THREE ESSAYS ON HUMAN CAPITAL AND LABOR SUPPLY

By

Cody Taylor Orr

A DISSERTATION

Submitted to

Michigan State University

in partial fulﬁllment of the requirements

for the degree of

Economics – Doctor of Philosophy

2021

ABSTRACT

THREE ESSAYS ON HUMAN CAPITAL AND LABOR SUPPLY

By

Cody Taylor Orr

This dissertation contains three chapters that study individuals’ willingness to work, factors

that inﬂuence their human capital development, and the interaction between their human capital

investment decisions and labor supply.

Chapter one examines how college students choose their credit hour enrollment, labor supply,

and borrowing, paying particular attention to the role of wages, ﬁnancial resources and beliefs.

To formalize these relationships, I construct a dynamic structural model where students choose

their credit hours, work hours, and borrowing to maximize lifetime utility. I collect data from

two sources to estimate the model: (1) a unique survey of Michigan State undergraduates eliciting

their employment history, family ﬁnancial support, beliefs about the returns to studying and be-

liefs about earning a high GPA, and (2) administrative data from the University. Estimates of the

model suggest that students’ credit hour decision is inelastic with respect to changes in ﬁnancial

aid, tuition, beliefs, or wages. Students’ labor supply and borrowing decisions are responsive to

changes in wages, and for a subset of students, changes in beliefs. I also conduct two counterfac-

tual simulations, increasing the minimum wage and making college tuition free, and evaluate how

these policy changes affect student decisions and outcomes.

The second chapter studies the relationship between the gender composition of a student’s

peers and two of their non-cognitive factors: sense of belonging and self-worth. Using data from

Add Health and exploiting idiosyncratic variation in the share of female peers across grades within

schools, I ﬁnd positive but small effects of a higher share of female peers for male students. I do

not ﬁnd statistically signiﬁcant effects for female students, but I can rule out large positive effects.

The third chapter, jointly written with Todd Elder and Steven J. Haider, estimates how the wage

elasticity of labor supply has changed for single and married men and women over the last two

decades. The wage elasticity of labor supply is arguably one of the most fundamental parameters

in economics, but despite the central role of this parameter, few studies have examined how it has

evolved past the early 2000s. We ﬁnd robust evidence that the labor supply elasticities for all four

demographic groups have increased modestly. For women, this ﬁnding is a substantial departure

from earlier evidence. We also contribute to the literature on the robustness of discrete choice

labor supply models by estimating elasticities under a variety of assumptions and speciﬁcations.

Our estimated trends are remarkably similar across speciﬁcations.

ACKNOWLEDGMENTS

This dissertation is the result of much guidance and support from my advisors, colleagues, and

friends. I would like to speciﬁcally acknowledge the contributions of the following individuals for

their role in helping this dissertation come to completion:

My dissertation chair, Steven Haider, who mentored me as a scientist and instructor, challenged

me to be the best I could be, and always made time to meet with me and discuss my research.

Steven was also a consistent advocate for me and my career, seeking opportunities for me to grow

as a researcher and helping me secure funding for my work.

My dissertation committee members, Scott Imberman, Michael Conlin, and Kris Renn, and

other faculty in the Economics Department at MSU, including Jeffrey Wooldridge, Todd Elder,

and Justin Kirkpatrick, who generously gave their time to review drafts of individual chapters,

provide extensive feedback, and help me become a more adept researcher.

My classmates, Dylan Brewer, Riley Acton, and Luke Watson, who never hesitated to help me

think through a challenging research question, share MATLAB and Stata code, sit in my practice

presentations, and read drafts of my work.

Administrators and staff at MSU, including Mark Largent, Karen Clark, Dean Valenti, Justin

Bruner, and Jim Murphy, who volunteered their time and resources to help me design and distribute

the Student Enrollment and Employment Survey and utilize university administrative records.

My parents, Don and Joni Orr, who raised me to have the curiosity and persistence necessary

to pursue a doctorate and made signiﬁcant sacriﬁces so I could receive a great education.

My family, Ed and Elyse Streit, Fred and Marla Meldrum, and Ginger and Sheridan Rampaul,

who never hesitated to give me good company and a place to stay when I wanted a break.

My friends, both old and new, who kept me sane and in good spirits: Matt and Meredith

Bateman, Kat Davis, Rachel Rosenberg, Matt Harding, Dylan and Amanda Brewer, Riley, Luke,

Alyssa Harben, Gabrielle Pepin, Bryce VanderBerg, Hannah Gabriel, and Nick Rowe.

Most importantly, my wife Miriam, who celebrated all my accomplishments as if they were

iv

her own, was patient and understanding when I worked long nights, taught me the ins and outs of

post-secondary ﬁnancial aid regulations and procedures, and made countless sacriﬁces so I could

pursue this goal.

v

TABLE OF CONTENTS

LIST OF TABLES .

LIST OF FIGURES .

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CHAPTER 1 CLOCKING INTO WORK AND OUT OF CLASS: COLLEGE STU-
DENT ENROLLMENT, LABOR SUPPLY, AND BORROWING DECI-
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1.3 Data .

Introduction .

1.4 Structural model .

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1.4.1 Model structure .

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1.2 Related literature .

1.2.1 Credit hour enrollment
1.2.2 Labor supply .
1.2.3

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Structural models of enrollment and employment
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1.3.1
Sampling frame and survey distribution . . . . . . . . . . . . . . . . . . .
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1.3.2 Observed credit hour enrollment and ﬁnancing choices . . . . . . . . . . .
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1.3.3 Cost of attendance and ﬁnancial need . . . . . . . . . . . . . . . . . . . . 10
Subjective expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.4
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1.4.1.1 Decision periods . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1.2 Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
State variables
1.4.1.3
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1.4.1.4
Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.1.5 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.1.6 Grades
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1.4.1.7 Maximization problem . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.2
Solution method .
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1.4.3 Model parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.4 Criterion function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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1.5.1 Auxiliary model estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.5.2
Structural model estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.3 Elasticities .
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1.5.4 Counterfactual simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.5.4.1 Minimum wage increase . . . . . . . . . . . . . . . . . . . . . . 30
1.5.4.2
Free in-state tuition . . . . . . . . . . . . . . . . . . . . . . . . . 31
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1.6 Conclusion .

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1.5 Results .

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CHAPTER 2 PEER GENDER COMPOSITION AND NON-COGNITIVE OUTCOMES . 35
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2.1 Disclaimer .
2.2

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Introduction .

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2.3 Data .
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2.4 Empirical strategy .
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CHAPTER 3 THE EVOLUTION OF THE WAGE ELASTICITY OF LABOR SUP-

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PLY OVER TIME .

3.4 Empirical methods

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Introduction .

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3.1 Disclaimer .
3.2
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3.3 Background and literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 The key elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.2 Why might elasticities vary over time? . . . . . . . . . . . . . . . . . . . . 45
3.3.3 Evidence on trends in labor supply elasticities . . . . . . . . . . . . . . . . 46
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4.1 A static discrete choice model of labor supply . . . . . . . . . . . . . . . . 48
3.4.2 Estimating the elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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3.6.1 Baseline results .
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3.6.2 Robustness to alternative utility function assumptions . . . . . . . . . . . . 56
3.6.3 Measurement error in wages . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6.4 Other elasticities
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3.7 Conclusion and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5 Data .
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APPENDICES .

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APPENDIX A CHAPTER 1 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . 63
APPENDIX B CHAPTER 2 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . 89
APPENDIX C CHAPTER 3 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . 101

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BIBLIOGRAPHY .

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vii

LIST OF TABLES

Table A.1.1

Summary Statistics for SEES Respondents and Recipients

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Table A.1.2 Credit Hour Enrollment by Semester . . . . . . . . . . . . . . . . . . . . 69

Table A.1.3

Expected Schoolwork Hours . . . . . . . . . . . . . . . . . . . . . . .

. 70

Table A.1.4 Data and Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 71

Table A.1.5 Auxiliary Model Parameters

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Table A.1.6

Structural Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . 73

Table A.1.7 Observed and Predicted Choice Probabilities . . . . . . . . . . . . . . .

. 74

Table A.1.8

Elasticities (Fall and Spring)

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Table A.1.9

Elasticities (Summer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Table A.1.10 Elasticity Heterogeneity (Fall and Spring)

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. 77

Table A.1.11 Counterfactual Simulation Results . . . . . . . . . . . . . . . . . . . . . 78

Table A.2.1

Predicting Wages for Non-Workers . . . . . . . . . . . . . . . . . . . . . 80

Table A.3.1

Family Financial Support: Education Expenses

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Table A.3.2

Family Financial Support: Living Expenses

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Table A.4.1 Michigan State and Peer Institutions . . . . . . . . . . . . . . . . . . .

. 88

Table B.1.1 Add Health Descriptive Statistics . . . . . . . . . . . . . . . . . . . . .

. 93

Table B.1.2 Non-Cognitive Factors (Count “Agree” or “Strongly Agree”) . . . . . .

. 94

Table B.1.3

Balance of Share Female on Control Variables . . . . . . . . . . . . . .

. 95

Table B.1.4

Baseline Regression Estimates . . . . . . . . . . . . . . . . . . . . . .

. 96

Table B.1.5

Regression Estimates without Controls . . . . . . . . . . . . . . . . . . . 97

Table B.1.6

Regression Estimates with Average Numerical Response . . . . . . . . . 98

viii

Table B.1.7 Disaggregated Regression Estimates for Each Non-Cognitive Factor

. . . 99

Table B.1.8

Regression Estimates Accounting for Measurement Error . . . . . . . . . 100

Table C.1.1 Distribution of Work Hours . . . . . . . . . . . . . . . . . . . . . . . . . 107

Table C.1.2

Baseline Model Elasticities for Select Years, Single Men and Women . . . 108

Table C.1.3

Baseline Model Elasticities for Select Years, Married Men and Women . . 109

Table C.2.1 Descriptive Statistics, Single Men and Women . . . . . . . . . . . . . . . 112

Table C.2.2 Descriptive Statistics, Married Men and Women . . . . . . . . . . . . . . 113

Table C.2.3 Heckman Selection Wage Model, Men . . . . . . . . . . . . . . . . . . . 114

Table C.2.4 Heckman Selection Wage Model, Women . . . . . . . . . . . . . . . .

. 116

Table C.4.1

Baseline Model Parameter Estimates, Single Men . . . . . . . . . . . .

. 120

Table C.4.2

Baseline Model Parameter Estimates, Single Women . . . . . . . . . . . 121

Table C.4.3

Baseline Model Parameter Estimates, Married Men and Women . . . .

. 122

ix

LIST OF FIGURES

Figure A.1.1 Distribution of Work Hours . . . . . . . . . . . . . . . . . . . . . . . . . 63

Figure A.1.2 Distribution of Borrowing Amounts

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Figure A.1.3 Grants and Family Support by Unmet Need Quintile . . . . . . . . . . . . 65

Figure A.1.4 Distribution of Expected Grades Conditional on Schoolwork . . . . . .

. 66

Figure A.1.5 Distribution of Expected Salaries Conditional on GPA . . . . . . . . . . . 67

Figure A.4.1 Expected Schoolwork Time Sample Question . . . . . . . . . . . . . . . 84

Figure A.4.2 Grade Distribution Sample Question . . . . . . . . . . . . . . . . . . .

. 85

Figure A.4.3 Distribution of Grades Conditional on Schoolwork . . . . . . . . . . . . 86

Figure A.4.4 Distribution of Salaries Conditional on GPA . . . . . . . . . . . . . . . . 87

Figure B.1.1 Distribution of Responses for Non-Cognitive Questions . . . . . . . . . . 89

Figure B.1.2 Distribution of Afﬁrmative Responses

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Figure B.1.3 Distribution of Average Numerical Responses . . . . . . . . . . . . . . . 91

Figure B.1.4 In-School Questionnaire Response Rates . . . . . . . . . . . . . . . . . . 92

Figure C.1.1 Labor Force Trends by Demographic Group . . . . . . . . . . . . . . . . 101

Figure C.1.2 Mean Own-Wage Elasticities, Baseline Estimates (1994-2017) versus

Estimates with No Beneﬁt Simulator (1979-2017) . . . . . . . . . . . .

. 102

Figure C.1.3 Mean Own-Wage Elasticities, Baseline Estimates versus Estimates from

Random-Slope Logit Model

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Figure C.1.4 Mean Own-Wage Elasticities, Baseline Estimates versus Estimates with

Different Treatments for Measurement Error . . . . . . . . . . . . . . . . 104

Figure C.1.5 Mean Own-Wage Elasticities Decomposed by Extensive and Intensive

Margins .

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Figure C.1.6 Mean Marshallian, Cross-Wage, Hicksian, and Income Elasticities . . . . 106

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Figure C.5.1 Mean Own-Wage Elasticities, Baseline Estimates versus Estimates from

Quadratic Utility Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xi

CHAPTER 1

CLOCKING INTO WORK AND OUT OF CLASS: COLLEGE STUDENT

ENROLLMENT, LABOR SUPPLY, AND BORROWING DECISIONS

1.1 Introduction

Post-secondary education yields signiﬁcant returns in the labor market (Oreopoulos and Petron-

ijevic 2013; Carneiro et al. 2011; Hussey and Swinton 2011). Nevertheless, there are many factors

that prevent a college enrollee from realizing the full return of a college degree. A third of students

who begin college will leave without earning a bachelor’s degree, thus incurring the direct ﬁnan-

cial and opportunity costs of college without the return to graduating (Shapiro et al. 2019). Even

among students that eventually complete their degree, their college’s quality (Black and Smith

2006), major ﬁeld of study (Altonji et al. 2012), cumulative grade point average upon graduation

(Hershbein 2019), cumulative credit hours (Arteaga 2018), net cost of attendance, level of student

loans, and time-to-degree (Dannenberg and Mugglestone 2017) can all alter the value of their in-

vestment. Recent research also highlights the non-monetary returns to attending college, which

can be diminished if students lack the leisure time to take advantage of their college’s amenities

(Jacob et al. 2018; Gong et al. 2019).

Many of the beneﬁts and costs to college are intrinsically linked to the student’s enrollment

intensity, time allocation and ﬁnancing decisions. The more classes a student takes, the quicker

she can complete her degree, reducing the direct costs of tuition, the opportunity costs of foregone

wages, and the likelihood that an unexpected life event necessitates her departure from college

(Belﬁeld et al. 2016; Attewell and Monaghan 2016). However, unless the student increases her

total time spent on schoolwork to maintain a similar level of effort across those additional classes,

her grades can suffer, increasing the likelihood of failing a course, delaying her time to graduation,

and adversely affecting prospective employers’ perceptions of her ability. Spending more time

on schoolwork carries a cost as well, reducing the time available for work and time available

1

for leisure. These complex tradeoffs make it difﬁcult to understand students’ behavior or predict

the effects of policies designed to improve student welfare, like reducing the cost of tuition or

increasing students’ wages.

This chapter studies how students navigate these tradeoffs to maximize their lifetime utility,

paying particular attention to the role of ﬁnancial resources and individuals beliefs. Unfortunately,

information on resources, such as family ﬁnancial support, and beliefs, such as expected returns

to studying, are not readily available in administrative data. To measure such factors, I developed

a survey that elicits students’ employment history, wages, family ﬁnancial support, and subjective

expectations on study hours, the returns to studying and returns to graduating with a high GPA.

After distributing my survey to a random sample of undergraduates at Michigan State Univer-

sity, I obtained administrative records from the University’s Ofﬁce of the Registrar and Ofﬁce of

Financial Aid containing students’ course history at MSU, ﬁnancial aid eligibility by term, and

borrowing history.

To analyze the data, I construct a dynamic model of student behavior. Students choose their

credit hour enrollment, labor supply, studying, and borrowing to maximize their lifetime utility

subject to time and consumption budget constraints. The model incorporates important features

of the college decision-making environment, including students facing borrowing constraints, re-

ceiving ﬁnancial support from their family, earning grades for their classes, and having individual-

speciﬁc beliefs about the returns to studying and returns to graduating with a high GPA. The

dynamics of the model also capture two important intertemporal tradeoffs. The choices of a stu-

dent in one period affects her behavior in future in-school periods (e.g., if a student takes a small

number of credit hours early in her tenure at college, she will need to make up for it with more

credit hours later). Additionally, students’ choices in college affect their future earnings and debt

obligations post-college.

The structural model allows me to estimate students’ preferences over in-school consumption,

leisure, grades, future earnings, and cumulative debt. I then derive individual-speciﬁc elasticities

for credit hour enrollment, labor supply, and borrowing with respect to changes in ﬁnancial aid,

2

tuition, beliefs, and wages. I ﬁnd that students’ credit hour enrollment is largely unresponsive to

changes in these variables. The labor supply decision, on the other hand, is much more responsive

with an average wage elasticity of 0.29 in the fall and spring semesters. This is similar to the wage

elasticity for working-age married women in the United States (McClelland and Mok 2012). Labor

supply is also responsive to beliefs about the returns to studying and returns to graduating with a

high GPA, speciﬁcally among students who expect they would substitute their work time for more

study time. Students’ borrowing choices are most responsive to changes in ﬁnancial aid and the

university’s tuition rate.

With the model estimates in hand, I simulate the effects of two policies which increase the

affordability of college but alter students’ incentives in very different ways: an increase in the

minimum wage to $15 per hour and making in-state tuition free for current students. An increase

in the minimum wage increases work hours by 0.75 hours a week in the fall and spring and by

1.14 hours a week in the summer. To a lesser extent students decrease their borrowing, and I do

not ﬁnd any signiﬁcant changes in credit hours or expected GPA. Free in-state tuition increases

credit hours by 0.09 hours in the fall and spring, which is not a large enough change to appreciably

decrease time-to-degree. While there are only minimal changes in work hours, average borrowing

decreases by $2,107 per year. As with the increase in minimum wage, making in-state tuition free

does not signiﬁcantly change expected GPA.

This chapter makes several contributions. It develops an estimable model that emphasizes the

credit hour decision and relationship between credits, grades, and future earnings. This is one of

the ﬁrst papers to propose such a structural model of the credit hour decision beyond the part-time

and full-time margins. This paper also contributes to the literature by estimating labor supply elas-

ticities speciﬁcally for college students. I pay particular attention to the unique ﬁnancial resources

and constraints students face and explicitly model the additional cost of labor on expected grades

and credit accumulation. Finally, this paper adds to the growing literature on dynamic discrete

choice estimation that incorporates subjective expectations, and it is the ﬁrst to do so with expec-

tations of the GPA returns to studying and labor market returns to graduating with a high GPA.

3

The standard approach to estimating dynamic models requires estimating laws of motion of state

variables from panel data, assuming heterogeneity in the process is fully captured by observable

characteristics of individuals, and imposing individuals’ expectations of the future match the pre-

dicted laws of motion (Aguirregabiria and Mira 2010). Eliciting subjective expectations allows one

to directly incorporate heterogeneity in beliefs. Furthermore, subjective expectations are required

to separately identify the role of preferences from beliefs, an important distinction for this research

(Manski 1993).

The chapter proceeds as follows. In Section 2, I summarize the existing literature on college

student credit hour enrollment intensity and labor supply. In Section 3, I introduce my data and

describe the sample. Section 4 details the structural model and my estimation procedure. Section 5

presents the estimated auxiliary model parameters, utility parameters, elasticities, and results from

counterfactual simulations. Section 6 concludes.

1.2 Related literature

1.2.1 Credit hour enrollment

The vast majority of research on college student credit hour enrollment uses reduced form

methods to estimate how changes in ﬁnancial aid affect student outcomes. For example, several

recent papers exploit discontinuities in students’ eligibility for need-based aid and ﬁnd small or

null effects on credit hours (Angrist et al. 2020; Denning et al. 2019; Denning and Jones 2019;

Denning 2019). When effects are present, they seem to be explained by changes in labor supply.

Most of this evidence is based on students from lower income households who qualify or are close

to qualifying for need-based aid, so it is unclear how students from more afﬂuent households might

respond to changes in aid.

Another potential determinant of credit hour enrollment is the price per credit hour. In one of

the few studies on the topic, Hemelt and Stange (2016) ﬁnd that students who face no marginal

cost to credit hours above the full-time minimum are seven percentage points more likely to enroll

in one to three credit hours above the full-time minimum, but they are also six percentage points

4

more likely to withdraw from a class during the semester, leading to no signiﬁcant increase in

credit attainment. This suggests that students are willing to experiment with taking more classes

when the monetary cost of doing so is low, but other factors make it difﬁcult to persist with heavier

schedules.

While it appears that students’ credit hour decision on the intensive margin is not signiﬁcantly

affected by their ﬁnancial resources, there is evidence that students respond to direct ﬁnancial

incentives to take more classes. These incentives come in the form of state or institutional aid

where students are required to complete 30 credit hours per year to renew their aid eligibility.

Miller et al. (2011) and Scott-Clayton (2011) both ﬁnd signiﬁcant increases in the probability that

students take 15 credit hours a semester when offered ﬁnancial aid with a credit hour requirement.

Even small monetary incentives can induce this behavior as Miller et al. (2011) ﬁnd in a study

evaluating a grant of only $1,000 per year.

1.2.2 Labor supply

Student labor supply has increased over the last half-century, mostly among students at four-

year colleges, on both the extensive and intensive margins (Bound et al. 2012; Scott-Clayton 2012).

Currently, 42% of full-time undergraduates work during the fall semester, up from 33% in the
1970s.1 Students work an average of 25 hours per week across the year. These changes in labor

are not inconsequential. The literature frequently ﬁnds that student labor supply decreases study

time, education enrollment, educational attainment, and to a lesser extent, grades. See the recent

literature review by Neyt et al. (2019) for more details.

Despite the frequency and ramiﬁcations of student employment, there is very little research on

wage elasticities for college students; in fact, many researchers that estimate labor supply elastici-

ties remove students from their sample to focus exclusively on prime-age workers. For examples,

see literature reviews by Bargain and Peichl (2016) and McClelland and Mok (2012). Elasticities

1Current results based on the author’s own calculations using the October Education Supple-
ment of the CPS for 2017 and 2018. These rates are similar to those reported by Scott-Clayton
2012, which end in 2009.

5

for students may differ from elasticities for non-students due to the added costs of working while

in school (e.g., fewer credit hours, lower grades) and the added need for money to pay for tuition.

Studies on the effects of increased ﬁnancial aid provide estimates of the relationship between

non-labor income and labor supply. Exploiting a discontinuity in ﬁnancial aid eligibility based

on age, Denning (2019) estimates that a $1,452 increase in ﬁnancial aid per year leads to a $511

reduction in labor market earnings per year. Broton et al. (2016) use random assignment of the

Wisconsin Scholars Grant, an award of $3,500 a year, and ﬁnd work hours decrease by 1.69 hour

per week, which is 14.35% of the mean. Studying an even larger grant, DesJardins et al. (2010)

estimate that receiving the $8,000 per year Gates Millennium Scholar award reduces labor supply

by 4.2 to 4.3 hours per week. Not surprisingly, larger grants appear to reduce labor supply by more

than smaller grants.

1.2.3 Structural models of enrollment and employment

Much of the literature on human capital investment and labor supply treats schooling and labor

as mutually exclusive actions (e.g., Arcidiacono 2004; Keane and Wolpin 1997; Altonji 1993).

When models allow individuals to work and enroll in school simultaneously, they typically do not

allow individuals to choose the intensity of their schooling (Joensen 2009; Ehrenberg and Sher-

man 1987). There are a few notable exceptions where researchers have modeled both the extensive

and intensive schooling and labor supply decisions. Gayle (2006) provides a ﬁnite-horizon model

where young adults (14 to 21 year olds) choose their schooling (enrollment and intensity), leisure,

and labor supply. Gayle documents inequalities in labor supply, intensity of schooling, and grade

progression by race. He then simulates the effect of a lump-sum transfer conditional on not work-

ing and ﬁnds minimal effects on labor supply or grade progression. Keane and Wolpin (2001)

provide a ﬁnite-horizon model where agents choose school attendance, work participation, and

borrowing. School attendance is restricted to no attendance, part-time, or full-time. Keane and

Wolpin pay particular attention to the role of family ﬁnancial support and borrowing constraints;

they conclude that family ﬁnancial support is a signiﬁcant determinant of part-time or full-time

6

attendance, but relaxing borrowing constraints only affects labor supply and consumption, not

attendance.

1.3 Data

For this chapter I use data from the Student Enrollment and Employment Survey (SEES), a

survey I developed and distributed to a random sample of undergraduates at Michigan State Uni-

versity in the spring of 2019. I also obtained administrative records from the Ofﬁce of the Registrar

and Ofﬁce of Financial Aid at the University for the SEES respondents, providing a detailed pic-

ture of students’ decisions and ﬁnancial resources. Together, the data contain students’ credit hour,

labor supply, and borrowing histories for their entire enrollment at MSU. In addition, they contain

students’ wages (expected wages for non-workers), cost of attendance, loan eligibility, grants and

scholarships, living situation, rent, and family ﬁnancial support for education and living expenses.

The data also contain students’ expected study hours conditional on credit hour and work sched-

ules, beliefs about the returns to studying on GPA, and beliefs about the returns to graduating with

a high GPA on future labor market earnings.

This section describes the sampling frame and presents summary statistics for particular vari-

ables of interest. A full text of the survey is available online.

1.3.1 Sampling frame and survey distribution

Michigan State University is a large, public research university in the United States.2 All MSU

undergraduate students who were 18 years old or older, were not on an athletic scholarship, and

had an expected graduation date of December 2019 or later were eligible to receive the SEES.

The Ofﬁce of the Registrar provided me with 6,000 randomly selected email addresses from this

sampling frame, and I emailed an invitation to take the survey to these students on March 12,

2019. Students were told the survey would take between 15 and 35 minutes to complete, and they

2Appendix table A.4.1 contains summary statistics for the MSU undergraduate population and

population of undergraduate students at other public four-year-degree-granting institutions.

7

would receive a $10 Amazon Gift Card upon completion. After two reminder emails, I closed the

survey on April 23, 2019 with 1,665 partial and complete responses. I restrict my analytic sample

to continuously enrolled domestic ﬁrst-time-in-college students who successfully completed the
survey.3 After these restrictions, I am left with 985 students and 2,943 student-period pairs (1,964

fall and spring and 979 summer).

Table A.1.1 presents summary statistics for the analytic sample and survey recipients. The

sample of respondents is more likely to be female, white (non-Hispanic) or Asian, in-state, and in

the honors college than the broader sample of domestic ﬁrst-time-in-college students who received

the survey invitation.

1.3.2 Observed credit hour enrollment and ﬁnancing choices

The Ofﬁce of the Registrar provided students’ credit hour enrollment by term. Table A.1.2

presents the proportion of students who enrolled in varying credit hour amounts. In the fall and

spring, almost half of students enrolled in 27 to 29 credits, and 95% of students enrolled in 24 to 32

credit hours. In the summer, 62% of students did not enroll in any credits, and among students who

did enroll, 40% took three to ﬁve credits and 42% took six to eight credits. Notably, many students

may not be enrolled in enough credits to graduate within four years of starting at MSU. Without

any transfer credits, the typical student needs to complete at least 120 credit hours to graduate, or

30 credits per year over four years. As shown in the last column of Table A.1.2, 46% of students

enroll in fewer than 30 credits across the entire year.

