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Xerox University Microfilms 300 North Z eeb Road Ann Arbor, M ichigan 48106 I I 74-6157 ULUSAN, Aydin Mustafa, 1941AN ECONOMETRIC ANALYSIS OF MICHIGAN'S WELFARE CASELOAD, 1968-71. Michigan State University, Ph.D., 1973 Economics, general U niversity Microfilm s, A XEROX Com pany , A nn A rbor, M ichigan AN ECONOMETRIC ANALYSIS OF MICHIGAN'S WELFARE CASELOAD, 19 6 8-71 By Aydin Ulusan A THESIS Submitted to M ichigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1973 ABSTRACT AN E CONOMETRIC ANALYSIS OF MICHIGAN'S WELFARE CASELOAD, 1968-71 By Aydm Ulusan The rapid increase in welfare rolls over the past few years has resulted in an increased recognition of the need for an explanation of the size and composition of this sector of the economy. This dissertation examines public a s s i s t a n c e , the alternatives to receiving public assistance, and the factors affecting the individual's choice among the available alternatives. The number of people choosing welfare over other alternatives, assistance, as we ll as those choosing to leave public determine the size of welfare rolls at any given point in time. Thus, time-series data are utilized in estimating equations on new recipients to and termina­ tions from Michigan's Ai d to Families w i t h Dependent Children (AFDC) and General Ass is ta nc e (GA) programs. Although past and present labor ma rk e t conditions as well as benefit levels seem to affect the decisions of individuals in any given month, neither the direction nor the m ag nitude of their impacts are consistent across s u b ­ groups of the welfare population that are examined. Aydm Ulusan To test the effects of some demographic c ha r a c t e r ­ istics on the pr obability of a recipient's employment, cross-section survey data on AFDC recipients are used in estimating a Logit Model. The results indicate that factors such as race, education, presence of pre-school children, and living in model cities neighborhoods affect the choices open to AFDC recipients. Finally, a Logistic Growth Model is estimated by using time-series data on female-headed AFDC families. It is seen that this model can be used with an acceptable degree of confidence for predicting caseloads and the associated p ro gram costs. To my father, Aziz Ulusan ii A CK NOWLEDGEMENTS I wish to thank Dr. Daniel H. Saks for his critique and help in making this dissertation a better product. I also wish to thank Dr. Mitchel Stengel, Mr. Vernon K. Smith, Mr. Daniel Kitchel, Schwartz and Mr. Leonard for their constructive comments on the drafts of this thesis. Special thanks go to Dr. Jan Kmenta, not only for his part in this work but also for his role as a mentor during my graduate studies in M ichigan State University. I w o ul d also like to thank Mrs. Pat Hansen for typing the ma ny drafts of this study and Mrs. Ann Brown for typing the final product. my wife, E n i s e , and my daughter, bearable. iii Finally, I mus t thank Cigdem, who made it all TABLE OF CONTENTS Page D E D I C A T I O N ................................... A CK NO WL ED GM EN TS ii ...................................... iii LIST OF T A B L E S .......................................... vi LIST OF F I G U R E S .......................................... viii Chapter I.PURPOSE AND ORGANIZATION ........................ II.AN ANALYSIS OF CASELOAD TUR NO VE R III. . . . . 1 6 Introduction ................................... A Model of Flows To and From the "Welfare Sector" ...................................... Module 1 ...................................... Mod ul e 2 ...................................... Module 3 ...................................... Module 4 . ........................... Mod ul e 5 ............................... Module 6 ...................................... Module 7 ....................................... Module 8 ....................................... Module 9 ...................................... M odule 1 0 ............................ Behavioral Considerations ..................... 8 8 10 10 10 11 12 12 13 13 13 15 AN ECONOMETRIC M ODEL OF FLOWS IN AND OUT OF WELFARE 33 I n t r o d u c t i o n ................................... ' The M o d e l ...................................... The Terminations Equation ................... The New Cases E q u a t i o n ..................... E s t i m a t i o n ...................................... R e s u l t s .......................................... Implications . . . . . Terminations ............................... N e w R e c i p i e n t s ............................... 33 33 35 39 44 44 49 49 53 iv 6 Chapter IV. V. VI. Page AN EMPIRICAL ANALYSIS OF THE EMPLOYED AFDC RECIPIENT: SOME EVIDENCE PROVIDED BY SURVEY D A T A .............................................. 66 ................................... Introduction The Shortcomings ofOrdinary Least Squares . A Logit Model ................................... E s t i m a t i o n ....................................... Implications ................................... 66 68 71 74 77 FLOWS INTO AFDC-R: A LOGISTIC GROWTH M O D EL . 85 The M o d e l ...................................... Specification ................................... E s t i m a t i o n ....................................... R e s u l t s .......................................... Implications ................................... 86 88 89 90 92 SOME CONCLUDING R E M A R K S ...................... 97 BIBLIOGRAPHY ............................................. A P P E N D I C E S ................................................ v 102 108 LIST OF TABLES Table 3.1 3.2 4.1 4.2 Page Time Series Analysis of Terminations from Michigan's AFDC-R, A F D C - U , and GA Programs . Time Series Analysis of New Recipients Coming Into Michigan's AFDC-R, A F D C - U , and GA P r o g r a m s .................................. 45 46 Frequency Distribution of Sample wit h Respect to Characteristics Categories and Employment 73 Relative Frequencies and the Implicit Estimates of P.. l 78 5.1 Predicted and Actual AF D C - R Caseload . . . . 93 5.2 AFDC-R Caseload Projections for 1973 . . . . 94 Appendix 3.A 3.B 3.C 3.D 3.E Breakdown of Occupational Categories that AFDC Recipients Currently or Usually Belong To . 113 Estimated Regression Coefficients for the Terminations Equations Using Different Labor Market V a r i a b l e s ..................... 114 Estimated Regression Coefficients for the New Recipient Equations With a Four Month Second, Third, and Fourth Degree Polynomial L a g ......................................... 115 Estimated Regression Coefficients for the New Recipient Equations With a Five Month Second, Third, and Fourth Degree Polynomial Lag . . 116 Estimated Regression Coefficients for the New Recipient Equations With a Six Month Second, Third, and Fourth Degree Polynomial Lag . . 117 vi Table Page 3.F Estimated Regression Coefficients for the New Recipient Equations With a Seven Month Second, Third, and Fourth Degree Polynomial L a g ..................................................118 3.G Estimated Regression Coefficients for the New Recipient Equations With an Eight M onth Second, Third, and Fou rt h Degree Polynomial L a g ..................................................119 3.H Correla ti on Matrix for Equation (3.4), Terminations from A F D C - R ..................... 120 C o r r e l at io n M at r i x for Equation (3.5), Terminations from AFD C- U ..................... 120 3.1 3.J C orrelation Ma tr ix for Equation (3.6), Terminations from G A .............................121 3.K Correla ti on M a t r i x for Equation (3.7a), New Recipient to A F D C - R ......................... 121 3.L Correlation Ma t r i x for Equation (3.8a), New Recipients to A F D C - U ......................... 122 3.M Co rrelation Matrix for Equation (3.9a), Ne w Recipients to G A .............................122 vii LIST OF FIGURES Figure 2.1 Page Flows between the labor market and welfare s e c t o r s ......................................... 9 3.1 Relative weights of lagged unemployment rates . 41 3.2 Weights of current and lagged unemployment rates in explaining flows into AFDC and G A . . 58 4.1 5.1 Monotonic transformation of a probability to the range + ° ° ) ................................. 70 A modified logistic growth curve 87 .............. C HA PTER I PURPOSE AND ORGANIZATION The size and composition of w el fa re rolls has b ee n the cause of growing concern to legislators, scientists, and taxpayers alike. explanations hav e been offered, social A l t h o u g h some heuristic they are of limited value in either forecasting or providing useful guidelines for w el fare policy. In this dissertation, the alternatives to receiving public assistance and the factors affecting the individual's choice b et ween the m will be examined. The n u m b e r of people choosing we l f a r e over other alternatives, as well as those choosing to leave public assistance, determine the size of w el fare rolls. The alternatives and the factors causing individuals to make decisions are r e p r e s en te d by the flow d i ag ra m in Chapter II.'*' The flows of people in and out of welfare and the flows of information upon w h i c h decisions are based are presen te d wi th the intention of de lineating the broader decisions implicit in m i c ro models of consumer choice. Chapter III develops an econo me tr ic model of people entering and leaving welfare rolls. The importance of pres en t as w e l l as past labor ma rk et conditions on the decision to choose welfare is incorporated into this 1 2 empirical m odel by the use of a d istributed lag structure. Using time-series data, the model is estimated and tested. Although labor m ar k e t conditions and benefit levels are seen to affect the decision of individuals, neither the d irection nor the magnitude of their impacts are consistent across sub-groups of the welfare population that are e x a m i n e d .^ The alternative to the welfare system that is of p ar ticular interest is the labor market; indeed, a major objective of the 1967 Social Security Amendments was to assure that recipients ". . .enter the labor force and 3 accept empl oy me n t so that they will become self-sufficient." Unfortunately for a large number of welfare recipients, the attainment of self-sufficiency as me as ur ed by their termination from the caseload has not followed the a c qu is i­ tion of employment. Rather, the ef f e c t of the 19 67 Ame nd me nt s has been to increase the number of persons who 4 are simultaneously employed and receiving welfare. This is a necessary consequence of the higher b reak even points 5 incorporated m the w e l f a r e reforms. As the number of people falling into this category are not accounted for by data on terminations or incoming r e c i p i e n t s , the empirical model pr es ented in Chapter III cannot analyze their decision to combine both labor mar ke t activity and welfare status. In order to provide insight into the factors affecting the probability of an A i d to Families wi th Dependent Children 3 (AFDC) recipient's employment, estimating a "Logit Model" survey data are used in in Chapter IV. This s p e c i f i c a ­ tion overcomes some of the statistical problems resulting from the use of a dichotomous dependent variable. results The indicate that demographic characteristics such as race, education, presence of pre-school children, and living in model cities neighborhoods affects the choices open to AF DC recipients. The rapid increase in the number of welfare recipients over the past few highly prosperous years has generated concern and frustration. A l though the number of persons receiving AFD C in M ichigan declined slightly during the 1 9 5 0 's, it increased by 143 p er cent in the next decade and has nea rl y doubled in the last three years. AFDC (nearly 70 p er cent of the total welfare population in December 19 72) is the largest category of public assistance in Michigan. Moreover in the past 15 years, it has shown the most dramatic increases of any welfare progr am in the state. w h o le picture however. the AF DC -R exhibits These statistics do not give the A closer look reveals that it is (female-headed) this trend. category in particular that Given these facts, the importance of an accurate predictive model of flows coming into the A FD C - R category becomes obvious. Based on the assumption that many n on -quantifiable occurances have been instrumental in the accelerated growth rate of this category of public 4 assistance, Model" Chapter V presents a modi fi ed "Logistic Growth for, essentially, predictive purposes. Time series data are used in the estimation of this model and the results indicate that it can be used wi th an acceptable degree of confidence for predicting caseloads and their implied costs to the state. The final chapter is devoted to a summary of findings and some conclusions. FOOTNOTES TO CHAPTER I ''"See Figure 2.1 below, p. 9. 2 The welfare categories included in our analysis are Aid to Families wi t h Dependent Children (AFDC), and General Assistance (GA). AFD C is a federal p r og ra m established to provide assistance to children who are deprived of parental support or care by the death, continued absence from the home, or physical or mental incapacity of a parent, or by the unemployment of the father. Here­ after, those cases where the father is present wi ll be called AFDC-U, Aid to Families with Dependent ChildrenUnemployed Father, and those cases where only the mother is present AFDC-R, Aid to Families with Dependent ChildrenRegular. W h e n e v e r a reference to the combined group is made, i.e., A F D C - U and AFDC-R, it will be denoted as AFDC. GA is a n on-federal p ro gr am administered by the county departments of social services. It provides assistance to persons where needs are not met by other programs or their own resources. These two programs, AFDC and GA, are the only ones that are significantly affected by labor market conditions, and e mp l oy me nt -r el at ed we l fare policy changes, and are therefore mo s t amenable to the kind of analysis we wi sh to undertake. 3 Social Security Amendments of 1967, Sec. 201 (C) (A), 90-248, January 2, 1968. 4 See Vernon K. Smith and Aydin Ulusan, The Employment of AF D C Recipients in M i c h i g a n , Studies in Welfare Policy, Publication 163 (Lansing: Michigan De partment of Social Services, 1972). P.L. ^The break ev en level is the point under a negative income tax scheme where the tax on earnings equals the income guarantee and is thus the p oi n t at which an i n d i v i d u a l ’s earnings w o u l d push him off of welfare. 5 CHAPT ER II AN ANALYSIS OF C ASELOAD TU RNOVER Introduction In this chapter, flows of people in and out of certain w e l f a re -r el a te d components of the economy are traced. These flows depend on decisions about the relative value of alternative courses of action and on information about those alternatives. The conceptual model to be presented is not proposed as an a lternative to the static micro models of consumer choice; broader choices it delineates the implicit in them. The flows of people coming into Michigan's AFDC-R, AFDC-U, and GA programs and the flows of people t e r m i n a t ­ ing from these programs are focused upon in our analysis. Besides comprising a very large p r oportion of the total welfare population, these categories are p robably the only ones that are significantly affected by factors presented below. to be These three categories will be analyzed jointly or separately depending upon the aspect of the p ro bl em under scrutiny and the availability of data. The information influencing decisions consists of data on labor mar ke t conditions, benefit levels, expected wages, welfare and costs and returns implicit in the 6 7 choice of one alternative over others. There also exist other factors such as changes in the rights of individuals to receive public assistance, graphic changes, socio-economic a n d d e m o ­ revisions of w el fare policy, and shifts in attitudes and tastes wi th re spect to pub l ic assistance. The broader scope of our model also enables us to i n c o r ­ porate a degree of " dy n a m i s m , " inherent in the response to flows of this information, not possible w it h i n the static framework of consumer choice models. The use of subscripted variables are imporant since some flows of information may lag be hi nd events; for example, the p e rception of relative opportunities, is ba sed on past as w e l l as pr esent events, as shown by the profound influence of the w o r k history of A F D C women on their choices between wo rk and w e l f a r e . ^ Similarly the dissemi na ti on of information is a dynamic p he nomenon resulting in an eve r- wi de ni ng response as it becomes available to mo re and more people. of information, The flood in the form of simplified we lfare manuals, w h i c h became available to slum and gh et to dwellers in the 19 60's is a good example of this. Such evi de nc e is pr ovided by a study w h i c h summarizes the impact as f o l l o w s : F r o m September of 19 65 to September of 19 66. . .[the] AF DC caseload in [a pa rticular anti-poverty] area grew by 36.6 percent; the total city A F D C caseload, during the same period, increased by only 8.6 p e r ­ cent. . . .All tne [anti-poverty] agency did. . .was to make people aware of the availability of AFDC [and] to stimulate the use of (it).