) (0.001) (0.001) Zoned School's % Special Education - 0.002 - 0.002 - 0.002 (0.002) (0.002) (0.002) Zoned School's % ELL 0.001 0.001 0.001 (0.001) (0.001) (0.001) All models include a student fixed effect as well as grade, year, and grade - year dummies. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students attended a school with a magnet program at some point in the dataset . 206 Table A. 9 . Value - Added Models for Reading Z - Scores (Full Estimates) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Poverty - 0.006 - 0.007 - 0.006 - 0.006 - 0.006 - 0.007 (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Free L unch - 0.004 - 0.004 - 0.004 - 0.004 - 0.004 - 0.004 (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Reduced L unch - 0.009* - 0.010* - 0.009* - 0.010* - 0.009* - 0.010* (0.005) (0.005) (0.005) (0.005) (0.005) (0.005) Home Language not Eng lish 0.038* 0.039* 0.038* 0.039* 0.038* 0.039* (0.020) (0.020) (0.020) (0.020) (0.020) (0.020) Immigrant 0.089*** 0.089*** 0.089*** 0.090*** 0.089*** 0.089*** (0.018) (0.018) (0.018) (0.018) (0.018) (0.018) Gifted and Talented - 0.112*** - 0.113*** - 0.113*** - 0.114*** - 0.112*** - 0.114*** (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) Special Education 0.052*** 0.053*** 0.052*** 0.054*** 0.052*** 0.054*** (0.011) (0.011) (0.011) (0.011) (0.011) (0.011) Parent Denial - 0.014 - 0.014 - 0.014 - 0.014 - 0.015 - 0.014 (0.013) (0.013) (0.013) (0.013) (0.013) (0.013) ELL 0.032*** 0.031*** 0.032*** 0.031*** 0.032*** 0.031*** (0.010) (0.009) (0.010) (0.009) (0.010) (0.009) Structural Move - 0.007 - 0.007 - 0.008 - 0.008 - 0.008 - 0.008 (0.013) (0.012) (0.013) (0.012) (0.013) (0.012) N onstructural Move 0.007 0.008 0.008 0.009 0.008 0.008 (0.008) (0.008) (0.009) (0.008) (0.008) (0.008) IB 0.017 0.020 0.021 0.023 0.014 0.018 (0.016) (0.017) (0.017) (0.018) (0.017) (0.018) Zoned Magnet - Student - 0.027** - 0.019* (0.011) (0.012) Nonprogram Magnet Student - 0.011 - 0.003 (0.007) (0.008) Magnet Chooser - 0.022*** - 0.009 (0.007) (0.009) 207 Table A.9. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Career prep - 0.046 - 0.040 (0.033) (0.032) College prep - 0.045*** - 0.044*** (0.012) (0.016) Vanguard - 0.010 0.005 (0.013) (0.017) Humanities or Literature - 0.062*** - 0.049*** (0.015) (0.017) STEM - 0.008 - 0.001 (0.008) (0.009) Language - 0.037*** - 0.024* (0.012) (0.013) Performing or Fine Arts - 0.018** - 0.013* (0.008) (0.007) Other - 0.014 - 0.001 (0.016) (0.018) SWP - 0.027*** - 0.018* (0.010) (0.010) SUS - 0.045*** - 0.021 (0.016) (0.023) SWAS - 0.009 - 0.002 (0.006) (0.007) Zoned School's % Chooser - 0.000 - 0.000 - 0.000 (0.000) (0.000) (0.000) Zoned School's % White 0.000 0.000 0.000 (0.001) (0.001) (0.001) Zoned School's % Hisp anic 0.001 0.001 0.001 (0.001) (0.001) (0.001) Zoned School's % Black 0.001 0.001 0.001 (0.001) (0.001) (0.001) Zoned School's % Poverty 0.000 0.000 0.000 (0.001) (0.001) (0.001) 208 Table A.9. (cont'd) (1) (2) (3) (4) (5) (6) Variable No Peer Comp Peer C omp No Peer Comp Peer Comp No Peer Comp Peer Comp Zoned School's % G ifted and T alented 0.000 0.000 0.000 (0.000) (0.001) (0.000) Zoned School's % Special Education - 0.003** - 0.003** - 0.003** (0.001) (0.001) (0.001) Zoned School's % ELL 0.000 0.000 0.000 (0.000) (0.000) (0.000) All models include a student fixed effect as well as grade, year, and grade - year dummies . Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 562,855 includes data for 207,684 students, and 144,894 of these students a ttended a school with a magnet program at some point in the dataset. 