3I limit the sample to domestic ﬁrst-time-in-college students, as international students (54) face
additional restrictions on their employment and borrowing and transfer students have unobserved
credit enrollment and borrowing histories from their prior institutions (296). I further restrict the
sample to students who were continuously enrolled at least part-time at MSU for the fall and spring
semesters, as students who temporarily “stop-out” (55) may do so for reasons that are outside of
the scope of this research, like serious illness, family emergencies, or having a child. I also exclude
students who failed to reach the end of the survey (87), failed the attention check question (75), or
skipped a question required to estimate the model (64). Finally, I exclude students who believe their
grades will decrease as they increase their time on schoolwork (23) or believe their future wage
will be lower after graduating with a 4.0 GPA as opposed to dropping out (26), as this strongly
suggests that the student did not properly understand the questions.

8

The SEES asked students to identify semesters they worked a part-time or full-time job, and if

they worked, how many hours they usually worked per week. Students were equally likely to work

during the fall and spring or summer terms – 52% of students worked at least one hour per week

in the fall and spring and 51% of students worked at least one hour per week in the summer – but

they did not work the same number of hours across terms. Student workers worked an average of

12 hours per week in the fall and spring term, while workers worked an average of 33 hours per

week in the summer term. As shown in Figure A.1.1, the modal number of hours worked per week

in the fall and spring was ten, though eight and 15 hours were also common. In the summer, 40

hours per week was the modal choice by a large margin.

The Ofﬁce of Financial Aid provided students’ borrowing history by term. Each year, students

receive a ﬁnancial aid offer that includes their subsidized and unsubsidized loan offers (collectively,

Stafford loans). Stafford loan limits are set by the federal government, ranging from $5,500 for

dependent freshmen to $12,500 for independent juniors and seniors, and students cannot receive

more in Stafford loans than their budget (expected cost of attendance minus non-loan ﬁnancial aid)

allows. In the fall and spring, 85% of students were eligible for Stafford loans, and 48% of students

accepted at least some non-zero loan amount. In the summer, only 23% were eligible for Stafford

loans, and only 9% borrowed some non-zero loan amount. This is not surprising – students must

be enrolled in at least six credit hours to be eligible for Stafford loans.

Students do not need to accept the full Stafford loan offer, though in the fall and spring only

8% of borrowers accept less. If students want to borrow beyond their Stafford loan offer, they

must apply for loans from private vendors. As with Stafford loans, students cannot take out more

private student loans than their budget allows, though the credit hour requirement may be lower

than the six credits required for Stafford loans. In the fall and spring, 17% of students accepted

private loans, and in the summer, 3% of students accepted private loans. Figure A.1.2 presents the

distribution of accepted student loan amounts.

9

1.3.3 Cost of attendance and ﬁnancial need

A student’s cost of attendance is the estimated amount of the money she will spend to attend

the university for a year. There are four broad components of cost of attendance: tuition, books,

fees, and living expenses. In my sample, the average fall-spring cost of attendance was $28,359
for an in-state student and $52,728 for an out-of-state student.4 Students have two main sources

of funding to cover their cost of attendance that does not require them to work or borrow: grants
and family ﬁnancial support.5 In the fall and spring, the average in-state student received $6,076

in grants and $15,956 in family ﬁnancial support, leaving $6,328 of unmet ﬁnancial need. The

average out-of-state received $16,608 in grants and $30,614 in family ﬁnancial support, leaving

only $5,505 of unmet ﬁnancial need.

Averages hide signiﬁcant heterogeneity across students as Figure A.1.3 shows. Each panel

presents the average amount of grant aid and family ﬁnancial support received by students in dif-

ferent quintiles of the unmet need distribution. For both in-state and out-of-state students, students

in the bottom two quintiles received enough aid and support to cover their cost of attendance. At

the other extreme, students in the highest quintile of unmet need required $21,364 (in-state) or

$35,557 (out-of-state) of additional income or loans to cover their expected costs.

1.3.4 Subjective expectations

The SEES contains three sets of subjective expectations: students’ beliefs of their time spent

on schoolwork conditional on work and credit hour enrollment, their distribution of class grades

conditional on schoolwork hours, and their distribution of post-school salaries conditional on GPA.

4For all years in my sample, MSU charged students tuition per credit hour attempted. Rates
varied by the student’s residence (i.e., in-state or out-of-state), independent status, college, and
class level. An in-state ﬁrst-year student, without any additional tuition modiﬁers, paid $14,640
for 30 credit hours; a similar out-of-state student paid $39,766. In addition to tuition, students
purchase textbooks and other supplies which the University budgets at 7% of the base per-credit
rate. Some students also paid program fees, ranging from $100 to $670 a semester depending on
their college. Expected living expenses ranged from $11,122 to $14,320 and included room and
board and smaller miscellaneous expenses.

5See Appendix Section A.3 for details on how the SEES measured family ﬁnancial support.

10

To elicit beliefs about time spent on schoolwork, I showed students six work hour and credit

hour schedules (e.g., working ten hours per week while enrolled in 15 credit hours) and asked them

how many hours they expect to spend on schoolwork during a typical non-exam week. Students

were instructed to include class attendance, completing assignments, and reviewing notes within

“schoolwork”, and they were given attention check questions to verify they understood what “time

spent on schoolwork” should include. Appendix Figure A.4.1 contains an example of what students

were given for one schedule, and Table A.1.3 presents the distribution of expected schoolwork

hours for all six schedules.

At 12 credit hours and no work hours, the average student expects to spend 21.98 hours on

schoolwork in a typical week. Students substitute schoolwork time for work time, as the average

expected time on schoolwork decreases to 18.48 hours with 20 hours of work. Students also expect

to spend less time on schoolwork per credit as they take more credits, as the average expected time

on schoolwork increases from 21.98 hours (1.83 per credit) to 27.71 hours (1.54 per credit) when

credits increase from 12 hours to 18 hours.

To elicit beliefs about the distribution of grades conditional on schoolwork, I followed the

method proposed by Delavande and Rohwedder (2008). Students were shown a set of bins repre-

senting different outcomes – 0.0 (F), 1.0 to 1.5 (D), 2.0 to 2.5 (C), 3.0 to 3.5 (B), and 4.0 (A) –

and asked to place ten balls across the bins where each ball represented the likelihood of observing
the outcome.6 This exercise was repeated for a series of scenarios: spending one hour on school-

work per course per week, three hours on schoolwork, six hours on schoolwork, and nine hours
on schoolwork.7 Appendix Figure A.4.3 presents the average reported probability of earning each

grade for each scenario. At only one hour of schoolwork, the average student believes they are

6Eliciting distributions with the balls-in-bins method has two advantages. First, the visual fre-
quency representation can be understood by a respondent with limited formal education of proba-
bility (Delavande et al. 2011). Second, the balls-in-bins method always yields a valid probability
distribution, as respondents cannot violate monotonicity of the cumulative distribution function or
the bounding of probabilities between zero and one. A sample response is provided in Appendix
Figure A.4.2.

7A typical course is three credit hours.

11

most likely going to earn a C grade. As time spent on schoolwork increases, so does the proba-

bility of earning higher grades. There is signiﬁcant heterogeneity in these beliefs as Figure A.1.4

shows. The interquartile range of expected grades in a course with only one hour of schoolwork is

1.40 to 2.75, which spans a third of all available grades. The range of expected grades decreases as

students spend more time on schoolwork, but there are still meaningful differences at nine hours

of schoolwork; a quarter of students believe they will earn less than a 3.25, while a quarter believe

they will earn a 4.0.

To elicit beliefs about the distribution of post-school salaries conditional on GPA, I again used

the balls-in-bins method. The SEES asked students to consider ﬁve scenarios: failing to graduate,

graduating with a cumulative GPA between 2.0 and 2.49, graduating with a cumulative GPA be-

tween 2.5 and 2.9, graduating with a cumulative GPA between 3.0 and 3.49, and graduating with a

cumulative GPA between 3.5 and 4.0. Students were given six bins of possible full-time salaries:

less than $40 thousand, $40 to $59 thousand, $60 to $79 thousand, $80 to $99 thousand, $100 to

$119 thousand, and greater than $120 thousand. Appendix Figure A.4.4 presents the average re-

ported probability of earning each salary for each GPA scenario. The majority of students believe

they will earn less than $40 thousand a year if they left MSU without a degree. Students believe

they are more likely to earn higher salaries as they increase their GPA. As with the distribution of

grades, there is signiﬁcant heterogeneity in these beliefs. Figure A.1.5 presents the distribution of

expected salaries across students. The interquartile range of expected salaries without a degree is

$26 to $44 thousand, and this spread only increases with graduating and receiving a higher GPA.

With a 3.5 to 4.0 GPA upon graduation, a quarter of students expect to earn less than $70 thousand

while a quarter believe they will earn more than $105 thousand.

1.4 Structural model

This section presents a dynamic structural model to formalize the relationship between a stu-

dent’s choices, ﬁnancial resources, and beliefs. The student begins with her ﬁrst year of college

and chooses her credit hour enrollment, labor supply, and borrowing to maximize the present dis-

12

counted value of her lifetime utility. She derives utility from consumption, leisure, and the grades

she earns from her classes. Grades also affect her future salary upon leaving college. The student

leaves college when she earns enough credits to graduate with a degree, reaches the maximum

allowable time in college, or chooses to permanently exit.

1.4.1 Model structure

1.4.1.1 Decision periods

I take the college entrance decision as given and begin the individual’s decision horizon at the

start of her ﬁrst year in college. Decision periods correspond with academic terms, with the fall

and spring as period one, summer as period two, fall and spring of the next year as period three,
etc.8 Individual i remains in college until she graduates, chooses to leave without a degree, or

reaches period T . Individual i graduates when her cumulative credit hours earned exceeds her
graduation threshold ¯Ki and her cumulative GPA exceeds a 2.0.9 After leaving college, either
voluntarily, due to graduation, or because she reached the maximum time permitted, individual i

enters the full-time labor market. I model the full-time labor market as an absorbing state where the
individual’s remaining lifetime utility is a function of her post-school wage and cumulative debt.10

8I choose to combine the fall and spring to align with the actual decision periods of students
at Michigan State University. Students enroll for their fall and spring classes at the same time and
accept their loan offer for the two semesters together. They are allowed to change their spring
classes and loans in the future, but I do not permit that here.

9I allow the graduation threshold to vary by individual for two reasons. First, some majors
have higher credit requirements than others. Second, some students enter college with Advanced
Placement, Dual-credit, or other transfer credits. The simplest way to account for these credits in
the model is reducing the graduation threshold. Changing the initial value of the state variable for
number of credits introduces error into the GPA calculation.

10By modeling the full-time labor market as an absorbing state, I do not permit individuals
to leave college and return at a later time. Per the National Student Clearinghouse, only 13%
of students re-enroll within ﬁve years of leaving school without a degree (Shapiro et al. 2019).
At a university like MSU, where the six-year completion rate is near 80% (U.S. Department of
Education 2020), it is unlikely that many students plan on temporarily leaving school and returning
in the near future.

13

This simpliﬁcation allows me to focus on the decisions made in college while still incorporating

intertemporal tradeoffs that involve post-college outcomes.

1.4.1.2 Choices

Each period in school, individual i decides whether to continue in school or drop-out and enter

the full-time labor market. If she chooses to continue in school, she makes three additional de-

cisions: her labor supply hit, credit hour enrollment kit, and new student loans bit. Individual i
chooses her labor supply from the discrete set of 0 hours, 300 hours, and 600 hours which corre-

sponds to 0, 10, and 20 hours per week in the fall and spring periods and 0, 20, and 40 hours per
week in the summer periods.11 Credit hour enrollment is also restricted to a discrete set. In the fall

and spring, individual i can choose 26 credits, 30 credits, or 34 credits; in the summer, individual

i can choose 0 credits, 3 credits, or 8 credits. In addition, she can choose not to borrow additional

loans, borrow her Stafford loan offer, or borrow her maximum student loan eligibility. I denote the
entire set of feasible choices in period t with At.12

1.4.1.3 State variables

Individual i enters each period with a set of state variables: cumulative credit hours earned Kit,
cumulative grade point average Git, cumulative debt Bit, and time-invariant characteristics Xi. I
denote this collection of state variables with Sit. Individual i begins college with no credit hours,
11Discretization of the choice set simpliﬁes the estimation procedure. It avoids the solving of
ﬁrst-order conditions, and it easily incorporates corner solutions (e.g., no work, no classes, and
no or maximum borrowing). One drawback is the modeler must specify the number of feasible
choices; however, previous work in the labor supply literature has found estimated utility parame-
ters are robust to this decision (L¨oefﬂer et al. 2018).

12At depends on t to reﬂect that the credit hour choice set differs in the fall and spring from the

summer.

14

GPA, or debt. State variables evolve according to the following laws of motion:

Ki,t+1 = Kit +

1[gikt > 0]

kit∑
(cid:19)

k=1

(cid:18) Kit

∑kit

k=1 gikt
Kit + kit



(1.1)

Gi,t+1 = Git

Kit + kit

+

Bi,t+1 = (1 + rt)(Bit + bit)

Cumulative credits earned is the number of credit hours where a passing grade (greater than 0.0)

was earned for that credit. Cumulative GPA is the weighted average of the individual’s previous
cumulative GPA and newly earned grades.13 I denote the grade earned for credit k by individual

i in period t with gikt. Cumulative debt is equal to prior debt plus new borrowing, after interest
accumulation.

1.4.1.4 Preferences

While enrolled in school, individual i has preferences over three payoff variables: consump-

tion c(a,Sit), leisure l(a,Sit), and semester grade point average git ≡ 1
of-period utility function that represents in-school preferences with Usch
the individual’s preferences can be separated into an observable component usch
(c,l,g) and unob-
servable (to the econometrician) choice-speciﬁc shock εit ≡ {εait : a ∈ At}. The choice-speciﬁc
preference shocks are independently distributed across choices, individuals, and time according to

k ∑k gikt. I denote the end-
(c,l,g,ε). I assume that

t

t

13The weighted average formula for cumulative GPA is not correct for students that earned a 0.0
(failing) grade in a course, as credits that received a 0.0 do not contribute to Kit, but fewer than
4% of student-term pairs include a 0.0 grade, so this formula is correct for the vast majority of
observations. A precise calculation requires tracking separately the number of credits attempted
and the number of credits passed and using credits attempted in the weights.
If this were the
only shortcoming, the current formula would over-estimate cumulative GPA; however, students
are allowed to retake a failed class and replace their 0.0 grade with a higher grade from a second
attempt. I do not record when students do this. If I did track cumulative credits attempted separately
and used it in place of Kit, I would not correctly replace 0.0 grades with their revised grade. In this
regard, the current formula underestimates cumulative GPA. Considering both factors together, it
is ambiguous whether the formula over- or under-estimates cumulative GPA, as the errors partially
cancel each other out.

15

a type I extreme value distribution, and the preference shocks are revealed to the individual at the

beginning of the period.

The utility from individual i choosing action a in period t is given by the below equation; for

notational convenience I have suppressed the payoff function arguments and replaced them with

subscripts to denote the individual, choice, and time period:

Usch
t

(cait,lait,git,εait) = usch

t

(cait,lait,git) + εait.

(1.2)

Once the individual leaves school and enters the post-school labor market, she receives a single

utility realization equal to the discounted present value of her lifetime utility in the labor market,
U post
(Sit). This utility sum is a function of her wage and cumulative debt upon entry into the
t
post-school labor market which jointly determine her “full income”.14 Finally, I use Ut(a,S,ε)
to denote individual i’s utility when her entrance into the post-school labor market is unknown ex

ante:

Ut(ait,Sit,εit) = 1[in-schoolit]Usch

t

(cait,lait,git,εait) + 1[post-schoolit]U post

t

(Sit).

(1.3)

1.4.1.5 Constraints

Individual i faces constraints on consumption, leisure, and borrowing. Her consumption is

equal to her labor income, changes in debt, and family ﬁnancial support less net (of grants) educa-
tion expenses. Labor income is the product of an hourly wage wsch
and hours worked. Both family
support f am(·) and net education expenses edut(·) can depend on individual i’s choices and state
variables.15

i

cit(ait,Sit) = wsch

i hit + bit + f am(ait,Sit)− edut(ait,Sit).

(1.4)

14Instead of modeling the individual’s entire lifetime labor supply problem, I assume she can
maximize her utility according to a two-stage budgeting model, and her lifetime value function is
simply a function of her wage and debt (e.g., Blundell and Walker 1986).

15Net education expenses depend on credit hour enrollment, cumulative credit hours, and time-
invariant student characteristics. Family ﬁnancial support varies with choices and states through
changes in net education expenses.

16

When an individual is still in school, her wage is a constant individual-speciﬁc part-time wage
. Once out of school, her full-time wage wpost

i (Sit). This
distribution is a function of her credit hours and GPA, and the distribution can vary across individu-

wsch
i

is drawn from the distribution Fw

i

als even if they have identical credit hours and grades (e.g., via differences in productivity). Family

support and net educational expenses are time-invariant functions and are known with certainty by

the individual. I do not permit individuals to have negative consumption. Instead, I impose a con-

sumption ﬂoor c such that any individual that would have consumption lower than c receives an

external transfer that brings her consumption up to c.

Individual i’s leisure time is equal to her total time endowment Lt less study hours studyi(ait)

and work hours:

lit(ait,Sit) = Lt − studyi(ait)− hit.

(1.5)

I model study hours as a time-invariant and deterministic function of individual i’s other choices,

speciﬁcally, her labor supply and credit hour enrollment. This is a strong restriction – holding credit
hours and labor supply ﬁxed, the individual cannot trade leisure for additional study time.16 To

increase study time, she must change one of her work hours or credit hours. There is also non-

negativity constraint on leisure – individuals cannot choose to study and work so much that their

leisure is negative.

1.4.1.6 Grades

At the end of each period, individual i receives a grade gikt for each credit hour she was enrolled
in. Grades enter the utility function directly and affect the evolution of state variables, and conse-
quently, future earnings. Grades are random variables drawn from the distribution Fg

i (studyi/kit).
16The purpose of this restriction is two-fold. First, modeling the study decision as an “outcome”
as opposed to a choice avoids introducing a fourth dimension in the choice problem, signiﬁcantly
reducing the computational burden of estimation. Second, specifying this as a time-invariant and
deterministic function of two other choices allows me to estimate study hours with data from the
SEES. The alternative involves solving for study hours as a best response function of the state
variables and other choices. Without a closed-form solution, I would need to solve for the best
response for every individual, instantiation of states, choice bundle, and parameter iteration in the
maximization routine.

17

This distribution is a function of individual i’s study hours per credit hour, and she does not know

what grades she will earn until the conclusion of the period. Thus, when she maximizes her life-

time utility, the uncertainty of what grade she will earn may affect her optimal decision. She may

choose a credit-work-borrowing bundle to reduce the risk of earning a low grade even if her ex-

pected grade does not signiﬁcantly change. As with the post-school wage distribution, the grade

distribution can vary across individuals even if they spend the same amount of time studying per

credit hour.

There are two important assumptions here. First, I assume that individuals have correct beliefs

about their grade distributions. This precludes individuals from learning about their own ability

or returns to studying. Second, I assume that the grade distribution does not vary over time. This

implies that individuals do not become more efﬁcient studiers, relative to course difﬁculty, as they

spend more time in college.

1.4.1.7 Maximization problem

Individual i maximizes the expected discounted value of her lifetime utility subject to the afore-

mentioned constraints. The solution to her lifetime maximization problem at period one is given

by the laws of motion for state variables and

(cid:34)T +1

(cid:35)

Vi1(Si1,εi1) ≡ max
{a∈At}T

t=1

∑
t=1
i hit + bit + f am(ait,Sit)− edut(ait,Sit),c}
s.t. cit(ait,Sit) = max{wsch

β t−1Ut(a,Sit,εit) | Si1,εi1

E

(1.6)

lit(ait) = Lt − studyi(ait)− hit
lit(ait) ≥ 0

where β is the discount factor.17 The expectation is taken with respect to future choice-speciﬁc

preference shocks, grades, and the future full-time wage offer.

17The above equation is a slight abuse of notation, as the individual does not make any further
choices once she leaves school, which can occur before T . The implicit assumption is that the
individual’s utility is ﬁxed after leaving school and her choice set is the null set.

18

1.4.2 Solution method

The maximization problem for individual i can be re-written at any period t ≤ T as a recursive

function of the future period value function:

Vit(Sit,εit) = max
{a∈At}

{Ut(a,Sit,εit) + β E[Vi,t+1(Si,t+1,εi,t+1)|a,Sit]}.

(1.7)

This recursive nature implies that the value function can be solved via backward induction. In

period T , the ﬁnal possible period in school, individual i solves:

ViT (SiT ,εiT ) = max
a∈AT

T (caiT ,laiT ,giT ) + εaiT + β E[U post
usch

(cid:110)

(cid:111)
T +1(Si,T +1)|a,SiT ]

(1.8)

where the expectation is with respect to grades and the post-school wage offer. With a solution

for ViT , individual i (or the econometrician) proceeds backwards to solve the remaining value
functions.

In the t < T value functions, the expectation generally does not have a closed-form solution.

So to proceed, I consider the expectation in two parts: the expectation of the value function with

respect to the choice-speciﬁc preference shocks but conditional on the future state variables (com-

monly referred to as the “Emax” function), and the expected Emax function with respect to the

future state variables. The Emax function has a closed-form solution given the distribution of the

choice-speciﬁc preferences shocks:

E[Vit(Sit,εit)|Sit] =

E.C. + log

 ∑

a(cid:48)∈At

(cid:110)

usch
t

exp

(ca(cid:48)it,la(cid:48)it,git) + β E[Vi,t+1(Si,t+1,εi,t+1)|a(cid:48),Sit]

(cid:111) (1.9)

where E.C. is Euler’s constant. The Emax function can theoretically be solved by backward induc-
tion; however, this is computationally infeasible in practice.18

18To see why, note that the value function must be solved at every possible combination of state
variables that can be reached in a given time period. Given the continuous nature of the state
space, a full-solution method would require discretizing the state space. With 985 individuals, 28
elements of the choice set, and ten choice periods, a coarse grid of 25 elements for each of the three
time-varying state variables would required evaluating 4.309 billion functions for each iteration of
parameter values.

19

A popular approach for estimating the Emax function in similarly complex models is an in-

terpolation method proposed by Keane and Wolpin (1994). Starting at the terminal period, I take

R values from the set of feasible state variables and solve for the exact Emax function for each

individual at all R states. I then ﬁt a ﬂexible individual-speciﬁc interpolating function to approx-

imate the value function for all other possible state variable combinations. Moving backward to
period T −1, I again take R values from the set of feasible state variables and solve for the approxi-
mate Emax function using the interpolating function for the period T Emax function. This process

continues until I have interpolating functions for every individual in all periods.

The interpolation method provides an approximation of the Emax function; the next step is

solving for the expected Emax function with respect to the future state variables. Given a distribu-

tion on the grade and post-school wage error terms, this is a straightforward exercise.

1.4.3 Model parameterizations

I specify individual i’s observable in-school utility function as:

usch
t

(cait,lait,git) = αc ln(cait) + αlt ln(lait) + αg ln(git)

+αh0t1[hit > 0] + αk01[kit = 0] + αk301[kit = 30]

(1.10)

+αb11[bit = Stafford only] + αb21[bit = Max eligiblity]

where αlt and αh0t are allowed to vary between fall / spring and summer periods.19 I restrict αc,
αl, and αg to positive values, and the log speciﬁcation imposes diminishing marginal utility from
consumption, leisure, and grades.20 In addition to the payoff variables, I include ﬁxed costs for
various alternatives.21

19In the fall and spring, I divide consumption and leisure by two and specify utility as
(cait/2,lait/2,git) + β usch
(cait/2,lait/2,git). This captures the difference in period length

usch
t
between the fall / spring period and summer period.

t

20Because semester GPA can take on the value of zero, I use the inverse hyperbolic sine function
in place of the natural log. The inverse hyperbolic sine yields nearly identical marginal utilities as
the natural log except when semester GPA is very close to zero.

21A ﬁxed cost of labor is common in the labor supply literature and can capture the additional
effort associated with attending a job regardless of hours worked (L¨oefﬂer et al. 2018). I include

20

The net tuition function edut(ait,Sit) is equal to expected fees, tuition, and textbooks less grants
and scholarships. Fees, tuition, and textbooks can vary based on attempted credit hours and the

individual’s characteristics in Xi, such as independence status and residency. Loan offers are also
based on net tuition. Neither Stafford loan offers nor private loan offers can exceed individual i’s

net tuition function plus expected living expenses. Furthermore, Stafford loans have a maximum

value speciﬁed by the federal government and require the individual is enrolled in at least six credit

hours.

Individual i’s family ﬁnancial support is given by:

f am(ait,Sit) = ﬂi + edut(ait,Sit)× fpi

(1.11)

where ﬂi ∈ Xi is the individual’s lump-sum family transfers and fpi ∈ Xi is the individual’s family
transfers for education expenses as a percent of education expenses.22

I model individual i’s study time function as:

(cid:16)

studyi(ait) =

δ0i + δ1ikit + δ2ihit + δ3ih2
it

(cid:17)

kit.

(1.12)

This speciﬁcation allows the individual to change her study time per credit hour as she changes her

credit hour enrollment or work hours.

I model the grade process with a heteroskedastic ordered probit. Individual i’s unobserved

“knowledge” for a particular credit hour g∗
ikt is a function of her knowledge without any studying
γ0i, her individual-speciﬁc return to studying rate γ1i, study hours per credit hour, and a normally
a ﬁxed utility term for attempting zero credit hours to capture similar ﬁxed costs associated with
enrolling in any classes regardless of the number of classes. Marx and Turner (2018) ﬁnd empirical
evidence that students face a ﬁxed non-monetary cost for borrowing, which I capture with αb1 and
αb2. I allow this cost to vary between Stafford loans and the maximum loan eligibility because
students have to actively seek out and apply for loans beyond the Stafford loan offer, and the search
costs may have a utility cost.

22This functional form reﬂects how the SEES measured family ﬁnancial support. Respondents
speciﬁed how much they received in support for living expenses as a ﬁxed dollar amount and how
much they received for education expenses as either a ﬁxed dollar amount or as a percentage of
education expenses. For students who receive both as a ﬁxed dollar amount, fpi is zero.

21

distributed error term νikt.23 When her knowledge passes particular thresholds, she earns higher
discrete grades. I assume all individuals face the same thresholds to earn each grade and the same

variance factor for the error term.