^ We shall now set up the conceptual model, and relate the be havioral models found in the literature to its components. 8 A M o d e l of F l o w s To a n d F r o m t he " W e l f a r e S e c t o r " W e h a v e e m p l o y e d w h a t m i g h t be science" approach to m o d e l b u i l d i n g . information are represented by respectively in F i g u r e t h e n th e b a h a v i o r a l 2.1. is d e s c r i b e d b y Module F l o w s of p e o p l e the solid a n d b r o k e n lines about the pe o p l e wit h i n thi s d i a g r a m is a s s u m e d to b e s t a t i o n a r y . 1 (t-1) assistance the c a s e l o a d for the p a r t i c u l a r under examination. w h o ar e n o t e m p l o y e d , in th e p r e v i o u s category of public Included are both recipient's a n d t h o s e w h o a r e e m p l o y e d and receiving welfare benefits simultaneously being represented by the shaded r e g i o n ) . alternatives are three G r o u p 1, remain unemployed, (ii) stayon welfare but become employed, or leave welfare. t h o s e w h o are e m p l o y e d r e c i p i e n t s , (ii) (iii) the can stayon welfare and (i) can s t a y on w e l f a r e a n d remain employed, s t a y on become unemployed, welfare but or l e av e w e l f a r e . If a l t e r n a t i v e s means There (i) (iii) 2, (the l a t t e r to c h o o s e f r o m f o r b o t h g r o u p s . unemployed recipients, Group and The p o p u l a t i o n w h o s e b e h a v i o r T hi s r e p r e s e n t s period "s y s t e m s - Each module will be defined, assumtpions them w i l l be explained. termed a (i) or (ii) a flow into Module 2, are c h o s e n by e i t h e r g r o u p t h e c a s e l o a d in p e r i o d (t). it FLOWS BETWEEN THE LABOR MARKET AND WELFARE SECTORS NEW WELFARE RECIPIENTS INT CASELOAD In T -1 CASELOAD IN T LABOR MARKET 8 STOCK OF INDIVIDUALS HAVING EXHAUSTED UNEMPLOY­ MENT INSURANCE STOCK OF INDIVIDUALS RECEIVING UNEYIPLOYMENT STOCK OF UNEMPLOYED OR UNDER EMPLOYED LABORERS STOCK OF EMPLOYED LABORERS INSURANCE NON-LABOR FORCE NON-WELFARE SECTOR FIGURE 2 I TERMINATIONS TRANSFERS TO OTHER PUBLIC ASSISTANCE PROGRAMS IN T 10 If, however, the decision to leave welfare (alternative (iii) for both groups) is made then a flow through the node represented by module 3, terminations is period (t-1), r e s u l t s . Module 2 The caseload in period component, (t) is represented by this and needs no further elaboration as it is identical to module 1 with respect to composition and alternatives. Module 3 Termination from welfare in period represented by this module. (t-1) is Alth ou gh it is not a component comprising a stock of people faced with a l te r ­ natives, it can be considered a "summation operator" on flows coming out of the we lfare sector or a node through which people flow. That is to say it represents the sum of recipients who have decided to terminate and flow into (i) Module 4: (ii) Module 5: the stock of employed laborers the non-welfare, sector, ■• (in) Module 10: non-labor market or other public assistance programs. Module 4 This represents However, the stock of employed l a b o r e r s . it intersects the other component of the overall labor market, the stock of unemployed or underemployed 3 11 laborers. As with modules 1 and 2, the status of e m p l o y ­ ment is differentiated by shading the appropriate area. The region of module 4 that does not intersect with module 6 is comprised of people who have two choices open to them (i) continuing their employment, or (ii) leaving the labor force. Those who chose to leave the labor force flow into module 5, the non-labor force non-welfare sector. women getting married, Retired people, and young people continuing their education wo uld be good e x a m p l e s . The area that intersects module 6 represents the underemployed and low-wage earners, and the choices open to them will be discussed in defining module 6. Module 5 The group of people who are neither on welfare nor in the labor mar ke t makes up module 5. deserted by her husband, A mother now people supported by relatives, retirees living off their pensions, and students are examples of members of this group. The alternatives they can choose from are (i) remaining in this group, (ii) joining the labor force, or (iii) becoming a welfare recipient. Alternative native (iii) (ii) implies a flow into module 4, and a l t e r ­ a flow into module 9. 12 Module 6 The low-wage empl oy me nt m a r k e t , the underemployed, and unemployed individuals seeking jobs make up this component of the model. The alternatives facing this group are (i) remaining in the labor m ar k e t which implies staying in module 6 or flowing into module 4, (ii) moving into the non-labor force, non-labor market sector, (iii) i.e., module 5, receiving unemployment insurance, which means a flow into module 7, or (iv) becoming a welfare recipient and flowing into module 9. Module 7 The stock of individuals receiving unemployment insurance is r epresented by module 7. This group can choose between (i) remaining in this component until they exhaust their benefits and then flow into module 8, (ii) getting back into the labor force, going into module (iii) i.e., 4, flowing into module 5, the non-labor force non-welfare sector, or (iv) becoming a welfare recipient and flowing 4 into module 9. 13 M od ul e 8 The flow of people from module 7, the stock of individuals receiving unemployment insurance, replenishes the stock of individuals having exhausted such benefits, and is re presented by module 8. It is really a node like module 3 (thought as a summation operator) and members are expected to be in passage to the following alternatives: (i) going ba ck into the labor force, (ii) going into the non-labor force non-welfare sector, (iii) A lt er na ti ve or receiving public assistance. (i) results in a flow into module 4, in a flow into module 5, and (iii) (ii) in a flow into module 9. Module 9 As w i t h module 3, this compon en t of the m o d el is a "summation operator." It represents the total flow coming into the welfare sector, welfare recipients in peri od i.e., the sum of new (t), coming from modules 5, 6, 7, and 8. Module 10 Module 10 is included for accounting reasons and represents transfers to other public assistance programs from GA. The choices available to this group need not be dwelt upon as they are incorporated into the caseload of other categories r epresented by module 2. 14 The definition of each component of the conceptual model, the flows of people among the components (solid lines), and the factors affecting their decisions, presented as information flows (broken lines), can be summarized in the following way. Denoting the stock of new public assistance recipients in period N. = I wj t j 5 where (t) by N^., we can write ; j = 5,6,7,8, (2.1) = inflow from the "non-welfare, non-labor market sector" in period t, = inflow from the "stock of unemployed and underemployed" in period t, N 7 = inflow from the "stock receiving unemploy­ ment benefits" in period t, and g N. = inflow from the "stock having exhausted unemployment benefits" in period t. Termination from welfare in period (t) are denoted by T , and can be summarized as Tfc = I T^ ; i = 4,5,10, i 4 T = outflow going into the labor force m t, (2.2) period 5 T t = outflow going into the "non-welfare, n o n ­ labor market sector" in period t, and T = outflow going into other public assistance programs in period t. 15 We can now represent the caseload in pe r i o d as follows (t) 5 ct-ct-i-I Tt-i+I Nt;1:V5 A°k (2-3) T t = f i^x l t ,x2 t ' ‘ '*'xn t ' £t ^ ' i = 4 '5 '1 0 ' (2.4) N (2.5) 1 jj ] — D/b , 1, 0 , where 9 j ^x it ,x2 t ' ’ ' ' • t * ^t ^ ^ 5/6,7,8, = a vector of variables representing the information flows, or factors affecting choices of leaving or entering the welfare sector,^ and = r an d o m variables representing unaccountable or unmeasurable information flows or factors affecting the decision process in period t. The task ahead of us is to define the x vector explicitly so that empirical evidence can be brought to bear on the question of caseload size. Behavioral Considerations Individuals in the modules face alternatives among which they must choose. Assu mi ng that they are rational, the choices made must result in wh at the decision makers feel is a better state of affairs. Let us say they have a preference function u ( , z ^ ,...,z ^ ) , the arguments of which are the alternatives they can choose from. There are, 16 however, constraints on these alternatives. This can formally be stated as follows: max. S .T .7 That is, u(Z); Z = [z^]; g J (Z) = 0 ; i = 1 , 2 , ...,n, j= 1 , 2 , (2.6) ( 2 . 7 ) the individual must combine the n alternatives in such a way that the m constraints are satisfied and his preference function is maximized. 8 The remainder of this section w i l l be devoted to a discussion of the elements of the Z vector, natives, the a l t e r ­ and the constraints plac ed upon them. Generally the elements of the Z vector are goods and s e r v i c e s , the consumption of w hich provide utility or satisfaction to the consumer. However, if it is assumed that various goods and services are purcha se d in fixed proportions at constant p r i c e s , then income can be treated as genera li ze d purchasing power. Thus, a consumer's satisfaction can be said to depend on income, Y, and leisure, L, i.e., U = u (Y ,L) . (2.8) The wage rate, w, and the amount of time worked, put limits on the income that can be earned; (24 -L ), therefore, the constraint on income is Y = w (2 4-L) . (2.9) 17 Studies of the economics of public assistance have almost e x clusively used the above model of consumer behavior. Modifications on the income constraint (2.9) are the only things differentiating these products. The pioneering application is that of B r e h m and Saving 9 who suggest the following q u a l i f i c a t i o n s : (a) a consumer who chooses to be on general assistance must either specialize in leisure or must earn less than some m i n i m u m income, Y g , deemed necessary by the state. (b) if there is a stigma at tached to being on welfare the grant that the consumer receives should be discounted by some factor k, where o0, (2.11a) 18 and (2.lib) if [Yg -w(24-L)]<0. Y = w(24-L) where w is the wage rate and L denotes leisure. The increment to the consumer's income for each additional hour of work w i l l depend upon the wage rate w and the stigma discount k, i.e., (2 .1 2 ) = w (k-1) . and w>0 As o0, and X (X ) X ' p ' if [ G - U - t j ) I-(l-tw )Pw (24-Hx -L) ]<0, where = p u r c h a s e d goods and services, X = home pro du ce d goods and s e r v i c e s , L = leisure (2.18) 22 G = welfare grant, 18 = welfare tax on unearned income (i.e., deductions from grant due to I ) , I T P = unearned, n on -g ra nt income, w w = we lfare tax on earned income 19 = ex pected wage, H = hours expended in produc in g home goods and s e r v i c e s , and P = expe ct ed price of all m ar k e t p r o d u c e d goods and services. Given that there are husbands in the home of AFDC-U, and GA c a s e s , this model may not be as relevant in a n a l y z ­ ing their behavior. For them, the income-leisure approach with a modi fi ca ti on of the income constraint is more appropriate. max. Their optimization p ro bl em will then be U = u(Y,L) (2.19) S.T. Y = G + ( l - t T )1 + (1-t )P (24-L) X w w if (2.20) [G-(l-tT )I-(1-t )P ( 24 -L)]>0, and 1 w w Y = P w (2 4-L) if [G-(l-t_)I-(l-t )P (24-L)]<0, X w w — where Y is total income, and t h e 'remaining variables are as defined above. If we assume that receiving public assistance means an increase in the total income of i n d i v i d u a l s , then the 23 "income effect" will imply an increased consumption of all "normal" goods and services. good, If leisure is a normal its increased consumption results effort. On the other hand, in reduced w o r k the imposition of a tax on earned and un earned income of w e l f a r e recipients reduces the price of leisure thereby reinforcing the income effect toward less wo rk effort. However, a stigma a ssociated wit h receiving w el fare w ould weaken this income effect. Furthermore, going on welf ar e m a y be associated w i t h a decrease in total income for some recipients; 20 if this loss is not made up for by the value of increased leisure or the substitution of home p ro d u c e d goods for p ur ch as ed g o o d s , the implied reduction in w o r k effort m i g ht not materialize. The imposition of additional constraints on the welfare choice such as a social m a x i m u m w o r k week, work r e q u i r e m e n t s , and m i n i m u m wages reduce the feasible set to such an extent that the optimization p r o b l e m either becomes ov e r c o n s t r a i n e d or, at best, very confusing. However, 21 the a p plicability of comparative static analysis is thrown into serious doubt when dynamic considerations are br o u g h t into light. If receiving pub li c assistance implies an increase in the total income of individuals, then some dynamic effects may lead to an increased wor k effort offseting the static effects po s tulated above. For example, Conlisk 22 suggests that a taste of higher income may lead to a desire for even more income thus increasing the work m ot ivation of recipients. Furthermore/ better nutrition and health and investment in the children's education made possible by the increased level of income may result in increased w o r k effort in the short as well as the 23 long-run. Alt ho ug h Saks 24 points out that the d e p re ci a­ tion of human capital resulting from the loss of industrial discipline and decay of skills is a p ossibility which m ig ht reduce the expected wage of a recipient/ programs (e.g., WIN) training available to welfare recipients w o u ld have the opposite long-run effect. Changes in labor mar k et conditions may also enter the individual's preference function in a dynamic way. P rolonged u ne mployment leading to a depletion of savings, the exhaustion of unemployment benefits, and a general reduction in exp ec te d income would, more than likely, increase the probability of applying for welfare. The dynamic effects of political, 25 legal, and sociological changes may also undermine the conclusions drawn from the static analysis. in particular, stress Piven and Cloward, this aspect of the p r o b l e m in explaining the rise in caseloads in the sixties. They h ypothesize that the rise in we lfare rolls was not just a direct result of eco no mi c depriviation inflicted on families as a consequence of agricultural modernization 25 leading to urbanization and chronic urban unemployment. Rather, the removal of traditional restrictions that had kept these people off the rolls in the past has led to the rapid increase in the number of public assistance recipients. With the emergence of w el fare rights as a national issue in the mid-19 60's, social workers, employees, student activists, lawyers, welfare church groups, Civil Rights o r g a n i z a t i o n s , and the poor themselves began to question previously unchallenged issues and practices. This in turn has led to court rulings and legislative changes which have enabled a great many persons who were previously excl ud ed to become w el fare recipients. Piven and Cloward contend that this upsurge in pressure was stimulated by the federal gove rn me nt through its i n t er ­ vention in local welfare arrangements. Specifically: --The es ta bl is hm en t of new services, both public and private, that offered the p oo r information about welfare entitlements and the assistance of experts in obtaining benefits. — The initiation of litigation to challenge a host of local laws and policies that kept people off of welfare rolls. — The support of new organizations of the poor which informed people of their entitl em en t to public welfare and moun t ed pressure on officials to approve their applications for a s s i s t a n c e .27 However, the Great Society programs had not been designed to increase the w el fa re rolls; indeed, it was hoped that education and training programs di rected at the poor would result in fewer recipients. 26 The "storefront service center" became the most p re va le nt welfare rights service in the 1960's. Most were sponsored by the Office of E qual Opportunity's (OEO) "community-action programs" by social workers, lawyers, the poo r themselves. (CAPs) churchmen, and w e r e staffed students, and These centers, w h i c h acted as advocates of the poo r in dealing w i t h local social service departments served hundreds of thousands of po or people. The impact of such services was summarized in a 1969 HEW study: A statistically s ignificant relation did exist betwe en CAP (Community Action Program) expenditures and the A FD C p o o r - r a t e — the higher the (per capita) ex penditure the hi g h e r the rate (at w hi c h poor families were on the r o l l s ) . Alt ho ug h there is no direct evidence, CAP programs may have he lp ed the poor unde rs ta nd their rights under ex is ti ng public assistance po licies and may have lowered the amount of p ersonal stigma recipients felt. There is evidence showing that CAP programs are associated wit h reduced feelings of helplessness. CAP e x pe nditures per 1,000 p oo r persons were inversely related to p o w e r ­ lessness (the mo re a city received CAP funds, the fewer the number of recipients feeling h e l p l e s s ) . A flood of information in the form of simplified welfare manuals s up pl emented the face-to-face dissemination pro vi de d by the C A P s . While an increasing number of people were coming to believe that they had a right to demand welfare, a series of judicial decisions were undermining some of the regulations by which relief rolls had bee n ke pt down in the past. The OEO's N e i g h b o r h o o d Legal Services P ro gr am gave impetus to this legal assult on the system. By 19 68, 27 250 legal service projects had been e st a bl is he d w h ic h op er at ed about 850 n ei g h b o r h o o d law offices staffed by approximately 1,800 attorneys. 