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Three Essays on the Economics of Higher Education

Thèse

Safa Ragued

Doctorat en économique

Philosophiæ doctor (Ph.D.)

Québec, Canada

© Safa Ragued, 2017

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Three Essays on the Economics of Higher Education

Thèse

Safa Ragued

Sous la direction de:

Sylvain Dessy, directeur de recherche

Bernard Fortin, codirecteur de recherche

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Résumé

Ma thèse relie deux littératures diérentes, à savoir, l'économie de l'éducation et l'économie du

travail. Ces deux littératures se rencontrent dans un cadre d'analyse de politiques publiques visant

à renforcer le capital humain et à prévenir les parcours scolaires inecaces.

Le premier chapitre propose un modèle d'équilibre général de participation aux études

su-périeures et d'ore de travail, dans un contexte de rendement incertain sur les études susu-périeures

et de mobilité internationale des capitaux. L'étude vise à comparer les performances de diérentes

propositions scales sur la formation des compétences. Les résultats montrent que l'impact sur la

formation de capital humain du passage d'un régime d'imposition proportionnel à un régime

d'impo-sition progressif varie selon le niveau de l'ecacité de la préparation des diplômés par l'enseignement

supérieur. Cet impact est négatif lorsque le niveau d'ecacité est faible et positif quand il est élevé.

Le deuxième chapitre aborde la question de l'inégalité des revenus. Le modèle considère

trois types d'interventions que le gouvernement peut adopter pour maximiser la bien-être social : le

nancement de l'éducation primaire et secondaire, la subvention de l'éducation postsecondaire et / ou

la redistribution des revenus par l'impôt sur les salaires. L'étude détermine simultanément le niveau

optimal de ces politiques en utilisant un modèle de participation aux études supérieures. Calibré

sur des preuves empiriques provenant de l'Ontario, le modèle prédit une combinaison optimale

caractérisée par la coexistence de la scalité redistributive, l'investissement public dans l'éducation

primaire et secondaire, et les subventions publiques pour l'éducation supérieure. Par rapport au

statu quo en Ontario, la combinaison optimale est caractérisée par une plus faible part des fonds

publics alloués à l'éducation primaire et secondaire, une plus grande part allouée aux subventions de

l'éducation postsecondaire, et un niveau plus élevé de taxation redistributive. De plus, les résultats

concluent que les études qui ne déterminent pas conjointement les niveaux optimaux de ces trois

options politiques ont tendance à surestimer ces niveaux.

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Alors que les deux premiers chapitres étudient l'optimalité des politiques publiques, le

troisième chapitre aborde empiriquement la question de l'interruption temporaire des études

postse-condaires, en particulier, son eet sur les salaires ultérieurs des diplômés. La plupart des études sur

les décrocheurs du postsecondaire et sur les conséquences économiques de leurs parcours scolaires

considère le décrochage comme étant une décision permanente. Peu d'attention a été accordée,

jus-qu'à présent, à l'eet de décrochage temporaire sur les revenus futurs des individus, et ce en dépit du

nombre important de décrocheurs qui, à un moment donné, décident de retourner à l'université et de

terminer leurs études. Ce chapitre contribue à la compréhension de cette question par, d'une part,

l'analyse de l'eet de l'interruption temporaire des études postsecondaires sur les salaires de sortie

des diplômés, et d'autre part, la vérication si ces derniers sont aectés diéremment par les raisons

de l'interruption. Cette question est examinée en utilisant les données de l'Enquête Nationale auprès

des Diplômés (END) de 2007. L'endogénéité de certaines variables du modèle est prise en compte à

l'aide de l'approche des instruments générés de Lewbel (2012). Cette approche impose des

restric-tions raisonnables sur les seconds moments conditionnels des données, sous l'hétéroscédasticité des

termes d'erreur des covariables endogènes. Compte tenu de ces restrictions, la méthodologie de

Lew-bel fournit des instruments générés qui sont utilisés avec des instruments externes supplémentaires

pour estimer le modèle. Sachant les niveaux de scolarité et de l'expérience, les résultats montrent

que l'interruption temporaire a un eet positif sur les salaires de départ des hommes qui avaient

occupé un emploi à temps plein au cours de leur interruption. L'eet est négatif si l'interruption

est associée à des problèmes de santé aussi bien pour les hommes que pour les femmes. Les femmes

subissent également une pénalité salariale si leur interruption est due à un emploi à temps partiel,

à un manque d'argent, ou à des raisons autres que la santé, le travail et l'argent.

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Abstract

My thesis bridges two dierent literatures namely, the Economics of Education and Labor Economics.