(1.13)

g∗
ikt = γ0i + γ1i

νikt ∼ N

0,exp

gikt =

(cid:18)

0

1.25

2.25

3.25

4



studyi

kit

(cid:18)studyi

+ νikt

(cid:19)(cid:19)

σ g
kit
if g∗
ikt ≤ 0
if 0 < g∗
ikt ≤ γC
γC < g∗
ikt ≤ γB
if
γB < g∗
ikt ≤ γA
γA < g∗
ikt.

if

if

Fg
i

is deﬁned by γi ≡ {γ0i,γ1i,σ g,γC,γB,γA}.
I specify individual i’s post-school value function as:

U post(Sit) = αw ln(wpost

i

(Sit)) + αB ln(Bit)

(1.14)

where the log speciﬁcation imposes diminishing marginal returns to post-school earnings and post-
school cumulative debt.24 I restrict αw to positive values and αB to negative values.

Individual i’s post-school wage offer is modeled as:

wpost
i

(Sit) = exp{ω0i + 1[Kit ≥ ¯K](ω1i + ω2i(Git − 2) + ω3i(Git − 2)2) + ξi}

(1.15)

where ξi ∼ N(0,σ w
ing with a GPA above the minimum for a degree.25 Fw
i

i ). This speciﬁcation includes a college degree premium and a return to graduat-
is deﬁned by ωi ≡ {ω0i,ω1i,ω2i,ω3i,σ w
i }.
23In practice, I model the error distribution such that there is perfect correlation between errors
in groups of three credits. This reﬂects that students earn grades at the course level, and courses
are typically three credit hours each.

24Because cumulative debt can take on the value of zero, I use the inverse hyperbolic sine func-

tion in place of the natural log.

25To reduce the computational burden of estimating the model, I assume there are no returns to
in-school work experience. Researchers have found conﬂicting evidence on the returns to in-school
work experience (e.g., see Baert et al. 2016; H¨akkinen 2006; Hotz et al. 2002).

22

I set T = 10 so individuals have ﬁve full years to complete college before entering the post-

school labor market. I set Lt = 3360 for the fall and spring period and Lt = 1680 for the summer

period corresponding to a time endowment of 112 hours per week or 16 hours per day. I assume an

annual interest rate of 4.44%, which is approximately the average interest rate on Federal Stafford

loans for in-sample years. I also specify a discount rate instead of estimating it, as it is typically

not well identiﬁed (Aguirregabiria and Mira 2010). Given existing research suggests that young

adults have higher discount rates than older adults (e.g., see Green et al. 1994), I choose an annual

discount rate of 0.8. Finally, I set the consumption ﬂoor at $50 per week.

1.4.4 Criterion function

Before estimating the structural model, I estimate the studying model parameters δi, grade
model parameters γi, and wage model parameters ωi using the subjective expectations elicited in
the SEES. With these individual-speciﬁc parameters in hand, I estimate the utility parameters α ≡
{αc, αlt, αg, αh0t, αk0, αk30, αb1, αb2, αw, αB} via maximum likelihood. This two-step approach
is common in the literature to reduce the computational burden of estimating the parameters jointly
(Aguirregabiria and Mira 2010).26

The log-likelihood function for individual i is given by:

lli(α) = logPr(ait, ˆSit,gikt : t = 1, . . .Ti | α)

(1.16)

where ait is the chosen bundle for individual i in period t, ˆSit is the set of observable state variables
and predicted auxiliary model parameters, gikt is the vector of earned grades for individual i in
credit hour k and period t, and Ti is the ﬁnal period observed in the data for individual i.

Because the choice-speciﬁc preference shocks are independently distributed over time and the

other state variables evolve independently from the preference shocks, I can re-write the likelihood

26I take the studying model, grade model, and wage model parameters as given for the second
estimation step; I do not incorporate the standard errors on those parameters into the estimation of
the utility parameters.

23

function as:

lli(α) =

t=1

Ti∑
logPr(ait| ˆSit,α) +
Ti−1
∑
t=1

+

logPr( ˆSi,t+1|ait, ˆSit,gikt) + logPr( ˆSi1|α).

Ti∑

t=1

logPr(gikt|ait, ˆSit)

(1.17)

The second and third terms are deﬁned by the grade model described previously and do not

depend on the parameters in α. The fourth term, the contribution of initial state variables to the

likelihood function, can also be ignored under the assumption that the choice-speciﬁc preference

shocks are independently distributed over time and uncorrelated with the initial states (Aguirre-

gabiria and Mira 2010). Thus, the only term relevant for the maximization problem is the ﬁrst term

– the log of the conditional choice probability.

Given the type I extreme value distribution, the probability that alternative a is chosen by

individual i in period t given states ˆSit is:

Pr(a| ˆSit,α) =

exp

usch
t
∑a(cid:48)∈At exp

(cid:110)

(cid:111)
(cid:111)
(cait,lait,git) + β E[Vi,t+1( ˆSi,t+1,εi,t+1)|ait, ˆSit]
(ca(cid:48)it,la(cid:48)it,git) + β E[Vi,t+1( ˆSi,t+1,εi,t+1)|a(cid:48), ˆSit]
usch
t

(cid:110)

(1.18)

where the expectations are taken with respect to the choice-speciﬁc preference shocks, grades, and

the post-school wage offer. I follow the procedure outlined in Section 1.4.2 to approximate these

expectations and then I estimate the utility parameters using maximum likelihood.

1.5 Results

1.5.1 Auxiliary model estimation

Table A.1.4 summarizes the variables in the structural model and speciﬁes the time periods

they are available in the data. The choice variables, time-varying state variables, and net education

expense function are available for all time periods. In-school wages and family ﬁnancial support

are only known at the time of the survey, and I assume that they do not change over time (Appendix

Sections A.2 and A.3 describe the calculation of these variables in more detail). In the rest of this

section, I brieﬂy describe how I use the survey responses to estimate students’ study time function,

grade production function, and post-school wage function.

24

As speciﬁed in equation 1.12, a student’s time spent on schoolwork is an individual-speciﬁc

function of their credit hours and labor supply. In the SEES, I asked students how much time they

expect to spend on schoolwork given six hypothetical credit hour enrollment and work hour sched-

ules. I use their responses to these six questions and estimate the study function parameters with a

linear regression. Panel A of Table A.1.5 presents the distribution of study function parameters.

Equation 1.13 speciﬁes that the relationship between schoolwork and grades follows a het-

eroskedastic order probit model with an individual-speciﬁc constant and return to schoolwork. I

use students’ reported probability of earning each discrete grade in the four schoolwork time sce-

narios to estimate this model. As described in Section 1.3.4, students placed ten balls in bins to

convey the likelihood of earning a particular grade. Each ball placed is a separate observation, so

there are 40 observations per student (ten balls placed in four schoolwork scenarios) to identify the

individual-speciﬁc parameters. I assume that the variance term and thresholds are common across

all students. I also normalize the lowest threshold to zero to report individual-speciﬁc constants

for every student. Panel B of Table A.1.5 presents the distribution of the grade production function

parameters.

Equation 1.15 speciﬁes that a student’s post-school wage is determined by an individual-

speciﬁc constant, degree premium, and return to GPA. The variance of the error term is also

individual-speciﬁc. To estimate these parameters, I use the conditional salary distributions elicited

from each student for ﬁve GPA scenarios. Similar to the conditional grade distribution questions,

students placed ten balls in bins to convey the likelihood of earning a particular post-school full-

time salary. Each ball placed is a separate observation, so there are 50 observations per student (ten

balls placed in ﬁve GPA scenarios) to identify individual-speciﬁc parameters. I estimate the wage

offer model with a separate linear regression for each student. Panel C of Table A.1.5 presents the

distribution of the post-school wage function parameters.

25

1.5.2 Structural model estimates

Table A.1.6 presents the estimated utility parameters and their standard errors.27 There are a

few takeaways worth noting. First, there is a signiﬁcant increase in how much students value their

leisure time in the summer relative to the fall and spring. This is not surprising, as students may

have more leisure options available to them during the summer semester (e.g., traveling, spending

time with family and friends from home) which makes their time more valuable. In addition to

consumption and leisure, students also value their contemporaneous semester GPA independent of

the future labor market returns.

The estimated parameters conﬁrm the existence of non-zero ﬁxed costs. Students have a non-

trivial ﬁxed cost of work that is similar in the fall / spring and summer periods. They also have a

ﬁxed cost of enrolling in classes during the summer period. Students have a ﬁxed cost of borrowing

the maximum amount of loans available to them which is expected given the additional steps

students need to take to borrow beyond their Stafford loan offer. However, students have a near-

zero ﬁxed cost for accepting the Stafford loan offer suggesting that students do not face a “psychic

cost of debt” when borrowing small amounts.

In isolation, utility parameters can only tell us so much, but before proceeding with further

analysis, I verify that the model achieves a reasonable ﬁt of the observed data. Table A.1.7 presents

the observed probabilities of each choice, average predicted probabilities of each choice, and the

difference between the two. Panel A conﬁrms that the model does a good job ﬁtting the observed

credit hour choice probabilities in the fall and spring periods, but it struggles to capture the u-

shaped pattern in the summer periods. Panel B tells a similar story; the model does well ﬁtting the

observed work hour probabilities in the fall and spring periods, but it does not capture the u-shaped

pattern of work hours in the summer. Panel C shows the goodness of ﬁt for borrowing choices. The

27Due to computation time, I estimate utility parameters with a random sample of 15% of ob-
servations. Goodness of ﬁt statistics are very similar for the 15% random sample and the entire
sample. I use the Berndt-Hall-Hall-Hausman (BHHH) algorithm for maximizing the log likeli-
hood function to avoid calculating ﬁnite differences required to estimate the Hessian (Train 2009).
I derive standard errors using the square root of the diagonal of the inverse outer product of the
gradient.

26

model does a good job matching the distribution of borrowing choices in the fall and spring periods,

and it correctly predicts that almost no students borrow in the summer. The model over predicts

students’ willingness to borrow up to their maximum loan eligibility in the summer, though this

is likely related to the model under-predicting students’ willingness to work 40 hours a week in

the summer. Overall, the model and estimated utility parameters ﬁt the observed distribution of

choices well.

1.5.3 Elasticities

Tables A.1.8 and A.1.9 present statistics for a series of elasticities of credit hour, work, and bor-

rowing behaviors. I derive these elasticities via simulation by comparing the weighted average of

choices (weighted by the model-derived probability of the choice) with the baseline variables and

with the simulated variables: a $1,000 increase in grants ($500 in the summer), a 10% increase in
the per-credit hour tuition rate, a 10% increase in students’ expected return to studying (γ1i), a 10%
increase in students’ expected return to earning a higher GPA (ω2i and ω3i), and a 10% increase in
students’ in-school wage.28 I estimate standard errors for the average elasticities across students

with a parametric bootstrap using 30 draws from the joint distribution of utility parameters.

As shown in Panel A, I do not ﬁnd evidence that students’ credit hour decisions vary strongly

with ﬁnancial aid, tuition, beliefs, or wages. Almost all of the estimated elasticities are near-zero

in both the fall and spring and summer periods. The largest elasticity, a 0.177 credit hour elasticity

with respect to the return to GPA in the summer, is not practically signiﬁcant. With a base of 2.43

average credit hours, a 10% increase in the returns to GPA increases the average student’s credit

hour enrollment by 0.04 credits. Furthermore, as the last three columns of the table show, credit

hour elasticities are practically insigniﬁcant across the 25th and 75th percentiles of the elasticity

distribution.

28Because these elasticities are numerically derived and not analytically derived “point elastici-
ties”, I use an arc elasticity formula where the percentage change in the numerator and denominator
of the elasticity are relative to the midpoint between the two numbers. For the returns to GPA elas-
ticity, I increase two parameters – ω2i and ω3i – so I use the percentage change in the marginal
effect of an increase in GPA at a GPA of 3.0 as the denominator.

27

Students are more responsive on the labor supply margin than the credit hour margin. As

shown in the last row of Panel B, the average wage elasticity is 0.29 in the fall and spring and 0.24

in the summer; for a 10% increase in wages, students work 2.9% and 2.4% more hours on average.

These wage elasticities are comparable to consensus estimates for prime-aged working adults in

the United States, particularly for married women (McClelland and Mok 2012). Students decrease

their labor supply with an increase in their subjective beliefs for the returns to studying and returns

to GPA, at least in the fall and spring when they are more likely to face grade penalties for devoting

more time to work; a 10% increase in students’ beliefs about the returns to studying decreases

hours worked by 1.19%, and a 10% increase in students’ beliefs about the labor market returns to

graduating with a higher GPA decreases hours worked by 2.11%. Worth noting, the distribution

of these elasticities across students is skewed right, so the average response is not indicative of

the median student’s response. I do not ﬁnd evidence that students’ labor supply decisions are

responsive to changes in ﬁnancial aid or tuition – across the interquartile range, elasticities are

near zero.

Panel C presents estimated elasticities for students’ borrowing decisions. On average, students

signiﬁcantly change their borrowing behavior in response to a change in ﬁnancial aid and tuition

in the fall and spring. A 10% increase in ﬁnancial aid reduces borrowing by 7.81%, and a 10%

increase in tuition increases borrowing by 2.33%. This response is only present in the fall and

spring, as students are unlikely to enroll in enough credit hours to be eligible for student loans.

But once again, the distribution of these elasticities is highly skewed, and the median student

does not change their borrowing to a meaningful degree.

In the summer, students do increase

their borrowing with a change in their beliefs about the returns to GPA. This likely reﬂects the

positive credit hour elasticity in the summer; beliefs about the returns to GPA increase, students

take marginally more credits in the summer when it is easier to earn a high GPA (fewer classes to

distribute study hours across), and the small increase may cross the minimum credit hour threshold

to begin borrowing. The ﬁnal elasticity, borrowing with respect to wages, is negative in both the

fall and spring (-0.09) and summer (-0.16), suggesting that students will substitute to labor from

28

debt when the value of labor is higher.

For the elasticities that are highly skewed, a question naturally arises – what students are in

the tail of the distribution? To answer this question, I conduct a series of two-sample t-tests on

potential explanatory factors by comparing students in the bottom and top terciles of their elasticity

distributions.

I choose factors that should affect the marginal utility or cost of changing labor

supply and borrowing such as unmet ﬁnancial need, wages, and expected studying time response
to work hours.29 Table A.1.10 presents the results for the fall and spring periods.

Panel A compares students in the bottom and top terciles of the returns to studying elasticity

of labor supply. The average elasticity is -0.12 but the median elasticity is only -0.02. Students in

the bottom tercile, who reduce their labor supply more with an increase in the returns to studying,

have larger expected increases in study time with their decrease in work hours and larger expected

returns to graduating with a high GPA. In addition, these students have lower expected returns to

studying originally, suggesting that there are diminishing marginal returns to studying. The more

elastic students also have less unmet ﬁnancial need and lower wages on average, so the opportunity

cost of giving up work hours is smaller.

Panel B compares students in the bottom and top terciles of the returns to GPA elasticity of

labor supply. The distribution of this elasticity is more skewed than the prior one, with a mean

elasticity of -0.21 and a median elasticity of -0.03. As with the prior elasticity, the more elastic

students here have larger expected study hours gains from work reductions; however, these students

have similar unmet need and wages as students with smaller (in absolute value) elasticities. In

addition, the more elastic students have higher returns to GPA originally, though it is difﬁcult to

draw conclusions from this correlation as a 10% increase in the returns to GPA is larger in absolute

terms when the base is higher.

29Unmet ﬁnancial need, in-school wage, return to studying, return to GPA, and cumulative credit
hours are self-explanatory or discussed previously. The “study cost of work” is how many study
hours per credit hour the student expects to give up with an increase in work hours; in other words,
the derivative of studyi(ait)/kit with respect to hit in equation 1.12. Because the derivative changes
with work hours, I use the derivative at 6 work hours, which is approximately the mean work hours
in the fall and spring.

29

Panels C and D compare students in the bottom and top terciles of two borrowing elasticities:

ﬁnancial aid elasticity and tuition elasticity. The average ﬁnancial aid elasticity is -0.78 (median

of -0.01), and the average tuition elasticity is 0.23 (median of 0.03). There is signiﬁcant overlap

between the more elastic students in each distribution – 70% of students in the bottom tercile of the

ﬁnancial aid distribution are in the top tercile of the tuition distribution, and 88% of students in the

top tercile of the ﬁnancial aid distribution are in the bottom tercile of the tuition distribution. When

the budget constraint becomes tighter (ﬁnancial aid decreases or tuition increases), the students

who increase their borrowing the most have larger studying costs of work. They also have fewer

cumulative credit hours and are further from graduating, so they are discounting the future repay-

ment of their loans more heavily. The two groups of elastic students are not identical, however,

as the more elastic students of the tuition distribution have signiﬁcantly less unmet ﬁnancial need

than the less elastic students while the elastic students of the ﬁnancial aid distribution have similar

unmet ﬁnancial need to the less elastic students.

1.5.4 Counterfactual simulations

Elasticities are helpful for predicting how small, equally sized (in percentage terms) changes

in particular variables affect students’ choices. I now turn to two counterfactual simulations that

involve much larger changes that are not felt equally by all students. The ﬁrst simulation models

an increase in the minimum wage to $15 per hour. The second simulation makes in-state tuition

free for all students. Both policies relax a student’s budget constraint, albeit in very different ways,

with different effects across the distribution of students.

1.5.4.1 Minimum wage increase

Federal and state minimum wage laws are a potential mechanism for reducing income inequal-

ity in the United States (Card and Krueger 2016, Dube 2019). Because of this, there is growing

pressure to raise the federal minimum wage from its current rate of $7.25 per hour, which has

not changed since 2009, to $15 per hour (Pramuk 2019). In Michigan, the state minimum wage

30

increased on September 1, 2014 from $7.40 to $8.15, and it is set to increase each year until

reaching $12.05 in 2030 (Michigan Michigan Senate 99th Legislature 2018). At the beginning of

spring 2019, the state minimum wage was $9.45. In this ﬁrst simulation, I model what would have
happened if Michigan raised their minimum wage to $15 per hour on September 1, 2014.30

A $15 minimum wage would raise hourly wages for 93% of students in my sample and increase

the average wage from $10.95 to $15.32. Notably, the wage increase is not signiﬁcantly correlated

with students’ unmet ﬁnancial need.

Panel A of Table A.1.11 presents the expected behaviors and outcomes for students under the
baseline and counterfactual simulations.31 Increasing the minimum wage to $15 per hour increases

average weekly work hours by 0.75 in the fall and spring and 1.70 in the summer. With the wage

and hour increase, the average student’s labor income increases by $1,115 in the fall and spring

year and $1,003 in the summer. There is a small decrease in average borrowing, $303 in the fall and

spring and $65 in the summer, which is not enough to offset the gains in labor income. There is no

observable change in attempted credit hours or expected cumulative GPA. Thus, the primary effect

of increasing the minimum wage is increasing students’ consumption (at the expense of leisure or

studying) as opposed to allowing students to maintain existing consumption with less debt or fewer

hours working.

1.5.4.2 Free in-state tuition

Another policy proposal gaining momentum in the United States is making college tuition free

(Murakami 2020). Multiple US presidential candidates in the 2020 election adopted free college

plans in their platforms, and many states already have grant programs that cover the cost of tuition

at two- and four-year colleges for low- to middle-income families (Dickler 2019). These programs

30I assume there are no changes in labor demand and only focus on the labor supply response.
Based on a recent review of the minimum wage literature, this is not an unreasonable assumption
(Belman and Wolfson 2014).

31The baseline simulation takes students’ state variables in their ﬁrst period as given and projects
out their optimal decisions and evolution of state variables according to the estimated utility func-
tion parameters.

31

can increase enrollment in eligible colleges, and additional requirements (e.g., minimum GPA or

minimum completed credits per year) can incentivize students to change their behavior (Quinton

2019). In this second simulation, I model what would happen to existing students if Michigan

State University unconditionally waived the cost of in-state tuition for all students enrolled after
September 2014.32

Free in-state tuition reduces the expected cost of attendance by $15,723 in the fall and spring

and $964 in the summer. Expected credit hours are much lower in the summer, so the expected

savings are less. Even with free in-state tuition, in-state students still have expected living costs

of $14,148 in the fall and spring and $7,074 in the summer, as well as smaller program fees and

textbook costs, and out-of-state students still have the remainder of their tuition ($24,483 in the

fall and spring, $1,632 in the summer, on average). Unlike increasing the minimum wage as in the

previous counterfactual, the actual beneﬁt of free college varies signiﬁcantly by students’ ﬁnancial

need. Students with sufﬁciently high ﬁnancial need beneﬁt from the entire tuition reduction while

students with sufﬁciently large grants, scholarships, and family ﬁnancial support do not beneﬁt at

all.

Panel B of Table A.1.11 presents the expected responses and outcomes for students with and

without free in-state tuition. Average credit hours attempted increase by 0.09 credits in the fall and

spring and 0.04 credits in the summer, but this is a small effect in practice. Over the course of four

years, this corresponds to less than one additional credit hour. There are similarly small changes

in work hours. Given these small effects, there is no observable difference in expected cumula-

tive GPA. Borrowing does change substantially, however, with average loan amounts decreasing

by $1,922 in the fall and spring and $185 in the summer. Taken together, this counterfactual

simulation suggests that making college tuition cheaper is largely a wealth transfer for Michigan

State’s already enrolled students; it reduces students’ reliance on loans but does not improve other

32I assume no changes in enrollment or shifts in the university budget. I also assume that families
do not change their family ﬁnancial support plans, and any money previously allocated toward ed-
ucation expenses is not given to students. Out-of-state students are charged the difference between
in-state and out-of-state tuition.

32

outcomes like credit accumulation or GPA.

1.6 Conclusion

In this paper, I show how wages, ﬁnancial resources and beliefs inﬂuence college students’

credit hour enrollment, labor supply, and borrowing decisions. I begin by presenting novel survey

data from a random sample of undergraduates at Michigan State University. The survey contains

students’ work history, expected study hours for varying enrollment and work schedules, family

ﬁnancial support, beliefs about the returns to studying, and beliefs about the returns to graduating

with a high GPA. The survey also contains administrative data on students’ credit hour history,

ﬁnancial aid eligibility, and borrowing history. After presenting the data, I develop a dynamic

structural model of college students’ credit hour enrollment, labor supply, and borrowing which

captures the key contemporaneous and future tradeoffs involving these decisions. I then estimate

students’ preferences for consumption, leisure, grades, future earnings, and future debt and derive

elasticities for the three behaviors of interest. Finally, I simulate the effects of two counterfactual

policies: a minimum wage increase and free college tuition.

Students’ credit hour decisions are highly inelastic; the estimated elasticities with respect to

changes in ﬁnancial aid, tuition, returns to studying, returns to GPA, and in-school wage are all

near zero. Students’ work decisions are more responsive to changes in their budget and beliefs than

their credit hour decisions. I estimate an average wage elasticity of 0.29 in the fall and spring and

0.24 in the summer which are both comparable to elasticities for prime-age workers in the United

States. I ﬁnd slightly smaller, but still practically signiﬁcant, labor supply elasticities with respect

to beliefs about the returns to studying and returns to GPA. The larger elasticities are driven by

students who expect to gain more study hours back from a decline in work hours. These students

also have large borrowing elasticities with respect to ﬁnancial aid and tuition. Coupled with a wage

elasticity of borrowing of -0.16, this supports that students substitute between labor income and

borrowing.

The counterfactual simulations reveal similar patterns as the elasticities. A $15 minimum wage

33

would increase average work hours by 0.75 hours per week in the fall and spring and 1.14 hours

per week in the summer. It would also lead to small decreases in borrowing. Making in-state

tuition free for all students would negligibly change credit hours or work hours, but it would reduce

average borrowing by $1,922 in the fall and spring and $185 in the summer. Neither counterfactual

policy leads to a signiﬁcant change in expected GPA.

These results suggest how colleges and universities may (or may not) be able to change student

behavior. Financial levers on their own do not appear to be effective in increasing students’ credit

hour enrollment and subsequently decreasing time-to-degree. Financial aid that is tied to maintain-

ing certain credit hour benchmarks may hold more potential. There are also non-monetary levers

not explored in this chapter that could be more effective, like utilizing academic advisors to change

students’ mindset about the default course schedule or offering more classes in the summer term

so students have more opportunities to reach 30 hours beyond the fall and spring.

It is not clear ex ante that institutions should prefer that college students increase or decrease

their labor supply, but it does appear that changing students’ wages would be effective in shifting

their willingness to work. Colleges can adjust pay scales for on-campus jobs, and policy makers

can focus on changing the minimum wage. Importantly, these wage increases apply equally to

high-need and low-need students, and because there does not appear to be strong income effects

present, both high-need and low-need students will change their behavior. An alternative policy,

such as increasing Federal Work-Study generosity, would be more targeted at high-need students

than raising wages for everyone.

34

CHAPTER 2

PEER GENDER COMPOSITION AND NON-COGNITIVE OUTCOMES

2.1 Disclaimer

This chapter uses data from Add Health, a program project designed by J. Richard Udry,

Peter S. Bearman, and Kathleen Mullan Harris, and funded by a grant P01-HD31921 from the

Eunice Kennedy Shriver National Institute of Child Health and Human Development, with co-

operative funding from 17 other agencies. Special acknowledgment is due to Ronald R. Rind-

fuss and Barbara Entwisle for assistance in the original design. Persons interested in obtaining

Data Files from Add Health should contact Add Health, The University of North Carolina at

Chapel Hill, Carolina Population Center, 206 W. Franklin Street, Chapel Hill, NC 27516-2524

(addhealth contracts@unc.edu). No direct support was received from grant P01-HD31921 for this

analysis.

2.2 Introduction

Non-cognitive factors are signiﬁcant determinants of both educational and labor market out-

comes, in some settings explaining more variation in these outcomes than cognitive skills (Almlund

et al. 2011; Borghans et al. 2008; Bowles et al. 2001). Despite their importance, we are still learn-

ing about the development of non-cognitive factors, particularly among adolescents (Kautz et al.

2014). Drawing from existing research that demonstrates how an adolescent’s peers affects their

cognitive skill formation, we may expect that an adolescent’s peers could affect their non-cognitive

factor formation, too (Epple and Romano 2011; Sacerdote 2011). This chapter investigates the re-

lationship between a particular type of peer effect, peer gender composition, and non-cognitive

factors.

Previous studies ﬁnd that students with a higher share of female peers do better in the classroom

(Gong et al. 2019; Hoxby 2000; Lavy and Schlosser 2011), and there are compelling reasons

35

to believe that this relationship exists for non-cognitive factor formation. Being surrounded by

similar peers may help a student feel like they belong in their community, make it easier to develop

friendships, and improve the student’s happiness and mental health. Dweck et al. (2014) and

Farrington et al. (2012) provide extended commentary on these non-cognitive factors and how

they may relate to peer groups. In two studies that examine the relationship between peer gender

and non-cognitive factors directly, Gong et al. (2019) ﬁnd that male students exhibit a higher

life fulﬁllment and conﬁdence for the future when they have more female classmates and female

students report lower levels of unhappiness, and Lavy and Schlosser (2011) ﬁnd that the self-

reported quality of inter-student relationships improves for both male and female students when

they have more female peers.

This chapter estimates the causal effect of peer gender composition on two additional non-

cognitive factors – sense of belonging and self-worth – using a data set that is ubiquitous in the peer

effects literature, the National Longitudinal Study of Adolescent to Adult Health (Add Health).