29 Pressure was also e xe rt ed by we lfare rights groups w hi ch banded together in a National Welf ar e Rights O r ga ni za ti on (NWRO) claiming more than 100,000 dues- p ay i n g members in some 350 local groups by 19 69. contribution to the rising we lfare rolls was 30 NWRO's in mak in g slum and ghetto families less fearful in applying for aid and demanding their rights. All of these pressures but definite finally lead to gradual legal and p ro cedural changes in the nation's we l f a r e system. Michigan's experience is summarized by a list of welfare policy changes p r e s e n t e d in the A p p e n d i x to this chapter. Before p r o c ee di ng w i t h the empirical a n a l y s e s , it will be useful to review w h a t has been p u t forth in this chapter. flows A f t e r the pres en ta ti on of a model of in and out of the we lfare sector, micro behavioral models of consumer choice were shown to apply to the d ecision process of individuals conceptual model. in the components of the Q u al if ic at io ns wit h respect to the a pp licability of these m i cr o models were then reviewed. A l t h o u g h the imposition of additional constraints on the w el fare choice introduced doubts as to the credibility of the comparative statics analysis, dynamic considerations 28 were seen to be considerably more damaging in this respect. Furthermore, dynamic forces outside the scope of t raditional ec on om i c analysis and sociological factors) (such as political, legal, wer e suggested as possible determinants of the choice to become a welfare recipient. The e mp ir ic al models to be p re se nt ed in the following chapters are tentative, and ex ploratory in nature. In Chapter III, time series data on incoming AFDC-R, AFDC-U, and G A recipients and terminations from these programs are u tilized in analyz in g some determinants of caseload size. Al though a degree of dyn am is m is incor­ p or at ed into the m o de l by the use of a di stributed lag structure, the state of the art plus the absence of data r estrict us fr om going any further here. The absence of data on people who are simultaneously e mployed and r ec ei vi ng welf ar e exclude this growing category from the m odel in Chapter III. It is, however, this sub-group of the w el fa re p op ulation that merits special attention. Tr ai ni n g programs and financial incentives to work, for example, sub-group. Thus, fall heavily on this rather than excluding the e mployed welfa re recipients completely from this examination, cross-sectional survey data are uti li ze d in Chapter IV to analyze some factors influencing their probabilities of employment. 29 Finally, in an attempt to incorporate the non- quantifiable legal, political, and sociological factors as determinants of caseload size, a "predictive" growth model is specified and estimated in Chapter V. Time series data are used in estimating this non-linear model of AF DC -R caseload growth. This was the category which we believe was most influenced by those factors mentioned above. FOOTNOTES TO CHAPTER II ^See Leonard Goodwin, Do the Poor W a n t to W o r k ?, (Washington, D.C.: Brookings I n s t i t u t i o n , J u n e , 1972) . 2 M aryland State Department of Public Welfare, A Report on Caseload Increase in the Aid to Families with Dependent Children Program, 1 9 6 0 - 6 6 , Research Report No. 2 (Baltimore: The Department, July 1967), p. 36. 3 GA reciprents may be transferred to any of the other welfare programs. 4 People receiving u ne mp loyment compensation are not eligible for the A F D C - U program. 5 In Eq u at ro n (2.3) t e r m x n a t r o n s , T^., is lagged one period due to the acc ou nt in g process used by the Michigan State Department of Social Services. The r educ­ tion in the caseload due to the number of recipients terminating from w e lf a re in period (t) is taken into account when p r e se nt i ng the caseload figure for period {t + 1) . ^It is p ossible for some elements in the X vector to be zero in either of Equations (2.4) or (2.5), i.e., the same variables may not determine both openings and closings. 7 S.T. will be used throughout as an abbreviation for "subject to." g This does no t rule out the possib il it y of one or more of the alternatives not b e ing chosen. 9 C. T. B r e h m and T. R. Saving, "The Demand for General Assistance Payments," Am er ic an Economic R e v i e w , Vol. 54(December, 1964), pp. 1002-18. "^Brehm and Saving concede that ot ) variable in the terminations equations. and salary empl oy m en t Wage (WSEt ) is one of these, and gives the total number of people receiving wages and salaries in Michigan. A lt ho u g h it is, of course, partially an indication of labor supply, it was considered to give a b etter indication of the overall demand for labor. Since m os t we l f a r e recipients do not have the skills that w ou ld qualify th em for employment in m a n u f ac tu ri ng industries, e m p l o y m e n t in n o n - m an uf ac tu ri ng industries (ENMI^.) seemed 7 to be another good choice for this measure. the total une mp lo ym e nt rate Finally, (U^.) was also used, in order to determine w h e t h e r it is a good measure of the demand for the services of welfare r e c i p i e n t s . choices of F r o m these three (D^_) , the statistically m o s t signif ic an t one for each category will be p re se nt ed in the results. The higher the demand for labor, the more people we w ould expect to terminate from public assistance, 3Tt 3WSEfc 3Tt - 0 ' and 3ENMIt - °' i.e., 37 Similarly, the lower the unem p lo ym en t rate, should be the terminations figure, the higher thus, 3T. to ; i°- The relative attractiveness of employment or the likely wage will also affect the choice between continuing assistance or terminating. however, It should be pointed out, that those w h o do terminate because of e m p lo ym en t do so because they expect higher earnings than the fixed b re ak-even income level for welfare recipients under negative tax schemes. Although m o s t investigators use m an uf a c t u r i n g wages or a similar p ro xy for this variable, we have tried to calculate a somewhat different measure using information on the oc cu pational distribution of employed welfare recipients in the late sixties to weight m a n u ­ facturing and service industry w ages in a particular period. The appendix to this chapter explains just how Q the w e i g h te d ex pected wage vari ab le It is not a satisfactory variable, other proxies. attractive (EW^) was derived. but may be better than Higher expected returns will make it more to be in the labor force, thus, 3T ■Se w ; > °- Although the variables (D^.) and (EW^_) are important in themselves, we also hypothesize an interaction b et ween 38 them. That is, terminations w o u l d be even higher if there were an increased demand for labor coupled with high ex pe ct ed wages. Conversely, some terminations resulting from an increased demand for labor wo uld be offset by low e xpected wages. Taking partial derivatives, this can be expressed as al + a 3 ^ t 9EW t — ^ ' an<^ “2 + °3 D t - 0> The supply of labor also has some bearing on the number of terminations. A large supply w o u l d imply more competition for the few available jobs. Thus, terminations can be exp ec te d to diminish w h e n the supply of labor increases. (NFLF^) Although M ic higan's n o n - f a r m labor force is not the b es t measure of the total supply, data limitations dictate its e mp l oyment in this model. We w o u l d expect 3NFLFt - °* The size of the caseload (C.) is included as an t explanatory variable to control for differences nu mb e r of potent ia l terminations over time. peo pl e who are on welfare, other things being equal, in the The more the more pe o p l e who could, leave welfare. Thus, w e expect 39 3T, The cost of terminating from pu bl ic assistance will also influence a client's decision. not take into account other benefits stamps, (G^) child care, etc.), Alt ho ug h it does (Medicaid/ food the average monthly grant is the be st measure of benefits foregone upon leaving welfare. The higher the grant level, recipients w il l be to leave welfare, the less w il l i n g i.e., The N e w Cases Equation Equation (3.3) relates the n e w cases coming into public assistance to the following variables Xt = (Ut ' U t - l ° t - m ' H F I *P t - l ' B X B t - l ' E W t - X ' T R t ' G t - l ' !:t ) The current and lagged values of the un em ployment rate (Ut ) and the n ex t three variables are generated by past and pr e s e n t labor m a r k e t conditions. GA variable The transfers from (TRt ) and the average mont hl y grant originate in the public assistance sector. (Cfc), again, (G^..^) The er ror term represents unaccountable and unmeasurable random factors in per io d t. All of the explanatory variables, with the exception of transfers from GA to other pu b l i c assistance programs (TRt ) and the unemployment rate (Ut ) , are lagged one month 40 for institutional reasons. Incoming recipients in m onth (t) would n o t appear in the caseload until month (t+1) due to the time required for pr oc essing of a pp l ic a­ tions, determining eligibility, etc. This does not apply to transfers from GA. As other writers have p o in te d out, 9 an assumption that worsening labor-market conditions causes a simultaneous increase in we lfare rolls w o u l d be, at best, simplistic. A more dynamic process seems to be at work. We hypothesize that p a s t as we ll as current labor m a r k e t conditions influence the st re a m of people coming onto welfare. Pro­ longed u n e mp lo ym en t w ould imply the exhaustion of savings, reduced job opportunities, and increased necessity of accepting public assistance. Furthermore, w e assume that there is some m a x i m u m p e r i o d of u n em ployment beyond which specific families public assistance. cannot subside unless they apply for Since our ec onometric m od el is specified to analyze aggregate behavior, this m a x i m u m per io d would have the m o s t w e i g h t in exp la in in g incoming welfare recipients. That is if people can h o l d out for, months before applying for assistance, say, 4 then the u n e m p l o y ­ m en t rate of four months ago w ould have the most we ig ht in explaining numbers of new recipients in the current month. For a large population, unemployment rates in months prior to and after the average ma x i m u m period would have lower weights reflecting the distribution of resources and alternative opportunities in the population. Figure 3.1 summarizes our assumptions in this respect. 41 RELATIVE W E IG H T S OF LAGGED U N E M P L O Y M E N T RATES WEIGHTS Wi i LAG -1 0 1 2 3 FI G U R E 3.1 m tn +1 42 The current u n e mp l oy me nt rate values (u .j._i) ' ^ t - 2 ^ ' * * * ' ^ t - m ^ r ecip ie nt (Ut ) and its lagged are ^-n ^-*ie ne w (Nt ) equations to test the above hypothesis. The "Pascal Lag/" and the "polynomial lag" are the only d istri bu te d lag structures that w o u l d b e ap propriate for the above c o n f i g u r a t i o n . ^ the polynomial, into Equ at io n The relative ease of est im at in g or Almon lag, led to its incorporation (3.3); the degree of the p o l y no mi al and the length of the lag to be dete rm in ed by the data. As implied by Figure 3.1 we expect the direction of the relationship to be such that 9N •777;--- •> t-i “ 0 ; i.— 1,2, • . • ,m. Follow in g the logic of our terminations equation the exp ec te d returns from be co mi ng a public assistance recipient are represented by the welfare grant level and the cost of dropping out of the labor ma r k e t is the exp e ct ed wa ge (EW^^) . W e expect: — > 0, and 3Gt-i 3N. 3 H T i °t The num be r of Mich ig an residents ex ha usting une mp lo ym en t benefits (EXBt _^) w i l l also affect the number 43 of new we lfare r e c i p i e n t s . ma r k e t conditions, Under unfavorable labor the process of b ecoming unemployed, receiving un em p loyment benefits, and unsuccessfully seeking em p l o y m e n t will culminate in the exhaustion of these benefits. received, Wh en the last unemployment check is and job prospects still look dim, the pr obability of applying for public assistance should be quite high; thus, we postulate that 9N - > 0. 3EXBt _ 1 G rowth in the supply of labor, by the n o n - f a r m labor force as represented (NFLFt _ ^ ) , should also have an affect on the nu mb er of new cases ( N ). the number seeki ng employment or employed, The larger the smaller the p r obability of adequate emp lo y me nt for the mar gi na l worker. Thus, we hypothesize that 3N, - > 0. 3NFLF, -> t-X Some gene r al assistance (GA) recipients are transferred to other pu bl i c assistance programs every month. A fraction of these e n d up on A F D C - R and AFDC-U, affecting the size of 12 (N^). 3N STR t - °* Thus 44 Estimation The new recipients (Nt ) , and terminations equations will be estimated for each category AFDC-U, and GA) (AFDC-R, separately using ordinary least squares. The new recipients with quadratic, (T^) cubic, (Nt ) equation will be estimated and quartic polynomial lag structures and for each degree of the polynomial a 4, 5, 6, 7, and 8 m o n th lag wi ll be specified. resulting estimates, F r o m the the "best" degree of polynomial and length of lag will be c h o s e n . ^ We have also assumed that the unemployment rate of the coming month, t+1, and the m o n t h p re c e d i n g the specified lag, t - ( m + l ) , will have no affect on (Nfc) . This will imply the following constraint on the weights. w m + l = w -l = The terminations (Tt ) equations will be estimated with the three alternative measures of the labor demand (D^.) explained above, the total unemployment rate wage and salary empl oy m en t (U^.) , (WSEt ) , and employment in non-manu fa ct ur in g industries (ENMI^). The variable having the h i g h e s t level of statistical significance will be presented m the next section of this chapter. 14 Results The estimated terminations and new recipients equations for each category are p r es en te d in Tables and 3.2 respectively. 15 3.1 TABLE 3.1.— Time Series Analysis of Terminations from Michigan's AFDC-R, AFDC-U, and GA Programs.a Eqn. Independent Variables Dep. Var* WSEt ENMI. l EW (WSE^) tfMIt) (EWt) (EWt) t Ct d.f. F R2 D-W Gt AFDC-R 3.4 T -116.52* 4.76** (2.67) 0.00 -0.38 (3.09) 0.10*** (0.03) -43.40*** (20.84) 6,36 20.82 0.78 1.61 0.07 (0.07) -5.90 (5.99) 0.34*** (0.08) -33.18*** (11.16) 6,36 16.19 0.73 2.03 49.31* (32.61) 6,36 220.50 0.97 1.58 (75.62) AFDC-U 3.5 T -185.77 (241.17) 8.84* (6.25) GA 3.6 Tt -48.63** (24.96) -604.17* (371.05) 0.36** 20.60*** 0.17*** (0.21) (9.96) (0.06) Standard errors are presented below the estimates of the coefficients, d.f. is degrees of freedom, F is the F statistic, is the coefficient of determination, and D-W is the Curbin-Watson statistic for tests of autoregression. The asterisks above the estimates of the coefficients give the level of significance; ‘denotes significance at better than the 10 percent level, **at better than the 5 percent level, and ***at better than the 2.5 percent level. TABLE 3.2.— Time Series Analysis of New Recipients Coming Into Michigan's AFDC-R, AFDC-U, and GA Programs.3 Eqn. Independent Variables Dep. Va r . w b t 3.7.a 3.8.a 3.9.a NFLF , t-1 EXBt-i TR t „ AFDC-R N t -2.54* (1.87) -0.49 (0.87) -0.16** (0.10) 0.54*** (0.24) „ AFDC-U -5.85** (3.20) 3.12 (5.84) -0.45*** (0.17) 1.85*** (0.41) -20.85** (12.60) 16.08* (10.85) GA Nt 0.08 (0.33) EV i 96.32*** (44.31) F R2 D-W 6,35 20.35 0.85 1.37 ri f Gt-1 13.96 (15.65) -108.97* (82.99) 0.43 (9.28) 6,35 6.61 0.54 2.07 -244.94* (166.24) 80.46* (50.28) 6,36 3.81 0.35 1.33 Standard errors are presented below the estimates of the coefficients, d.f. is degrees of freedom, F is the F statistic, R2 is the coefficient of determination, and D-W is the Durbin-Watson statistic for tests of autoregression. The asterisks above the estimates of the coefficients give levels of significance; *denotes significance at better than the 10 percent level, **at better than the 5 percent level, and ***at better than the 2.5 percent level. Coefficients for the constant are not presented. W is the composite polynomial lag variable, which will be expanded in the text. It represents^ 7 month quadratic polynomial for AFDC-R, and AFDC-U, and a 5 month quadratic polynomial for GA. 47 A lthough some variables in the terminations equations have the e xpected signs, i nconsistent with expectations. expected wages variable negative. some seem to be The coefficient of the (E W^), for example, is consistently Even though it is only significant at the 10 percent level for A F D C - R and GA, this result is disturbing. Similarly, variable level, the negative c oefficient of the demand for labor (ENMI^), significant at better than the 5 percent for the GA terminations is surprising. The only coefficient that is significant for all categories and exhibits the hypothesized relationship with terminations is that of caseloads. Grant levels also see m to affect terminations in the expected direction for AFDC r e c i p i e n t s . Before getting into the implications of the estimates the expansion of the (Wfc) terms into current and lagged unemployment rates will be useful, coefficients of the as the (W^.) term by themselves give us no information about the impact of pas t labor mar ke t conditions 16 AFD C- R NT + 5 0 .80Ut _ 4+ 4 6 . 