These two literatures are brought together to bear on public policy aimed at enhancing human capital

and preventing inecient schooling paths.

The rst chapter proposes a general equilibrium model of enrollment in higher education

and labor supply, in the context of uncertain return on higher education and internationally mobile

capital. The study aims to contrast the performances of dierent wage tax proposals on skill

forma-tion. The results suggest that the quantitative impact on skill formation of switching from the at to

the progressive tax varies with the level of eciency with which higher education imparts graduates

with suitable skills. This impact is negative when the level of eciency of higher education is low

and positive when it is high.

The second chapter raises the issue of income inequality. The model considers three types

of interventions on which the government could take action to maximize social welfare: nancing

early education, subsidizing college tuition and/or redistributing income through taxation. The

study jointly determines the optimal level of these policies using a model of college enrollment.

When calibrated to empirical evidence from the Canadian Province of Ontario, the model predicts

an optimal policy mix characterized by the coexistence of redistributive taxation, public investment

in K-12 education, and public subsidies for college tuition. Compared to the Status Quo policy

scenario in Ontario, the optimal policy mix exhibits a lower share of public funds allocated to K-12

education, a higher share allocated to college tuition subsidies, and a higher level of redistributive

taxation. More importantly, the results conclude that studies that do not jointly determine the

optimal levels of the three policy options tend to overestimate these levels.

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empirically tackles the issue of temporary interruption of higher education, particularly, its eect

on subsequent wages. Most of the studies that address the issue of the economic consequences of

schooling interruption, examine dropping-out as a permanent decision. Little attention has so far

been given to the eect of temporary drop out on earnings despite the substantial number of dropouts

who at some point decide to re-enroll and complete their education. This chapter contributes

to the understanding of this issue by investigating the extent to which schooling discontinuities

aect post-graduation starting real wages and whether the latter are dierently inuenced by the

reasons behind these discontinuities. This subject is examined using data from the 2007 National

Graduate Survey. The covariates endogeneity is taken into account using Lewbel's (2012) generated

instrument approach. The latter imposes some reasonable restrictions on the conditional second

moments of the data, under heteroscedasticity of the error terms of the endogenous covariates. Under

these constraints, the Lewbel framework provides generated instruments which are used along with

additional external instruments, to estimate the model. Conditional on the levels of schooling and

experience, the results nd a positive eect on wages of temporary schooling interruption for men

who had held a full-time job during their out-of-school spell(s). Both men and women witness a

wage decrease if their interruption is associated with health issues. Women also bear a wage penalty

if their interruption is due to a part-time job, to lack of money, or is caused by reasons other than

health, work, and money.

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Contents

Résumé

iii

Abstract

v

Contents

vii

List of Tables

viii

List of Figures

ix

Acknowledgments

xii

Introduction

1

1 Whither the Progressive Tax?

6

1.1 Introduction

. . . .

7

1.2 Preliminaries

. . . .

12

1.3 Equilibrium Analysis

. . . .

26

1.4 Concluding Remarks

. . . .

36

2 Optimal Fiscal and Education Policies when Educational Abilities Are

En-dogenous

38

2.1 Introduction

. . . .

39

2.2 Economic Environment

. . . .

43

2.3 Mapping the Model To the Data

. . . .

53

2.4 Optimal Policy Mix

. . . .

63

2.5 Concluding Remarks

. . . .

67

3 Does Temporary Interruption in Postsecondary Education Induce a Wage

Penalty? Evidence from Canada

69

3.1 Introduction

. . . .

70

3.2 Literature Review

. . . .

75

3.3 Data and Descriptive Statistics

. . . .

79

3.4 Specication of the Baseline Wage Equation

. . . .

83

3.5 Lewbel's Approach

. . . .

85

3.6 Empirical Results

. . . .

86

3.7 Robustness Checks

. . . .

90

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Conclusion

102

A

105

A.1 Proof of Proposition 2

. . . .

105

A.2 Proof of Proposition 3

. . . .

106

B

107

B.1 Proof of Proposition 1

. . . .

107

C

108

C.1 Controlling for Current Health Status

. . . .

108

C.2 Box-Cox Test

. . . .

109

C.3 Quadratic Education and Quartic Work Experience Function

. . . .

110

C.4 Non-Separability in Education and Experience

. . . .

111

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List of Tables

1.1 Parameter Values

. . . .

30

2.1 Independence Test with Empirical Copula

. . . .

55

2.2 Goodness of Fit and Model Selection Tests

. . . .

58

2.3 Estimates of the Margins'Parameters

. . . .