Based on the aggregation of eight different measures, I ﬁnd that male students report a stronger

sense of belonging and self-worth when they have more female peers, but the effects are small in

magnitude. The results also suggest that there are no appreciable effects for female students.

2.3 Data

Add Health is a nationally representative longitudinal survey of seventh to twelfth graders in the

United States (Harris 2009). The ﬁrst survey instrument, an in-school questionnaire, provides data

on student demographics, peer groups, and non-cognitive factors for 90,118 students. I create a

subset of this sample for my analysis by excluding the following students. One student is missing

a valid school identiﬁer, 803 students are missing a valid grade, 6,849 students are missing a

survey weight, and 17,325 students did not provide a valid answer to at least one of the outcomes

or control variable questions. I also exclude 3,767 students who attended schools that required

explicit parental consent to take the in-school questionnaire; these schools tend to have lower in-

school questionnaire participation rates which makes the calculation of the share of female peers

36

more prone to measurement error. Finally, I exclude 100 students who had fewer than ten total

students in their grade and 1,144 students who attended schools that were exclusively male or

female, as there is no variation in peer gender across grades. I am left with 60,129 observations.

My explanatory variable of interest is the share of female peers in a student’s school and grade

which I calculate by dividing the number of students who answered the question, “what sex are

you?” with “female” by the total number of students who answered the question either “male”
or “female” in that student’s school and grade.1 To avoid correlations between the student’s own

gender and the share of female peers in their school and grade, I use a leave-out mean, where I

do not include the student in the calculation of their peer group’s mean. In addition to the share

of female peers, I include the following control variables in my baseline model: biological sex,

Hispanic or Spanish ethnicity, race (e.g., Black or African American, Asian or Paciﬁc Islander,

American Indian or Native American, White, other), if the student’s age (in years) is above the

median age for their grade across all schools, if the student reported being born in the United

States, and dummy variables for the number of people that live in the student’s household. Table

B.1.1 presents descriptive statistics for the sample.

The in-school questionnaire contains four questions that measure sense of belonging – “I feel

socially accepted”, “I feel loved and wanted”, “I feel close to people at this school”, “I feel like

I am part of this school” – and four questions that measure self-worth – “I have a lot of good

qualities”, “I have a lot to be proud of”, “I like myself just the way I am”, “I feel like I am doing

everything just alright”. Each question was asked on a 5-point Likert scale with options ranging

from “Strongly disagree” to “Strongly agree”. Given the ordinal nature of the responses, there is

no obvious way to aggregate the individual questions into their broader non-cognitive factor. As

my primary speciﬁcation, I use the count of questions that a student answered in the afﬁrmative

(“Agree” or “Strongly agree”) as my outcome variable. Table B.1.2 presents the probability of an

afﬁrmative response for each of the eight questions and the mean number of afﬁrmative responses

for the two broader categories. I also consider a speciﬁcation where I assign a numerical value
1I calculate the share of female peers from the full sample of in-school questionnaire respon-

dents before I remove students for my analytic sample.

37

to each possible response (e.g., Strong disagree = 1, Disagree = 2, . . .

, Strongly agree = 5) and

estimate the effect of an increase in female peers on the average numerical response for the broader

non-cognitive factor. Figures B.1.1 through B.1.3 present histograms of responses for each survey

question, the count of afﬁrmative responses, and the average numerical response.

2.4 Empirical strategy

I employ a similar method as Hoxby (2000) and Lavy and Schlosser (2011) to isolate plau-

sibly exogenous variation in the share of female peers; I assume that variation in the share of

female students within a school and across grades is uncorrelated with unobserved determinants

of non-cognitive factors. By focusing on within school variation, this assumption is not violated

by endogenous sorting into schools if the sorting occurs equally in all grades. I conduct a balance

test to check for observable violations of this assumption by regressing the share of female peers

in a school and grade on the aforementioned control variables, school dummy variables, and grade

dummy variables. As shown in Table B.1.3, only one relationship is statistically signiﬁcant at the

10% level which is to be expected given the number of control variables even if no true correlations

exist in the population.

I estimate a linear-in-means model with school and grade dummy variables to measure the

relationship between peer gender composition and non-cognitive factors. Let yi be a non-cognitive
factor for student i, female−isg the share of female peers in student i’s school s and grade g,
excluding student i, Xi a vector of student characteristics, φs a vector of school-speciﬁc effects, and
ψg a vector of grade-speciﬁc effects. The estimating equation is:

yi = β f emale−isg + Xi + φs + ψg + εisg.

(2.1)

I use the Add Health adjusted sample weights in all regressions, and I estimate standard er-

rors using a Taylor linearization adjusting for the survey’s regional stratiﬁcation and clustering by

school as prescribed by Chen and Chantala (2014).

38

2.5 Results

Table B.1.4 contains the estimated effect of a unit increase in the share of female peers in a

student’s school and grade on the count of afﬁrmative sense of belonging and self-worth survey

responses. Each pair of columns presents results for a different sample: the total sample, female

students only, and male students only.

I do not ﬁnd signiﬁcant evidence that female students are more or less likely to have a higher

sense of belonging or self-worth with an increase in the share of female peers, but the coefﬁcients

and standard errors rule out practically signiﬁcant positive effects. I do ﬁnd evidence that male stu-

dents report both stronger belonging and self-worth, but while the effect is statistically signiﬁcant,

it is not large. A ﬁve percentage point increase in the share of female peers, (roughly equivalent to

a one-standard deviation increase) leads to male students reporting 0.036 and 0.032 more afﬁrma-

tive responses to the four belonging and four self-worth questions, respectively. This corresponds

to 1.4% and 1.1% of the mean or 2.6% and 2.6% of the standard deviation. These effect sizes for

male students are comparable to those found by Lavy and Schlosser (2011) and Gong et al. (2019).

In addition, while Gong et al. ﬁnd that a higher share of female peers results in lower rates of

reported unhappiness among female students, they ﬁnd that only male students report greater life

fulﬁllment, conﬁdence for the future, and private recreation with their classmates.

I also examine speciﬁcations without individual level controls, using the average numerical

response as opposed to the count of afﬁrmative responses, and using the probability of an afﬁr-

mative response for each individual non-cognitive question. Tables B.1.5 through B.1.7 contain

the results. Across each speciﬁcation, the results are similar. Male students report slightly higher

sense of belonging and self-worth when exposed to more female peers while female students do

not report sense of belonging or self-worth changes that are statistically different from zero.

Finally, I use simulation methods to test the robustness of the results to measurement error in

the share of female peers. Share of female peers is based on individual-level responses to the in-

school questionnaire and is not a precise measure of the true share of female students in a school

and grade, as not every student in every school was in attendance or agreed to take the survey.

39

School administrators did report how many students were on their roster for the in-sample grades,

allowing me to calculate the percentage of students who responded to the survey. As shown in

Figure B.1.4, most students in my sample attended schools that had an 80% response rate or higher,

and every student in my sample attended a school with at least a 50% response rate. The effect of

measurement error on the point estimates is unknown ex ante, as the measurement error does not

satisfy the classical assumptions. To account for this bias, I follow a multiple imputation procedure

and adjust the standard errors according to the formula proposed by Rubin and Schenker (1986).

I assume that the observed share of female students in a school and grade is an unbiased es-

timate for the true share of female students, which would be true if in-school questionnaire par-

ticipation is uncorrelated with gender. Next, I estimate the number of missing students in a grade

by multiplying the number of missing responses in a school by the share of the grade within each

school. I then create 100 simulated data sets ﬁlling in the missing students with draws from a Bi-

nomial distribution using the probability of being female and number of missing students in each

school and grade. I re-estimate my model for each data set, replacing the observed share of female

peers with a simulated share of female peers. The average point estimate is a consistent estimate

for the theoretical point estimate without measurement error in the share of female peers, and the

average standard error, plus a term to correct for the variation across simulations, is a consistent

estimate for the standard error without measurement error. As shown in Table B.1.8, the point

estimates for the share of female peers are slightly smaller than in the baseline model. The primary

ﬁnding is unchanged.

2.6 Conclusion

Although many researchers have established the importance of non-cognitive factors, the liter-

ature on how to develop these factors is still growing. This chapter ﬁnds evidence that a mechanism

for cognitive skill development, peer gender composition, is a minor input into the formation of

two non-cognitive factors, sense of belonging and self-worth, for adolescent males. While I do

not ﬁnd evidence that peer gender composition is also a determinant of sense of belonging and

40

self-worth for female adolescences, it may play an important role for other non-cognitive factors

and should be explored further in subsequent research.

41

THE EVOLUTION OF THE WAGE ELASTICITY OF LABOR SUPPLY OVER TIME

CHAPTER 3

3.1 Disclaimer

This chapter was co-authored with Todd Elder (telder@msu.edu) and Steven J. Haider

(haider@msu.edu). Both authors have approved that this work be included as a chapter in my

dissertation.

3.2 Introduction

The wage elasticity of labor supply is arguably one of the most fundamental parameters in

economics. This parameter captures how a change in the net wage, perhaps induced by a change in

taxes, retirement credits, or productivity, affects labor supply, measured by the number of workers

or work hours. With such a parameter in hand, and especially with knowledge of how it varies

with observable characteristics, one can readily forecast how labor supply will respond to policy

changes that affect wages. Moreover, the magnitude of the wage elasticity has implications for

numerous questions, such as optimal taxation, the causes of business cycles, and the role of human

capital formation, to just name a few.

Despite the importance of the wage elasticity of labor supply, there exists limited evidence

about how this parameter has changed over time. Several papers have studied changes in women’s

elasticities, documenting a strong decline for both married (Kumar and Liang 2016; Blau and

Kahn 2007; Heim 2007;) and single (Bishop et al. 2009) women. Most of these papers do not

include data for years beyond the early 2000s, and one paper in particular ﬁnds that the declining

trend slowed at the turn of the century, suggesting that newer estimates might tell a different story

(Kumar and Liang 2016). A recent meta-analysis also ﬁnds declining elasticities for women in

both Europe and the US (Bargain and Peichl 2016), but the authors conjecture that changes in how

researchers have estimated labor elasticities may account for some of the intertemporal variation in

42

the estimates. There is little formal analysis of the trend in labor supply elasticities for men outside

of meta-analysis and cross-paper comparisons.

In this chapter, we use a consistent econometric approach to examine how the wage elasticity of

labor supply has changed over time. First, we provide a theoretical discussion on why elasticities

might evolve over time and a review of the existing literature on labor supply elasticity trends.

We then propose a static discrete choice model and estimation strategy that exploits variation in

wages due to variation in marginal tax rates across households and income ranges. At the same

time, we critically examine the importance of our modeling decisions and test the robustness of our

estimated trends to these decisions. In doing so, we contribute to the methodological literature that

assesses the sensitivity of labor supply research to its modeling assumptions. See L¨oefﬂer et al.

(2018) for an excellent recent example.

We have two primary ﬁndings. One, there is robust evidence that the labor supply elasticities

for married and single men and women have increased modestly over the last two decades. For

women, this is a reversal of previous trends. Second, our results suggest that many computationally

costly decisions, like using maximum simulated likelihood to include time-invariant idiosyncratic

preference heterogeneity and to integrate out measurement error in wages, do not signiﬁcantly alter

the estimated trends in elasticities.

3.3 Background and literature review

Numerous integrative surveys have summarized the vast literature on labor supply elasticities;

see Blundell and MaCurdy (1999) and Keane (2011) for just two examples. In this section, we

brieﬂy lay out the basic issues related to our research question, heavily relying on the exposition

in Keane (2011).

43

3.3.1 The key elasticities

In a static model, two key wage elasticities arise. The ﬁrst is the Marshallian (or uncompen-

sated) elasticity eM, which measures how hours worked h change with a change in wage w:

eM =

w
h

∂ h
∂ w.

(3.1)

The second is the Hicksian (or compensated) elasticity eH, which measures how hours change with
a change in wage, holding utility u constant:

(cid:12)(cid:12)(cid:12)u

eH =

w
h

∂ h
∂ w

.

(3.2)

Letting eI denote the income elasticity of labor supply and s denote the share of income accounted
for by labor income, the Marshallian and Hicksian elasticities are related to each other based on

the Slutsky equation when labor supply is a continuous choice:

eM = eH +

s
1− s

eI.

(3.3)

Under the assumption that leisure is a normal good, the income elasticity is negative, implying that

the Hicksian elasticity is greater than the Marshallian elasticity.

In a life-cycle model, these two elasticities measure the effect of a permanent (or parametric)

change in wages – the Marshallian elasticity when the permanent wage change is uncompensated

and the Hicksian elasticity when the permanent wage change is compensated. In addition, the life-

cycle model introduces the Frisch (or intertemporal) elasticity, which measures how labor supply

responds to known wage changes between two periods. Based on the standard assumption of

diminishing marginal utility, we know that the Frisch elasticity is greater than the other two.

Which elasticity is relevant depends on the particular policy being considered. The effect of a

newly imposed tax to fund a public good might be best approximated with the Marshallian elastic-

ity, whereas the imposition of a tax to fund a universal income transfer might be best approximated

by the Hicksian elasticity. The evaluation of a change in tax rate with age, such as that with the

Social Security retirement earnings test, might be best approximated with the Frisch elasticity.

44

Regardless of which elasticity is most targeted, the econometrician’s assumptions and empir-

ical speciﬁcations may signiﬁcantly affect their estimates of labor supply elasticities. Key issues

include the simultaneity of wages and hours, the treatment of taxes, measurement error in wages

and non-labor income, the treatment of missing wages for non-workers, the possibility of non-

separabilities between consumption and leisure and over time, the choice of control set, what is

considered to be exogenous, and the sources of dynamics like human capital accumulation. Blun-

dell and MaCurdy (1999) and Keane (2011) include detailed discussions of these and other econo-

metric issues. The literature is large and complex, and given this complexity, empirical studies

often must make compromises at various points in their analysis.

3.3.2 Why might elasticities vary over time?

Within the canonical model of labor supply where jobs are only indexed by the wage rage

and workers can freely choose their hours, a few hypotheses exist that can explain why labor sup-

ply elasticities might change. Secular changes in wages or non-labor income, including changes

in government programs that provide income to non-workers and compositional changes in the

population (e.g., age distribution, marriage rates, and number of children) that alter eligibility for

existing programs, could affect the Marshallian elasticity (Bishop et al. 2009; Heim 2007). Com-

positional changes in the population can also affect the distribution of preferences for consumption

and leisure even if the underlying conditional preferences are unchanged. For example, prefer-

ences for leisure might increase with number of children. As family size increases or decreases, so

might the wage elasticity even if the relationship between children and utility of leisure does not.

A less satisfying explanation is that preferences themselves have changed over time.

Additional explanations for evolving labor supply elasticities arise outside of the canonical

model. Certain hours-wage bundles may be restricted by the demand side of the labor market, and

these restrictions can loosen or tighten over time. Similarly, their could exist time-varying ﬁxed

costs of work (e.g., commuting) that make certain hours-wage bundles particularly unappealing.

The composition of non-pecuniary job attributes can also change over time, affecting individuals’

45

willingness to work at all or work long hours (Blau and Kahn 2007; Atrostic 1982). While we do

not include non-pecuniary job attributes in this research, we are able to incorporate ﬁxed costs of

part-time work.

3.3.3 Evidence on trends in labor supply elasticities

Several papers have examined changes in the labor supply elasticities of women, and the title of

one notable example succinctly summarizes the literature: “The Incredible Shrinking Elasticities:

Married Female Labor Supply, 1978-2002” (Heim 2007). Based on March Current Population

Survey (CPS) data from 1979 through 2003, Heim ﬁnds that the wage elasticity declined by about
60 percent from an initial base of 0.36.1 Blau and Kahn (2007) examine changes for married

women using 1980 through 2000 March CPS data. They ﬁnd that the wage elasticity dropped

by just over 50% from an initial base of about 0.80. Both papers use a continuous labor supply

model with a Heckman selection correction to account for unobserved wages among non-working

women. Important for our ﬁndings, neither paper ﬁnds that the downward trend diminished in later

years. Kumar and Liang (2016) also examine the labor supply elasticities of married women, but
they use the 1980 through 2006 Panel Study of Income Dynamics (PSID).2 Kumar and Liang ﬁnd

large declines in elasticities, but they provide some evidence that the declines level off during the

very last years of their sample period.

Moving from married women to single women, Bishop et al. (2009) estimate changes in the

wage elasticity for single women using the March CPS from 1979 through 2003. With a continuous

choice model, they conclude that the wage elasticity of labor supply declined by about 80 percent

from an initial base of about 0.20. There is little evidence that the downward trend diminished

towards the end of their sample period.

1Unless otherwise speciﬁed, we report Marshallian elasticities when referencing results from

previous studies.

2Although the authors provide some estimates that exploit the panel nature of their data, we
focus on the estimates obtained from pooled models that are similar to those estimated by Heim
(2007) and Blau and Kahn (2007).

46

Several systematic literature reviews also provide evidence about how the wage elasticity has

changed over time. Keane (2011) provides a list of estimates from eight different studies that

exhibit little change from 1980 to 2001 in the wage elasticity for men. Based on an exhaustive

list of studies from both the United States and Europe, Bargain and Peichl (2016) do not ﬁnd ev-

idence of a systematic trend in wage elasticities for men, but they do observe a downward trend

in elasticities for married and single women. Interestingly, Bargain and Peichl (2016) demonstrate

that researchers are increasingly using discrete choice estimation methods to estimate wage elas-

ticities, and the downward trends in female elasticities are somewhat ﬂatter when using estimates

from these discrete choice studies as opposed to estimates from continuous choice studies.

3.4 Empirical methods

We rely on a static model of labor supply throughout our analysis. The motivation for doing

so is that static models continue to play a prominent role in assessing the responsiveness of hours

to wages. Bargain and Peichl (2016) list numerous examples of recent papers that estimate a

static model, and two prominent papers that provide a synthesis of our understanding of Hicksian

elasticities rely on estimates from static models (Keane 2011; Chetty et al. 2011). In addition, we

are able to use the methods from other papers that allow us to isolate plausibly exogenous variation

in wages that stems from between-state and intertemporal variation in marginal tax rates.

Many of the recent papers that estimate the wage elasticity of labor supply do so using a dis-
crete choice framework pioneered by van Soest (1995).3 This approach is particularly well-suited

to examining our question. First, it directly incorporates non-participation into the labor supply de-

cision, allowing us to study the extensive and intensive margins in a common framework. Second,

it allows us to utilize plausibility exogenous variation in wages caused by variation in the marginal

tax rate across states and across time. Third, it allows us to incorporate ﬁxed costs of working as

well as other nonconvexities of the wage-hours locus.

3In a recent literature review, Bargain and Peichl (2016) compile papers that have estimated
wage elasticities by time and the method used. Pooling across European and US studies, there is a
clear trend towards using the discrete choice framework.

47

3.4.1 A static discrete choice model of labor supply

For notational ease, we ﬁrst describe our discrete choice model for single (non-married) in-

dividuals. Suppose an individual i chooses hours of work per week hi j from a set of J different
alternatives. For singles, J = 7 and hi j ∈ {0,10,20,30,40,50,60}. We assume that the individual
earns a constant pre-tax hourly wage wi regardless of their hours choice. Each choice of weekly
work hours delivers a different level of weekly consumption ci j and leisure li j. Consumption is
equal to the sum of household labor income (wi × hi j) and non-labor income (yi), after taxes and
government beneﬁts. Leisure is equal to the total time endowment per week (112 hours) less
weekly work hours.4 Thus, each individual has the choice of seven different bundles {ci j,li j} j∈J.
The portion of utility that depends on the hours-consumption bundles and individual taste

shifters xi is denoted by ui j(ci j,li j,xi). Total utility is deﬁned by:

vi j = ui j(ci j,li j,xi) + εi j

(3.4)

where εi j is an i.i.d. extreme value type I error term. Based on this error assumption, the probability
of individual i choosing choice j, denoted pi j, is given by the closed-form expression:

pi j(wi,yi) ≡ Pr(vi j ≥ vik, ∀k (cid:54)= j) =

.

(3.5)

exp(cid:0)ui j(ci j,li j,xi)(cid:1)

∑J
k=1 exp (uik(cik,lik,xi))

This expression is the familiar conditional logit form for choice probabilities.

For our baseline model, we adopt the translog function for ui j, as speciﬁed by van Soest

(1995):5

ui j = β c lnci j + β cc(lnci j)2 + β l

i lnli j + β ll(lnli j)2 + β cl lnci j lnli j + f (xi,hi j).

(3.6)

We allow the parameter β l

i to vary with several individual characteristics (a quadratic in the loga-
rithm of age, the number of dependents aged 0 to 2 years, and the number of dependents aged 18 or

younger) as we discuss in more detail below. The term f (xi,hi j) allows for ﬁxed utility decrements

4We assume that individuals have 112 total hours per week to devote to work or leisure with

the remaining 56 hours spent on sleep and personal care.

5Other authors who use a translog function include Flood et al. (2004) and Haan (2006).

48

of working ten, twenty, and thirty hours per week; these utility decrements might arise due to the

true ﬁxed costs of working part time, or they might capture employers’ choices to not offer these

hours packages (van Soest 1995).

For married households, we amend the basic speciﬁcation to include a quadratic function of the

logarithm of leisure for both spouses, as well as an interaction between the logarithms of leisure of

each. Each spouse has their own ﬁxed utility decrements of working ten, twenty, and thirty hours

per week. The choice set for married couples is all combinations of the seven hours choices for

each spouse, delivering 49 different hours choices for the couple.

At this point, one could estimate the model via maximum likelihood, but researchers routinely

incorporate two extensions. The ﬁrst is in recognition that a conditional logit functional form

imposes the independence of irrelevant alternatives property (IIA), which implies that if one choice

is taken away, an individual must substitute towards all other choices proportionally. Introspection

suggests that an individual would be more likely to substitute towards a “nearby” hours choice. To

allow for richer substitution patterns, a random term is included in the individual-speciﬁc slope on

leisure:

β l
i = δ0 + δ1 lnagei + δ2(lnagei)2 + δ3dep2i + δ4dep18i + ξi

(3.7)

where dep2i and dep18i are the number of dependents under the ages of two and 18, respectively,
and ξi ∼ N(0,σ 2
ξ ) is idiosyncratic preference heterogeneity for leisure (random slope). This spec-
iﬁcation avoids imposing IIA for the pooled sample of observations; however, IIA is still present

at the individual level once we condition on ξi.

The second extension reﬂects that wages must be predicted for non-workers (and possibly

for workers, too), which generates measurement error in the wages used for elasticity estimation.
Speciﬁcally, suppose true wages w∗

i are given by:

w∗
i = ˆw(xi) + ηi

(3.8)

where ˆw(xi) are expected wages based on covariates xi and ηi is the idiosyncratic component to
wages. We follow the common practice of “integrating out” measurement error. In practice, this

49

amounts to pre-specifying the distribution of ηi, taking draws from this assumed distribution, and
integrating over the draws when we maximize the simulated likelihood function (see van Soest

(1995) for a more rigorous description). We specify that the measurement error in wages is nor-

mally distributed with zero mean and variance given by a Heckman selection model. We describe

our Heckman selection procedure in Appendix Section C.2.

To accommodate the random slope on leisure and measurement error in wages, we estimate our

utility parameters using maximum simulated likelihood (MSL). Deﬁne the likelihood contribution

for a single individual as:

Li =

(cid:90) (cid:90) (cid:104)

(cid:105)
pi j(wi,yi | ξi)1[ j= j∗] f (ξi)

dFη (ηi)dFξ (ξi)

(3.9)

where pi j(wi,yi|ξi) is the probability of individual i choosing work hours j conditional on the
random slope term ξi, j∗ is the observed work hours choice, f (ξ ) is the density of ξ , Fη is the
cumulative density of η, and Fξ is the cumulative density of ξ . This likelihood contribution can be
approximated by taking R independent draws of (ξi,ηi) from their joint distribution and averaging
over the draws. Speciﬁcally:

LiR =

R
∑
r=1

pi j(wir,yi | ξir)1[ j= j∗]; wir ∼iid Fη;

ξir ∼iid Fξ .

(3.10)

Our baseline estimation uses 100 draws from a Halton sequence for the wage error and random
slope.6

3.4.2 Estimating the elasticities

With parameter estimates in hand, we can directly simulate counterfactuals and compute elas-

ticities. Speciﬁcally, we use the parameter estimates and Equation 3.5 to predict the probability

that each individual i choices each choice j. We then calculate the expected hours worked for

6Halton sequences are deterministic sequences that cover domains of integration more evenly
than do independent pseudo-random draws. As Train (2009) argues, simulations using Halton
draws exhibit greater accuracy than those using pseudo-random draws, particularly in the context
of logit choice models.

50

each individual as the probability-weighted average of hours. Next, we vary the wage or non-labor

income for each individual, depending on the elasticity, and recalculate the predicted probabilities

of each choice and expected hours worked. The percent change in expected hours worked is the

numerator for our elasticity, and the percent change in wages or non-labor income is the denomina-

tor. We report the mean elasticity across individuals and derive standard errors using a parametric

bootstrap with 50 draws from the joint distribution of utility parameters.

For the Marshallian own-wage elasticity, our estimated elasticity for each individual is given

by:

eM =

∑ j h j ∗(cid:16)

(cid:17)
p j(w1)− p j(w0)

∑ j h j ∗ p j(w0)

∑ j h j ∗(cid:16)

(cid:17)
p j(w1)− p j(w0)
∆w∗ ¯h(w0)

∗ 1
∆w =

(3.11)

where w0 is the individual’s original wage, w1 is a counterfactual wage that is ∆w% higher, and
¯h(wk) is the estimated hours worked when an individual is faced with wage wk, i.e., ¯h(wk) =
∑ j h j ∗ p j(wk). The quantities are evaluated for individual i with a non-labor income of y, which
we suppress to simplify notation. For all of our reported elasticities, ∆w is one percent, though our

observed trends are nearly identical for ∆w equal to ten percent.

To provide further information about the underlying source of hours changes, we decompose

the Marshallian elasticity into extensive (eEXT

eINT
M =

(3.13)
where q j(wk) = p j(wk)/(1− p0(wk)). This decomposition ensures that the underlying compo-
nents sum to the Marshallian elasticity (eM = eEXT
M ), with the ﬁrst component measuring
the change in the probability of not working and the second measuring the change in expected

M + eINT

∆w∗ ¯h(w0)

hours conditional on working.

We estimate income elasticities by increasing each individual’s after-tax non-labor income by

$1,000 in nominal value, but because some individuals have no non-labor income, we compute

51

eEXT
M =

and

M ) and intensive (eINT

M ) components:

(cid:104)(cid:16)
1− p0(w1)
(cid:104)(cid:16)
1− p0(w1)

1− p0(w0)
∆w∗ ¯h(w0)

(cid:17)−(cid:16)
(cid:17)(cid:105)∗ ∑ j(cid:54)=0 h j ∗(cid:16)

(cid:17)(cid:105)∗ ∑ j(cid:54)=0 h j ∗ q j(w0)
(cid:17)
q j(w1)− q j(w0)

(3.12)

an arc elasticity by using the average non-labor income (pre- and post-$1,000 increase) in the

denominator, as opposed to the percentage change.