209 Table A. 10 . Levels Models for Math Z - Scores: Restricting Sample to Middle School and High School Variable MS or HS Only Full Sample MS or HS Only Full Sample MS or HS Only Full Sample Zoned Magnet Student - 0.186** - 0.041** - 0.077 - 0.018 Nonprogram Magnet Student - 0.017 - 0.006 - 0.026 - 0.014 Magnet Chooser 0.01 0.01 - 0.023 - 0.013 Career Prep - 0.097** - 0.149*** - 0.047 - 0.047 College Prep - 0.268*** - 0.177*** - 0.033 - 0.039 Vanguard 0.01 - 0.062* - 0.054 - 0.034 Humanities or Literature - 0.026 - 0.058 - 0.033 - 0.04 STEM 0.053*** 0.027 - 0.017 - 0.017 Language 0.070* - 0.004 - 0.038 - 0.025 Performing or Fine Arts 0.018 - 0.031** - 0.015 - 0.013 Other 0.067** 0.090*** - 0.03 - 0.025 SWP - 0.175** - 0.059*** - 0.075 - 0.02 SUS - 0.051 - 0.109*** - 0.06 - 0.034 SWAS 0.030*** 0.029*** - 0.01 - 0.01 All models include the full set of control variables and a student fixed effect. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample size of 287,9 96 includes data for 129,468 students, and 109, 282 of these students attended a school with a magnet program at some point in the datase t. 210 Table A. 1 1 . Levels Models for Reading Z - Scores: Restricting Sample to Middle School and High School Variable MS or HS Only Full Sample MS or HS Only Full Sample MS or HS Only Full Sample Zoned Magnet Student - 0.037 - 0.040*** - 0.036 - 0.013 Nonprogram Magnet Student 0.011 - 0.011 - 0.015 - 0.009 Magnet Chooser 0.045*** 0.002 - 0.015 - 0.009 Career Prep - 0.017 - 0.064** - 0.029 - 0.032 College Prep - 0.091*** - 0.121*** - 0.02 - 0.024 Vanguard 0.053* - 0.01 - 0.031 - 0.013 Humanities or Literature 0.034 - 0.090*** - 0.023 - 0.025 STEM 0.052*** 0.011 - 0.008 - 0.009 Language 0.044* - 0.026 - 0.026 - 0.019 Performing or Fine Arts 0.018** - 0.003 - 0.009 - 0.011 Other 0.041*** 0.025 - 0.014 - 0.018 SWP - 0.056 - 0.041*** - 0.048 - 0.011 SUS - 0.029 - 0.066*** - 0.032 - 0.022 SWAS 0.039*** 0.024*** - 0.006 - 0.007 All models include the full set of control variables and a student fixed effect. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample si ze of 287,996 includes data for 129,468 students , and 109, 282 of these students attended a school with a magnet program at some point in the dataset . 211 Table A. 1 2 . Value - Added Models for Math Z - Scores: Restricting Sample to Middle School and High School Variable MS or HS Only Full Sample MS or HS Only Full Sample MS or HS Only Full Sample Zoned Magnet Student - 0.179*** - 0.017 - 0.056 - 0.018 Nonprogram Magnet Student - 0.036 - 0.001 - 0.026 - 0.013 Magnet Chooser - 0.04 - 0.022* - 0.025 - 0.012 Career Prep - 0.047 - 0.084** - 0.038 - 0.041 College Prep - 0.146*** - 0.108*** - 0.041 - 0.031 Vanguard - 0.015 - 0.045** - 0.026 - 0.022 Humanities or Literature - 0.034 - 0.002 - 0.031 - 0.028 STEM 0.012 - 0.016 - 0.019 - 0.013 Language - 0.009 - 0.045*** - 0.035 - 0.014 Performing or Fine Arts - 0.014 - 0.035*** - 0.016 - 0.011 Other 0.000 0.023 - 0.028 - 0.028 SWP - 0.076*** - 0.040** - 0.028 - 0.018 SUS 0.046 - 0.044 - 0.054 - 0.031 SWAS - 0.013 - 0.015* - 0.011 - 0.008 All models include the full set of control variables and a student fixed effect. Standard errors are clustered by school and shown in parentheses. *, **, and *** denote statistical significance at the 0.1, 0.05, and 0.01 levels, respectively. The sample si ze of 287,996 includes data for 129,468 students , and 109, 282 of these students attended a school with a magnet program at some point in the dataset . 212 Table A. 1 3 . Value - Added Models for Reading Z - Scores: Restricting Sample to Middle School and High Scho ol Variable MS or HS Only Full Sample MS or HS Only Full Sample MS or HS Only Full Sample Zoned Magnet Student - 0.09 - 0.019* - 0.082 - 0.012 Nonprogram Magnet Student 0.002 - 0.003 - 0.017 - 0.008 Magnet Chooser 0.01 - 0.009 - 0.018 - 0.009 Career Prep - 0.006 - 0.04 - 0.029 - 0.032 College Prep - 0.043* - 0.044*** - 0.022 - 0.016 Vanguard 0.012 0.005 - 0.03 - 0.017 Humanities or Literature - 0.041 - 0.049*** - 0.028 - 0.017 STEM 0.036*** - 0.001 - 0.011 - 0.009 Language - 0.031 - 0.024* - 0.019 - 0.013 Performing or Fine Arts - 0.037*** - 0.013* - 0.009 - 0.007 Other 0.030** - 0.001 - 0.015 - 0.018 SWP - 0.076* - 0.018* - 0.046 - 0.01 SUS 0.001 - 0.021 - 0.036 - 0.023 SWAS 0.007 - 0.002 - 0.007 - 0.007 All models include the full set of control variables and a student fixed effect. 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