60

2.4 Parameter Values

. . . .

63

2.5 Optimal Policy Under Dierent Scenarios

. . . .

64

2.6 Sensitivity Analysis

. . . .

65

3.1 Descriptive Statistics

a

. . . .

96

3.2 Underidentication, Weak Identication, and Overidentication Tests for the Baseline

Specication

. . . .

97

3.3 Breusch-Pagan Test for Homoskedasticity

. . . .

98

3.4 OLS and Lewbel's Estimates of the Wage Equations for Men and Women (With

Dummies for Reasons of Interruption)

. . . .

99

3.5 Underidentication, Weak Identication, and Overidentication Tests for the Second

Specication

. . . .

100

3.6 OLS and Lewbel's Estimates of the Wage Equations for Men and Women (With No

Dummies for Reasons of Interruption)

. . . .

101

C.1 Controlling for Current Health Status

a

. . . .

108

C.2 Statistics for the Box-Cox Test

. . . .

109

C.3 Quadratic Education and Quartic Work Experience Function

a

. . . .

110

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List of Figures

1.1 Worker b's Decision Tree

. . . .

15

1.2 The Equilibrium Supply of Skilled Workers

. . . .

31

1.3 The Equilibrium Level of Capital Inows

. . . .

33

1.4 The equilibrium Skill Premium

. . . .

34

1.5 The Average Student Debt

. . . .

35

2.1 Normalized Ranks

. . . .

56

2.2 Gaussian Copula

. . . .

59

2.3 Histograms and Density Functions

. . . .

61

2.4 Social Welfare as a Function of (α, τ

c

)

. . . .

63

2.5 Sensitivity Analysis with Respect to λ

. . . .

65

2.6 Measure of College Graduates as a Function of (α, τ

c

)

. . . .

66

3.1 Potential Wage Proles for Interrupters and Non-interrupters

. . . .

71

3.2 Two-Stage Quantile Regression and GMM Linear Lewbel's Coecients, and

Con-dence Intervals for the Interruption-Related Variables - Men

. . . .

93

3.3 Two-Stage Quantile Regression and Linear Lewbel's Coecients and Condence

In-tervals for the Interruption-Related Variables - Women

. . . .

94

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To my mother Fatma, to my father Mosbah. May God, the Almighty,

grant you health, long life, and happiness.

In loving memory of my grandmother Bebba.

You are always in my thoughts.

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You know, sometimes all you need is twenty seconds of insane courage. Just literally twenty seconds of just embarrassing bravery, and I promise you, something great will come of it.

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Acknowledgments

I would rst like to thank my thesis advisor Sylvain Dessy, whose vast expertise, understanding,

advice, and motivation added considerably to my graduate experience. I would also like to express

my sincere gratitude to my thesis co-advisor Bernard Fortin for his immense knowledge, support,

energy, and great sense of humor. The guidance, availability, and insights of Professors Dessy and

Fortin have helped me over the course of my thesis. In addition to their intellectual rigor and

technical expertise, I have appreciated their kindness, caring and paternal attitude. I thank them

for such a wonderful experience. I could not have imagined having better advisors and mentors for

my Ph.D study.

I would also like to thank Marie-Louise Leroux for taking time out from her busy schedule

to serve as my external reader. My sincere thanks also go to Vincent Boucher and Luca Tiberti who

kindly accepted to act as readers for my thesis.

I wish to thank Arthur Lewbel for his valuable input on some technical aspects of my

econometric model. I am also grateful to Ali Yedan for helping me develop a program of quantile

regression with a large number of endogenous variables.

I would like to address all my gratitude to the Department of Economics and its faculty

as well as to all my professors from the Department for providing a very high quality education.

I wish to thank Ginette Therrien, Martine Guay, Josée Desgagnés, Jocelyne Turgeon, and all the

personnel of the Department for their help and professionalism. I thank my fellow colleagues at the

Department for the stimulating discussions and for all the fun we have had in the last years.

My deepest gratitude goes to my parents Mosbah and Fatma for their unconditional support

and sacrice so that my siblings and I attain the highest levels of education. Most importantly, I

thank them for the values that they instilled in us and for encouraging us to be the best that we

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can be. My thanks also go to my twin brother Mohamed, the brightest man I know. I also thank

my beautiful sister Marwa, and my two little brothers Omar and Ismail. My profound appreciation

goes also towards my dearest, darling husband Walid who has been supporting me every step of the

way. No words can describe all the gratitude I have towards such a smart, kind, and lovely person.