7 2 U t_ 5+ 3 5 . 5 6 U t_ 6+2 0 . 32 Ut_ ? + 0 . 49NFLFt _ 1- 0 .1 6 E X B t_ 1+ 0 .54TRt+ 9 6 .32EWt_ 1 +13.96G t-1 +e t* (3.7b) 48 This tells us that the unem pl o ym en t rate of 3 to 4 months ago has the m o s t impact on c ur re n t flows into the A F D C - R category. The lag structure for the AFD C- U new recipi en t equ at io n is the same as that for AFDC-R, however, the unemp lo ym en t rate is seen to affect this p r o g r a m more. AFnr-n =-8041.73+48. 80U.+81. 9 0 U . .+1 05 .30U,. 0 t t t“ 1 X.— 2. + 1 1 7 . 00 U t _ 3+ 1 1 7 . 0 0 U t _ 4+ 1 0 5 .3QUt _ 5 +81.90U, ,+ 48.80U. -.+ 3.12NFLF. t-6 t-7 t-1 -0.45EXB. .+1 •85 T R .— 10 8.97 E W , ^ t-JL t t-1 +0.43G, , + e , . t_1 Labor m a r k e t conditions, m e n t rate, (3.8b) as me as u r e d by the u n e m p l o y ­ seem to have the gr e at es t impact on GA recipients, wi th the situation 2 to 3 months ago being most influential. GA N. =-34266 .82 + 125 .10U.+208 .50U, ..+250.20U., 0 t t t-1 t-2 + 2 5 0 .20Ut _ 3+ 2 0 8 . 5 0 U t _ 4+12 5 . 1 0 U t_ 5 + 16.0 8NFLF .+ 0 .0 8 E X B , .-244 .94EW,. , t-1 t-1 t-1 + 80 . 46G. ,+e,.. t_1 (3.9b) 49 Implications Even though some of our results, part ic ul ar ly for the terminations e q u a t i o n s , do n o t see m theoretically plausible, the fact that this is w h a t the data points is in itself significant. conditions accurate? recipients? Are the measures of labor mar ke t Are they appropriate for welfare Unfortunately we cannot give an emphatic "yes" to ei t he r question. Ev en more important, however, is the question of specification. c or re ct relationships? this manner? to Have we p o s t u l a t e d the Do welfare recipients behave in All that can be h o pe d for is that we have come close en ou gh to reasonably approximate w h a t we wis h to explain. Terminations 17 Contrary to Saks 1 re su lt for New York City that a s ignificant relationship did n o t e x is t be tween labor m ar k e t conditions and the proba bi li ty of an A F D C - R case terminating, we sugge st that an increase in the demand for labor (WSE^,, for example) terminations from AFDC-R, does not hold for GA. w i l l significantly increase and AFDC-U. This result, however, A l t h o u g h the co efficient for the demand for labor vari ab le (ENMI^) is si gnificant at b e t t e r than the 5 p er ce nt level, it is negative. 18 A n increasing demand for labor result in g in less terminations is quite i nc on sistent w i t h w h a t w e w o u l d expect. Although employ­ m e n t may not be the only reason for terminating, there are some people wh o do so for e m p l o y m e n t - r e l a t e d reasons. 50 One explanation of this phenomenon is provided by Saks. 19 He suggests that welfare payments may only provide a tolerable existence wh e n supplemented by private t r a n s f e r s , e.g., financial assistance from friends and relatives. As the demand for labor increases, in private a resultant increase transfers may be expected causing terminations from GA to decline. A l t h o ug h this w o ul d seem to hold, p ar ti cularly for GA recipients since they receive a relatively small grant, data. 20 it is not supported by existing Eith e r the data are misleading, which w ould imply a hi gh level of fraud in reporting income, or we must seek the ex p l a n a t i o n elsewhere such as in the possibility of a dual labor market. The next labor-market variable of interest is expected w ages (EW^). The tentative implications drawn from our estimates are again contradictory to those of Saks. 21 His results indicate that expected wages are important in pu lling w om en off of welfare. Although only s ignificant at the 10 percent level for AFDC-R and GA, terminations for all programs are ne ga tively related to e xpected wages. As was explained above, the possibility of increased levels of transfer payments resulting from higher wages m ig ht make welfare more tolerable and thereby reduce the number of terminations. On the tenuous assumption that m a r g i n a l productivity factor pricing applies, when the going wage exceeds the m arginal products 51 of employable welfare recipients, increasing wages may also result in fewer people terminating from public assistance. The c oe ff ic ie n t for the interaction term ( E W ^ ) (D t ) p ro ve d to be statistically insignificant in the A F D C equations and, alt ho ug h significant at better than the 5 percent level for GA, the magnitude of the eff ec t is s uf fi ciently small so as not to change the implications mentioned above. Specifically, ~ _GA Unmi^ = ~48*63 + °*36 EWt 3TGA = -604.17 + 0.36 E N M I t , and if we use the me an values of 3t GA &ENMI 3TG A Thus, = -48.63 + = -604.17 + (EW^) and (0.36) (85.54) (0.36) (1408.98) the direction of the relationships (ENMI^) we get = -17.84 = -96.93. remain the same, a lthough the impacts of the coefficients are somewhat reduced. M i c hi g an 's n o n - fa rm labor force (NFLF^) has the p o st ul at ed relationship with terminations from A F D C - R and 52 A FDC-U (an increase in the supply of labor causes a reduction in terminations.) However, are not statistically significant. have an unexpected result; (NFLF^.) variable, the coefficients For GA, we again the coefficient for the the supply of labor, s ignificant and positive. is statistically This result is unexpected, but the p os s ib il it y of having mis sp ec i fi ed the model m u s t also be considered. If the number of terminations from GA hap pe ne d to be an a rgument in the labor supply function, such a relationship w ou ld be po ssible as terminated GA recipients w o ul d end up in the labor force and the n o n ­ farm labor force figure w o u ld thus increase. The opportunity cost of terminating from public assistance is given by the respective average monthly grant levels. The coefficients for these variables are statistically significant and have the expected negative signs for A F D C - R and AFDC-U. Saks' 22 results: b ei ng on AFDC, them. These are consistent with the higher the benefits received by the less w il ling recipients are to forego The p o i nt elasticity of terminations wit h respect to changes in the grant level is -5.6 6 for A F D C - R and -21.32 for AFDC-U. 23 The difference in magnitudes is also in line with Saks who suggests that this may be due to relatively lower day care costs for A FD C - U families so that a one dollar increase in the grant level w ould induce more of them to stay on welfare. Here again the 53 implied behavior of GA recipients d i f f e r s : the higher the m on thly g r a n t , the greater the number of terminations from the program. The reason for this result may again be found either in model specification or administrative peculiarity. Higher GA grants may imply more effort by counties to get recipients off of welfare by transfers to other pu bl ic assistance programs or outright removal. Counties, 24 operating w it h i n fixed budgets may also vary the grant levels according to caseload size, e.g., benefits when caseloads are smaller. increase Of course the possibility of spurious correlation m u s t also be considered. New Recipients B r e h m and Saving's pioneering article was the first of relatively few empirical studies of public assistance. 25 As m en ti on ed ea rlier in the review of theoretical models, they analyze the demand for General Assistance (GA) as a special case of the dem an d for leisure and estimate the parameters of their demand equation in an econometric study. 26 Their results indicate that the demand for public assistance is positively and si gnificantly related to the level of be nefit payments rather than to labor m a r k e t conditions. As p oi nted out by Albin and Stein, 27 the dependent variable in the B r e hm -S av in g equations is described as the number of GA recipients as a percentage of the state's population, w he re as what was actually used was the number 54 of GA cases. Since definitions of a GA case differ from state to state, a case cannot be identified wi th a decision unit such as a h ou sehold or a family. Given the considerable st ate-to-state v a ri ation in the number of persons per case, Albin and Stein 28 adjust the case data to a recipi en t b asis and recalc ul at e the Brehm-Saving regressions. Their results indicate that the relationship between recipients and b en efit levels disappears, thus throwing into qu estion the theoretical underpinnings of the Bre h m- Sa vi ng model. They conclude that the variation in the prop or ti o n of the p o pu l a t i o n receiving GA benefits is bet te r e xp la in ed by labor m a r k e t conditions as measured by the insured une mp lo ym en t rate. In their reply to A lb in and Stein's comment, B rehm and Saving 29 concede to the error p o i n t e d out by the authors b u t do not agree with their "correction." They make a valid p o i n t by e x p l ai ni ng that the removal of p o t e n ti al ly employable recipients from GA wi th the implementation of the A F D C - U p r o g r a m caused Stein and Albin to estimate a model w hich did not p e r f o r m we ll as it was not applicable to the recipients to w h o m the data applied. A f te r correcting the "correction" by adjusting the data to a recip ie n t basis, e li mi na ti ng single-person cases, and using p r e - AF DC -U data, they come up with results similar to their original ones. The implications of our estimates are more in line wi th those of Al bin and Stein. A l t h o u g h the coefficient 55 for the grant level (Gt_^) is positive for GA cases, it is only significant at the 10 percent level. categories, however, For all the prime labor market variable, current and lagged unemployment rates, have the postulated relationships and are statistically significant (at better than the 5 percent level for AFDC-U and GA, and at better than the 10 percent level for A F D C - R ) . Our results with respect to grant levels, are also corraborated by Saks. 30 His coefficients for AFDC-R and AFDC-U grant levels have the expected positive signs, but are not statistically significant in explaining the probability of receiving welfare. Similarly, we get positive but statistically insignificant grant-level coefficients in our AF D C - R and AFDC-U new recipient equations. Although the coefficients are n o t statistically significant, the presentation of grant elasticities of demand for welfare might give some insight into the problem. Evaluated at the m e a n s , the point elasticities are respectively 0.87, 0.12, and 1.09 for AFDC-R, AFDC-U, and G A . 31 A percentage increase in the grant level seems to induce more than a percentage increase in new recipients only for GA. The impacts are quite small for the other two programs. However, recalling the grant elasticities of terminations, we see that a percentage increase in grant levels reduces the percentage of terminations by 5.6 6 percent for AFDC-R, and 21.32 percent for AFDC-U. Thus, even though changes 56 in the g r a nt levels do n ot induce proport io na te flows into welfare, they do m a k e it less probable for recipients to leave welfare. The use of the insured u ne mp l o y m e n t rate, by B rehm a n d Saving 32 as w e ll by Albin and Stein, 33 as a measure of labor ma r k e t conditions rel ev an t to public assistance recipients out, is hi gh l y questionable. As Kasper the long duration of this unemployment, industries where they work, 34 points the marginal and the relatively low wages r e c e i v e d by we lfare recipients w o u l d more than likely p reclude their e l i g i bi li ty for u n e m pl o ym en t insurance. Using various combinations of e xp la na to ry variables, K asper 35 estimates a set of bet te r specified models, p ar ti cularly w i t h r es pect to labor m a r k e t c o n d i t i o n s , and comes up with results similar to ours and contrary to those of B r e h m and Saving w i t h re spect to the importance of labor ma r k e t conditions versus grant levels in causing t h e flows into welfare. The fact that the unemployment rate of previous periods may explain the number of recipients presently on we l f a r e is also put forth by Kasper and incorporated into his model by the use of variables such as the pe r c e n t a g e change in total and insured u n e mp lo ym en t r a t e s . His results substantiate the thesis that the lag b et ween the p e r i o d w h e n a loose labor m ar k e t is confronted and when families have to resort to public assistance is quite long. 57 F ur th er support of this is p r o v i d e d by Saks. Taking a more so phisticated approach, 36 he uses a quadratic Almon d istributed lag and comes up w i t h significant coefficients in equations that apply to A FD C - U applicants. Our results imply that the u ne mp l o y m e n t rates of pas t periods are important determinants of new welfare recipients ent er in g the AFDC-R, AFDC-U, in the current month. and GA programs The ma gnitudes of the impact of c u r r e n t and lagged u ne mp l o y m e n t rates on the different p ub l i c assistance categories are also as w e expected. Looking at Figure 3.2, we see that the largest impact is on potential GA recipients; the we i g h t s are smaller for AF DC - U and the least impact is on AFD C mothers. Furthermore, our data indicate that GA is characterized by very large inflows and outflows relative to the other programs. The shorter lag, five months, w o u l d tend to refle ct this m or e v olatile response. A no ther labor m a r k e t variable of interest is the e x p ec te d wage (EW^_^). Saks found that the expected wage xs a p o w e r f u l d e t e r m in an t of welfare applications. This is also implied by our estimates 37 for AF D C - U and GA. The coefficients for e x p e c t e d wages are ne gative and statist ic al ly significant at the 10 p e r c e n t level for these two categories. H ig h e r e x p e c t e d wages seem to reduce or defer the neces si ty for w el fare benefits. The wage e la s ticities of demand for welfare are -9.59, and 58 HEIGHTS OF C U R R E N T A N D LAGGED U N E M P L O Y M E N T RATES IN EX PL AIN IN G F L O W S INTO A F D C A N D GA rs wt 260 240 220 200 180 160 140 120 AFDC-U 100 80 60- AFDC-R 40- 20 - 0 i FIGURE 3.2 LAG 59 -2.30 for AFD C- U and GA recipients respectively. elasticities are quite high to those calculated by Saks 38 These {especially whe n compared 39 ); however, as he points out, these results are comforting in that g rant levels can go up by many more p er centage points than the expe c te d wages w i t h o u t affecting caseloads demand w er e 0.12 for AFDC-U, (the grant elasticities of and 1.09 for G A ) . Given the fact that A F D C mothers are usually characterized by low skill levels and that their e m p l o y ­ ment is usually co nc e ntrated in service industries and low skilled jobs, the significantly positive relationship between new A F D C - R recipients and expected wages is not too startling. The suggested explanations given to explain the unexpected r el at ionship between terminations and e x p e c t e d wages may also apply to this result. An increase in the supply of labor, farm labor force a higher n o n ­ (NFLFt _ ^ ) , has the exp ec te d positive relationship with inflows to A F D C - U and GA. A lthough only the co efficient for the GA e q u at io n is statistically significant, our hypothesis that looser labor market conditions, labor, c ha racterized by a hig he r excess supply of induce a greater flow into the welfare sector seems to be consistent with the data. The contention that potential AFDC mothers wo uld not tend to be as responsive to labor ma r ke t conditions as the other two categories m i g h t be reflected in the 60 statistically insignificant c oefficient for in the A F D C - R new recipients equation. (NFLF^._^) Although the negative relationship is not in line w i t h w h a t we expected, it m i g ht be caused by (NFLF^_^) b ei ng a demand rather than a supply variable. Furthermore, the "added worker" effect might be operating, in w h i c h case (NFLF^_^) w o u l d be partially depend en t upon the choice be t w e e n welf ar e and labor force participation, and not vice versa. One of the most pe rplexing results is the highly significant n egative relationship be tween the number of people exha u st in g unemployment benefits inflows into A F D C - R and AFDC-U. (EXB^._^) Although, and as Kasper 40 points out, the probabi li ty of a po te n ti al welfare recipient be ing eligible for u n e m pl oy me nt benefits is quite small, it should n o t lead to such results. Incoming GA recipients exhib it the expe ct ed p o sitive relationship w it h the (EXB^__^) variable, however, the coefficient is not statistically significant. The last implication to be drawn from the estima te d equations pertains to the transfer variable, (TR,), t included in the two AFDC new recipi en t equations. The n um b e r of GA recipients b e in g transferred to other public assistance programs are seen to play a significant role in determining A F D C - R and AFDC-U caseloads. Both equations show a statistically significant po sitive relationship between the transfers variable, and AFDC-U. (TR^_) , and inflows to A F D C - R FOOTNOTES TO C H AP TE R III C . , N. , T D The sources of the data used are as follows: , G ,: Social Service Statistics publi sh ed m on th ly by the M ichigan Department of Social Services; , U , , E W . , NFLF : E X B ,: Michigan Manp ow e r R e vi e w published monthly by the M i c h i g a n E m p l o y m e n t Security Commission. W e l f a r e Review pu bl is he d monthly by the U.S. D e p ar tm en t of Health, Education and Welfare. 