Rather than use the Slutsky decomposition in Equation 3.3 to derive the Hicksian elasticity, we

calculate the Hicksian elasticity using an income compensation so individuals’ expected earnings
at ¯h(w1) and w1 are attainable at ¯h(w1) and the original wage w0:

∑ j h j ∗(cid:110)

p j

w1,y

eH =

(cid:17)− p j(w0,y +

(cid:16)
∆w∗ ¯h(w0,y +(cid:2) ˜w(w1,y)− ˜w(w0,y)(cid:3)∗ ¯h(w1,y))

˜w(w1,y)− ˜w(w0,y)

(cid:104)

(cid:105)∗ ¯h(w1,y))
(cid:111)

(3.14)

where ˜w(wk,y) denotes the expected after-tax earnings when an individual faces wage wk and non-
labor income y.7 Equation 3.14 shows that, in order to calculate the Hicksian elasticity, we should
compute the choice probabilities at the original wage w0 while increasing non-labor income by the
expected increase in after-tax income due to the wage change from w0 to w1. This adjustment to
non-labor income allows us to remove the income effect caused by the higher wage.8

3.5 Data

Our primary data source is the 1979 through 2017 Annual Social and Economic March Sup-

plement of the Current Population Survey (CPS). These surveys provide total earnings and hours

worked for the previous year, as well as demographic information like number of dependents and

state of residence. We list all results by survey year throughout the paper.

The sample is restricted to adults in single-family households as deﬁned by Census Bureau.

Single adults must be between 26 and 55 years old, and couples must have one spouse between

26 to 55 years old and the other spouse between 22 and 59 years old. We exclude individuals

7The fact that the Slutsky equation may not hold in a discrete choice model is well-developed
elsewhere, including Dagsvik and Karlstr¨om (2005) and Dagsvik et al. (2014). The formulation we
implement is simpler than the approaches laid out in these studies, in part because we use income
compensation rather than utility compensation for the worker.

8An alternative approach to the one stated here involves increasing the wage rate but reducing
after-tax income by the difference between expected earnings at the higher wage and original
wage. For some individuals, the non-labor income decrease results in negative consumption and
undeﬁned utility. However, for individuals with well deﬁned utility under both approaches, the
estimated Hicksian elasticities are nearly identical.

52

who are enrolled in school, disabled, self-employed, members of the armed forces, earn farm or

business income, work unpaid in a family business, report wages less than $4 per hour or more

than $150 per hour, or report non-labor income less than $0 or greater than $1,000,000. We do not

exclude individuals with imputed survey responses. If either spouse meets our exclusion criteria,

we exclude the entire household. For married couples, if the age-year sample is greater than 10,000

households, we take a random sample of 10,000 households to reduce the computational burden of

estimating our models.

We use usual hours worked per week from the prior year and discretize hours into seven

choices: 0, 10, 20, 30, 40, 50, and 60 hours per week. We compute the hourly wage from wage

and salary income in the prior year divided by the usual work hours multiplied by weeks worked

in the prior year. Non-labor income is the sum of dividend income, interest income, rental income

and other property income, alimony, child support, and other non-property income. Wages, of

course, are unobserved for non-workers, so we impute wages for non-workers based on a stan-

dard Heckman selection procedure. Appendix Section C.2 contains complete details of the sample

construction, basic descriptive statistics, and parameters from the Heckman corrected wage esti-

mation.

We supplement the CPS with two additional data sources. The ﬁrst is NBER’s TAXSIM,

which allows us to calculate after-tax income by state and year utilizing micro-level information on

earnings, state of residence, and household structure. The second is the Urban Institute’s TRIM3,

which allows us to calculate the social program beneﬁts a household qualiﬁes for (e.g., AFDC,

SNAP, SSI) based on their household earnings, state of residence, and household structure. Data

from TRIM3 is available from survey years 1994 to 2000 and 2002 onward, so we restrict most
of our analysis to this time frame.9 See Appendix Section C.3 for further details on how we

incorporate TAXSIM and TRIM3.

As an initial look at the data, Figure C.1.1 shows the labor force participation rate, average

9While TRIM3 beneﬁt simulations are available for 2001, they do not include observations
from the SCHIP expansion, and the individual identiﬁers which are normally used to merge the
TRIM3 data to the ASEC data do not match.

53

annual hours worked conditional on working, average wage conditional on working, and average

non-labor income for our primary sample period and for four demographic groups (single and

married men and women). The well-documented changes are readily apparent. Labor force partic-

ipation decreased modestly for men, increased for single women during the 1990s, and remained

relatively constant for married women. Among the employed, annual hours worked and wages

increased for all four demographic groups despite a brief decline in the late 2000s. Non-labor

income is very sensitive to broader business cycles and does not have a clear upward or downward

trend over time.

For a more detailed look at labor force behavior, Table C.1.1 shows the distribution of hours

worked for select years across our primary sample period. The modal choice of each demographic

group is 40 hours per week, and for every group except for married women, approximately 60%

choose 40 hours. Men, both single and married, are more likely to work 50 or more hours per

week than work 30 or fewer hours. Married women are consistently more likely to work 30 or

fewer hours than 50 or more hours.

3.6 Results

We ﬁrst present our baseline results for Marshallian own-wage elasticities in Section 3.6.1,

followed by results based on different utility function assumptions in Section 3.6.2. Section 3.6.3

contains results based on different approaches for addressing measurement error in wages. Finally,

Section 3.6.4 presents results for other elasticities, including extensive and intensive Marshallian

elasticities and Hicksian elasticities. Parameter estimates for our baseline speciﬁcation are pro-

vided in the Appendix Section C.4

3.6.1 Baseline results

the variance on the random slope for leisure is zero (σ 2

For our baseline results, we estimate the model outlined previously, except we impose that
ξ = 0). While this implies that we are
estimating a typical “conditional logit” model as opposed to a “random slope logit” model, we still

54

utilize MSL to integrate out the measurement error in predicted wages for non-workers. We relax

this assumption in the next subsection.

Figure C.1.2 presents in dark blue the mean own-wage elasticities from 1994 through 2017 as

estimated from our baseline model. The same estimates are reported for select years in Tables C.1.2

and C.1.3. For three groups – single men, married men, and married women – we observe small

increases in the labor supply elasticity over time. For example, the own-wage elasticity increases

from 0.050 (standard error: 0.012) to 0.113 (0.012) for single men from 1994 to 2017, from 0.090

(0.004) to 0.118 (0.005) for married men, and from 0.261 (0.009) to 0.340 (0.010) for married

women. For the fourth group, single women, the estimates increase after 2000, from 0.141 (0.011)

in 2000 to 0.231 (0.012) in 2017, but given the decline in the elasticity from 1994 to 2000, the

elasticity is relatively ﬂat over the full time period. The modest increase in the own-wage elasticity

over the last two decades across various groups represents one of the key ﬁndings of our paper.

The conclusion that own-wage elasticities were declining for single women up to 2000 is not

surprising given previous work (e.g,. Heim 2007). But because our baseline estimates use a beneﬁt

simulator that begins in 1994, they are only partially comparable to previous papers that examine

trends in own-wage elasticities. We can produce a consistent set of elasticity estimates, going back
as early as 1979, by ignoring government assistance.10 These estimates are presented in Figure

C.1.2 with dark red lines and triangular markers.

The removal of the beneﬁt simulator has little affect on the estimated elasticities for most

demographic groups and years, especially for men. Elasticities for single and married women are

more sensitive to removing the beneﬁt simulator, but the trends observed from 1994 onward are

still apparent. Additionally, the inclusion of data from 1979 to 1993 reveals a steady upward trend

in the mean own-wage elasticity for single and married men and a downward trend for single and

married women lasting until 2000. These patterns are similar to those found in previous studies

10Many previous papers that calculate own-wage elasticities do not include government assis-
tance, such as Heim (2007), Blau and Kahn (2007), and Bishop et al. (2009). By excluding gov-
ernment assistance, not only do we obtain a consistent time series over a longer period, we also
produce estimates that are more comparable to the existing literature.

55

that examined this earlier time period.11

3.6.2 Robustness to alternative utility function assumptions

A simplifying assumption that we made for our baseline results is that the variance of the

idiosyncratic preference heterogeneity for leisure is zero. Although this assumption is at odds with

the existing literature, it is not at odds with previous empirical ﬁndings – numerous papers report
results that are consistent with the random slope being unimportant.12 Regardless, we compare our

baseline conditional logit results to results from a random slope logit model where the variance on

the leisure preference heterogeneity term is not restricted to be zero.

As shown in Figure C.1.3, the effect of adding random slopes to leisure varies by demographic

group. For single women, neither the level nor the trend are sensitive to this modeling change,

though the standard errors are signiﬁcantly noisier. This occurs because the estimated variance

on the random slope for leisure is near zero in almost every year, but the standard errors on the

variance are quite large. Elasticity estimates are nearly identical for married men with a random

slope, but the estimates shift upward (while preserving the same the trend over time) for married
women, and the standard errors are often incalculable.13 The group for whom the random slope

11For single women, our baseline results suggest that the own-wage elasticity declined by 47%
from 1979 to 2000, from 0.261 (standard error: 0.019) to 0.138 (0.011). In Bishop et al. (2009),
the authors ﬁnd an 80% decline from a base of 0.20 over a similar period.

12van Soest (1995) estimates random slopes with variances that are not statistically different
from zero and very small relative to the mean value. Callan and van Soest (1996) estimate random
slopes with variances that are not statistically different from zero, but the variance for women
could be practically signiﬁcant. van Soest et al. (2002) estimate a precise zero for random slope
variances for women. Brewer et al. (2006) include random slopes on income, female hours, ﬁxed
costs of work, and welfare participation. For single mothers and couples, the ﬁrst three variances
are precisely estimated zeroes, and the fourth is large but statistically insigniﬁcant from zero. Two
papers, Haan (2006) and L¨oefﬂer et al. (2018), examine this issue directly and conclude that labor
supply elasticities tend to change very little when allowing for random slopes on just consumption
or leisure individually, although both papers ﬁnd that allowing for more unrestricted unobserved
heterogeneity can have some small effects on point estimates.

13In some years, after including a random slope, the estimated hessian from the ﬁnal evaluation
of the likelihood function is invertible, but its inversion is not positive semideﬁnite. We use the in-
verse hessian as the covariance matrix when drawing parameter values for our bootstrap procedure,

56

speciﬁcation seemingly matters the most is single men, as the elasticities are consistently larger

and the trend over time is steeper. For single men, the random slope is large enough to roughly

double the mean own-wage elasticity in most years.

In addition to the introduction of random slopes for leisure, we also test the robustness of our

ﬁndings to a quadratic utility function, as used in Bargain et al. (2014), as opposed to our baseline

translog utility function. We present these results in Appendix Section C.5. Both utility functions

yield very similar elasticity estimates.

3.6.3 Measurement error in wages

In Figure C.1.4, we compare elasticity estimates with different strategies to address measure-

ment error in wages. First, we compare estimates using the expected wage for non-workers as

opposed to drawing from the conditional distribution of wages. Across all demographic groups,

both methods yield similar elasticity estimates. One important caveat is both methods only use

predicted wages for non-workers. Because most individuals in our samples are working, this pro-
cedure treats few individuals as having error-laden wages.14 Some previous studies use predicted

wages for both workers and non-workers alike, and accounting for measurement error in those
circumstances likely matters more.15

To analyze this possibility, Figure C.1.4 also presents results that use predicted wages for ev-

eryone. The series labeled “All, 100 Draws” integrates out measurement error using 100 Halton

draws, while the series labeled “All, 0 Draws” ignores measurement error and uses the mean pre-

dicted earnings for everyone. Our results suggest that the decision to predict wages for everyone

or for only non-workers matters, as elasticities tend to be larger when we predict wages for ev-

so when this matrix is not positive semideﬁnite, it cannot be used as a valid covariance matrix.

14In 2014, the percent working is 93% among single men, 88% among single women, 95%
among married men, and 74% among married women. See Appendix Tables C.2.1 and C.2.2 for
the percentage of non-workers in other years.

15Studies that predict wages only for non-workers include van Soest (1995), Blundell et al.
(1998), and Haan (2006). Studies that predict wages for the full sample include Flood et al. (2004)
and Bargain et al. (2014). See L¨oefﬂer et al. (2018) for a discussion and analysis of this issue.

57

eryone; however, the estimated trends are insensitive to this choice. Once again, integrating out

measurement error as opposed to using the mean predicted earnings preserves the estimated trends,
especially for married men and women.16

This ﬁnding has two important implications. First, to the extent that adjusting for measure-

ment error in wages is not necessary, we can use standard maximum likelihood estimation pack-

ages rather than the more computationally costly maximum simulated likelihood methods outlined

above. Second, our analysis of measurement error has ignored the fact that, when adjusting for

measurement error, we were pre-specifying its distribution. By instead relying just on the condi-
tional mean wage, we need to make no such decision about the size of the variance.17

3.6.4 Other elasticities

We now provide estimates of other elasticities beyond the Marshallian total own-wage elastic-

ity: extensive and intensive margin own-wage elasticities, cross-wage elasticities, Hicksian own-

wage elasticities, and income elasticities. All of the following results are based on our baseline

model.

Figure C.1.5 contains estimates for the extensive and intensive margin own-wage elasticities.

Across all four demographic groups, the intensive margin elasticities are small and vary little over

16Why does accounting for measurement error matter little? For the case at hand, a reasonable
representation of the measurement error process is w∗ = w + η, where w denotes expected wages
and w∗ denotes actual wages. This measurement error process differs from the standard classical
measurement error form (which reverses the role of w and w∗) because we are correcting for mea-
surement error in cases where we utilize predicted wages based on a Heckman selection equation.
In other words, we are using predicted wages w in estimation, whereas the actual wages w∗ include
an individual component η that is unobserved. While analytic results are not available for the non-
linear labor supply function we use for estimation, this alternative form of measurement error leads
to little or no effects in other settings. For example, it is straightforward to show that the OLS es-
timate of a regression of y on w is consistent for an OLS regression of y on w∗(assuming that η is
i.i.d. in both cases), which is contrary to the usual attenuation result under classical measurement
error from the use of an error-ridden variable.

17Changes in the assumption on the size of the variance of the measurement error can apprecia-
bly change the results depending on its relative size compared to other parameters in the model.
For example, when predicting wages for everyone (which leads to a large estimated variance),
elasticities tend to be more sensitive to the assumption of its size.

58

time. Thus, changes in the total elasticities are driven almost exclusively by changes at the exten-

sive margin. This ﬁnding aligns with the existing literature; for example, Heim (2007) studying

married women and Bishop et al. (2009) studying single women ﬁnd that the total own-wage elas-

ticity and the extensive margin elasticity decline by the same magnitude during the 1980s and

1990s.

Figure C.1.6 contains estimates for cross-wage elasticities, Hicksian own-wage elasticities,

and income elasticities. Cross-wage elasticities (an individual’s hours response to a change in

their spouse’s wage) are small and relatively stable from 1994 to 2017 for married men (-0.019 to

-0.035) and women (-0.144 to -0.157).

As expected, we ﬁnd that the Hicksian elasticity is consistently larger than the Marshallian

elasticity, and the two follow similar trends over time. The difference between the two elasticities

is signiﬁcantly larger for single men and women relative to married men and women, as individual

labor income makes up a smaller share of total income for married households and the income

elasticities for married couples are smaller. For single men, the Hicksian elasticity increases more

rapidly than the Marshallian elasticity over the entire time period – a 0.152 increase versus a 0.062

increase – but slower in percentage terms – a 54.8% increase versus a 123.0% increase. For single

women, the two have similar percentage declines from 1994 to 2000, but from 2000 onward, the

Hicksian elasticity increases faster in both levels and percentages – a 0.189 (68.0%) increase versus

a 0.058 (33.4%) increase.

The trends in income elasticities vary by demographic group. For single men, income elas-

ticities oscillated up and down until steadily growing more negative after 2000, decreasing from

-0.029 (standard error: 0.008) to -0.092 (0.014) in 2017. Income elasticities for single women

increased rapidly between 1994 to 1999, from -0.369 (0.036) to -0.109 (0.017), before reversing

throughout the 2000s back down to -0.264 (0.026) in 2017. For married men and women, income

elasticities were relatively stable over the entire period with small increases from 1994 to 2005 and

equally small decreases from 2005 to 2017.

59

3.7 Conclusion and discussion

In this paper, we examine trends in labor supply elasticities for four demographic groups: single

and married men and single and married women. Our results suggest that own-wage elasticities

have steadily increased over the last two decades for all four groups. For single and married

women, this ﬁnding is a remarkable reversal of the “incredible shrinking elasticities” reported for

the 1980s and 1990s in previous studies. These reversals were sufﬁciently large to reverse all of

the previous declines for single women and about half of the previous declines for married women.

For all groups, changes in the extensive margin account for nearly all of these trends; the intensive

margin contributes little to overall elasticities regardless of group or time period.

Our results also show that the estimated trends are robust to some of the common alternative

modeling assumptions used in the literature, including computationally demanding assumptions

like the use of random slope logit and integrating out measurement error. This ﬁnding is signif-

icant because researchers who make simpliﬁcations in these dimensions can choose to increase

complexity in other dimensions, like the size of the choice set or non-convexities in the budget set.

Taken together, our results raise an important question: why did labor supply elasticities in-

crease over the last two decades? Because the extensive margin accounted for nearly all of the

increases for all four groups, likely candidates include those factors that affect the decision to

work. Abraham and Kearney (2020) suggest that one potential driver of labor force participation

trends involves increases in the generosity of safety net assistance, namely through federal disabil-
ity insurance, SNAP beneﬁts, or publicly provided health insurance.18 They argue that the latter

two factors likely play small roles in participation trends because of timing inconsistencies, and

that seems likely to be the case for the trends in elasticities as well. For example, the Affordable

Care Act, which went into effect in 2009, cannot explain the increase in estimated elasticities be-

18Abraham and Kearney (2020) examine changes in labor force participation rates among young
and prime-age adults between 1999 and 2018, assessing the evidence for a host of factors that could
explain declining participation rates among men and women younger than 55. While the factors
underlying trends in extensive margin elasticities and in participation rates are not necessarily
identical, it would be surprising if they were wholly unrelated.

60

tween 1999 and 2008 that we ﬁnd for each of the four demographic groups. On the other hand,

federal disability caseloads grew steadily from 1999 to 2015, and Abraham and Kearney (in addi-

tion to Binder and Bound 2019) suggest that this growth may account for as much as ﬁve percent

of the decline in participation rates over the same period. Increased access to disability assistance

may have also contributed to rising extensive margin elasticities over that period by reducing the

relative appeal of working for low wages.

Of course, the increasing trends in (pre-tax) labor supply elasticities may also stem from poli-

cies that increase, rather than decrease, participation rates. The primary candidates involve the

expansions of the Earned Income Tax Credit in 1993, 1996, 2001, and 2009. However, our es-

timated elasticities for both single and married women decline until roughly 2000 (in agreement

with previous estimates) before reversing, which is inconsistent with the steady expansions of the

EITC. Moreover, the expansions cannot explain the evolution of elasticities for single (and, to some

extent, married) men, who are largely ineligible for EITC beneﬁts.

In sum, we ﬁnd clear evidence that labor supply elasticities have increased in the last twenty

years, but convincing explanations for these trends have not emerged. Our estimates suggest that

social program beneﬁts inﬂuence elasticities for women, but accounting for intertemporal variation

in those beneﬁts does not markedly inﬂuence trends. For men, we ﬁnd that the treatment of beneﬁts

has no effect on either the estimated levels or trends in elasticities.

61

APPENDICES

62

APPENDIX A

CHAPTER 1 APPENDIX

A.1 Main text ﬁgures & tables

Figure A.1.1 Distribution of Work Hours

Notes: This ﬁgure presents the distribution of work hours among students with non-zero work
hours. Hours worked in the fall and spring semesters are averaged together. Number of
observations: 1,013 (fall and spring) and 503 (summer).

63

010203040Percent010203040506070Work hours per weekFall/SpringSummerFigure A.1.2 Distribution of Borrowing Amounts

Notes: This ﬁgure presents the distribution of accepted student loans. Number of observations:
1,964 (fall and spring) and 979 (summer).

64

020406080100Percent05101520253035404550Loan amount (thousands)Fall/SpringSummerFigure A.1.3 Grants and Family Support by Unmet Need Quintile

Notes: This ﬁgure presents the average amount of grants and family ﬁnancial support received in
the fall and spring term by quintile of unmet ﬁnancial need. Unmet need is equal to cost of
attendance less grants and family support. The dashed line denotes the average cost of attendance.
Results are separated by residency status (in-state versus out-of-state). Number of observations:
1,767 (in-state) and 197 (out-of-state).

65

Average cost of attendance010,00020,00030,00040,000Average dollars12345Unmet need quintileIn-state studentsAverage cost of attendance020,00040,00060,00080,000Average dollars12345Unmet need quintileOut-of-state studentsGrantsFamily supportFigure A.1.4 Distribution of Expected Grades Conditional on Schoolwork

Notes: This ﬁgure presents the distribution of expected grades conditional on schoolwork time.
Schoolwork time is measured as hours per class per week. Expected grades are calculated from
students’ probabilities of earning each discrete letter grade. Number of observations: 985.

66

0.511.522.533.54Expected grade1 hour3 hours6 hours9 hoursSchoolwork hours per class per weekMean25-75 pct5-95 pctFigure A.1.5 Distribution of Expected Salaries Conditional on GPA

Notes: This ﬁgure presents the distribution of post-school full-time salaries conditional on GPA
upon graduation. Expected salaries are calculated from students’ probabilities of receiving salary
offers in particular ranges. Number of observations: 985.

67

0255075100125150Expected salary ($000s)No degree2.0 to 2.492.5 to 2.993.0 to 3.493.5 to 4.0Graduation status and GPAMean25-75 pct5-95 pctTable A.1.1 Summary Statistics for SEES Respondents and Recipients

Respondents Recipients

0.683
0.813
0.069
0.050
0.093
0.008
0.007
0.107
0.171
0.263
0.285
0.308
0.144
0.253
0.136
0.062
0.031
0.491
0.265
0.014
3.485
985

Variable
Female
White, non-Hispanic
Black or African American
Hispanic
Asian
American Indian or Alaskan Native
Native Hawaiian or Paciﬁc Islander
Out-of-state
First generation
Freshman
Sophomore
Junior
Senior
Honors college
Business
Humanities
Health
STEM
Social Science
Undecided major
Cumulative GPA
Observations
Notes: This table presents summary statistics for the sample of sur-
vey respondents and the continuously enrolled domestic ﬁrst-time-
in-college survey recipients. Each respondent is only counted once
regardless of how many terms they were enrolled at MSU. Class
code, ﬁeld of study, and cumulative GPA are current as of the end of
spring 2019.

0.534
0.778
0.104
0.054
0.088
0.013
0.005
0.136
0.188
0.267
0.286
0.301
0.146
0.159
0.181
0.053
0.025
0.453
0.267
0.020
3.270
4,356

68

Table A.1.2 Credit Hour Enrollment by Semester

Credits

Summer

Full Year

Fall and
Spring
0.00
0.00
0.00
0.00
0.10
0.20
0.51
0.87
19.30
46.59
28.67
3.11
0.61
0.05
0.00
1,964

0.00
0.00
0.00
0.00
0.10
0.10
0.10
0.41
10.83
34.83
25.64
12.46
9.91
3.47
2.15
979

61.70
15.22
16.14
4.90
1.12
0.61
0.31
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
979

0 to 2
3 to 5
6 to 8
9 to 11
12 to 14
15 to 17
18 to 20
21 to 23
24 to 26
27 to 29
30 to 32
33 to 35
36 to 38
39 to 41
42 to 52
Observations
Notes: This table presents the proportion of students en-
rolled in the speciﬁed number of credit hours for both fall
and spring terms and summer terms. Credits hours are
based on enrollment at the quarter point in the semester,
which is the ofﬁcial census date for the University. The
last column, credit hours for the full year, does not include
the fall 2018-spring 2019 academic year because the data
does not contain summer 2019 enrollment data.

69

Table A.1.3 Expected Schoolwork Hours

Work Hours

0 hours 10 hours
21.98
(10.87)

–
–

20 hours

30 hours

18.48
(9.41)

–
–

–
–

21.81
(10.13)

–
–

17.78
(10.21)

12 hours

15 hours

s
r
u
o
H

t
i

d
e
r
C

18 hours

27.71
(11.23)

–
–

20.81
(11.60)

–
–

Notes: This table presents the mean (standard deviation in
parentheses) expected schoolwork hours for each hypothetical
schedule of credits and work hours. Number of observations:
985.

70

Table A.1.4 Data and Model Parameters

Choice variables
Labor supply
Credit hours
Borrowing

Time-varying state variables

Cumulative credits earned
Grade point average (GPA)
Total debt

Other variables

In-school wages
Family ﬁnancial support
Net education expenses

Auxiliary model parameters
Expected study hours
Returns to studying
Wage model

Notation Periods Observed

hit
kit
bit

Kit
Git
Bit

t = {1, . . . ,Ti}
t = {1, . . . ,Ti}
t = {1, . . . ,Ti}

t = {1, . . . ,Ti}
t = {1, . . . ,Ti}
t = {1, . . . ,Ti}

wsch
i
f am(·)
edut(·)

max{t|hit > 0}
t = {1, . . . ,Ti}

t = Ti

δi
γi
ωi

Notes: This table summarizes the key variables in the structural
model and for what periods I observe them in the data. The student’s
ﬁrst semester at MSU is denoted by period 1, and the semester of the
survey is Ti. For example, if the student enrolled in the fall of 2017, I
observe them for three periods, fall 2017-spring 2018, summer 2018,
and fall 2018-spring 2019.

71

Table A.1.5 Auxiliary Model Parameters

Parameter

Mean

Std. Dev.

25th Pct.

75th Pct.

Constant: δ0i
Credit hours: δ1i
Work hours: δ2i
Work hours2: δ3i

Constant: γ0i
Study hours: γ1i
C threshold: γC
B threshold: γB
A threshold: γA
Error variance: σ g

Panel A: Studying function

2.525
-0.056
-0.020
0.00014

1.767
0.086
0.046
0.00128

1.260
-0.106
-0.046
-0.00057

3.667
-0.002
0.006
0.00083

Panel B: Grade production function

1.551
0.319

0.451
0.193

2.263
0.453

1.279
0.367
1.183
2.423
3.768
-0.0017

Panel C: Post-school salary offer

0.338
0.419
0.595
0.292
0.144

10.352
0.302
0.186
0.114
0.359
985

Constant: ω0i
Degree premium: ω1i
GPA x Degree: ω2i
GPA2 x Degree: ω3i
Error variance: σ w
i
Observations
Notes: This table presents summary statistics for the distribution of parameters
estimated before the structural model. The studying function can be found in
Eq. 1.12, the grade production function in Eq. 1.13, and the post-school salary
offer function in Eq. 1.15.