Last but not least, I recognize that this research would not have been possible without the

Support of the Fonds de Recherche du Québec - Société et Culture (FRQ-SC) and the Canada Chair

in Economics of Social Policies and Human Resources. The analysis presented in this thesis was

conducted at the Quebec Interuniversity Centre for Social Statistics which is part of the Canadian

Research Data Centre Network (CRDCN). The services and activities provided by the QICSS are

made possible by the nancial or in-kind support of the Social Sciences and Humanities Research

Council (SSHRC), the Canadian Institutes of Health Research (CIHR), the Canada Foundation for

Innovation (CFI), Statistics Canada, the Fonds de recherche du Québec - Société et culture

(FRQ-SC), the Fonds de recherche du Québec - Santé (FRQS) and the Quebec universities. The views

expressed in this thesis are those of the authors, and not necessarily those of the CRDCN or its

partners.

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Introduction

Income inequality in advanced democracies has increased over the past 30 years, especially in Canada.

Indeed, according to a report by the Organisation for Economic Co-operation and Development

(OECD), Canada experienced the second highest growth in inequality, as measured by the Gini

coecient, among the member countries of the organization

1

. At the same time, the college wage

premium has also increased in recent years (Autor, 2014; Boudarbat et al., 2010). Paradoxically,

individuals from poor socioeconomic backgrounds are under-represented in the population of

college-educated workers (Lochner and Monge, 2011). With this in view, the literatures highlights two types

of strategies that are capable of addressing income inequality; redistributing to the poor later (i.e.

equalization of outcomes) and investing in their skills now (i.e. equalization of opportunities).

On the one hand, a policy intervention that equalizes outcomes may be implemented

through dierent tools such as, for example, redistributive taxation, transfers, and/or a minimum

wage legislation. Such policies, although redistributive in character, are likely to have a dissuasive

eect on labor and schooling.

On the other hand, the rising earnings gap between those with a university education and

those without is seen as an important source of growing inequality (Autor, 2014). Accordingly,

increasing educational attainments would be an eective strategy to redress inequality (see, for

ex-ample McCall and Kenworthy 2009 and Krugman 2015). It follows that encouraging participation

in higher education remains among the government's high priorities. Public policies need to

partic-ularly target individuals that are under-represented in higher education. Such individuals are most

prone to come from disadvantaged households. Furthermore, the focus of policymakers should not

be limited to broadening access to higher education as access means not just entrance, but

comple-tion of that educacomple-tion. Attencomple-tion should hence be paid to the issues of persistence in schooling and

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successful participation. Recall that both educational attainment and later earnings are determined

by cognitive ability, which are mainly formed at early educational stages. It must therefore be

rec-ognized that nancing k-12 education is a key determinants of the children's outcomes. Hence, an

examination of how to eectively allocate public funds between the dierent stages of education is

deemed appropriate. This aspect is modelled in my work.

In essence, studies that separately tackle these two strategies namely equalization of

out-comes and of opportunities, yield an incomplete analysis of the issue of reducing income inequality.

In other words, public policies that seek to curb income inequality must rely on a joint assessment

of the implications of both strategies. Such analysis allows to take into account all the feedbacks

and policy implications that could occur between the dierent tools used by the two approaches.

Such study is provided in my thesis.

The rst chapter of my dissertation tackles the issue of enabling equitable access to quality

learning for all members of society. Particularly, the chapter presents a general equilibrium model

of enrollment in higher education and labor supply, in the context of uncertain return on higher

education and internationally mobile capital. The study aims to contrast the performances of

dif-ferent wage tax proposals on skill formation. The literature outlines a single channel through which

distortionary taxation impacts individuals' decision on whether or not to pursue higher education:

a wage tax reduces the reward from being skilled, and thus tends to create a disincentive to pursue

costly higher education as a skill-imparting mechanism. The main contribution of the study is that

the general equilibrium model highlights a second channel. More precisely, when a fraction of the

tax revenue collected through wage taxation is invested in enhancing access to higher education, for

example, through tuition subsidies, a second channel for the impact of wage taxation on the decision

to pursue higher education opens up, working through the level of tax revenue collected.