2 Michigan's total unemployment rate (Ut), wage and salary e m pl oy me nt in Mi ch ig an (WSE-f-) t and e m p l oy me nt in n o n - m a nu fa ct ur in g industries in Michigan (ENMIt ) are used, and the ones that are statistically significant p re s e n t e d in the results. ^U.S. Dep ar tm en t of HEW, Findings of the 1971 AF DC Study (Washington, D . C . : Center for Social Statistics, December, 19 71). 4 See David Franklin, "A L on g itudinal Study of WIN Dropouts: Pr o g r a m and Policy Implications," (Los Angeles: Regional Institute in Social Welfare, April, 1972), (DOL Con tr ac t N u m b e r 51-05-70-05); E dw a r d Opton, "Factors A s s oc i at ed with E mp l o y m e n t A mo ng Welfare Mothers," (Berkeley: The Wr ig h t Institute, 1971), (DOL C ontract Numb er 51-05-69-04); Sydney Bernard, "The Ec on om ic and Social A d j us tm en t of LowIncome F em al e- He ad e d F a m i l i e s ," (The Florance Heller Graduate School for A d v a nc ed Studies in Social Welfare, Brandies University, May, 1964), (Grant Number 0 0 4 ) ; Samual Meyers and Jennie McIntyre, "Welfare Policy and Its Consequences for the Recipient Population: A Study of the AF DC Programs," (Bureau of Social Science Research, December 1969), (Grant Num b er 4 0 5 - W A - O C - 6 7 - 0 7 ) ; Elaine Burgess and Daniel Price, An A m e ri ca n Dependency Challenge (Chicago: Ame ri ca n Public We l f a r e A s s o c i a t i o n , 1963); Lawrence Podell, "Families on W el fare in N ew York City," (New York: City University of Ne w York, Center for the Study of Urban Problems, 1963). 61 62 5 . . . . . As was explai ne d pr eviously this generalization does n o t seem to h o l d for M ichigan w h e r e the nu mb er of emp lo ye d welfare recipients has been on the rise. However, we shall defer any further comments to the pr e se ntation of the empir ic al r e s u l t s . ^See Tilford Gaines, " E m p l o y m e n t - U n e m p l o y m e n t ," E c o n o m i c Report of Manufac tu re rs Hanover T r u s t , April, 1972; Jacob Mincer, "Labor Force Participation of M a rr ie d Women: A Study in L abor Supply," Aspects of Labor E c o n o m i c s , Nat io na l Bu re a u of E c o n o m i c Research! (Pr in ce to n: Princeton University Press, 1962), pp. 63-105. Among labor supply responses to demand, the m o s t no teworthy refer to "discouraged" and "added" workers. The "discouraged w o r k e r hypothesis" suggests that at any m o m e n t there e x is t a large number of pe op le who are m a r g i n a l workers in the sense that they accept e m p l o y m e n t w h e n jobs are very easy to find, b u t stop looking w h e n the dem an d for labor diminishes. A force w o r k i n g in the opposite direction and known as the "added w o r k e r hypothesis" applies to the same group of pe op le and claims that whe n labor m a r k e t conditions are b a d and re su lt in the primary wag e earner in a family losing his job, then the secondary workers in the family enter the labor m a r k e t to seek employment. These forces are said to apply p a r ti cu l ar ly to housewives, retired people, and y ou ng er people. 7 This assumption is ve rified by the distribution of empl oy ed welfare recipients in different industries given in Mic hi ga n De partment of Social S e r v i c e s , Profile of Michigan's AFDC C a s e l o a d , Research P a per Number 1, (Lansing, Michigan: The Department, October, 1969). g . The w ei ghts were calculated from Profile of Michigan's AF DC Caseload quot ed in the pr eceeding f o o t n o t e . See A p p e n d i x to this chapter. 9 See Daniel H. Saks, "Economic Analysis of an Urban P ublic Ass is t an ce Program: Aid to N e w York City Families of Dependent Children in the Sixties," (unpublished Ph.D. dissertation, Princeton University, 1 S 7 3 ) ; and Hirsehel Kasper, "Welfare Payments and W o r k Incentives: Some Determinants of the Rates of General As sistance Payments," Journal of H um an R e s o u r c e s , III{Winter, 1968), pp. 86-110. "^The curve in Figure 3.1 touches the horizontal axis, becomes zero, at lag -1 and lag m+1. This implies that the un em ployment rate of n e x t month, lag -1, and the unemployment rate of m+1 months ago have n o affect in the aggregate decision to e n te r welfare. 63 ■^See Jan K m e n t a , Elements of E c o n o m e t r i c s , (New York: The M a cm il la n Company, 1971) , pp. 4"87 - 9 5. 12 The number of transfers fr om GA could no t be subtracted out of the appropriate programs because the data are n o t disaggregated. "^The "best" lag structure is defined as having the degree and length of lag that produces the highest value of , the co efficient of determi na ti on corrected for d e g r e e s of freedom, and po sitive we ights for current and lagged une mp lo ym en t r a t e s . 14 All of the e st imated equations, (Nt ) as well as (Tt ) ,will be p re se nt ed in the A p p e n d i x to this chapter. 15 The correlation matrices for all sented in the results section can be found to this chapter. equations p r e ­ in the A p p e nd ix X6 It should be n oted that when a (W-j-) coefficient is e x p a n d e d its negative c oefficient implies positive coefficients for each u n em pl oy me nt rate. See Kmenta, o p . c i t . , p. 493. 17 Saks, o p . c i t ., Chapter V. 18 The GA terminations e quation was also run wi th the u n em p lo ym en t rate (Ut), and wage and salary empl oy me nt (WSEt ) w i t h identical r e s u l t s . See the A p p e n d i x to this chapter for the full set of estimates. 19 Saks, op. c i t ., C ha pter II. 20 See Lynn Savage and Sherry D a h l k e , "The General Assistance Pr ogram in Four Counties in Michigan," (unpublished study of the Mich i ga n Dep ar tm en t of Social S e r v i c e s ) . 21 Saks, op. c i t . , Chapt er V. 99 “ “ I b i d ., Chapter V. 2 ^The elasticities are (3 T / 3 G t ) ( G / T ) , w h e r e _ ( 3 T t / 3 G t ) is the coefficient for the grant level (G^) and T, G are the me an values for terminations and g r an t levels respectively, 24 Savage and Dahlke, o p . c i t . , observed that one county even attempted to inforce a m an da to ry m a x i m u m period that a GA family could receive assistance. 64 25 C. T. B r eh m and T. R. Saving, "The Demand for General As sistance Payments," Am erican Economic R e v i e w , Vol. 5 4 (December, 1966), pp. 1002-18. 26 It can be seen from the specification of their model that they use cross-sectional observations from 4 8 states for each of nine years. Alt ho ug h they claim to be pooling cross-section and time series data and e s t i m a t ­ ing via Zellners technique (Arnold Zellner, "An Efficient Me th o d of E s t im at i ng Seemingly U nr el at ed Regressions and Test for A g g r e ga ti on Bias," Journal of the American Statistical A s s o c i a t i o n , Vol~ 57 (June, 1962) , pp. 343-48) as it applies to Aitkeh's G e n e r al iz ed Estimation, this does not see m to be the case. In p r e se nt in g their results B r e h m and Saving give nine d if fe re nt estimates for each equation, i.e., they have ei th e r e st im at ed different equations for each of the nine years, implying that they did n o t in fact pool cross-section and time series data, or they have pooled the data for each state and monthly dat a for each year and applied G en er al iz ed Least Squares to this. Thus, they have either p re se nt ed their model in a m is l e a d i n g way, or have not used the estimation technique wh ich they claim. UllCj « «< J . A Jiill t 27 ^Peter P eter S. Albin and B ru no Stein, "The Demand for fo3 General Ass: ssistance P a y m e n t s — Comment," American Economic Review, Vol. Dl. 57 (June, 1967), pp. 575-89. 28Ibid. 29 C. T. B r e h m and T. R. Saving, "The Demand for General As s istance Payments: Reply," A m e r i c a n Econ om i c R e v i e w , Vol. 57(June, 1967), pp. 585-88. 30 S a k s , op. c i t . , Chapter I I . 31 - The elasticities are (9Nt/9Gt-l) (G/N) where (3Nt/ 9 G t_i) is the coeffi ci en t for the g ra nt level (G^._^) , and G, N are the mean values for grant levels and new recipients. 32 33 34 B r e h m and S a v i n g , op. Albm and Stein, Kasper, op. cit. op. c i t . cit. 35 , . , Ibid. 36 Saks, o p . c i t ., Chapter II. 65 37 I b i d ., Ch apter I I . 38 T hese el as ti c i t i e s are also c a l c ul at ed at the me ans and are (9Nt/ 3 E W t ) ( E W / N ) . 39 40 S a k s , o p . c i t ., c h ap te r II. Kasper, op. cit. C HA PT ER IV AN E MP IR IC A L ANALYSIS OF THE EM PL OY ED AFDC RECIPIENT: SOME EVIDENCE P ROVIDED BY SURVEY DATA Introduction The replacement of the 100 pe rcent welfare tax^ by a less confiscatory 66 2/3 p er ce nt and the break-even levels of income 2 implied by the 19 67 amendments to the Social Security A c t 3 have resulted m a growing number of persons who are combining the alternatives of simul4 taneously wo rking and receiving welfare. This sub-group of the welfare popu la ti on is of pa rticular interest in light of the emphasis pl ac ed on e m p lo ym en t by policy makers. Even though this group's labor force p a r t i c i ­ pation has not lead to self-sufficiency, goal of many welfare reforms, the ultimate the importance of this first step in the possible at tainment of economic independence is obvious. Av ai l a b l e time series data on new recipients and terminations provide no information on the employed recipient. Furthermore, to our knowledge, there exists no other data on this sub-group in Michigan. situation, we were Given this faced with the alternative of completely 66 67 excluding the employed welfare recipients from our empirical analysis or utilizing a cross-section survey that was available to provide insight into some factors that affect 5 the p robability of a recipient's employment. Many researchers have tried to isolate factors conducive and detrimental to e m p l oy me nt and the use of a dichotomous dependent variable lends itself quite g readily to such undertakings. Models of this kind are usually referred to as "linear p r o b a bi li ty models" and have the following form: Y ± = a + & X L + £._, where {4.1) Y. = 1 if the I*"*1 individual is employed, = 0 otherwise, X^ = a vector of explanatory v a r i a b l e s , and e. = disturbance term. l In this chapter a linear pr ob ab il it y model wil l be used for analyzing the em p l o y m e n t probability of A F D C recipients. Alt h ou gh the elements be specified below, of the vector, to could be more numerous and more relevant to the theoretical model, we were constrained by the availability of computer pr ograms for categorizing a larger set of variables in the survey. and by the information contained 68 The Shortcomings of Ordinary Least Squares 7 Consider the relationship given by Equation (4.1). This equa ti o n states that the conditional distribution of Y^, given X ^ , has a mean of a+$X^ and a variance e qual to a 2 . However, different values, since Y^ can only assume two 0 and 1, we have, by the definition of mathe ma ti ca l expectation, E ( Y ± ) = l x fi (l)+0xfi (0) = f i (l), where f ^ (1) is the p r o b a b il it y that an individual wit h characteristics r e pr es en te d by X^ is employed. E (Y ^ ) = a+3X^, the probab il it y f^(l) will be different for different vectors of characteristics. therefore, think of E(Y^) Since We can, as m e as u ri ng the proportion of all individuals w i t h characteristics x^ who are employed. Thus, 0<_a+6Xi£ l . F r o m E q u at io n (4.1), we get e. = Y ± - a - 6 X i and since Y^ can only be equal to 0 or 1, it follows that for any given ve ct o r of characteristics, e:^ can only take on two d if fe re nt values, (l-a-PX^). This X ^ , the disturbance (-a-|3X^) and is a violation of the normality assumption of the classical n or m a l regression model and discretely distri bu te d a s : is Since we are assuming that is distributed with zero mean, w e can determine the probabilities f and (1-f) as follows: (-a-0x± )f + d - a - e x ^ (1-f) = 0, which after solving for f gives f = l-a-0Xi . Therefore the variance of E { e i2 ) = is (-a-3X± )2 (l-a-0Xi) + (1-a-eXj^) 2 (a+SX^ = ( a + B X ^ (l-a-eXj^) = E ( Y ± ) [l-E(Yi ) ]. Hence, the variance of e^ and is therefore h e t e r o s k e d a s t i c . is dependent on E(Y^) Although the least squares estimators of a and 6 will be unbiased, their estimated standard errors will have a bias so that classical tests of significance will not necessarily be reliable. Some of the researchers cited in the beginning of this chapter qualify their results by explaining that 70 the assumption of homoskedasticity is violated. however, None, se e m to note the non-normal and discrete d i s t r i ­ bution of The task at hand is to transform Equation (4.1) in such a w a y as to make it consistent with the classical assumptions of ordinary least squares estimation. We desire a m o n o t o n i c transformation such as that shown in Figure 4.1. MONOTONIC TRAN S F O R MATION OF A PROBABILITY TO THE RANGE Probability P (-»,+<») . 71 The probability, p, is measured along the horizontal axis and its transformation along the vertical axis. W h e n p increases from 0 to 1, its transform increases from -°° to +°°, thereby allowing us to correct the p roblem of finite range. There are an infinite number of t r a n s ­ formations with this property, but the most populat are Q the probit, tobit, and logit transformations. As the logit model is the least theoretically complicated and computationally the easiest, we shall use it for our empirical analysis. A Logit Model Consider the following regression equation: Y. = CH-6X.+YZ.+6U. + SW.+E . l where i ' i = 1 if the i l th l l (4.2) AFDC r ecipient is employed, = 0 otherwise; = 1 if the i th recipient is white, = 0 otherwise; Z. = 1 if the i 1 years old, tih recipient has children 0-5 = 0 otherwise; U. = 1 if the i ^ recipient has at least a high school education, = 0 otherwise; i W. = 1 if the i recipient lives in a model cities neighborhood, = 0 otherwise; and e. = disturbance term. i 9 72 We can define the odds in favor of being employed as the ratio p / ( l - p ) , where p is the probability of employment. The odds may be regarded as a monotonic t r a n s ­ formation of p with range from 0 to 00. negative values, As this excludes it is still restrictive, therefore we describe odds as a long-linear function of c h a r a c t e r i s t i c s : P± ln(i— =-) f “P i - a+3X.+yZ, + 5U. + 5 W . . 1 The left-hand side of 1 (4.3a) 1 1 (4.3a) is known as the logit of e m p l oyment and is a transformation of probability illustrated in Figure 4.1: — 00 at p=0 0 at p=.5 + CO at P=1 = -p i name to the relationsh when (4 .3a) is solved 1 Pi _ ^1-0X± „QV — -v/1? .-6U.-CW — ^T1 _rT»T -yZ 1+e 1 1 • * (4.3b) i Since our explanatory variables are dichotomous, we can display all combinations of possible states in Table 4.1. Using the elements in the first two rows of Table 4.1, our model becomes TABLE 4.1.— Frequency Distribution of Sample with Respect to Characteristics Categories and Employment. Categories* Number of Cases Number Employed Relative Frequency (0000) (0001) (0010) (0011) (0100) (0101) (0110) (0111) (1000) (1001) (1010) (1011) (1100) (1101) (1110) (1111) 129 584 337 1203 41 138 244 370 881 522 1549 990 136 107 576 245 20 90 27 154 8 43 20 72 108 49 115 108 20 19 83 40 0.155 0.154 0.080 0.128 0.195 0.312 0.082 0.195 0.123 0.094 0.074 0.109 0.147 0.178 0.144 0.163 ★ The categories can be interpreted as follows: (0000) = > X = 0, Z - 0 , U=0, W = 0 = > individuals who are black, have no children 0-5 years old, have no high school education, and do not live in model cities. (0001) = > X = 0, Z - 0, U = 0, W = 1 = > individuals who are black, have no children 0-5 years old, have no high school education, and live in model cities. (0010) = > X = 0, Z - 0 , U = 1, W = 0 = > individuals who are black, have no children 0-5 years old, have high school education or more, and do not live in model cities. (1111) = > X = 1, Z - 1, U = 1, W = 1 = > individuals who are white, have children 0-5 years old, have high school education or more, and live in model cities. 74 1 0 0 0 0 El in [n22/(n12 - n ^ ) ] 1 0 0 0 1 e2 In (n23/(n13 * n 23>] 10 0 10 1" tn21/(nu - n21)] a 6 Y (4.4) 6 C 10 1 1 1 ln ^n 2 8 ^ tn!8 ” n 28J ^ 1 1 11 1 ln [n2,16/{nl,16 " n2,16)] where is the element in the i e 16 row and j column of Table 4.1. Following Theil's lead, we assume that the relative frequencies in the third line of Table 4.1 are based on independent samples drawn from binomial distributions so that the es are i n d e p e n d e n t . the It can then be shown that are asymptotically normally distributed with zero mean and variance equal to [nik f ^ d - f ^ ) ] ^ n lk e<3u a ^s t^ie total number of cases in the k ^ where column of the first row and f 3^ equals the corresponding relative 11 frequency in the k column of the third row. Estimation Taking the natural logarithms of the relative frequencies assures the asymptotic normality of the 75 disturbances and applying w e i g h t e d least squares estimation to the transformed data eliminates heteroskedasticity. The weights are pro p o r tional to the reciprocals of the approximate standard deviations of the Thus, the assumptions of the classical normal regression model are A satisfied. A A A A Then by s u bstituting a,6,y,6, and C into /\ Equation (4.3b), we can get implicit estimates of p ^ , i.e., i _ p. = -- A A A A (4.3) . -a-BX.