10.087
0.028
-0.101
-0.016
0.267

10.579
0.556
0.473
0.260
0.461

72

Table A.1.6 Structural Model Parameters

Coefﬁcient Std. Err.

In-school utility

Log(Consumption)
Log(Leisure)

Summer
Log(GPA)
1[Work > 0]

Summer

1[Credits = 0]
1[Credits = 15]
1[Stafford loan]
1[Max loan]

Post-school utility

Log(Post-school wage)
Log(Post-school debt)

(0.033)
(0.062)
(0.151)
(0.022)
(0.064)
(0.185)
(0.394)
(0.070)
(0.118)
(0.206)

(1.083)
(0.040)

Observations
Notes: This table presents the estimated parameters
to the utility functions speciﬁed in Eq. 1.10 and Eq.
1.14. To reduce computation time, I use a 15% sample
of the data to estimate the parameters.

0.578
0.465
2.637
0.899
-0.638
0.023
1.750
0.859
-0.040
-0.826

26.646
-1.213
142

73

Table A.1.7 Observed and Predicted Choice Probabilities

Observed
Panel A: Credit hours

Predicted

Difference

Fall and spring
26 credits
30 credits
34 credits
Summer
0 credits
3 credits
8 credits

Fall and spring
0 hours
10 hours
20 hours
Summer
0 hours
20 hours
40 hours

0.332
0.630
0.038

0.613
0.147
0.240

0.382
0.570
0.048

0.647
0.256
0.097

Panel B: Work hours

0.539
0.280
0.181

0.495
0.138
0.367

0.587
0.191
0.222

0.563
0.269
0.167

Panel C: Borrowing

Fall and spring
No new loans
Stafford loans
Maximum loans
Summer
No new loans
Stafford loans
Maximum loans

0.558
0.363
0.079

0.924
0.066
0.009

0.598
0.348
0.054

0.893
0.037
0.070

-0.050
0.060
-0.010

-0.034
-0.109
0.143

-0.048
0.089
-0.041

-0.068
-0.132
0.200

-0.040
0.015
0.025

0.031
0.029
-0.061

Notes: This table presents the observed and predicted probabilities
of each discrete choice in the model. Number of observations: 1,964
(fall and spring) and 979 (summer).

74

Table A.1.8 Elasticities (Fall and Spring)

Elasticity

Mean

25th Pct. Median 75th Pct.

Panel A: Credit hours elasticities (Mean: 28.36)

Financial aid
Tuition rate
Return to studying
Return to GPA
Wage

0.0032
-0.0028
-0.0082
0.0035
-0.0010

(0.0005)
(0.0003)
(0.0007)
(0.0005)
(0.0001)

-0.0024
-0.0007
-0.0100
-0.0003
-0.0016

-0.0002
0.0000
-0.0008
0.0019
-0.0005

Panel B: Work hours elasticities (Mean: 6.29)

Financial aid
Tuition rate
Return to studying
Return to GPA
Wage

0.0012
0.004
-0.119
-0.211
0.291

(0.0029)
(0.003)
(0.005)
(0.006)
(0.033)

-0.0093
-0.007
-0.217
-0.201
0.188

0.0000
0.000
-0.022
-0.034
0.262

0.0001
0.0003
0.0049
0.0082
0.0001

0.0023
0.018
0.094
0.000
0.357

Panel C: Borrowing elasticities (Mean: $3,947)

-0.781
0.233
-0.059
0.0057
-0.092

-0.166
-0.005
-0.063
-0.0232
-0.140

-0.009
0.027
-0.006
-0.0025
-0.044

0.001
0.172
0.009
0.0059
-0.022

(0.043)
(0.013)
(0.012)
(0.0080)
(0.013)

Financial aid
Tuition rate
Return to studying
Return to GPA
Wage
Notes: This table presents estimated elasticities for the fall and spring periods.
Elasticities estimated via simulation with (1) a $1,000 increase to ﬁnancial aid
(2) a 10% increase to tuition (3) a 10% increase to the return to studying param-
eter γ1i (4) a 10% increase to the return to GPA parameters in the post-school
wage function ω2i and ω3i (5) a 10% increase to the in-school wage rate. All
elasticities are calculated as arc elasticities where percentage changes are based
on the midpoint between the original and simulated variables. Standard errors
estimated via a parametric bootstrap with 30 draws from the joint distribution of
utility parameters. Number of observations: 1,964.

75

Table A.1.9 Elasticities (Summer)

Elasticity

Mean

25th Pct. Median 75th Pct.

Panel A: Credit hours elasticities (Mean: 2.43)

Financial aid
Tuition rate
Return to studying
Return to GPA
Wage

-0.028
-0.0058
0.011
0.177
-0.051

(0.004)
(0.0020)
(0.033)
(0.011)
(0.007)

-0.040
-0.0171
-0.004
0.033
-0.076

-0.022
-0.0056
0.075
0.126
-0.043

-0.010
-0.0031
0.181
0.273
-0.020

Panel B: Work hours elasticities (Mean: 17.01)

Financial aid
Tuition rate
Return to studying
Return to GPA
Wage

-0.0029
-0.0077
-0.0084
-0.019
0.238

(0.0010)
(0.0008)
(0.0019)
(0.002)
(0.031)

-0.0174
-0.0065
-0.0226
-0.026
0.173

-0.0060
0.0001
-0.0032
-0.010
0.236

0.0192
0.0006
0.0096
-0.001
0.291

-0.049
0.038
-0.019
0.142
-0.164

(0.009)
(0.009)
(0.040)
(0.010)
(0.020)

-0.067
-0.012
-0.019
0.015
-0.242

-0.020
0.041
0.176
0.208
-0.062

Panel C: Borrowing elasticities (Mean: $325.69)
-0.038
0.007
0.063
0.092
-0.165

Financial aid
Tuition rate
Return to studying
Return to GPA
Wage
Notes: This table presents estimated elasticities for the summer periods. Elas-
ticities estimated via simulation with (1) a $500 increase to ﬁnancial aid (2) a
10% increase to tuition (3) a 10% increase to the return to studying parameter
γ1i (4) a 10% increase to the return to GPA parameters in the post-school wage
function ω2i and ω3i (5) a 10% increase to the in-school wage rate. All elas-
ticities are calculated as arc elasticities where percentage changes are based on
the midpoint between the original and simulated variables. Standard errors es-
timated via a parametric bootstrap with 30 draws from the joint distribution of
utility parameters. Number of observations: 979.

76

Table A.1.10 Elasticity Heterogeneity (Fall and Spring)

Variable

Bottom Tercile Top Tercile Difference

Panel A: Work hours and returns to studying (N = 1,308)
-727∗
-0.40∗
-0.014∗∗∗
-0.046∗∗∗
0.055∗∗∗
-0.27

Unmet ﬁnancial need
In-school wage
Study cost of work
Return to studying
Return to GPA at 3.0
Cumulative credit hours

3,400
11.23
-0.015
0.403
0.411
21.63

2,673
10.82
-0.029
0.357
0.466
21.36

Panel B: Work hours and returns to GPA (N = 1,315)

Unmet ﬁnancial need
In-school wage
Study cost of work
Return to studying
Return to GPA at 3.0
Cumulative credit hours

2,844
11.16
-0.040
0.390
0.515
23.32

3,038
11.16
0.003
0.382
0.354
20.51

-194
0.00
-0.043∗∗∗
0.008
0.161∗∗∗
2.81∗

Panel C: Borrowing and ﬁnancial aid (N = 1,311)

Unmet ﬁnancial need
In-school wage
Study cost of work
Return to studying
Return to GPA at 3.0
Cumulative credit hours

2,931
11.08
-0.022
0.373
0.392
17.30

3,344
10.95
-0.016
0.376
0.421
27.55

-413
0.13
-0.007∗∗∗
-0.003
-0.028
-10.26∗∗∗

Panel D: Borrowing and tuition (N = 1,309)

3,828
10.93
-0.015
0.380
0.417
27.87

Unmet ﬁnancial need
In-school wage
Study cost of work
Return to studying
Return to GPA at 3.0
Cumulative credit hours
Notes: This table presents the means for particular variables separately
for students in the bottom tercile and top tercile of the speciﬁed elasticity
distribution. Statistical signiﬁcance based on two-sample t-tests with un-
equal variances. ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

1,734
11.01
-0.022
0.357
0.391
17.86

2,095∗∗∗
-0.08
0.007∗∗∗
0.023
0.026
10.01∗∗∗

77

Table A.1.11 Counterfactual Simulation Results

Outcome

Baseline Counterfactual Difference Std. Err.

Panel A: Increase minimum wage to $15

Credit hours
Fall and spring
Summer
Work hours
Fall and spring
Summer
Borrowing
Fall and spring
Summer
Cumulative GPA

28.85
1.76

6.24
11.80

28.85
1.70

6.99
12.94

4,294.39
790.69
2.96

3,991.78
725.87
2.95

-0.004
-0.065

0.748
1.142

-302.61
-64.82
-0.011

(0.023)
(0.027)∗
(0.056)∗∗∗
(0.062)∗∗∗
(110.85)∗∗
(25.65)∗
(0.037)

Panel B: Set in-state tuition rate to $0

(0.023)∗∗∗
(0.028)

4,294.39
790.69
2.96

2,372.50
605.85
2.95

0.088
0.044

-0.094
0.101

28.94
1.81

6.15
11.90

28.85
1.76

6.24
11.80

Credit hours
Fall and spring
Summer
Work hours
Fall and spring
Summer
Borrowing
Fall and spring
Summer
Cumulative GPA
Notes: This table presents the projected credit hour enrollment, work hours,
borrowing, and terminal-period cumulative GPA under the baseline model
and counterfactual model. The baseline model takes the state variables for
individuals as given in the ﬁrst period and simulates their choice history and
outcomes for the remaining periods. The counterfactual models vary indi-
viduals’ wage or tuition rate for all periods and simulate their choice history
and outcomes given the changes. The ﬁnal column presents the standard er-
rors from a two-sided t-test with unequal variances. ∗p < 0.05, ∗∗p < 0.01,
∗∗∗p < 0.001.

(0.053)
(0.057)
(86.69)∗∗∗
(20.17)∗∗∗
(0.037)

-1,921.89
-184.84
-0.012

78

A.2

In-school wage estimation

The SEES asked students to report their earnings from their most recent semester working. If

students were paid hourly, they were asked to report their average hourly wage, including tips and

after taxes. If students were paid a salary, they were asked to report their frequency of payment

(e.g., weekly, bi-weekly, or monthly) and their typical payment, after taxes. I convert salary earn-

ings to hourly wages using the student’s reported frequency of payment and typical hours worked.

I use a student’s most recent hourly wage for their in-school wage across all in-school periods

To predict a wage for non-workers, the SEES asked students for their expected wages in fall

2019 if they were to work. Students were not asked this question if they were certain that they

were not going to work in fall 2019 because I did not have conﬁdence that these students had fully

formed beliefs about the wage offers for college workers. For non-workers who did not provide an

expected wage, I predict their potential wage using data from non-workers by regressing expected

log wage on gender, race, residency, ﬁrst-generation status, age, class level, honors status, and

broad categories for major (e.g., Business, Humanities). The regression coefﬁcients are presented

below.

79

Table A.2.1 Predicting Wages for Non-Workers

Ln(Wage)
Female
Black or African American
Hispanic
Asian
American Indian or Alaskan Native
Native Hawaiian or Paciﬁc Islander
Out-of-state
First generation
Age (months)
Sophomore
Junior
Senior
Honors college
Business
Humanities
Health
STEM
Undecided major
Constant
Observations
Notes: This table presents the estimated coefﬁcients from
a regression of log wage (expected by non-workers) on a
vector of student characteristics.

Std. Err.
(0.019)
(0.035)
(0.039)
(0.027)
(0.088)
(0.145)
(0.028)
(0.024)
(0.001)
(0.021)
(0.036)
(0.077)
(0.021)
(0.028)
(0.040)
(0.051)
(0.020)
(0.086)
(0.321)

Coef.
-0.048
0.030
0.039
-0.050
-0.029
-0.101
-0.021
-0.037
0.002
-0.005
-0.008
0.118
-0.015
0.024
-0.018
0.045
0.004
0.162
1.872
296

80

A.3 Measuring family ﬁnancial support

The SEES elicits family ﬁnancial support for education expenses and living expenses sep-

arately. For education expenses, student could report that their family provides no support for

educational expenses, a ﬁxed dollar amount of support for educational expenses, a percent of edu-

cation expenses, enough support to pay for their tuition but not their textbooks, or enough support

to pay for all of their education expenses. Responses were adjusted upward if the student’s parents

received a Direct PLUS loan from the Federal government in excess of the family ﬁnancial support

the student indicated.

For living expenses, students could report that their family provides no support, a ﬁxed dollar

amount of support for living expenses, or support for all of their living expenses. To convert “all

of living expenses” to a dollar amount, I ﬁrst estimate the student’s expected living expenses. I

use the student’s self-reported monthly rent and calculate the ratio of her rent to the cost of a

standard double-bed room on campus ($2,121 per semester). I then multiply this ratio by the total

expected living expenses as speciﬁed by the University in their cost of attendance calculations.

The assumption is that students who spend x% more on rent than they would if living on campus

also spend x% more on other living expenses than they would if living on campus. This product

is the student’s expected living expenses and the dollar amount I assign to family ﬁnancial support

when the student reports their family pays for all of their living expenses. For students who live at

home, I assume they receive 150% of the standard double-bed room on campus worth of support

for rent.

81

Table A.3.1 Family Financial Support: Education Expenses

Percent
25.89
8.32
13.50
16.65
35.63
985

Education Support
No support
Dollar amount
Percentage
All tuition, no books, etc.
All education costs
Observations
Notes: This table presents the pro-
portion of students who reported each
level of family ﬁnancial support for ed-
ucation expenses.

82

Table A.3.2 Family Financial Support: Living Expenses

Percent
33.91
28.32
37.77
985

Living Support
No support
Dollar amount
All living costs
Observations
Notes: This table presents the pro-
portion of students who reported
each level of family ﬁnancial support
for living expenses.

83

A.4 Supplemental ﬁgures & tables

Figure A.4.1 Expected Schoolwork Time Sample Question

Notes: An example question in the SEES eliciting how much time the student expects to spend on
schoolwork in a typical week. Respondents answered among a discrete set of possible answers:
“0 to 5”, “6 to 10”, “11 to 15”, “16 to 20”,“21 to 25”, “26 to 30”, “31 to 35”,“36 to 40”, “41 to
45”, or “More than 45”.

84

Figure A.4.2 Grade Distribution Sample Question

Notes: A sample response in the SEES module eliciting students’ beliefs about how their time
spent on schoolwork affects their distribution of grades. Respondents could ﬁll each row with
balls representing the likelihood that they would earn the speciﬁed grade.

85

Figure A.4.3 Distribution of Grades Conditional on Schoolwork

Notes: This ﬁgure presents the average probability that students believe they will receive each
letter-grade conditional on time spent on schoolwork. Number of observations: 985.

86

0.2.4.6Probability1 hour3 hours6 hours9 hoursABCDFABCDFABCDFABCDFWeekly schoolwork hours per courseFigure A.4.4 Distribution of Salaries Conditional on GPA

Notes: This ﬁgure presents the average probability that students believe they will earn a salary
within each range conditional on GPA upon graduation (or leaving MSU without a degree).
Number of observations: 985.

87

0.2.4.6ProbabilityNo degree2.0 to 2.492.5 to 2.93.0 to 3.493.5 to 4.0$0 to 39k40 to 59k60 to 79k80 to 99k100 to 119k$120k+$0 to 39k40 to 59k60 to 79k80 to 99k100 to 119k$120k+$0 to 39k40 to 59k60 to 79k80 to 99k100 to 119k$120k+$0 to 39k40 to 59k60 to 79k80 to 99k100 to 119k$120k+$0 to 39k40 to 59k60 to 79k80 to 99k100 to 119k$120k+GPA upon graduationTable A.4.1 Michigan State and Peer Institutions

Carnegie Peer
S.D.
Mean
25,029
9,268
0.060
0.515
0.200
0.541
0.073
0.067
0.134
0.148
0.095
0.110
0.0081
0.0040
0.0017
0.0030
0.082
0.291
18,178
52,782
0.636
0.203
1,261
26,306
16,649
11,522
0.280
15,713
0.492
0.713
0.872
15,146

4,377
3,923
3,564
0.099
2,506
0.171
0.128
0.066
6,970

88

S.D.
6,671
0.117
0.259
0.206
0.193
0.057
0.0566
0.0208
0.092
18,298
0.180

MSU
Mean
39,208
0.507
0.681
0.075
0.048
0.057
0.0018
0.0008
0.210
70,982
0.777
1,224
28,194
18,984
9,235
0.219
21,250
0.535
0.800
0.919
17,975

Variable
Number of undergraduates
Female
White
Black or African American
Hispanic
Asian
American Indian or Alaskan Native
Native Hawaiian or Paciﬁc Islander
First generation
Median family income
Admissions rate
Average SAT (ACT equivalent)
Average annual cost of attendance
Average net price
Average net price (income < $48k)
Pell Grant recipients
Median debt
Four-year completion rate
Six-year completion rate
Retention rate
Instructional spending per FTE
Observations
Notes: This table presents the mean and standard deviation of statistics for Michigan State
University, four-year public universities with the same Carnegie Classiﬁcation as MSU (doc-
toral universities with very high research activity), and four-year public universities regard-
less of Carnegie Classiﬁcation. Data come from the U.S. Department of Education College
Scorecard (2020), most recent institution-level year.

Public Four-Year
Mean
6,978
0.575
0.551
0.150
0.151
0.040
0.0117
0.0029
0.356
42,691
0.717
1,103
21,091
13,956
10,886
0.404
14,641
0.274
0.476
0.734
10,956

85

4,397
4,491
3,821
0.142
3,650
0.156
0.153
0.095
14,519

1

93

514

88

APPENDIX B

CHAPTER 2 APPENDIX

B.1 Figures & tables

Figure B.1.1 Distribution of Responses for Non-Cognitive Questions

Notes: Each cell plots the percentage of students who answered the speciﬁed non-cognitive
question with each of the ﬁve possible answers. Number of observations: 60,129. The
distributions do not utilize survey weights.

89

01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeSocially accepted01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeLoved and wanted01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeClose to people01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreePart of school01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeHave good qualities01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeHave a lot to be proud of01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeLikes self01020304050PercentStr. disagreeDisagreeNeitherAgreeStr. agreeDoing everything rightFigure B.1.2 Distribution of Afﬁrmative Responses

Notes: Each cell plots the percentage of students who answered in the afﬁrmative (“Agree” or
“Strongly Agree”) for zero, one, two, three, or all four of their non-cognitive questions. The top
row contains the count of afﬁrmative responses for the four sense of belonging questions: I feel
socially accepted, I feel loved and wanted, I feel close to people at this school, and I feel like I am
a part of this school. The bottom row contains the count of afﬁrmative responses for the four
self-worth questions: I have a lot of good qualities, I have a lot to be proud of, I like myself just
the way I am, and I feel like I am doing everything just about right. The left column contains the
count of afﬁrmative responses for the entire sample of 60,129 students, the middle column
contains the count of afﬁrmative responses for the 31,445 female students, and the right column
contains the count of afﬁrmative responses for the 28,684 male students. The distributions do not
utilize survey weights.

90

010203040Percent01234Count "Agree" or "Strongly agree"Sense of belonging: All010203040Percent01234Count "Agree" or "Strongly agree"Sense of belonging: Female010203040Percent01234Count "Agree" or "Strongly agree"Sense of belonging: Male010203040Percent01234Count "Agree" or "Strongly agree"Self-worth: All010203040Percent01234Count "Agree" or "Strongly agree"Self-worth: Female010203040Percent01234Count "Agree" or "Strongly agree"Self-worth: MaleFigure B.1.3 Distribution of Average Numerical Responses

Notes: Each cell plots the distribution of the average numerical response across the two broad
non-cognitive questions. “Strongly disagree” was assigned a value of 1, “Disagree” a value of 2,
“Neither agree nor disagree” a value of 3, “Agree” a value of 4, and “Strongly agree” a value of 5.
The top row contains the average numerical response for the four sense of belonging questions: I
feel socially accepted, I feel loved and wanted, I feel close to people at this school, and I feel like
I am a part of this school. The bottom row contains the average numerical response for the four
self-worth questions: I have a lot of good qualities, I have a lot to be proud of, I like myself just
the way I am, and I feel like I am doing everything just about right. The left column contains the
average numerical response for the entire sample of 60,129 students, the middle column contains
the average numerical response for the 31,445 female students, and the right column contains the
average numerical response for the 28,684 male students. The distributions do not utilize survey
weights.

91

051015Percent12345Average numerical responseSense of belonging: All051015Percent12345Average numerical responseSense of belonging: Female051015Percent12345Average numerical responseSense of belonging: Male051015Percent12345Average numerical responseSelf-worth: All051015Percent12345Average numerical responseSelf-worth: Female051015Percent12345Average numerical responseSelf-worth: MaleFigure B.1.4 In-School Questionnaire Response Rates

Notes: This ﬁgure plots the distribution of in-school questionnaire response rates for each
participating school. Response rates are calculated by dividing the number of in-school
questionnaire responses in the school by the number of students listed on a school’s roster. The
distribution does not utilize survey weights.

92

Table B.1.1 Add Health Descriptive Statistics

Weighted
S.D.
0.054
0.500
0.309
0.376
0.199
0.189
0.150
0.474
0.235

Mean
0.503
0.516
0.107
0.170
0.041
0.037
0.023
0.339
0.059

Unweighted
S.D.
Mean
0.503
0.045
0.499
0.523
0.349
0.142
0.366
0.159
0.059
0.236
0.178
0.033
0.154
0.024
0.338
0.473
0.280
0.086

Variable
Share female
Female
Hispanic or Latino
Black or African American
Asian or Paciﬁc Islander
American Indian or Native American
Other race
Above median age
Born outside the United States
Household size
One
Two
Three
Four to six
Shelter or group home
Observations
Notes: Each column presents the mean or standard deviation for the ex-
planatory variable of interest and control variables used in the regressions.
The ﬁrst two columns correspond to the unweighted sample of students, and
the last two columns correspond to the sample weighted by the inverse prob-
ability of their selection using weights provided by Add Health.

0.005
0.053
0.183
0.756
0.003

0.071
0.223
0.387
0.429
0.057

0.005
0.053
0.185
0.754
0.003

0.073
0.224
0.388
0.431
0.056

60,229

60,229

93

Table B.1.2 Non-Cognitive Factors (Count “Agree” or “Strongly Agree”)

Survey Question
Sense of belonging
I feel socially accepted
I feel loved and wanted
I feel close to people at this school
I feel like I am part of this school

Female

Male

All

Mean S.D. Mean S.D. Mean S.D.
1.38
2.59
0.68
0.45
0.44
0.73
0.49
0.58
0.60
0.49

2.63
0.71
0.73
0.59
0.61

1.42
0.48
0.45
0.50
0.50

2.54
0.65
0.73
0.58
0.59

1.40
0.47
0.45
0.49
0.49

Self-worth
I have a lot of good qualities
I have a lot to be proud of
I like myself just the way I am
I feel like I am doing everything just about right
Observations
Notes: Each column presents the mean or standard deviation for number of afﬁrmative responses
(“Agree” or “Strongly Agree”) to the corresponding survey question. Sense of belonging and self-
worth include the sum of the relevant individual questions. Observations are weighted by the
inverse probability of their selection using weights provided by Add Health.

1.20
0.35
0.38
0.43
0.50

1.33
0.40
0.43
0.49
0.49

2.95
0.86
0.82
0.76
0.51

1.28
0.38
0.41
0.47
0.50

2.54
0.80
0.76
0.60
0.37

2.74
0.83
0.79
0.68
0.44

60,229

31,445

28,684

94

Table B.1.3 Balance of Share Female on Control Variables

Female

Male

Coeff.
0.0012
-0.0001
0.0007
0.0008
0.0011
0.0016
0.0006

Coeff.
-0.0010
0.0001
-0.0002
0.0003
0.0004
-0.0020∗
-0.0005

Std. Err.
(0.0016)
(0.0010)
(0.0026)
(0.0028)
(0.0028)
(0.0013)
(0.0015)

Share Female
Hispanic or Latino
Black or African American
Asian or Paciﬁc Islander
American Indian or Native American
Other race
Above median age
Born in the United States
Household size
One
Two
Four to six
Shelter or group home
Constant
Observations
Notes: This table contains estimates from regressions of the share of female peers on in-
dividual control variables, school dummy variables, and grade dummy variables. The ﬁrst
two columns correspond to the sample of female students, and the last two columns cor-
respond to the sample of male students. Standard errors are adjusted for the stratiﬁcation
and clustering of the survey design. Observations are weighted by the inverse probability of
their selection using weights provided by Add Health. ∗p < 0.10, ∗∗p < 0.05, ∗∗∗p < 0.01.

Std. Err.
(0.0013)
(0.0011)
(0.0019)
(0.0025)
(0.0021)
(0.0011)
(0.0015)

(0.0084)
(0.0037)
(0.0011)
(0.0040)
(0.0092)

-0.0295
0.0037
0.0012
0.0051
0.5492∗∗∗

(0.0363)
(0.0024)
(0.0012)
(0.0064)
(0.0084)

0.0062
0.0025
0.0013
0.0016
0.5599∗∗∗

31,445

28,684

95

Table B.1.4 Baseline Regression Estimates

All

Female

Male

Belonging Self-worth Belonging Self-worth Belonging Self-worth

(3)

(4)

-0.00550
(0.408)

-0.197
(0.258)

(5)
0.714∗
(0.352)

(6)
0.633∗
(0.270)

Share female

Female

(1)
0.295
(0.318)
-0.107∗∗∗
(0.0149)

(2)
0.242
(0.176)
-0.427∗∗∗
(0.0173)

Y

Y

Y

Y

Y

60,129

60,129

31,445

31,445

Controls
Observations
Notes: This table contains estimates from regressions of the number of afﬁrmative responses
(“Agree” or “Strongly Agree”) to the sense of belonging and self-worth question categories on
the share of female peers within a student’s school and grade, individual covariates, and school
and grade dummy variables. Standard errors are adjusted for the stratiﬁcation and clustering of
the survey design. Observations are weighted by the inverse probability of their selection using
weights provided by Add Health. ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

28,684

28,684

Y

96

Table B.1.5 Regression Estimates without Controls

All

Female

Male

Belonging Self-worth Belonging Self-worth Belonging Self-worth

(1)
0.335
(0.317)
3.211∗∗∗
(0.162)

(2)
0.455∗
(0.177)
2.799∗∗∗
(0.102)

(3)

(4)

-0.0356
(0.423)
3.503∗∗∗
(0.219)

-0.191
(0.267)
3.223∗∗∗
(0.147)

(5)
0.736∗
(0.348)
2.900∗∗∗
(0.188)

(6)
0.635∗
(0.273)
2.626∗∗∗
(0.165)

Share female

Constant

N

N

N

N

N

60,129

60,129

31,445

31,445

Controls
Observations
Notes: This table contains estimates from regressions of the number of afﬁrmative responses
(“Agree” or “Strongly Agree”) to the sense of belonging and self-worth question categories on
the share of female peers within a student’s school and grade and school and grade dummy
variables. Standard errors are adjusted for the stratiﬁcation and clustering of the survey design.
Observations are weighted by the inverse probability of their selection using weights provided by
Add Health. ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

28,684

28,684

N

97

Table B.1.6 Regression Estimates with Average Numerical Response

All

Female

Male

Belonging Self-worth Belonging Self-worth Belonging Self-worth

Share female

Female

(1)
0.215
(0.196)
-0.107∗∗∗
(0.0116)

(2)
0.134
(0.128)
-0.349∗∗∗
(0.0137)

(3)

(4)

-0.0790
(0.246)

-0.204
(0.169)

(5)
0.561∗
(0.248)

(6)
0.486∗
(0.186)

Y

Y

Y

Y

Y

60,129

60,129

31,445

31,445

Controls
Observations
Notes: This table contains estimates from regressions of the average numerical responses (e.g.,
“Strongly Disagree” = 1, “Strongly Agree” = 5) to the sense of belonging and self-worth question
categories on the share of female peers within a student’s school and grade, individual covariates,
and school and grade dummy variables. Standard errors are adjusted for the stratiﬁcation and
clustering of the survey design. Observations are weighted by the inverse probability of their
selection using weights provided by Add Health. ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

28,684

28,684

Y

98

Table B.1.7 Disaggregated Regression Estimates for Each Non-Cognitive Factor

Socially

cepted

ac-

(1)

Loved
and

wanted

(2)

Close

people

to

(3)

Part of
school

(4)

Good
quali-
ties
(5)

Proud
of a lot

Likes
self

(6)

(7)

Doing
things
right
(8)

Share female

Constant
(0.133)

Controls
Observations

Share female

Constant

Panel A: Female
0.0924
-0.0816
(0.302)
(0.175)

-0.129
(0.193)

-0.0914
(0.238)

0.0380
-0.325
(0.246)
(0.192)
3.911∗∗∗ 4.751∗∗∗ 4.305∗∗∗ 4.507∗∗∗ 4.283∗∗∗ 4.565∗∗∗ 4.488∗∗∗ 3.627∗∗∗
(0.107)

0.0530
(0.171)

-0.461
(0.276)

(0.0964)

(0.130)

(0.101)

(0.145)

(0.105)

(0.160)

Y

Y

Y

Y

Y

Y

Y

Y

31,445

31,445

31,445

31,445

31,445

31,445

31,445

31,445

0.458
(0.299)

Panel B: Male
0.441∗
0.121
(0.219)
(0.169)

0.631∗
(0.274)

0.469∗
0.341
(0.208)
(0.227)
3.928∗∗∗ 4.051∗∗∗ 3.768∗∗∗ 4.115∗∗∗ 4.284∗∗∗ 4.513∗∗∗ 3.712∗∗∗ 2.913∗∗∗
(0.126)
(0.117)

0.634∗∗
(0.240)

0.304
(0.167)

(0.0966)

(0.168)

(0.103)

(0.162)

(0.114)

(0.133)

Y

Y

Y

Y

Y

Y

Y

28,684

28,684

28,684

28,684

Controls
Observations
Notes: This table contains estimates from regressions of the probability of afﬁrmative response
(“Agree” or “Strongly Agree”) to each non-cognitive question on the share of female peers within
a student’s school and grade, individual covariates, and school and grade dummy variables. Panel
A contains estimates for the subsample of female students, and Panel B contains estimates for the
subsample of male students. Standard errors are adjusted for the stratiﬁcation and clustering of
the survey design. Observations are weighted by the inverse probability of their selection using
weights provided by Add Health. ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

28,684

28,684

28,684

28,684

Y

99

Table B.1.8 Regression Estimates Accounting for Measurement Error

All

Female

Male

Belonging Self-worth Belonging Self-worth Belonging Self-worth

Share female

Female

(1)
0.247
(0.315)
-0.107∗∗∗
(0.0149)

(2)
0.197
(0.192)
-0.427∗∗∗
(0.0173)

(3)

(4)

-0.00112
(0.398)

-0.182
(0.268)

(5)
0.613∗
(0.367)

(6)
0.537∗
(0.276)

Y

Y

Y

Y

Y

Y

60,129

60,129

31,445

31,445

Controls
Observations
Notes: This table contains estimates from regressions of the number of afﬁrmative responses
(“Agree” or “Strongly Agree”) to the sense of belonging and self-worth question categories on
the share of female peers within a student’s school and grade, individual covariates, and school
and grade dummy variables using 100 simulated data sets to account for measurement error in
the share of female students. Standard errors are adjusted for the stratiﬁcation and clustering of
the survey design and for the uncertainty introduced by measurement error in the share of female
peers. Observations are weighted by the inverse probability of their selection using weights
provided by Add Health. ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001.

28,684

28,684

100

APPENDIX C

CHAPTER 3 APPENDIX

C.1 Main text ﬁgures & tables

Figure C.1.1 Labor Force Trends by Demographic Group

Notes: This ﬁgure presents trends in labor force participation, annual hours worked, hourly
wages, and non-labor income separately by sex and marital status. Annual hours worked are the
product of usual hours worked per week in the prior year and weeks worked in the prior year.
Hourly wages are quotient of pre-tax wage and salary income in the prior year and annual hours
worked. Hourly wages and non-labor income are in 2017 dollars. Observations are weighted by
their ASEC person-level survey weight.

101

70%80%90%100% 19951998200120042007201020132016Survey yearLabor Force Participation16001800200022002400 19951998200120042007201020132016Survey yearAnnual Hours for Workers141822263034 19951998200120042007201020132016Survey yearHourly Wages for Workers10002000300040005000 19951998200120042007201020132016Survey yearNon-Labor IncomeSingle MenSingle WomenMarried MenMarried WomenFigure C.1.2 Mean Own-Wage Elasticities, Baseline Estimates (1994-2017) versus Estimates
with No Beneﬁt Simulator (1979-2017)

Notes: This ﬁgure presents the estimated trends in mean own-wage elasticities separately by sex
and marital status. Our baseline model (blue) has a translog utility function, no random slopes,
beneﬁt simulator from TRIM3, and predicted wages for non-workers using 100 draws from their
conditional wage distribution. Our model without the beneﬁt simulator (red with triangle
markers) is identical to the baseline model except for the absence of the beneﬁt simulator.
Standard errors, computed with a parametric bootstrap of 50 draws from the joint distribution of
parameters, are denoted by dashed lines.

102

-.10.1.2.3.4.5Own-Wage Elasticity1979198519911997200320092015YearSingle Men-.10.1.2.3.4.5Own-Wage Elasticity1979198519911997200320092015YearSingle Women-.10.1.2.3.4.5Own-Wage Elasticity1979198519911997200320092015YearMarried Men-.10.1.2.3.4.5Own-Wage Elasticity1979198519911997200320092015YearMarried WomenBaselineNo benefitsFigure C.1.3 Mean Own-Wage Elasticities, Baseline Estimates versus Estimates from Random-
Slope Logit Model

Notes: This ﬁgure presents the estimated trends in mean own-wage elasticities separately by sex
and marital status. Our baseline model (blue) has a translog utility function, no random slopes,
beneﬁt simulator from TRIM3, and predicted wages for non-workers using 100 draws from their
conditional wage distribution. Our random-slope logit model (red with triangle markers) is
identical to the baseline model except for the addition of random slopes on the leisure term in the
utility function. Standard errors, computed with a parametric bootstrap of 50 draws from the joint
distribution of parameters, are denoted by dashed lines. Standard errors are missing for years
where the estimated covariance matrix is not positive semi-deﬁnite.

103

-.10.1.2.3.4.5.6Own-Wage Elasticity199519992003200720112015YearSingle Men-.10.1.2.3.4.5.6Own-Wage Elasticity199519992003200720112015YearSingle Women-.10.1.2.3.4.5.6Own-Wage Elasticity199519992003200720112015YearMarried Men-.10.1.2.3.4.5.6Own-Wage Elasticity199519992003200720112015YearMarried WomenBaselineRandom-slope logitFigure C.1.4 Mean Own-Wage Elasticities, Baseline Estimates versus Estimates with Different
Treatments for Measurement Error

Notes: This ﬁgure presents the estimated trends in mean own-wage elasticities separately by sex
and marital status. Our baseline model (in blue) has a translog utility function, no random slopes,
beneﬁt simulator from TRIM3, and predicted wages for non-workers using 100 draws from their
conditional wage distribution. The three other models are identical to the baseline model except
they use the mean wage for non-workers as opposed to drawing from the distribution (red with
triangle markers), predicted wages for workers and non-workers using 100 draws from their
conditional wage distribution (green with square markers), and predicted wages for workers and
non-workers using the mean wage (orange with round markers).

104

-.20.2.4.6.81Own-Wage Elasticity199519992003200720112015YearSingle Men-.20.2.4.6.81Own-Wage Elasticity199519992003200720112015YearSingle Women-.20.2.4.6.81Own-Wage Elasticity199519992003200720112015YearMarried Men-.20.2.4.6.81Own-Wage Elasticity199519992003200720112015YearMarried WomenBaselineNon-workers, 0 drawsAll, 100 drawsAll, 0 drawsFigure C.1.5 Mean Own-Wage Elasticities Decomposed by Extensive and Intensive Margins

Notes: This ﬁgure presents the estimated trends in mean total, extensive margin, and intensive
margin own-wage elasticities separately by sex and marital status. We decompose the total
own-wage elasticity (blue) into the extensive margin elasticity (red with triangle markers) and
intensive margin elasticity (green with square markers) according to the formulas in Section 3.4.2.
Estimates based on our baseline model.

105

-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearSingle Men-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearSingle Women-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearMarried Men-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearMarried WomenTotalExtensiveIntensiveFigure C.1.6 Mean Marshallian, Cross-Wage, Hicksian, and Income Elasticities

Notes: This ﬁgure presents the estimated trends in mean Marshallian own-wage (blue),
cross-wage (red with triangle markers), Hicksian (green with square markers), and income
(orange with round markers) elasticities separately by sex and marital status. Estimates based on
our baseline model.

106

-.4-.20.2.4.6Elasticity199519992003200720112015YearSingle Men-.4-.20.2.4.6Elasticity199519992003200720112015YearSingle Women-.4-.20.2.4.6Elasticity199519992003200720112015YearMarried Men-.4-.20.2.4.6Elasticity199519992003200720112015YearMarried WomenMarshallianCross-wageHicksianIncomeTable C.1.1 Distribution of Work Hours

2008

2012

2016

7.06
0.72
2.18
4.18
60.45
16.46
8.95
4,254

12.44
1.19
4.57
7.66
59.54
10.27
4.33
7,013

5.98
0.32
1.26
2.12
59.50
19.66
11.16

5.19
0.61
2.24
3.33
59.96
18.70
9.98
3,690

10.20
1.01
4.07
7.79
60.32
11.40
5.21
5,733

3.89
0.22
0.97
1.62
61.62
21.16
10.52

1996

3.25
0.38
1.97
3.62
56.73
21.59
12.47
2,930

11.02
1.03
3.88
6.62
58.57
12.02
6.86
4,651

2.52
0.31
0.80
1.40
58.21
23.70
13.05

0 hours
10 hours
20 hours
30 hours
40 hours
50 hours
60 hours
Observations

0 hours
10 hours
20 hours
30 hours
40 hours
50 hours
60 hours
Observations

0 hours
10 hours
20 hours
30 hours
40 hours
50 hours
60 hours

2004

2000
Panel A: Single Men
2.39
0.45
1.85
2.13
57.09
24.84
11.24
3,159

4.50
0.57
2.30
3.11
61.00
18.77
9.74
4,260

4.65
1.04
2.01
2.36
61.72
18.41
9.80
4,374

Panel B: Single Women

5.98
0.78
4.15
6.11
62.53
13.78
6.67
4,763

8.54
1.14
4.29
6.17
63.53
11.50
4.83
7,658

8.51
0.97
4.10
5.98
64.06
11.44
4.94
7,300

Panel C: Married Men
2.25
0.19
0.75
1.11
57.59
24.66
13.46

3.61
0.20
0.82
1.46
60.57
22.17
11.18

3.50
0.11
0.82
1.61
60.66
21.76
11.53

Panel D: Married Women

21.61
2.73
8.55
8.22
48.67
7.74
2.49
12,251

21.30
2.59
7.35
7.64
49.69
9.10
2.35
12,722

0 hours
10 hours
20 hours
30 hours
40 hours
50 hours
60 hours
Observations
Notes: This table contains the percent of individuals within each demographic
group that worked the speciﬁed number of hours per week in the prior year.
Observations are weighted by their ASEC person-level survey weight.

25.39
1.68
5.79
6.26
48.85
9.01
3.01
14,414

23.36
2.17
6.33
6.88
50.66
8.03
2.57
18,802

24.12
2.34
7.05
7.61
48.95
7.58
2.35
20,417

25.52
2.22
6.35
7.27
48.12
7.88
2.63
17,383

107

Table C.1.2 Baseline Model Elasticities for Select Years, Single Men and Women

Own-wage

Extensive margin

Intensive margin

Hicksian

Income

1996

2000

2004

2008

2012

2016

Panel A: Single Men

0.045
(0.012)
0.037
(0.008)
0.008
(0.005)
0.236
(0.030)
-0.035
(0.010)

0.050
(0.010)
0.037
(0.007)
0.013
(0.004)
0.217
(0.027)
-0.029
(0.008)

0.074
(0.011)
0.061
(0.008)
0.013
(0.004)
0.430
(0.031)
-0.054
(0.009)

0.078
(0.010)
0.061
(0.008)
0.017
(0.004)
0.375
(0.030)
-0.047
(0.008)

0.112
(0.012)
0.094
(0.010)
0.019
(0.004)
0.473
(0.034)
-0.073
(0.012)

0.105
(0.012)
0.084
(0.009)
0.021
(0.004)
0.397
(0.027)
-0.076
(0.013)

Observations

2,930

3,159

4,260

4,374

4,254

3,690

Own-wage

Extensive margin

Intensive margin

Hicksian

Income

Panel B: Single Women

0.210
(0.013)
0.165
(0.010)
0.045
(0.004)
0.350
(0.016)
-0.256
(0.032)

0.141
(0.011)
0.101
(0.008)
0.039
(0.004)
0.253
(0.015)
-0.124
(0.018)

0.203
(0.010)
0.152
(0.008)
0.051
(0.003)
0.374
(0.014)
-0.180
(0.019)

0.197
(0.010)
0.149
(0.008)
0.048
(0.003)
0.343
(0.015)
-0.136
(0.016)

0.273
(0.012)
0.217
(0.010)
0.056
(0.003)
0.466
(0.018)
-0.205
(0.022)

0.252
(0.012)
0.205
(0.010)
0.048
(0.003)
0.464
(0.017)
-0.289
(0.028)

4,763

7,658

7,300

4,651

Observations
Notes: This table contains the estimated elasticities for single men and women
in a subset of years. Elasticity derivations are provided in Section 3.4. Standard
errors are calculated using a parametric bootstrap with 50 draws from the joint
distribution of utility parameters.

7,013

5,733

108

Table C.1.3 Baseline Model Elasticities for Select Years, Married Men and Women

Own-wage

Extensive margin

Intensive margin

Cross-wage

Hicksian

Income

1996

2000

2004

2008

2012

2016

Panel A: Married Men

0.075
(0.004)
0.045
(0.003)
0.030
(0.002)
-0.008
(0.002)
0.097
(0.005)
-0.040
(0.006)

0.081
(0.004)
0.050
(0.003)
0.032
(0.002)
-0.016
(0.002)
0.108
(0.005)
-0.040
(0.006)

0.090
(0.004)
0.059
(0.004)
0.030
(0.002)
-0.031
(0.002)
0.129
(0.007)
-0.034
(0.004)

0.095
(0.004)
0.062
(0.004)
0.034
(0.002)
-0.011
(0.002)
0.118
(0.006)
-0.039
(0.006)

0.134
(0.006)
0.095
(0.005)
0.039
(0.002)
-0.016
(0.002)
0.182
(0.008)
-0.036
(0.004)

0.106
(0.005)
0.076
(0.004)
0.031
(0.002)
-0.035
(0.003)
0.160
(0.005)
-0.056
(0.005)

Observations

10,000

10,000

10,000

10,000

10,000

10,000

Own-wage

Extensive margin

Intensive margin

Cross-wage

Hicksian

Income

Panel B: Married Women

0.206
(0.008)
0.159
(0.006)
0.047
(0.002)
-0.094
(0.011)
0.247
(0.009)
-0.043
(0.005)

0.248
(0.009)
0.194
(0.008)
0.054
(0.002)
-0.148
(0.011)
0.301
(0.011)
-0.047
(0.006)

0.291
(0.010)
0.229
(0.008)
0.062
(0.002)
-0.187
(0.013)
0.352
(0.011)
-0.036
(0.004)

0.257
(0.009)
0.206
(0.007)
0.051
(0.002)
-0.163
(0.012)
0.314
(0.010)
-0.043
(0.005)

0.297
(0.009)
0.241
(0.008)
0.056
(0.002)
-0.161
(0.012)
0.371
(0.011)
-0.047
(0.004)

0.331
(0.009)
0.272
(0.008)
0.059
(0.002)
-0.175
(0.013)
0.393
(0.011)
-0.063
(0.005)

10,000

10,000

10,000

Observations
10,000
Notes: This table contains the estimated elasticities for married men and women
for a subset of years. Elasticity derivations are provided in Section 3.4. Standard
errors are calculated using a parametric bootstrap with 50 draws from the joint
distribution of utility parameters.

10,000

10,000

109

C.2 Construction of variables from March CPS

As described in the main text, we use data from the 1979 through 2017 Annual Social and

Economic March Supplement of the Current Population Survey (CPS). In this section, we describe

how we construct our variables from the CPS. Tables C.2.1 and C.2.2 present the basic descriptive

statistics for all four demographic groups, and Tables C.2.3 and C.2.4 present the results from the

Heckman corrected wage models for men and women.

Household construction We restrict our sample to single-family households, which are house-

holds that the Census Bureau deﬁnes as having only one sub-family. Within these households,

we match spouses using the sploc variable from IPUMS. We identify dependents as any child,

stepchild, grandchild, other relative under the age of 18, or sibling under the age of 18 that resides

in the household. We topcode the number of dependents at nine.

Educational attainment We use the method proposed in Jaeger (1997) to map different edu-

cation levels into ﬁve categories: did not complete high school, completed high school, attended

some college, earned a college degree, earned an advanced degree.

Hours worked We use usual hours worked per week from the prior year as our continuous hours

variable. We then discretize hours as follows: less than ﬁve hours, 0 hours; between ﬁve and 14

hours, 10 hours; between 15 and 24 hours, 20 hours; between 25 and 34 hours; 30 hours, between

35 and 44 hours, 40 hours; between 45 and 54 hours, 50 hours; greater than 54 hours, 60 hours.

Non-labor income We calculate non-labor income as the sum of dividend income, interest in-

come, rental income and other property income, alimony, child support, and other non-property

income. For years 1998 and later, dividend income and other property income are separately

recorded in the CPS. Prior to 1998, they are recorded together in one category. If the combined

category is positive, we assume that 16.5% of the combined category is dividend income and 83.5%

is other property income. If the combined category is negative, we assume 100% of the combined

110

category is other property income. This split approximates the relative ratio of dividend income to

other property income from 1998 and later. We also assume that non-labor income is shared for

the entire household.

Hourly wage We calculate hourly wages as pre-tax wage and salary income for the prior year

divided by the product of usual hours worked per week in the prior year and weeks worked for pay

in the prior year. We code hourly wage as “missing” if usual hours worked or weeks worked are

zero or if wage and salary income is missing. Throughout our analysis, we use imputed wages for

these non-workers (and occasionally for the workers, too). We use the standard Heckman selection

model to estimate wages while accounting for selection into employment. First, we divide the

sample into men and women and pool across ﬁve-year bins (e.g., 1979-1983, 1984-1988, etc.) for

improved power. Then for each sex and pooled year sample, we jointly estimate a wage model

(log wage as a function of a cubic in age, educational attainment, marital status, and number of

dependents) and selection model (probability of working as a function of the wage variables with

selection instruments of non-labor income and indicators for having children between the ages

of zero to two, three to seven, eight to 13, 14 to 17, 18, and 19+). This procedure provides us

with estimated wages for non-workers (and workers) and the variance of the conditional wage

distribution.

Real wages and income We use the Consumer Price Index Research Series Using Current Meth-

ods (CPI-U-RS) to convert all after-tax wages and non-labor income to 2017 dollars.

111

Table C.2.1 Descriptive Statistics, Single Men and Women

Working
Hours (> 0)
Hourly wage
Non-labor income
Age
Dependents (under 18)
Dependents (under 2)
High school completed
Some college
Bachelor’s degree
Advanced degree
Observations

1980

1988

1996

2000

2008

2016

Panel A: Men

0.97
42.34
22.06
1,536
37.60
0.18
0.01
0.30
0.21
0.19
0.10
2,648

0.96
42.89
24.22
1,982 2,025
37.49
0.18
0.01
0.35
0.20
0.21
0.11
3,097

0.97
0.98
43.57 43.91
22.84 25.78
2,995
39.00 39.69
0.17
0.20
0.01
0.01
0.32
0.32
0.28
0.29
0.22
0.20
0.10
0.10
2,930 3,159

0.95
0.95
42.70
42.86
24.90 26.14
2,140 2,268
40.63 40.75
0.18
0.19
0.01
0.01
0.32
0.30
0.29
0.29
0.23
0.22
0.09
0.12
4,374 3,690

0.84
39.54
18.45
2,583 2,834
38.27
0.96
0.08
0.38
0.21
0.15
0.07
5,373

0.89
0.94
40.23 40.57
19.25 20.94
3,812
39.68 40.38
0.85
0.94
0.07
0.06
0.31
0.32
0.31
0.31
0.17
0.19
0.08
0.09
4,651 4,763

Panel B: Women
0.84
38.54
15.65
2,659
38.91
1.21
0.09
0.40
0.18
0.12
0.05
5,316

Working
0.90
0.92
Hours (> 0)
39.85
39.73
Hourly wage
21.36 22.31
Non-labor income
2,803 2,338
Age
40.94 40.64
Dependents (under 18)
0.87
0.88
Dependents (under 2)
0.07
0.07
High school completed
0.25
0.27
Some college
0.32
0.34
Bachelor’s degree
0.20
0.22
Advanced degree
0.11
0.14
Observations
7,300 5,733
Notes: This table contains descriptive statistics for our analytic sample
across time. Panel A presents statistics for single men and Panel B presents
statistics for single women. Years correspond to the survey year in the CPS.
Working is a binary variable equal to one if the observation had positive
hours worked per week in a typical week last year. Hours (> 0) is the
average hours worked for workers. Hourly wages and non-labor income
are in 2017 dollars. Observations are weighted by their ASEC person-level
survey weight.

112

Table C.2.2 Descriptive Statistics, Married Men and Women

1980

1988

1996

2000

2008

2016

Panel A: Men

Working
Hours (> 0)
Hourly wage
Non-labor income
Age
Dependents (under 18)
Dependents (under 2)
High school completed
Some college
Bachelor’s degree
Advanced degree
Bachelor’s degree
Advanced degree
Observations

0.99
43.31
25.37
2,218
40.09
1.50
0.20
0.37
0.17
0.12
0.03
0.16
0.07
17,619

0.98
43.74
27.23
2,815
39.66
1.33
0.21
0.38
0.19
0.15
0.05
0.18
0.09
14,944

0.98
44.43
27.10
3,236
40.71
1.31
0.20
0.33
0.27
0.19
0.08
0.19
0.11
12,251

0.98
44.68
29.78
4,884
41.44
1.30
0.19
0.32
0.27
0.21
0.09
0.21
0.12
12,722

0.97
44.05
29.41
3,309
42.16
1.30
0.20
0.29
0.26
0.25
0.12
0.23
0.13
18,802

0.96
43.63
32.10
3,169
42.91
1.31
0.19
0.27
0.25
0.28
0.17
0.24
0.17
14,414

Panel B: Women

0.66
43.31
9.66
2,218
37.42
1.50
0.20
0.49
0.16
0.12
0.03
17,619

0.79
44.43
15.31
3,236
38.58
1.31
0.20
0.36
0.28
0.19
0.08
12,251

0.79
44.68
16.71
4,884
39.36
1.30
0.19
0.33
0.29
0.21
0.09
12,722

0.77
44.05
17.37
3,309
40.18
1.30
0.20
0.27
0.28
0.25
0.12
18,802

0.74
43.74
12.79
2,815
37.24
1.33
0.21
0.47
0.20
0.15
0.05
14,944

Working
0.75
Hours (> 0)
43.63
Hourly wage
18.80
Non-labor income
3,169
Age
40.99
Dependents (under 18)
1.31
Dependents (under 2)
0.19
High school completed
0.23
Some college
0.25
Bachelor’s degree
0.28
Advanced degree
0.17
Observations
14,414
Notes: This table contains descriptive statistics for our analytic sample across
time. Panel A presents statistics for married men and Panel B presents statistics
for married women. Years correspond to the survey year in the CPS. Working is
a binary variable equal to one if the observation had positive hours worked per
week in a typical week last year. Hours (> 0) is the average hours worked for
workers. Hourly wages and non-labor income are in 2017 dollars. Observations
are weighted by their ASEC person-level survey weight.