-yZ.-6U.-CW. . , l 1 l i i 1+e Results Utilizing the data p r e s e n t e d in Table 4.1 and applying Theil's transformation to purge heteroskedast icity to the resulting 16 observations gave the following e s t i m a t e d equation: I n C p ■ / ( 1 - p ■)] = - 9 .30-0.62 X.+1.03 Z.-0.85 U. 1 1 (0.20) N O . 26) N o . 20) 1 -0 .14 W.+e. ; R 2=0.85. (0.20) 1 1 As can be seen, we (4.5a) have a high coefficient of d e t e r m i n a ­ tion and three out of four coefficients are statistically s i g n i f i c a n t at bet t e r than the 0.5 percent level. However, when we solve for p^, ~ Pi _ 1 . . 1+e 9.30+0.62X.-1.0 3Z.+0 .85U .+0 .14W“. 1 1 1 1 , A (4.5b) 76 we e n d up w i t h n o n s e n s ical results. For example, the proba b i l i t y of a b l a c k person, w i t h no preschool children, no high school education, (X=0, Z = 0 , U=0, W=0) and n o t living in model cities b ecoming e m p loyed is: pi = " 9.3^ " °*00009' 1+e w h i c h does n o t even come close to the observed relative frequency of 0.155 for this group. The dilemma was p artially resolved after we r e estimated Theil's own example. 12 Ordinary least squares and w e i g h t e d least squares estimates showed that the results p r e s e n t e d in his example are n ot those of w e i g h t e d least squares even though they are claimed to be so. A n o t h e r a t t empt at purging the data of h e t e r o s k e ­ dasticity, this time by a two step procedure, was undertaken b u t to no avail. Specifically, we ran ordinary least A squares to obtain Y ^ s and, 2 since E ( e ^ )=E (Y^)[1-E(Y^)], e a c h observation was w e i g h t e d by w i= [ E ( Y ± ) (1 - E (Y ± ) and r e e s t i m a t e d by ordinary least squares. were The results just as n o n s e n s i c al as those prese n t e d in Equation (4 . 5 a ) . Alt h o u g h the v iolation of the h o m o s k edasticity a ssumption leads to insufficient estimates of the regression coefficients and bia s e d e stimates of the standard errors, 77 w hich in turn affect the t - r a t i o s , the esti m a t e d coefficients are unbiased an d consistent. Therefore, we will use the ordinary least squares results for the logit model. l n t p •/(1 ”P ■)] = - l •94-0.22 X.+0.4B Z.-0.39 U.+0.33 W .+ e .;R 2= 0 .70 1 1 (0.14) 1 (0.14) 1 (0.14) 1 (0.14) 1 (4.6a) We see that S is s i g n i ficant at the 10 percent, than the 1 percent, pe r c e n t level. 6 at better and y and x, at better than the 0.5 However, as e xplained above, the estimated s t andard errors p r e s e n t e d in parentheses below the estimated coefficients are biased. The classical tests of significance A may still be reasonable approximations. Solving for p ^ , we get _ 1 __________________________ 1. 9 4+0 .22X .-O''.48Z .+0 .39U .-0 .33W . ' = pi 1+e 1 1 1 1 from which the entries in Table 4.2 have been computed. A It shows that the e s t i m a t e d p^S approximate the observed relative frequencies in T a ble 4.1 quite closely. I m p l i c a t i o n s 2-2 Due to the limited information c ontained in the data and the qualifications our estimates are subject to, the implications drawn are tentative and should only be taken as pos s i b l e s u g gestions in identifying the factors influencing the p r o b a bility of an AFDC recipient's employment. TABLE 4.2.— Relative Frequencies and the Implicit Estimates of p^. Categories* (000C) (0001) (0010) (0011) (0100) (0101) (0110) (0111) (1000) (1001) (1010) (1011) (1100) (1101) (1110) (1111) Actual Relative Frequency 0.155 0.154 0.0B0 0.128 0.195 0.312 0.082 0.195 0.123 0.094 0.074 0.109 0.147 0.178 0.144 0.163 0.127 0.167 0.089 0.120 0.189 0.246 0.137 0.181 0.103 0.138 0.072 0.098 0.157 0.206 0.113 0.151 Estimated p i'S The categories can be interpreted as follows: (0000) = > X = 0, Z = 0 , U = 0, W = 0 = > individuals who are black, have no children 0-5 years old, have no high school education, and do not live in model cities. (0001) = > X = 0, Z = 0 , U = 0, W = 1 = > individuals who are black, have no children 0-5 years old, have no high school education, and live in model cities. (0010) = > X = 0 , U=l, Z=0, W = 0 = > individuals who are black, have no children 0-5 years old, have high school education or more, and do not live in model cities. (1111) = > X = 1, Z = 1, U = 1, W = 1 = > individuals who are white, have children 0-5 years old, have high school education or more, and live in model cities. 79 First, we see that non-white AFDC recipients have a higher p r o b a b i l i t y of b e ing employed across all categories. Given that a large portion of the caseload is composed of A F D C mothers/ it is easy to find other data confirming this conclusion. For example, the overall civilian labor force participation rate for women age 16 and over was non-whites 40.7 p e r c e n t for whites and 49.3 percent for (in 1960). The higher participation rates of non-white w o m e n seems to hold for all age groups except teenagers and is m o s t pron o u n c e d in the age brackets 25 to 34 and 35 to 44 (16.0 and 11.8 percentage points above 1 A that for white women, respectively). The fact that two-thirds of all AF D C mothers fall between the ages of 25 to 44 lends more credence to our results. 15 Alt h o u g h a number of reasons have been offered p u r p o r t i n g to explain the higher labor force p a r t i c i p a ­ tion of non-white women, they are quite ad hoc and unc o r ro b o r a t e d propositions. 16 We will simply say that the higher p r o b a b i l i t y of being employed for non-white A F D C recipients m i g h t be due to the relatively higher supply of labor that this group seems to offer. A second implication of ou r results is that AFDC families wi t h p r e s c h o o l children have higher probabilities of employment. This is contrary to the findings of other investigators as w e l l as to the expected direction of the relationship. Cohen found that by far the single most 80 important d e m o g r a p h i c characteristic influencing the labor force p a r t i c i p a t i o n decisions of w omen was the presence and age composition of children. 17 Further, the presence of children under six was found to have the strongest inhibiting effect on labor force participation. 18 A peculiarity in the sample or some statistical quirk are the only e x p l a nations possible for our results. The b a s i c assumption underlying recent proposals and policy decisions with respect to welfare has been that if recipients are given the required education and training, jobs are readily available. of our estimates s u g g e st the opposite. A third implication While there is much evidence that labor force participation rates are positively related to educational attainment for m o s t d e mographic groups, the single important exception to this gene r a l i z a t i o n is the group composed of non-white women. For this group, no systematic relationship appears to e x ist b e t ween labor force p a r t icipation and educational attainment 19 (except for higher rates for college g r a d u a t e s ) . Further evidence is a c cumulating that for a b road range of occupations i n s t itutional training or e ducational attainm e n t is a poor p r e d i c t o r of job performance. same token, 20 By the several studies suggest that the increase in the p r obability of e m p loyment is negligible, especially for m i n o r i t y group w o r k e r s , w h e n they are provided with vocational training and education. 21 Thus, our result that 81 AFDC recipients with less than high school education have a higher probability of being in the labor force does not run against the grain of these findings. The affects of residing in a model cities area of a city is something about which little is known. The inclusion of this category into our analysis was based on the thought that special transportation, health, information, and other services available to model cities residents might act to increase employment. results appear to support such a claim, Although the this could also be due to the effect of poverty on labor force participation. Model cities neighborhoods are, of course, the poorest acreas of cities and it is not possible to distinguish between the programs and the poverty in understanding the role of this variable. 22 FOOTNOTES TO C HAPTER IV A 100 p e r c e n t welfare tax implies that the basic grant is reduced by one dollar for every dollar of income e arned by a welfare recipient. 2 The level of income at or above w h ich a pers o n is no longer e ligible for pub l i c assistance is called the break-even level of i n c o m e . 3 Social Security Amendments of 1967, Sec. 201(C) (A), P.L. 90-248, January 2, 1968. 4 See Vernon K. Smith and Aydin Ulusan, The E m p loyment of A F D C Recipients in M i c h i g a n , Studies in We l f a r e Policy, Publication 16 3 ( Lansing: Michigan D e p artment of Social Services, 1972). 5 The cross-sectional data were obtained from a survey conducted by the Michigan D e p artment of Social Services of a sample of A F D C recipients in Ing h a m and Genesee counties in July, 1970. Besides o b t ained i n f o r m a ­ tion on the e m p l o y m e n t status of individuals on welfare, other demographic, and econo m i c characteristics were recorded. g See, for example, M a l c o m S. Cohen, Samuel A. Rea, Jr., and Robert I. Lerman, "A M i cro M odel of L abor Supply," BLS Staff P a p e r 4, (Washington, D . C . : U.S. Department of Labor, 19 70); Leonard J. Hausman, "The Impact of W e l f a r e on the W o r k E f f o r t of AFDC Mothers," in The President's Commission on Income M a i n t enance Programs, Technical S t u d i e s , (Washington, D . C . : U.S. G o v e r n m e n t Pr i n t i n g Office. 1970) ; Ronald E. Fine, Director, Final Report: AF D C E m p l o y m e n t and Referral G u i d e l i n e s , M i n n e a p o l i s , M i n n e s o t a : Institute for Interdisciplinary Studies, June, 1972); and Daniel H. Saks, "Economic Analysis of an Urban Public Assistance Program: A id to New York City Families of Dependent Children in the Sixties," (Unpublished Ph.D. dissertation, Princeton University, 1973). 7 This section draws heavily on Jan Kmenta's Elements of E c o n o m e t r i c s , (New York: The Macmillan C o m p a n y , 1971), Chapter 11. 82 83 g For an application of the prob i t analysis m o del see, e.g., James Tobin, "Estimation of Relationships for L i m ited D e p e n d e n t Variables," E c o n o m e t r i c a , Vol. 26 (January, 1958), pp. 24-36; and for the logit m o d e l see H enri Theil, Principles of E c o n o m e t r i c s , (New York: John W i l e y and Sons~J Inc. , 19 71) , Chapter 12. 9 A lt h o u g h all of the explanatory variables are d i c h o t o m o u s , this is no t due to the use of the logit model. Continuous variables can also be used, however, we have had to make due with w h a t was in the survey. ■^Theil, o p . c i t . , p. 635. 1 1 I b i d . , p. 635 . 12 I b i d . , p. 6 35. 13 I am grateful to Mr. V e r n o n K. Smith for his assistance in the p r eparation of this section. His valuable comments, and knowledge in the field were extremely helpful. 14 U.S. D e p a r t ment of Labor, Statistics on M a n p o w e r , Supplement to M anpower Report of the P resident (Washington, D.C.: U.S. G o v ernment Printing Office, March, 1969), Table A-4. 15Mic h i g a n Department of Social Services, Profile of M i ch igan's A F D C Caseload. Research Paper Number 1, TlTansing: The Department, October, 1969), Table 16. 16 See W i l l i a m G. Bowen and T. Aldrich Finnegan, The Economics of Labor Force P a r t i c i p a t i o n , (Princeton: Pr i n c e t o n University Press, 1969) , pp. 2^2-259; and Glen G. C a i n , M a r r i e d W o m e n in the Labor F o r c e , (Chicago: University of Chicago Press, 1966) , pp. 81-3, 103-4. 17 M a l c o m Cohen, "Married W o m e n in the Labor Force, An Ana l y s i s of Pa r t i c ipation R a t e s ," Monthly Labor R e v i e w , ( O c t o b e r , 1969). 18 Bowen and Finegan, 19I b i d . , pp. 20 o p . c i t ., pp. 9 6-10 3. 122-7. See Daniel Diamond and Hrach Bedrosian, "Hiring Standards and Job Performance," M a n p o w e r Research Monograph No. 18 (Washington, D.C.: U.S. D e p a r t m e n t of Labor). 84 21 See Edward Opton, "Factors Asso c i a t e d with E m p l o y m e n t A mong Welfare Mothers," (Berkeley, California: The W r i g h t Institute, 1971), (DOL Contract Number 51-05-69-04); and P e t er Doeringer, e d . , Programs to Employ the Disadvantaged (Engelwood Cliffs, New Jersey: P r e n t l c e - H a 11, I n c ., 1969) . 22 See Joseph D. Mooney, "Urban Poverty and Labor Force Participation," American Economic R e v i e w , Vol. 5 7 (March, 1967), pp. 104-19. CHAPTER V FLOWS INTO AFDC-R: A LOGISTIC GROWTH MODEL Introduction The A F D C - R category has, by far, caseload of any welfare programs. the largest In December, 19 71, there w e r e 128,644 A F D C - R cases as compared to 11,766 A F D C - U and 45,712 G A cases.^ Besides carrying the most w e i g h t in terms of the state's social services budget, it is one of the mo s t rapidly growing public assistance programs. G i ven these f a c t s , the importance of an accurate predictive m o del of the A F D C - R caseload becomes obvious. It was p o i n t e d out in Chapter II that many legal, political, and sociological factors were instrumental in the growth of w e l f a re caseloads. Furthermore, m o s t of these factors we r e seen to be n o n - q u a n t i f i a b l e . One way of dealing w i t h this w o u l d be to use a time trend as an e x planatory variable in an equation explaining A F D C - R caseloads. This w o u l d n o t be satisfactory since a time trend implies indefinite growth. explanatory variables m a x i m u m AF D C grants, The use of dichotomous (e.g., X^=0 before the increase in and X^.=l after the increase) would, on the other hand, require a very large set of o b s e r v a ­ tions if there were to be adequate degrees of freedom since the number of events that w o u l d have to be dichotomized 85 86 are so numerous. dichotomized, Even if m o s t of these events could be such an analysis w o u l d only detect changes in the intercept and slope of a linear model. 3 (if interaction is specified) Therefore, we will attempt to predict A F D C - R caseloads by using a logistic growth model in which caseload asymptotically approaches some limit. The asymptote for the A F D C - R caseload is the number of female headed families and subfamilies w i t h related children under 18 in Michigan. Altho u g h such an analysis could very well apply to A F D C - U and GA cases also, the definition of an asymptote for GA and A F D C - U cases w o u l d be almost impossible even if data on such an asymptote were a v a i l ­ able. Furthermore, the growth curve for A F D C - U and GA cases show ma n y fluctuations whereas A F D C - R cases exhibit a smooth growth similar to the curve in Figure 5.1 p r e s e n t e d below. The Model The m o d e l to be employed for p r e dicting AFDC-R 4 caseloads is a m o d i f i e d logistic growth curve and can be specified as follows: C t = 1+ea+6t+et where ' (5'la) C^ = A F D C - R c a seload in M i c higan in month t, F. = female-headed families and sub-families with related children under 18 in Michigan in month t, 87 e = the natural logarithm b a s e , t = time, i.e., t = l , 2,...,42 December 1971), and (July 1968 to e.t = disturbance term, The population regression line is given by the m o d ified logistic growth curve shown in Figure 5.1. A M O D IF IE D LOGISTIC G RO W TH CURVE CASELOAD FIGURE 5 7 As we are dealing w i t h female-headed AFDC families, the upper b o und to the A F D C - R caseload is the total n umber of female-headed families and sub-families with related children under 18 in Michigan (F^.) . We hypothesize that the dynamic processes previously m entioned led to a 88 no n -linear growth of A F D C - R caseloads as p resented in Figure 5.1. The statistical test of significance, the coefficient of determination, R 2 and , p resented with the results will help to judge the soundness of this hypothesis. Furthermore, predicting caseloads and comparing them wi t h actual figures will also be useful in determining the validity of our model. Specification The logistic model can be specified in two ways: one is the form given in Equation (5.1a), and the other is F c = t L_ i+e a + 3 t + e (5.2) t The values of C t can extend from is specified as (5.2) to +°° if the model and therefore the normality assumption of the classical normal regression m odel is not violated. Unfortunately obtaining m a x i m u m likelihood estimates for the parameters of this non-linear equation requires m a x i m i z i n g the following logarithmic likelihood function w i t h respect to its p a r a m e t e r s : L = - |ln(27T)- flrtJ2 2a T F 2 £ [C.