113

Table C.2.3 Heckman Selection Wage Model, Men

1979
to
1983

1984
to
1988

1989
to
1993

1994
to
1998

1999
to
2003

2004
to
2008

2009
to
2013

2014
to
2018

-0.135
(0.068)
0.418
(0.164)
-0.044
(0.013)
0.189
(0.024)
0.293
(0.031)
0.465
(0.035)
0.569
(0.050)
0.408
(0.028)
-0.088
(0.018)
0.064
(0.039)
0.047
(0.036)
0.127
(0.036)
0.145
(0.035)
0.104
(0.045)
0.119
(0.029)
-0.010
(0.001)
2.794
(0.898)

-0.207
(0.065)
0.573
(0.158)
-0.055
(0.012)
0.298
(0.023)
0.415
(0.029)
0.617
(0.033)
0.695
(0.044)
0.342
(0.026)
-0.133
(0.017)
0.105
(0.037)
0.115
(0.035)
0.153
(0.034)
0.225
(0.033)
0.168
(0.046)
0.142
(0.028)
-0.006
(0.001)
3.764
(0.869)

-0.176
(0.069)
0.483
(0.166)
-0.048
(0.013)
0.325
(0.024)
0.475
(0.029)
0.606
(0.033)
0.711
(0.042)
0.327
(0.025)
-0.114
(0.019)
0.028
(0.039)
0.093
(0.037)
0.157
(0.036)
0.193
(0.035)
0.183
(0.050)
0.148
(0.029)
-0.007
(0.001)
3.537
(0.924)

-0.108
(0.071)
0.352
(0.170)
-0.040
(0.013)
0.269
(0.028)
0.387
(0.030)
0.503
(0.034)
0.629
(0.043)
0.268
(0.026)
-0.125
(0.020)
0.007
(0.039)
0.089
(0.037)
0.182
(0.037)
0.263
(0.037)
0.212
(0.054)
0.124
(0.030)
-0.005
(0.000)
2.573
(0.947)

-0.145
(0.064)
0.452
(0.155)
-0.048
(0.012)
0.178
(0.028)
0.303
(0.029)
0.379
(0.031)
0.420
(0.037)
0.150
(0.023)
-0.043
(0.019)
0.079
(0.036)
0.109
(0.034)
0.149
(0.033)
0.220
(0.032)
0.245
(0.048)
0.204
(0.028)
-0.004
(0.001)
3.207
(0.870)

-0.201
(0.057)
0.577
(0.136)
-0.056
(0.011)
0.183
(0.025)
0.289
(0.026)
0.390
(0.028)
0.520
(0.034)
0.114
(0.020)
-0.022
(0.017)
0.175
(0.032)
0.026
(0.029)
0.183
(0.029)
0.170
(0.028)
0.156
(0.040)
0.168
(0.024)
-0.005
(0.000)
3.852
(0.760)

-0.206
(0.052)
0.531
(0.126)
-0.047
(0.010)
0.229
(0.022)
0.357
(0.023)
0.545
(0.025)
0.636
(0.030)
0.095
(0.018)
-0.021
(0.014)
0.141
(0.027)
0.067
(0.025)
0.128
(0.025)
0.179
(0.024)
0.138
(0.034)
0.159
(0.021)
-0.003
(0.001)
3.876
(0.701)

-0.131
(0.059)
0.355
(0.143)
-0.033
(0.011)
0.127
(0.027)
0.260
(0.028)
0.395
(0.030)
0.554
(0.035)
0.045
(0.020)
0.040
(0.017)
0.080
(0.032)
0.035
(0.029)
0.066
(0.029)
0.087
(0.028)
0.056
(0.039)
0.195
(0.024)
-0.002
(0.001)
3.036
(0.801)

Selection equation
Age

Age2/100

Age3/1000

H.S. completed

Some college

Bachelor’s degree

Advanced degree

Married

Dependents

1[Dep. 0-2]

1[Dep. 3-7]

1[Dep. 8-13]

1[Dep. 14-17]

1[Dep. 18]

1[Dep. 19+]

Non-labor income
(in $1000s)
Constant

114

Table C.2.3 (cont’d)

1979
to
1983

1984
to
1988

1989
to
1993

1994
to
1998

1999
to
2003

2004
to
2008

2009
to
2013

2014
to
2018

Wage equation
Age

Age2/100

Age3/1000

H.S. completed

Some college

Bachelor’s deg.

Advanced deg.

Married

Dependents

Constant

0.117
(0.010)
-0.201
(0.026)
0.011
(0.002)
0.270
(0.004)
0.344
(0.005)
0.483
(0.005)
0.523
(0.006)
0.134
(0.005)
0.001
(0.001)
0.456
(0.136)
95,631

0.069
(0.012)
-0.077
(0.029)
0.001
(0.002)
0.281
(0.005)
0.390
(0.006)
0.579
(0.006)
0.656
(0.007)
0.129
(0.005)
-0.003
(0.001)
1.001
(0.153)
91,741

0.097
(0.012)
-0.154
(0.030)
0.008
(0.002)
0.289
(0.005)
0.414
(0.006)
0.633
(0.006)
0.737
(0.007)
0.138
(0.005)
-0.003
(0.002)
0.603
(0.159)
90,746

0.139
(0.013)
-0.252
(0.033)
0.015
(0.003)
0.305
(0.006)
0.436
(0.006)
0.668
(0.007)
0.820
(0.008)
0.137
(0.005)
-0.001
(0.002)
-0.018
(0.177)
81,091

0.099
(0.011)
-0.157
(0.028)
0.008
(0.002)
0.306
(0.006)
0.468
(0.006)
0.741
(0.006)
0.908
(0.007)
0.141
(0.004)
0.012
(0.001)
0.540
(0.152)

0.075
0.113
(0.014)
(0.012)
-0.114
-0.196
(0.035)
(0.030)
0.005
0.011
(0.003)
(0.002)
0.313
0.328
(0.007)
(0.006)
0.484
0.487
(0.007)
(0.006)
0.807
0.751
(0.008)
(0.006)
1.012
0.904
(0.008)
(0.007)
0.137
0.143
(0.005)
(0.004)
0.012
0.009
(0.002)
(0.001)
0.894
0.375
(0.161)
(0.191)
110,212 120,014 111,194 93,621

0.056
(0.013)
-0.059
(0.031)
0.000
(0.002)
0.301
(0.007)
0.473
(0.007)
0.775
(0.007)
0.960
(0.008)
0.146
(0.005)
0.013
(0.002)
1.098
(0.169)

Observations
Notes: This table contains parameter estimates from the Heckman selection wage model described
in Appendix Section C.2. The outcome variable is logged hourly wage in 2017 dollars. Standard
errors in parentheses.

115

Table C.2.4 Heckman Selection Wage Model, Women

1979
to
1983

1984
to
1988

1989
to
1993

1994
to
1998

1999
to
2003

2004
to
2008

2009
to
2013

2014
to
2018

-0.047
(0.029)
0.113
(0.075)
-0.015
(0.006)
0.369
(0.011)
0.575
(0.014)
0.716
(0.016)
1.037
(0.032)
-0.500
(0.011)
-0.168
(0.007)
-0.492
(0.015)
-0.337
(0.014)
-0.020
(0.013)
0.153
(0.014)
0.148
(0.018)
0.003
(0.012)
-0.008
(0.000)
2.483
(0.358)

0.009
(0.032)
-0.018
(0.083)
-0.005
(0.007)
0.490
(0.012)
0.752
(0.015)
0.885
(0.017)
1.207
(0.029)
-0.365
(0.011)
-0.249
(0.008)
-0.403
(0.015)
-0.247
(0.015)
0.071
(0.014)
0.233
(0.015)
0.207
(0.021)
0.013
(0.013)
-0.007
(0.000)
1.455
(0.398)

-0.048
(0.035)
0.141
(0.091)
-0.018
(0.008)
0.538
(0.013)
0.820
(0.016)
0.946
(0.018)
1.236
(0.028)
-0.307
(0.012)
-0.241
(0.008)
-0.396
(0.016)
-0.244
(0.015)
0.087
(0.015)
0.203
(0.016)
0.232
(0.023)
0.001
(0.014)
-0.007
(0.000)
2.013
(0.437)

0.032
(0.038)
-0.038
(0.099)
-0.004
(0.008)
0.544
(0.016)
0.862
(0.017)
0.931
(0.019)
1.202
(0.028)
-0.340
(0.013)
-0.239
(0.009)
-0.346
(0.017)
-0.234
(0.016)
0.086
(0.016)
0.222
(0.017)
0.225
(0.025)
-0.007
(0.015)
-0.005
(0.000)
0.896
(0.482)

-0.009
(0.032)
0.063
(0.084)
-0.011
(0.007)
0.507
(0.015)
0.754
(0.015)
0.767
(0.017)
0.990
(0.022)
-0.578
(0.012)
-0.209
(0.008)
-0.324
(0.014)
-0.190
(0.014)
0.122
(0.014)
0.228
(0.014)
0.233
(0.021)
0.062
(0.014)
-0.004
(0.000)
1.811
(0.410)

-0.004
(0.031)
0.041
(0.078)
-0.008
(0.006)
0.537
(0.014)
0.828
(0.015)
0.824
(0.016)
1.037
(0.019)
-0.553
(0.011)
-0.213
(0.007)
-0.310
(0.014)
-0.165
(0.013)
0.122
(0.013)
0.255
(0.013)
0.241
(0.020)
0.037
(0.013)
-0.004
(0.000)
1.547
(0.389)

0.086
(0.032)
-0.189
(0.081)
0.012
(0.007)
0.481
(0.016)
0.783
(0.016)
0.822
(0.016)
1.060
(0.019)
-0.471
(0.011)
-0.223
(0.007)
-0.215
(0.014)
-0.097
(0.013)
0.133
(0.013)
0.251
(0.013)
0.208
(0.019)
0.055
(0.013)
-0.005
(0.000)
0.150
(0.413)

0.165
(0.035)
-0.369
(0.088)
0.026
(0.007)
0.477
(0.018)
0.805
(0.018)
0.881
(0.018)
1.144
(0.021)
-0.537
(0.012)
-0.186
(0.008)
-0.198
(0.015)
-0.125
(0.014)
0.069
(0.014)
0.192
(0.014)
0.205
(0.021)
0.005
(0.013)
-0.002
(0.000)
-0.969
(0.450)

Selection equation
Age

Age2/100

Age3/1000

H.S. completed

Some college

Bachelor’s degree

Advanced degree

Married

Dependents

1[Dep. 0-2]

1[Dep. 3-7]

1[Dep. 8-13]

1[Dep. 14-17]

1[Dep. 18]

1[Dep. 19+]

Non-labor income
(in $1000s)
Constant

116

Table C.2.4 (cont’d)

1979
to
1983

1984
to
1988

1989
to
1993

1994
to
1998

1999
to
2003

2004
to
2008

2009
to
2013

2014
to
2018

Wage equation
Age

H.S. completed

Some college

Bachelor’s deg.

Advanced deg.

Age2/100

Age3/1000

0.147
(0.013)
-0.292
(0.034)
0.018
(0.003)
0.283
(0.007)
0.493
(0.008)
0.735
(0.008)
0.933
(0.010)
-0.018
(0.004)
-0.077
(0.002)
0.073
(0.165)

0.175
(0.012)
-0.376
(0.033)
0.025
(0.003)
0.267
(0.006)
0.448
(0.008)
0.634
(0.008)
0.841
(0.010)
-0.046
(0.004)
-0.079
(0.002)
-0.150
(0.155)

0.183
0.139
(0.015)
(0.011)
-0.384
-0.302
(0.038)
(0.030)
0.026
0.021
(0.003)
(0.003)
0.318
0.219
(0.008)
(0.006)
0.532
0.368
(0.008)
(0.007)
0.807
0.537
(0.009)
(0.008)
1.036
0.727
(0.011)
(0.011)
-0.007
-0.075
(0.004)
(0.005)
-0.064
-0.069
(0.002)
(0.002)
-0.497
0.441
(0.140)
(0.186)
107,867 104,221 102,231 90,810

0.178
0.137
(0.015)
(0.013)
-0.370
-0.272
(0.038)
(0.033)
0.026
0.017
(0.003)
(0.003)
0.322
0.314
(0.010)
(0.007)
0.543
0.517
(0.010)
(0.007)
0.887
0.808
(0.010)
(0.008)
1.162
1.040
(0.011)
(0.009)
0.016
-0.007
(0.005)
(0.004)
-0.040
-0.051
(0.002)
(0.002)
-0.569
0.168
(0.162)
(0.200)
Observations
123,240 135,599 124,668 103,915
Notes: This table contains parameter estimates from the Heckman selection wage model described
in Appendix Section C.2. The outcome variable is logged hourly wage in 2017 dollars. Standard
errors in parentheses.

0.157
(0.013)
-0.318
(0.034)
0.021
(0.003)
0.330
(0.008)
0.551
(0.008)
0.861
(0.009)
1.124
(0.009)
0.006
(0.004)
-0.039
(0.002)
-0.228
(0.173)

0.116
(0.013)
-0.215
(0.032)
0.012
(0.003)
0.316
(0.007)
0.531
(0.008)
0.823
(0.008)
1.064
(0.009)
-0.012
(0.004)
-0.046
(0.002)
0.373
(0.161)

Married

Dependents

Constant

117

C.3 Using TAXSIM and TRIM3 to predict after-tax wages and social assistance beneﬁts

To fully exploit variation in the tax system, we would like to calculate after-tax income for each

hours choice a household could make (seven for single men and women, 49 for married couples).

Given we are using simulation methods that rely on 100 wage draws for each household, this

entails calculating post-tax income 700 times for each single man and woman and 4,900 times for

each married couple in our sample. This amounts to calculating after-tax income upwards of 1.35

billion times (700*93,330 for single men, 700*153,494 for single women, and 4,900*240,000 for

married couples).

To make this computationally feasible with TAXSIM, we rely on a strategy similar to that

described by L¨oefﬂer et al. (2018), estimating a ﬂexible parametric tax function and then using the

tax function to predict after-tax wages. For each observation, we use NBER’s TAXSIM version

27 to calculate after-tax income at seven weekly work hours choices conditional on working 50

weeks a year and their observed (or predicted) hourly wage and non-labor income. For single

men and women, the seven hours choices comprise their entire choice set. For married couples, we

specify that both spouses work the same number of hours and span the seven discrete hours choices

(e.g., 0 and 0 hours, 10 and 10 hours, etc.). Using each observation’s simulated after-tax income

from TAXSIM, we ﬁt an observation-speciﬁc function of after-tax income as a quadratic function

of before-tax income. To ensure that taxes are zero when income is zero, we do not include a

constant in the regression. Finally, when we use the observation-speciﬁc function to predict after-

tax income, we do not allow after-tax income to be less than 60% of before-tax income, which

should not happen in practice but would eventually happen for large enough before-tax income

due to the negative quadratic term.

For social beneﬁts, we use the Urban Institute’s TRIM3 and a ﬂexible regression to predict gov-

ernment assistance. TRIM3 provides information on eligibility and receipt of government assis-

tance (i.e., SNAP/Food Stamps, TANF/ADFC, and SSI) for each household in our sample. TRIM3

requires users to input assumptions and/or interpretations about economic behavior and the rules

118

governing federal programs. Therefore, the conclusions presented in this chapter are attributable

only to the authors and not any researcher at the Urban Institute. We estimate a state-year-marital

status-number of dependents-speciﬁc kinked regression model to predict beneﬁts given counterfac-

tual labor income bundles. The slope between household income and beneﬁts received is allowed

to change after the ﬁrst $10k and $20k of (nominal) income. Between $30k to $50k, $50k to $70k,

and $70k+, we use the average beneﬁts received in the range. When we use these ﬂexible functions

to predict beneﬁts received, we truncate beneﬁts at $0 and $50,000 in nominal dollars.

119

C.4 Utility function parameter estimates

Table C.4.1 Baseline Model Parameter Estimates, Single Men

Log(Consumption)

Log(Leisure)

× Log(Age)

× Log(Age)2

× Dep. (under 18)

× Dep. (under 2)

Log(Consumption)2

Log(Leisure)2

Log(C) × Log(L)

Hours = 10

Hours = 20

Hours = 30

1996
2.23
(1.37)
135.02
(38.29)
-19.75
(20.41)
3.12
(2.80)
-0.22
(0.20)
2.32
(1.11)
0.06
(0.02)
-11.22
(0.86)
-0.55
(0.27)
-3.31
(0.27)
-2.72
(0.14)
-2.58
(0.11)

2000
3.87
(1.25)
192.00
(39.47)
-42.29
(20.95)
6.24
(2.87)
-0.15
(0.22)
-1.10
(1.38)
0.08
(0.01)
-12.59
(0.80)
-0.96
(0.26)
-3.53
(0.30)
-2.80
(0.14)
-3.05
(0.12)

2004
3.43
(1.05)
167.55
(32.46)
-33.76
(17.26)
4.82
(2.36)
-0.36
(0.15)
0.66
(1.05)
0.10
(0.01)
-11.03
(0.72)
-0.88
(0.22)
-3.45
(0.20)
-2.97
(0.11)
-2.91
(0.09)

2008
4.29
(1.03)
271.43
(31.32)
-85.50
(16.45)
11.90
(2.25)
-0.35
(0.16)
-0.66
(0.74)
0.09
(0.01)
-11.97
(0.68)
-1.07
(0.21)
-2.94
(0.16)
-3.07
(0.12)
-3.14
(0.10)

2012
4.26
(1.15)
159.24
(30.16)
-27.56
(15.95)
4.06
(2.18)
-0.44
(0.16)
1.33
(0.81)
0.11
(0.02)
-11.20
(0.73)
-1.08
(0.22)
-3.50
(0.18)
-3.00
(0.11)
-2.74
(0.08)

2016
5.08
(1.05)
107.57
(34.23)
0.69
(18.18)
0.23
(2.48)
-0.39
(0.16)
1.02
(0.81)
0.13
(0.01)
-10.96
(0.73)
-1.30
(0.22)
-3.55
(0.22)
-2.98
(0.12)
-2.81
(0.09)

Observations
Notes: This table contains parameter estimates for our baseline model for single
men in a subset of years. The speciﬁc utility function is described in Section 3.4.1.

4,260

4,254

3,690

2,930

3,159

4,374

120

Table C.4.2 Baseline Model Parameter Estimates, Single Women

Log(Consumption)

Log(Leisure)

× Log(Age)

× Log(Age)2

× Dep. (under 18)

× Dep. (under 2)

Log(Consumption)2

Log(Leisure)2

Log(C) × Log(L)

Hours = 10

Hours = 20

Hours = 30

1996
10.63
(1.14)
320.14
(29.51)
-88.52
(15.83)
12.42
(2.18)
0.46
(0.10)
1.51
(0.28)
0.13
(0.02)
-15.31
(0.58)
-2.45
(0.22)
-3.18
(0.14)
-2.49
(0.08)
-2.25
(0.06)

2000
11.21
(1.09)
255.76
(31.38)
-43.64
(16.93)
6.34
(2.32)
0.57
(0.10)
1.05
(0.35)
0.13
(0.01)
-17.31
(0.60)
-2.60
(0.22)
-3.31
(0.17)
-2.35
(0.08)
-2.28
(0.06)

2004
13.56
(0.85)
308.36
(24.20)
-61.02
(12.96)
8.49
(1.78)
0.25
(0.08)
1.41
(0.26)
0.16
(0.01)
-18.42
(0.52)
-3.15
(0.18)
-3.11
(0.11)
-2.56
(0.06)
-2.46
(0.05)

2008
14.09
(0.89)
255.64
(24.86)
-29.22
(13.36)
4.22
(1.83)
0.28
(0.08)
1.00
(0.24)
0.14
(0.01)
-19.11
(0.53)
-3.24
(0.18)
-3.27
(0.12)
-2.57
(0.06)
-2.45
(0.05)

2012
15.76
(0.99)
269.93
(24.25)
-38.78
(12.90)
5.47
(1.77)
0.28
(0.08)
0.99
(0.25)
0.19
(0.01)
-17.93
(0.58)
-3.70
(0.19)
-3.38
(0.11)
-2.62
(0.06)
-2.27
(0.05)

2016
14.16
(1.02)
246.72
(27.65)
-36.50
(14.76)
5.19
(2.02)
0.08
(0.09)
0.75
(0.28)
0.20
(0.01)
-16.14
(0.60)
-3.34
(0.21)
-3.42
(0.13)
-2.78
(0.07)
-2.35
(0.05)

4,651

Observations
Notes: This table contains parameter estimates for our baseline model for single
women in a subset of years. The speciﬁc utility function is described in Section
3.4.1.

7,013

5,733

4,763

7,658

7,300

121

Table C.4.3 Baseline Model Parameter Estimates, Married Men and Women

Log(Consumption)

Log(Leisurem)
× Log(Agem)
× Log(Agem)2
× Dep. (under 18)

× Dep. (under 2)

Log(Leisure f )
× Log(Age f )
× Log(Age f )2
× Dep. (under 18)

× Dep. (under 2)

Log(Consumption)2

Log(Leisurem)2

Log(Leisure f )2

1996
12.59
(1.16)
277.64
(30.38)
-76.69
(16.47)
10.68
(2.26)
5.91
(1.24)
4.22
(3.52)
251.58
(25.58)
-50.35
(14.10)
7.06
(1.96)
6.68
(1.17)
5.29
(3.32)
0.14
(0.01)
-14.86
(0.32)
-17.95
(0.34)

2000
14.20
(1.13)
287.01
(30.55)
-86.62
(16.47)
12.18
(2.25)
9.26
(1.27)
2.31
(3.54)
233.39
(24.84)
-46.41
(13.68)
6.56
(1.90)
9.67
(1.21)
3.52
(3.34)
0.20
(0.01)
-14.46
(0.34)
-17.46
(0.33)

2004
14.04
(1.14)
278.50
(30.88)
-87.14
(16.59)
12.32
(2.26)
12.13
(1.28)
3.50
(3.46)
227.36
(25.64)
-45.25
(14.01)
6.39
(1.94)
12.50
(1.23)
4.79
(3.27)
0.22
(0.01)
-14.30
(0.34)
-17.50
(0.35)

2008
17.19
(1.14)
282.67
(29.39)
-74.71
(15.79)
10.46
(2.15)
9.85
(1.28)
1.10
(3.31)
206.19
(24.77)
-27.77
(13.53)
3.96
(1.87)
10.42
(1.22)
2.46
(3.12)
0.16
(0.01)
-15.49
(0.33)
-17.82
(0.34)

2012
18.83
(1.01)
254.86
(29.90)
-64.85
(16.06)
8.96
(2.18)
10.24
(1.14)
-3.94
(3.08)
250.87
(24.99)
-59.14
(13.59)
8.02
(1.87)
10.77
(1.09)
-2.79
(2.92)
0.17
(0.01)
-14.33
(0.33)
-16.39
(0.34)

2016
16.63
(1.02)
186.89
(31.52)
-40.29
(16.94)
5.71
(2.30)
11.23
(1.23)
-3.81
(3.35)
233.96
(26.03)
-54.46
(14.13)
7.63
(1.94)
11.81
(1.18)
-3.00
(3.20)
0.24
(0.01)
-13.80
(0.33)
-16.13
(0.32)

122

Table C.4.3 (cont’d)

Log(C) × Log(Lm)
Log(C) × Log(L f )
Log(Lm) × Log(L f )
× Log(Avg. Age)

× Log(Avg. Age)2

× Dep. (under 18)

× Dep. (under 2)

Hoursm = 10

Hoursm = 20

Hoursm = 30

Hours f = 10

Hours f = 20

Hours f = 30

1996
-1.88
(0.17)
-1.08
(0.14)
2.42
(6.37)
-0.44
(3.53)
0.12
(0.49)
-1.36
(0.28)
-0.98
(0.79)
-3.59
(0.19)
-3.22
(0.11)
-3.33
(0.08)
-2.86
(0.06)
-2.16
(0.04)
-2.18
(0.04)

2000
-2.25
(0.17)
-1.16
(0.13)
-0.88
(6.32)
2.77
(3.49)
-0.37
(0.48)
-2.10
(0.29)
-0.51
(0.79)
-3.90
(0.24)
-3.34
(0.12)
-3.71
(0.10)
-2.89
(0.07)
-2.28
(0.04)
-2.30
(0.04)

2004
-2.11
(0.17)
-1.29
(0.13)
-6.39
(6.47)
6.87
(3.54)
-0.96
(0.49)
-2.80
(0.29)
-0.76
(0.78)
-3.88
(0.21)
-3.51
(0.12)
-3.32
(0.08)
-2.88
(0.06)
-2.26
(0.04)
-2.24
(0.04)

2008
-2.69
(0.17)
-1.26
(0.13)
-3.79
(6.23)
4.31
(3.41)
-0.60
(0.47)
-2.30
(0.29)
-0.30
(0.74)
-4.62
(0.30)
-3.63
(0.12)
-3.32
(0.08)
-3.03
(0.07)
-2.43
(0.04)
-2.37
(0.04)

2012
-2.91
(0.15)
-1.41
(0.13)
-15.90
(6.22)
11.34
(3.40)
-1.52
(0.46)
-2.41
(0.26)
0.89
(0.69)
-3.87
(0.18)
-3.23
(0.09)
-3.21
(0.07)
-3.00
(0.07)
-2.40
(0.04)
-2.29
(0.04)

2016
-2.09
(0.16)
-1.90
(0.12)
-7.53
(6.57)
8.18
(3.58)
-1.14
(0.49)
-2.66
(0.28)
0.91
(0.76)
-3.95
(0.20)
-3.46
(0.10)
-3.50
(0.08)
-3.23
(0.07)
-2.52
(0.05)
-2.50
(0.04)

10,000

Observations
10,000
Notes: This table contains parameter estimates for our baseline model for mar-
ried men and women in a subset of years. The speciﬁc utility function is de-
scribed in Section 3.4.1.

10,000

10,000

10,000

10,000

123

C.5 Quadratic versus translog utility results

While our baseline model uses a translog utility function, another common choice in the liter-

ature is a quadratic utility function (e.g., Bargain et al. 2014; Blundell et al. 2000). L¨oefﬂer et al.

(2018) show that labor supply elasticity estimates tend to be robust to the choice of utility function,

and when we estimate our baseline model with a quadratic utility function, we ﬁnd similar results.

Following Bargain et al. (2014), our quadratic utility function for single men and women is:

ui j = β c

i ci j + β cc(ci j)2 + β l

i li j + β ll(li j)2 + β clci jli j + f (xi,hi j)

(C.1)

where ci j is weekly household consumption, li j = 168−hi j is weekly leisure, and f (xi,hi j) are
ﬁxed costs of working more than zero hours. Three parameters vary with individual characteristics:
i varies with a quadratic function of age and number of dependents under the age of 18, β l
β c
i varies
with a quadratic function of age and an indicator for having dependents under the age of 2, and

f (xi,hi j) varies with number of dependents under 18, an indicator for having dependents under
two, and an indicator for having earned a college degree.

For married men and women, we add a quadratic function of leisure for the spouse, an interac-

tion between household consumption and leisure for the spouse, the interaction of leisure for the

head of household and leisure for the spouse, and a ﬁxed cost of work for the spouse:

ui j = β c

i ci j + β cc(ci j)2 + β lm
i
i j + β cl f ci jl f
i jl f
β clmci jlm
i j + β lm f lm

lm
i j + β lmm(lm

i j )2 + β l f
l f
i j + β l f f (l f
i j)2+
i
i j) + f f (x f
i ,h f
i ,hm
i j + f m(xm

i j).

(C.2)

Modeled preference heterogeneity is the same for the spouse as for the head of household,

but now the quadratic function of age included in β c
i

is based on the average age of the head of

household and spouse.

Figure C.5.1 presents our estimated elasticities from the baseline model and model with quadratic

utility. Wages are predicted for non-workers using 100 Halton draws, and random slopes are set

to zero. As expected, the estimated elasticities are very similar between the two models, and the

trends we observe over time are unchanged.

124

Figure C.5.1 Mean Own-Wage Elasticities, Baseline Estimates versus Estimates from Quadratic
Utility Model

Notes: This ﬁgure presents the estimated trends in mean own-wage elasticities separately by sex
and marital status. Our baseline model (blue) has a translog utility function, no random slopes,
beneﬁt simulator from TRIM3, and predicted wages for non-workers using 100 draws from their
conditional wage distribution. Our quadratic model (red with triangle markers) is identical to the
baseline model except for quadratic utility function as described in Section C.5.

125

-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearSingle Men-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearSingle Women-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearMarried Men-.10.1.2.3.4.5Own-Wage Elasticity199519992003200720112015YearMarried WomenBaselineQuadratic utilityBIBLIOGRAPHY

126

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