----- ~7"tj ] . (5.3) t=l r 1+e t This could be done on a computer; however, the returns from such an undertaking did not seem to be w orth the costs 89 it would entail. in Equation Therefore, the specification implicit {5.1a) was adopted, and l n ( ^ -1) = a + 8 t+ e t (5.1b) was estimated by ordinary least squares. violating the normality assumtpion (since As this means can now only take on values between 0 and F ^ ) , our results must be qualified. Although non-normality makes the least squares coefficients less efficient in small samples, they retain all desirable asymptotic properties. Furthermore, the distribution of the disturbances is not radically different from the normal and therefore classical tests of significance may be reasonable approximations.^ Estimation^ The estimation of Equation (5.1b) would be straight-forward if monthly data on female headed families and sub-families with related children under 18 were available. However, these figures are only published in each Decennial Census and we have two data points, and 19 70, for our (F t > variable. 1960 Although the number of marriages, divorces, desertions, and illegitimate children of single women, and other socio-economic and demographic factors determine the size of ( ) , the absence of data forces us to make the simplifying assumption that the growth rate of female-headed families between 1960 and 1970 was exponential: 90 F where t F = F ert, o ' (5.4a) = number of female h e a d e d families and sub-families w i t h related children in M ic h i g a n in m onth t, Fq = initial value of F fc (in our case 1960), e = natural logarithm base, r = growth r a t e , and t = t i m e , i.e., t = 1,2,...,T. As the rate of growth, we can solve r, is the only for it after expressing (5.4a) unknown, in logarithmic form as In F -1 F „ = _ -----T n o r ,r- jil \ (5.4b) , where F T is the last observation, F q the first observation, and T the number of months be t w e e n the two. r . ln(142,. 4 3 ^ - 1 ^ 8 2 , 0 0 0 ) Thus, . 0 „ 046- (5 4o) A N o w we can e s t imate the value of (F^) , say (Ffc) , for any m o n t h b e t ween 1960 and 19 70 by entering the appropriate Ft « (t) into (82,000)e°*0046t These estimates will be used in E q u a t i o n (5.5) (5.1b). Results The e s t i m a t e d logistic growth curve for Michigan's A F D C - R caseload is 91 Ft ln(— ^ - 1 ) = 0 . 9 6 7-0.049t+It; H (0.002) 2 R=0.93 (5.6a) Subject to the q u alifications implied by the violation of the normality assumption, we see that the coefficient for (t) seems highly s i gnificant statistic is -24.5) (the value of Student's t- and 93 p ercent of the variation in the dependent va r i a b l e is expl a i n e d by the estimated *7 A relationship. We can solve for (double hat because an e s timate for was used) to get A F. C. = --------------------r 0.9 6 7 - 0.049t+e. l+e t The negative c o e f f i c i e nt for time time goes by (i.e. (t) (5.6b) (t) implies that as i n c r e a s e s ) , the ratio of the c a s e ­ load to the asymptote will approach one. That is, in the limit as . ^ t **■ 00 , e A A and . n 0 A C , ----- > t This, of course, 0.967-0.049t F ,. t is just for purposes of exposition as we w o u l d not expect F fc to retain the same growth rate or, for that matter, demographic, even the same shape. Socio-economic, and political changes w o uld more than likely induce changes in the number of female hea d e d families. The e s t i m a t e d equation seems to support our reasons for the use of such a model. main p u r p o s e was to be prediction, However, since our generating caseload 92 figures for months after December 19 71 p o i n t used in estimation) (our last data and comparing them with actual caseload figures w i l l give us a bet t e r idea of the model's performance. As can be seen from Table 5.1, the model performs quite well, with the hi g h e s t percentage error being only 5.2. Given the extremely naive way the female-headed families were estimated, may be considered quite close. the predictions It is true that we seem to be consistently under-predicting caseload size. This may be attributed to m i s s p e c ification or a host of other factors. valid. However, the following e xplanation may also be Since we are estimating the logarithmic t r ans­ formation of Eq u a t i o n in our estimates, (5.1a) this m i ght produce a bias since e v e n though E(Y±) = a+3X± , E (lnYi )7fln(a+exi ) . Q A Taylor series expansion of InY^ w o u l d make this clearer. Implications As our goal is to p redict A F D C - R caseload sizes, the obvious implication of the logistic growth curve is that it can be us e d to ge t reasonably accurate short run estimates of the size of this category of public assistance. The p r e d i cted caseload sizes for the year 19 73 are given in Table 5.2. It can be seen that the growth TABLE 5.1.— Predicted and Actual AFDC-R Caseload. Predicted Caseload Actual Caseload Error (ct ) (ct ) January 1972 119,984 120,580 -596 -0.5 February 121,936 123,993 -2,057 -1.7 March 123,869 127,839 -3,970 -3.1 April 125,802 130,489 -4,687 -3.6 May 127,651 132,765 -5,114 -3.9 June 129,512 134,698 -5,186 -3.9 July 131,349 136,799 -5,450 -4.0 August 133,160 140,187 -7,027 -5.1 Septeinber 134,938 142,231 -7.293 -5.2 October 136,705 142,794 -6,089 -4.3 November 138,435 143,233 -4,798 -3.4 December 140,148 143,860 -3,712 -2.6 Month Percentage 94 TABLE 5 . 2 . — A F D C - R Ca seload Projections for 1973 Month Projected Number of A F D C - R Cases January 1973 141,841 February 143/500 March 144,951 April 146,764 May 148,351 June 149,931 July 151,477 Aug u s t 153,006 September 154,511 O c t ober 155,997 N o vember 157,454 D e cember 158,897 rate will diminish and the upper bound for A F D C - R c a s e s , female headed families and sub-families with related children under 18, approached asymptotically. These results are only tentative and exploratory as they depend crucially on the not very realistic assumptions made about the asymptote, (F^.) . FOOTNOTES TO CHAPTER V This can also be compared with Aid to the Blind (AB), Aid to the Disabled (AD), and Old Age Assistance (OAA) cases which were respectively 1,555, 37,689, and 41,320 in December, 1971. 2 Although all econometric models can be used for prediction, the use of a model such as the one presented in Chapter 3 would entail making predictions as to the future values of the explanatory variables. Therefore, the accuracy of the predicted dependent variable w ould depend upon the accuracy of the values assigned to the explanatory variables in future periods. 3 See Jan Kmenta, Elements of E c o n o m e t r i c s ,(New York: The Macmillan Company, 1971), Ch. 11, pp. 409-25. 4 It is modified in that the unmodified logistic growth curve has a horizontal asymptote whereas ours has an increasing one. C f . Kmenta, o p . c i t ., pp. 461-2. 5 See E. Malinvaud, Statistical Methods of Econometrics, (Chicago: Rand McNally, 1966), pp. 195-197, and "2'5i-2S'4. g Data for A F D C - R caseloads were obtained from Social Service S t a t i s t i c s , published monthly by the Michigan State Department of Social Services, Data on (F t ) were obtained from the 19 60 and 1970 Decennial Census 7 The F-statistic with 1,40 degrees of freedom is 494.83. 3 I am grateful to Dr. Jan Kmenta for pointing out this possibility. 96 C H A P T E R VI SOME CONCLUDING REMARKS The p u r p o s e of this dissertation was to analyze the decision of choosing between we l f a r e and other alternatives process. and to isolate some factors affecting this To this end, a conceptual model was presented to define the flows to and from Michigan's welfare sector. Then, the m i c r o be h a v ior implicit in the conceptual model was ana l y z e d within the framework of a constrained o p t i m ization p r o b l e m w here individuals choose among the a lternatives open to them. Finally, empirical models were fo r mulated and hypotheses w i t h respect to the w e l fare decision tested. Data limitations and the p a r t i c u l a r aspects of the p r o b l e m di c t a t e d the use of three separate econometric models. The first utilized time-series data in analyzing the aggregate decisions resulting in new welfare recipients and terminations from public assistance. results, which are tentative, The can be summarized as follows: 1. Although both labor market conditions and welfare b e n e f i t levels play important roles in the decision to leave or e nter public assistance, 97 their 98 impacts are not uniform over the different sub-groups examined. Terminating AFD C - R and AFDC-U recipients are seen to be influenced as expected by the measured demand and supply of labor, while nothing in this respect can be said for GA. Similarly, the level of welfare benefits has a definite and strong impact on the decision of terminating from AF D C - R and AFDC-U but not on the decision of new recipients. On the other hand, expected wages are an important determinant of the flows into welfare, but shows an unexpected and non-significant relationship with t e r m i n a t i o n s . 2. Current as well as past labor market conditions have a significant influence on the decision to accept public assistance. The distributed lag structure specified in the new recipient equations yielded signifi­ cant and expected results for all categories. however, Again, the magnitude of the impact is different for AFDC-R, AFDC-U, and GA. As was pointed out earlier, some inconsistent results were obtained from the estimated relationships. This was particularly true for terminations and has reduced the validity of our results considerably. However, as the model, to our knowledge, is the second of only two attempts at an empirical analysis of termina­ tions, we have presented the results as they stand.^ A better specification and/or the employment of statistical 99 techniques such as "principal components analysis" to alleviate the problems of m u l t i c o l linearity could possibly 2 lead to a be t t e r set of results. The p r o b a b i l i ty of correlation across the new r e c i p i e n t and terminations equations for all categories is quite high. It is quite possible that terminations affect new recipients and that new recipients in one category influence the inflows into other programs. such a possibility# Given the gain in statistical efficiency implied by est i m a t i n g the w h o l e syst e m jointly is worthy of consideration. A technique such as "Seemingly Unrelated Regressions" w o u l d be appropriate for such a future 3 undertaking. Similarly, the specification of a simultaneous equation system is also in the r e alm of p o s sible improve­ ments in analyzing the w elfare choice. The second e c onometric m o d e l analyzed the e m p l o y ­ m e n t probab i l i t i e s of welfare recipients. The results from the logit model specified in C hapter IV, can be summarized as follows: 1. B l a c k AFDC recipients have higher probabilities of employment than whites. This result is consistent with other studies of labor force participation, suggesting that the possible reason for this is the greater supply of labor typically offered by b l ack women. 2. Contrary to the primary goal of m a n y proposals and p o l i c y changes, education by itself does n o t imply 100 higher probabilities of employment for AFDC recipients. This result is also supported, or at least not contra­ dicted, by many studies. However, the problems of finding an appropriate estimator makes this one of our most tentative findings. 3. AFDC recipients living in model cities neighborhoods have higher probabilities of employment than non-model cities residents. This can be attributed to either the programs provided for model cities n e i g h b o r ­ hoods or the affects of the poverty so prevalant in those neighborhoods on labor force participation. The last econometric model was specified to account for the gradual accumulation of non-quantifiable factors affecting the decision to enter the A F D C - R program and to provide a reliable means of predicting the caseloads of this category. Comparisons of caseloads generated by the estimated model indicate that it can be used with reasonable accuracy for this purpose. FOOTNOTES TO CHAPTER VI Daniel H. Saks, "Economic Analysis of an Urban Public Assistance Program: Aid to New York City Families of Dependent Children in the Sixties," (Unpublished Ph.D. dissertation, Princeton University, 1972). This is the only study, to our knowledge, that examines terminations from welfare. 2 For a discussion of principal components analysis, see Henri Theil, Principles of E c o n o m e t r i c s , (New York: John Wiley and Soiis^ Inc^ , 1971) , p p . 46-55. 3 See Jan Kmenta, Elements of E c o n o m e t r i c s , (New York: The Macmillan C o m p a n y , 1971) , pp . 517-29. 101 BIBLIOGRAPHY 102 I BIBLIOGRAPHY Public Documents State of Maryland. Department of Public Welfare. A Report on Caseload Increase in the A i d to Families with Dependent Children Program, 1 9 6 0 - 6 6 . Baltimore, Maryland: Department of Public Welfare, July, 1967. State of Michigan. Department of Labor. Michigan E m p l o y ­ ment Security Commission. Michigan Manpower R e v i e w . Detroit, Michigan: Michigan Employment Security Commission, 1968-1971. _________ . Department of Social Services. Fiscal 1 9 6 9 . Lansing, Michigan: Social Services, 1969. Annual Report Department of . Fifteenth Biennial Report July, 1966-June, 1 9 6 8 . Lansing, Michigan: Department of Social S e r v i c e s , 1968. . Profile of Michigan's AFDC C a s e l o a d . Lansing, Michigan: Department of Social Services, October, 1969. _________ . Social Service S t a t i s t i c s . Lansing, Michigan: Department of Social Services, May, 1 9 6 9 - D e c e m b e r , 1971. U.S. Congress. Social Security Amendments of 1 9 6 7 . 90th Congress. P.L. 90-248. Washington, D . C . : U.S. Government Printing Office, January, 1968. U.S. Department of Commerce. Bureau of the Census. 1960 Census of Population: General Population Characteristics: M i c h i g a n . Washington, D.C.: U.S. Government Printing Office, 1961. _________ . 19 70 Census of Population: General Population Characteristics: M i c h i g a n . Washington, D . C . : U.S. Government Printing Office, 1971. 103 104 U.S. Department of Health, Education, and Welfare. A Report on Caseload Increase in the Ai d to Families with Dependent Chi l dren in New York City, November" 19 68-February7, l96~9~l W a s h i n g t o n , D.C. : Department of Health, Education, and Welfare, 1969. Center for Social Statistics. Findings of the 1971 AFDC S t u d y . Washington, D.C.: D e p artment of Health, Education, and Welfare, December, 1971. . Welfare R e v i e w . Washington, D.C.: D e p artment of Health, Education, and Welfare, July 1968-January 1972. _ _ . Books Appel, Gary L. Effects of a Financial Incentive on AFDC Employment: M i chigan's E x p erience Between July 1969 and July 19^0 ■ M i n n e a p o l i s , M i n n e s o t a : Institute for Interdisciplinary Studies, March, 1972. The Economics B o w e n , W i l l i a m G. and Finnegan, A ldrich T. of Labor Force P a r t i c i p a t i o n . Princeton, N e w Jersey: P r i n ceton Uni v e r s i t y Press, 1969. Burgess, Elaine and Price, Daniel. A n A m e r i c a n Dependency C h a l l a n g e . Chicago: A m e rican Public Welfare Association, 1963, Cain, Glen G. M a r r i e d W o m e n in the L a bor F o r c e . University of Ch i c a g o Press, 1966 ^ Chicago: Doeringer, Peter, ed. Programs to Employ the D i s a d v a n t a g e d . En g land Cliffs, Ne w Jersey: P r e n t i c e - H a l l , Inc., 1969. Fine, Ronald E . , director. Final Report: AFDC Employment and Referral G u i d e l i n e s . Minneapolis: Institute for I n t e r d i s c i plinary Studies, June, 1972. Goodwin, Leonard. Do the Poor Want to W o r k ? Washington, D.C. : Brookings I n s t i t u t i o n , J u n e , 1972. Kmenta, Jan. E l ements of E c o n o m e t r i c s . Ma c m i l l a n Company, 1971. Ne w York: Malinvaud, E. S t atistical Methods of E c o n o m e t r i c s . Rand McNally, 1966. The Chicago: 105 Piven, Frances Fox and Cloward, Richard A. Regulating the P o o r . New York: Random House, 1971. Smith, Vernon K. and Ulusan, Aydin. The Employment of AFDC Recipients in M i c h i g a n . Lansing, Michigan: Department of Social Services, 1972. Theil, Henri. Principles of E c o n o m e t r i c s . John Wiley and Sons, I n c . , 1971. New York: Articles and Periodicals Albin, Peter S. and Stein, Bruno. "The Demand for General Assistance Payments." American Economic R e v i e w , Vol. 57 (June, 1967), 575-89. _________ . "The Constrained Demand for Public Assistance." Journal of Human R e s o u r c e s , III(summer 1968), 300-11. Becker, Gary. "A Theory of the Allocation of Time." Economic J o u r n a l , LXXV (September, 1965), 492-517. Bernard, Sydney. "The Economic and Social Adjustment of Low-Income Female-Headed Families." The Florance Heller Graduate School for Advanced Studies in Social Welfare, Brandies University, May, 1964. Boskin, Jay. "The Negative Income Tax and the Supply of Work Effort." National Tax Journal, XX (December, 1967), 353-67. Brehm, C. T. and Saving, T. R. "The Demand for General Assistance Payments." American Economic R e v i e w , Vol. 51 (December, 1964)"^ 1002-X8. _________ . "The Demand for General Assistance Payments: Reply." American Economic Review, Vol. 57 (June, 1967) , 585-8S'; C o h e n , M a l c o m S . "Married Women in the Labor F o r c e : An Analysis of Participation Rates." Monthly Labor R e v i e w , (October, 1969) . _________ . , Samuel A., Jr. and Lerman, Robert I. "A MicroModel of Labor Supply." BLS Staff Paper 4, 1970. Conlisk, John. "Simple Dynamic Effects on Work-Leisure Choice: A Skeptical Comment on the Static Theory." Journal of Human Resources, III (summer, 1968), 329-26. 106 Diamond, Daniel and Bedrosian, Hrach. "Hiring Standards and Job Performance." U.S. Department of Labor M a npower R esearch Monograph 18, Franklin, David. "A Longitudinal Study of WIN Dropouts: P r o g r a m and Policy I m p l i c a t i o n s ." Regional Institute in Social Welfare, April, 1972. Gaines, Tilford. " E m p l o y m e n t - U n e m p l o y m e n t ." Economic Report of Manufacturers Hanover Trust, April, 1972. Green, Christopher. "Negative Taxes and Money Incentives to Work: The Static Theory." Journal of Human R e s o u r c e s , III {Summer, 1968), 280-88. Hausman, L e o n a r d J. "The Impact of Welfare on the Work E ffort of AF D C Mothers." The President's Commission on Income Maintenance Programs, Technical Studies, 1970. Kasper, Hirshel. "Welfare Payments and Work Incentives: Some Determinants of the Rates of General Assistance Payments." Journal of Human Resources, III (Winter, 1968) , 8 6-lXtn Meyers, Samuel and McIntyre, Jeanie. "Welfare Policy and Its Consequencas for the Recipient Population: A Study of the AFDC Programs." Bureau of Social Science Research, December, 1969. Mincer, Jacob. "Labor Force Participation of Married Women: A Study in L a b or Supply." Aspects of Labor E c o n o m i c s , 1962, 63-105. Mooney, Joseph D. "Urban Poverty and Labor Force Pa r t i c i ­ pation." A m e r ican Economic Review, Vol. 57 (March, 1967), 104=19“: Opton, Edward, "Factors Associated with Employment Among Welfare Mothers." The Wrig h t Institute, 1971. Tobin, James. "Estimation of Relationships for Limited Depen d e n t Variables." E c o n o m e t r i c a , Vol. 26 (January, 1958), 24-36. Zellner, Arnold, "An E fficient Method of Estimations Seem­ ingly U n r e l a t e d Regressions and Test for Aggregation B i a s ." Journal of the American Statistical Association, Vol. 57 (June, 1962), 343-48. 107 Un p ublished Materials Saks, Daniel H. "Economic Analysis of an Urban Public Assistance Program: A i d to Ne w York Families w i t h Dependent Children in the Sixties." Unpublished Ph.D. Dissertation, Princeton University, 1972. Savage, L y n n and D a h l k e , Sherry. "The General Assistance P r o g r a m in Four Counties in Michigan." Unpublished study of the Michigan D e p artment of Social Services, March, 1973. APPENDICES 108 APP ENDIX TO CHA P T E R II 109 APPENDIX TO CHAPTER 2 IMPORTANT CHANGES IN MICHIGAN'S WELFARE POLICY Policy Change Effective Date 7-3-61 Simplified budgeting and increased maximum grants for AFDC. 9-1-63 AFDC Foster Care program began. 4-64 AFDC Unemployed Fathers program began. 8-15-66 Increase in maximum AFDC grants. 1-67 AFDC ceilings removed; laundry, special diets, telephone, upkeep of owned home, and household operations allowance added. 2-12-69 Step-parent income disregarded. 4-30-69 Emergency Assistance program began. 6-4-69 Durational residency requirement eliminated. \* 7-1-69 Income disregard implemented in AFDC; $24 WIN Training allowance. 7-1-69 Update of AFDC standards, $3 per person before receiving grant. 12-15-69 AFDC-Foster Care eligibility expanded per 1967 Social Security Act amendments. 1-20-70 Grandparent not legally responsible for support of grandchildren. 6-1-70 Expansion of AFDC-Foster Care to potential AFDC cases. 6-S-70 No grants cancelled because home unsuitable. 7-70 Per Act 88 of 1970, only relative responsibility is that of spouse for spouse, and parent for child under 21. 9-1-70 New shelter maximums. 9-1-70 Special needs items for laundry, telephone, special diet, and water incorporated into basic AFDC standards. 110 ill Effective Date Policy Change 10-14-70 Per Act 89 of 1970, client's statement of age and relationship of children is prima facia evidence of eligibility for AFDC. 11-12-70 G.M. Strike; strikes eligible for GA, Food Stamps, AFDC, and Medicaid. 4-1-71 AFDC-Incapacity - 3 months duration no longer required; method of eligibility simplified. 7-27-71 Presumptive Eligibility program established in some counties. 9-13-71 Simplified Method of Eligibility Determination implemented statewide in AFDC. APP ENDIX TO CHAPTER III 112 APPENDIX TO CHAPTER 3 Table 3.A Breakdown of Occupational Categories that AFDC Recipients Currently or Usually Belong Toa Percent Current or Usual Occupational Class AFDC-R Cl) Professional, semi-professional, proprietors, managers and officials AFDC-U (2) 1.1 1.4 11.6 2.6 Craftsmen, formen, and kindred workers 0.7 4.2 Operatives and kindred skilled and semi-skilled workers 3.4 16.8 Service workers, except private household 23.5 3.7 Private household service workers 10.2 0.0 Unskilled laborers 14.4 30.2 Clerical, sales, and kindred workers This table was constructed from Table No. 22 and 30 in Michigan Depart­ ment of Social Services, Profile of Michigan AFDC Caseload, Research Paper No. 1 (Lansing, Michigan: the Department, October, 1969). The first three categories were combined and manufacturing wages weighted by this proportion, and the weight derived from the last four categories were applied to service wages. The expected wages derived from Column 1 were used for AFDC-R, and those derived from Column 2 for AFDC-U and GA. It is true that the occupational and industrial classifi­ cations cannot be well matched in this way, but it was the best that could be done at the time. 113 Table 3.B Estimated Regression Coefficients for the Terminations equations Using Different Labor Market Variables3 Independent Variables UUpCUUUilL Variable rq. So. AFDC-R 1.1 ‘t AFDC-U 1.2 t _ GA t 1.3 T AFDC-R 1.4 T AFDC-U 1.5 ? GA T AFDC-R 1.7 T AFDC-U 1.8 T GA 1.9 (ENMIt) (WSEt) R- Standard trror of the Estimate UR t WSE 7.87 (16.51) — --- -0.07 (0.14) — — - -0.76 (268.72) 0.51 (7.05) *** 0.08 (0.03) ** -41.46 (21.87) 0.75 18.42 1,143.07 14.55 (23.53) — --- -0.01 (0.19) — — -50.51 (324.73) -2.46 (9.51) *** 0.28 (0-10) *** -26.31 (13.24) 0.62 9.76 1,556.24 -48.63*** (24.96) — — --- -604.17* (371.05) * *■* 20.60 (9.96) 49.31* (32.61) 0.97 220.54 1,560.32 (0.06) -45.06*** 0.78 21.83 1,070.69 (EWt) (EWt) ** 0.36 (0.21) ... EW NFLFt *** -595.50** (257.33) — — -112.99 (533.04) — ... 1053.59** (546-65) — — — (76.46) (1.89) (0.02) (20.49) — 35.11 (178.22) 11.69 (77.62) 1.80 (1.54) *** 0.27 (0.10) -28.76 (13.01) 0.62 9.74 1,557.11 — 198.84 (172.81) -120.36** (72.65) 0.44 (1.58) 0.11*** (0.05) 34.62 (29.19) 0.97 252.14 1,521.73 0.00 (0.00) -116.52* (75.62) -0.39 -43.40*** (20.84) 0.78 20.82 1,090.77 (3.09) 0.10 (0.03) 0.34 (0.08) -33.18 (11.16) 0.73 16.19 1,311.50 45.03* (31.57) 0.97 221.18 1,557.99 *** 4.76 (2.67) --- — — 0.07 (0.07) -185.77 (241.17) -5.90 (5.99) --- ... 0.09 (0.09) -393.32 (333.74) 14.04 (7.25) — — 8.84* (6.25) --- — -13.83** (7.59) — *** Standard errors are presented in parentheses below each coefficient. * Significant at better than the 10 percent level. ** Significant at better than the 5 percent level* it * Significant at better than the 2.5 percent level. _ , *** 0.10 -71.37 — 4.28 0.17*** -111.96 (118.17) — ** — Gt Ct A* *** *** 0.16 (0.06) 114 1.6 EiNMI r Ratio Table 5.C Estimated Regression Coefficients for the New Recipient Equations With a four Month Second, Third, and Fourth Degree Polynomial Laga Independent Variables Equation Number Dependent Variable n tj "t- 2.1 2.2 2.3 „ AFDC-R t v AFDC-U z .. GA i AFDC-R •VL 2.5 N AFDC-U t 2.6 n GA t 2.7 2.8 2.9 N AFDC-R v AFDC-U t GA Z ... 28.14 (32.22) -4.44 (5.19) 28.95 (55.42) -4.06 (8.11) -15.46 (11.13) __ 64.16 (62.96) -12.75 (10.18) 123.97** (64.41) 14.58 (15.06) -35.61** (19.55) — -65.78 (113.03) 4.63 (18.30) -49.45 (126.48) 10.30 (28.16) ___ __ -0.04 (0.68) — _— _ * ** -2.99 (1.28) — ___ -0.64 (2.40) N FLFt.i EXBt _i -11.79*** (2.82) -0.15* Significant at better than the 10 percent level. * * Significant at better than the 5 percent level. ** * Significant at better than the 2.5 percent level. FW c t-i G t-1 Ri *** 202.41 (41.44) 15.41 (15.49) 0.84 50.25 741.47 (0.10) *★* 0.65 (0.21) -10.61 (3.15) -0.10 (0.10) *** 0.66 (0.21) *** 195.69 (42.34) 11.75 (14.20) 0.84 25.82 744.37 -10.66*** (3.30) -0.10 0.66 (0.21) 195.23*** 11.88 0.84 21.93 755.52 (0.11) 1.01 (5.80) *** -0.43 (0.19) 4.12 (6.25) 1.06 (6.02 *** (43.66) (14.59) *** 1.84 (0.45) -46.49 (85.22) -1.51 (9.40) 0.51 6.00 1,504.73 *** -0.36 (0.20) *** 1.78 (0.43) -68.43 (86.40) -4.19 (9.58) 0.53 5.44 1,493.89 *** -0.53 (0.20) 1.68*** (0.40) -97.91 (91.13) 0.62 (9.23) 0.57 6.08 1,403.64 0.02 (0.34) — -240.24* (158.06) 81.32* (49.93) 0.36 5.99 2,686.59 (10.66) 14.42 (11.59) -0.01 (0.35) _ _ _ -231.44* (163.85) 83.38* (51.25) 0.36 3.25 2,722.01 13.69 (12.06) -0.04 (0.38) -238.13* (167.97) 83.80* (51.96) 0.36 2.72 2,758.84 15.48* aStandard errors are presented in parentheses below each coefficient. * TRt Standard Error of the Estimate 115 2.4 1.07 (5.55] w 4 t4 C r Ratio Table 5.D Estimated Regression Coefficients for the New Recipient Equations Kith a Five Month Second, Third, and Fourth Degree Polynomial Lag3 Independent Variables Equation Number nrtTVfsrwi fin f ULJJL. 1IU L M L Variable h t2 2.10 .. AFDC-R t w I tj "t4 ____ -0.90 (3.55) 2.11 2.12 AFDC-U t GA t 2.14 2.16 N AFDC-U L AFDC-R Nt AFDC-U 2.17 L GA 2.IS L 26.23 -1.46 (3.68) ** -11.81 (7.08) ____ -0.12 (0.20) *** 0.65 (0.20) *** 191.80 (42.68) *** -10.54 (2.96) -0.11 (0.10) *** 0.66 (0.20) 187.99 -11.34 (3-24) -0.14 (0.11) 1.99 (5.75) 35.46 (38.48) -6.08 ____ 3.85 (5.88) 49.51 (39.51) 0.15 (7.20) ** -20.85 (12.60) — -70.49 (71.17) 6.42 (9.06) -66.70 (74.88) 8.22 (13.20) 1.28 (6.24) Significant at better than the 10 percent level. ** Significant at better than the 5 percent level. * * Jr Significant at better than the 2.S percent level. G t-1 R" 16.45 (13.34) 0.S4 30.26 741.18 11.34 (13.90) 0.85 26,50 736,16 (42.51) *** 0.65 (0.21) ** * 187.11 (42.91) 12.98 (14.26) 0.85 22.83 742.77 * +* -0.47 (0.18) *** 1.82 (0.42) -78.38 (87.83) -0.51 (9.27) 0.52 6.43 1,478.62 *★* -93.40 -1.65 0.55 5.88 1,462.29 (0.19) *** 1.84 (0.42) (87.65) (9.22) *** -0.49 (0.20) + ** 1.89 (0.42) -108.60 (87.95) -2.75 (9.85) 0.57 5.39 1,453.68 -0.39 ... 16.08* (10.85) 0.08 (0.33) — -244.94* (166.24) 80.46* (50.58) 0.35 5.81 2,709.08 _ __ 14.09 (11.28) 0.00 (0.35) ____ -288.44* (169.01) 82.75* (50.84) 0.36 3.21 2,727.99 15.38 (12.03) -0.02 (0.38) __ -251.42* (172.10) 85.13* (53.06) 0.36 2.68 2,766.55 -0.14 (0.74) aStandard errors are presented in parentheses below each coefficient. * E W t-l ** -0.16 (0.09) ____ -0.49 (0.40) TK *** *11.60 (2.84) ____ (4.88) EXBt-l Standard Error of the Estimate _ 116 2.15 -3.12 (2.56) (20.96) AFDC-R 2.13 23.40 (20.29) .VFLFt _i C r Ratio Table 3.E Estimated Regression Coefficients for the New Recipient Equations h'ith a Six Month Second, Third, and Fourth Degree Polynomial Lag3 Independent Variables Equation Number 2.19 Dependent Variable ,, AFDC-R Nt 2.20 „ AFDC-U Nt 2. 21 N GA K 6 t2 -1.44 2.23 ., AFDC-R \ ,, AFDC-U Nt 2.25 2.26 2.2/ s AFDC-R s AFDC-U to -— i K 6 t4 --- NFLFt-l ★ ** -11.36 (2.85) EXB„ _ 1.“ 1 it** TR EWt-l (0.09) *** 0.62 (0.20) *** -10.43 (2.87) -0.11 (0.10) 0.67 (0.20) *** -10.65 (3.13) -0.12 (0.11) 0.67 -0.18 G t-1 R‘ Ratio *** 182.45 16.59 (13.17) 0.84 30.60 737.70 (42.65) *** 184.18 (42.00) 10.00 (13.74) 0.85 27.38 726.09 10.33 0.85 23.29 736.57 (0.20) *** 184.25 (42.60) (14.05) 21.32* (15.76) -2.40* (1.65) --- 22.13* -2.15 (2.09) -0.02 (0.08) ... ... 2.56 (5.75) *** -0.47 (0.18) *** 1.84 (0.41) -95.15 (89.66) 0.39 (9.26) 0.53 6.64 1,465.90 12.05 (30.25) -2.18 (3.16) ... 3.32 (5.90) *** -0.42 (0.19) *** 1.87 (0.42) -99.36 (90.52) 0.18 (9.33) 0.54 5.68 1,477.03 13.32 (32.17) -1.84 -0.02 (0.18) 5.06 (6.29) ** * -0.43 (0.21) *** 1.88 (0.43) -100.92 (92.60) 0.67 0.54 4.83 1,498.85 (10.17) -12.60* (8.44) ... 0.54 3.66 2,727.35 0.56 3.23 2,725.58 0.36 2.75 2,754.58 ** -8.59 (4.63) (4.15) — * ** 0.14 16.40* (11.01) (0.32) ... -241.41* (172.46) 82.00* (50.99) -68.13 (55.26) 5.90 (5.80) ... 14.28 (11.21) -0.00 (0.35) — -252.02* (172.30) * 83.55 (51.01) -59.23 (58.45) 8.29 (7.47) -0.16 (0.31) 12.64 (11.77) -0,06 (0.37) — -240.58* (174.89) 91.11 (53.60) aStandard errors are presented in parentheses below each coefficient. * Significant at better than the 10 percent level. ** Significant at better than the 5 percent level. ** * Significant at better than the 2.5 percent level. 117 2.24 J (2.29) (16.51) 2.22 W Standard Error of the Estimate Table 3.F Estimated Regression Coefficients for the New Recipient Equations Kith a Seven Month Second, Third, and Fourth Degree Polynomial Lag Independent Variabl es Equation Number Dependent Variable W t47 W t2 2.28 ., AFDC-R \ 2.29 AFDC-U Nt 2.30 k\ 2.51 AFX-R Nt .. AFDC-U Nt 2 .33 ., GA \ 2.34 2.35 2.56 ^ AFDC-R .. AFDC-U N tGA — 18.40* (12.96) ★ -1.75 (1-17) 18.66* (13.57) -1.69 (1.40) ... NFLFt _i EXBt _1 -0.49 (0.87) -0.16* (0.10) *** 0.54 (0.24) *** 96.32 (44.31) 13.96 (15.65) 0.85 20.12 874.00 *** -8.50 (2.86) *** -0.10 (0.10) 0.70 (0.21) *** 182.07 (44.84) 6.70 (14.50) 0.84 25.09- 753.37 *** 0.70 (0.21) 182.41 (45.72) 6.77 (14.74) 0.84 21.31 764.62 -108.97* 0.43 (9.28) 0.54 6.61 1,467.65 (82.99) 3.51 1,488.52 *** -1.90 (23.92) -0.36 (2.14) -4,01 (25.23) -0.77 (2.56) ... 3.12 (5.84) -0.45 (0.17) 1.85 (0.41) 3.30 (6.04) *** -0.44 (0.19) *** 1.86 (0.42) -97.91 (92.39) 0.36 (9-42) 0.55 *** **★ 1.86 (0.43) -95.13 (94.10) -0.28 (9.78) 0.53 4.71 1,508.83 — -241.04* (175.71) 82.70* (51.32) 0.33 3.60 2,734.69 0.35 5.18 2,753.13 0.37 2.83 2,740.29 ... 0.02 (0.08) 3.53 (6.17) 17.16* (11.22) 3.98 (3.90) -40.14 (45.53) 6.15* (4.60) ... *4* -0.13 (0.15) 14.77* Significant at better than the 10 percent level. ★ it Significant at better than the 5 percent level. *** Significant at better than the 2.S percent level. -0.42 (0.21) 0.18 (0.31) 0.02 (0.35) — - (11.46) -239.58* (175.61) 83.22* (51.29) 13.75 (11.54) -0.09 (0.37) — -256.94* (177.12) ** 92.48 (52.43) aStandard errors are presented in parentheses below each coefficient. * R2 -0.10 (0.11) -8.29* (5.84) -52.19 (43.42) G t-1 -8.58 (3.08) ** * — EWt-l -0.00 (0.04) * it -5.85 (3.20) TR 118 2.32 -2.54* (1.87) Ratio Standard Error of the Estimate I 1 i Table 3.G Estimated Regression Coefficients for the New Recipient Equations With an Eight Month Second, Third, and Fourth Degree Polynomial Lag Independent Variables Equation Number 2.37 Dependent Variable N AFDC-R 2.38 .. AFDC-U Nt 2.39 „ « 2.40 2.41 .. AFDC-U Nt N ga 2.43 .. AFDC-R Nt 2.44 AFDC-U Nt 2.45 GA Nt -1.24 (1.14) — 15.90* (10.03) ** 1.34 (0.79) 15.56* (10.31) -1.44* (0.92) 0.19 (1.47) -7.28 (19.30) -0.11 (1.75) Ratio 14.84 (13.02) 0.84 31.42 729.56 181.70** (44.39) 5.26 (14.67) 0.84 26.08 741.29 *** 0.69 (0.21) ** # 180.09 (45.67) 3.56 (14.95) 0.84 22.18 751.58 *** 0.43 (0.17) *** 1.82 (0.42) -90.31 (91.66) -0.26 (9.29) 0.53 6.45 1,477.27 *** -0.44 (0.19) 1.82 (0.43) -91.24 -0.12 (9.49) 0.53 5.38 1,498.52 (93.31) -92.90 (94.71) -0.01 (9.62) 0.53 4.59 1,518.65 EXBt-l --- *** '10.69 (2.92) ** * -0.19 (0.08) *** 0.60 (0.20) *** 171.87 (41.86) --- *«* -7.94 (2.87) -0.10 (0.10) • *»* 0.68 (0.21) *** -7.88 (2.92) -0.10 (0.10) 3.51 (5.99) 0.00 (0.02) +* -3.95 (2.34) -6.35 (18.84) 7 R" — 3.33 (6-21) *** -6.01* (4.21) TRt NFLFt-l 0.01 (0.04) 3.23 (6.50) -0.42 (0.20) EWt-l G t-1 *** *** 1.86 (0.45) — 17.97* (11.39) 0.19 (0.31) — -241.37* (175.40) 80.42* (51.00) 0.33 3.61 2,733.84 -38.59 (33.89) 2.58 (2.66) --- 15.49* (11.68) 0.04 (0.34) — -251.26* (175.85) 81.85* (51.07) 0.35 3.16 2,736.17 -35.15 (34.69) 3.52 -0.04 (0.07) 15.79* (11.80) -0.03 (0.37) --- -251.77* (177.49) 82.95* (51.58) 0.36 2.71 2,761.66 (3.11) aStandard errors are presented in parentheses below each coefficient. * Significant at better than the 10 percent level. * * Significant at better than the S percent level. #* * Significant at better than the 2.5 percent level. 119 2.42 ., AFDC-R w 8 t4 Standard Error of the Estimate 120 Table 3.H Correlation Matrix for Equation (3.4), Terminations from AFDC-R Tt 1.000 EWt (WSEt)(EWt) NFLFt 0.750 0.778 0.731 0.753 0.835 0.767 1.000 0.995 0.947 0.991 0.945 0.996 1.000 0.947 0.906 0.972 0.999 1.000 0.948 0.907 0.948 1.000 0.951 0.998 1.000 0.966 WSEt Ct Gt 1.000 Table 3.1 Correlation Matrix for Equation (3.5), Terminations from AFDC-U Tt 1.000 WSEt EWt (WSEt)(EWt) NFLFt 0.326 0.346 0.345 0.330 0.658 0.274 1.000 0.995 0.996 0.997 0.707 0.994 1.000 0.997 0.996 0.757 0.994 1.000 0.997 0.749 0.995 1.000 0.719 0.994 1.000 0.696 Ct Gt 1.000 121 Table 3.J Correlation Matrix for Equation (3.6), Terminations from GA Tt 1.000 ENMIt EWt 0.971 0.978 0.978 0.970 0.979 0.974 1.000 0.997 0.996 0.995 0.962 0.997 1.000 0.995 0.996 0.977 0.997 1.000 0.994 0.978 0.996 1.000 0.960 0.996 1.000 0.968 (ENMIt)(EWt) NFLFt ct Gt 1.000 Table 3.K Correlation Matrix for Equation (3.7a), New Recipient to AFDC-R N t 1.000 IV t NFLF. . t-1 EXB. , t-1 TR^ t EW. . t-1 G. . t-1 -0.807 0.265 0.680 0.771 0.839 0.748 1.000 -0.260 -0.884 -0.758 -0.892 -0.779 1.000 0.315 0.284 0.400 0.385 1.000 0.719 0.804 0.752 1.000 0.751 0.711 1.000 0.822 1.000 122 Table 3.L Correlation Matrix for Equation (3.8a), New Recipients to AFDC-U Nt 1.000 wt NFLFt l EXBt l TRt EWt-l Gt-1 -0.408 0.297 0.252 0.632 0.361 -0.081 1.000 -0.530 0.884 -0.758 -0.892 -0.246 1.000 0.481 0.532 0.709 0.192 1.000 0.719 0.804 0.247 1.000 0.751 0.064 1.000 0.385 1.000 Table 3.M Correlation Matrix for Equation (3. 9a), New Recipients to GA Nt 1.000 wt NFLFt-l EXBt-l EWt-l T t-1 -0.528 0.373 0.486 0.459 0.399 1.000 -0.549 -0.901 -0.892 -0.541 1.000 0.481 0.709 0.319 1.000 0.804 0.492 1.000 0.649 1.000