The second chapter focuses on income inequality which is largely shaped by the growing

wage premium associated with higher education. Expanding education plays a vital role in redressing

inequality. In this vein, some scholars (e.g., Restuccia and Urrutia, 2004) suggest that biasing public

investment in education towards the early stages of education is more eective at enhancing college

participation by poor social groups as the ability required to eectively cash in on the college

premium is formed at the early stages of education. Yet, some argue that most of the ability gaps

between low-income and high-income children was already evident before entering school age, say

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due to intergenerational correlation of abilities. Other scholars (e.g., Hanushek et al. 2003) suggest

that redistributive taxation might be a more eective equalizing strategy. Yet, redistribute taxation

has an adverse eect on the incentive to enroll in higher education as it reduces the after-tax college

premium in wage. In this vein, Krueger and Ludwig (2013) suggest that both redistributive taxation

and subsidization of college tuition may comprise a welfare-maximizing policy mix. None of these

existing studies, however, jointly determine the optimal levels of all these three forms of public

intervention, namely public investment in K-12 education, public subsidization of college tuition,

and redistributive taxation. The second chapter is an attempt to quantitatively determine the

optimal scal and education policies using a model of enrollment in postsecondary education. The

model integrates the joint role played by parental education and level of income in the production

of cognitive ability that determines a K-12 graduate's college premium in the event of participation

in postsecondary education. Using data from the Young in Transition Survey (YITS), the model is

calibrated to empirical evidence from Ontario.

The third chapter focuses on the issue of schooling persistence. In particular, it attempts

to shed light on the behavior of temporary interruption in postsecondary education by focusing

on its eect on subsequent wages. The relevance of the topic of discontinuous schooling arises

in consideration of the eects that this behavior may have on discontinuously enrolled graduates

(interrupters). This suggests that the timing of events in the process of socioeconomic achievement

of individuals can be as important as the events themselves (Duncan and al., 1972). Schooling

interruption, and the delayed graduation that it may imply, can thus aect various aspects of the

professional achievements and social lives of interrupters (level of income, number of children, etc).

In the same context, Featherman and Carter (1976) suggest that discontinuities in schooling impede

socio-economic achievement for a number of reasons, including the fact that "societies normally

process age-specic cohorts, failure to retain membership in a cohort as it is processed into the labor

market handicaps men vis-à-vis their former associates".

A survey of previous studies reveals that research on the implication of permanent dropout

on subsequent wages has been more extensive compared to temporary attrition. This could be partly

due to the perception that temporary schooling interruption followed by degree completion does not

necessarily impact future wages of interrupters as permanent dropout unambiguously leads to a

wage penalty. Temporary dropout, however, is quite common among young students as reported

by various studies. In Canada, one of the reasons why this phenomenon received little interest was

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the lack of data. The availability of new data sets [e.g., the Youth in Transition Survey (YITS), the

National Graduate Survey (NGS)], enabled researchers to explore this subject in Canada in more

depth than ever before. For example, Finnie and Qiu (2008) use the YITS and report that about

40% of university attrition and 54% of college attrition are temporary. Lambert et al. (2004) also

use information from the YITS and nd that almost 40% of those who left postsecondary education

between the ages of 18 and 20 had returned within two years. As reected by the numbers above,

temporary schooling interruption seems to reach a quite important part of the student population.

Given the observed commonness of such a behavior, a further investigation of its impact on future

wages is deemed appropriate.

Of course, the reason why a student temporarily interrupts her studies is likely to play a

crucial role on skill depreciation and therefore on subsequent real wages. Therefore, the third chapter

does not only investigate the impact of temporary schooling interruption on post-graduation starting

real wages but also explores whether the latter are dierently inuenced by the reasons behind

this interruption. In order to run the econometric analysis, the study uses the retrospective 2007

National Graduates Survey (NGS) data targeting Canadian men and women who graduated from a

postsecondary public institution in 2005. The endogeneity of schooling and covariates reecting the

reasons of schooling interruption is taken into account when examining their impact on wages. Due to

the unavailability of a sucient number of valid external instruments to circumvent the endogeneity

problem (at least six instruments are needed), the Lewbel (2012) two-stage heteroskedasticity-based

instrument approach is applied. To identify the model, this method exploits the conditional second

moments of the data, under heteroskedasticity of the error terms of the endogenous regressors. As

shown by Lewbel, these assumptions are satised by (but not limited to) models in which error

covariances across equations arise due to an unobserved common factor. As an example, learning

motivation may inuence both schooling interruption and subsequent real wage rates.

This chapter covers various contributions. It is the rst study to address this issue using

recent Canadian data (the National Graduate survey (NGS)) as previous work that investigates this

subject uses American data from 1979 to 1989. Besides, while existing studies only examine the eect

of interrupted schooling on white men's outcomes, the current chapter extends the analysis to include

women and control as well for racial identity. Furthermore, the modeling strategy pursued in the

chapter does not only test the extent to which schooling discontinuities aect subsequent earnings,

but also investigates whether labor market outcomes are also aected by the reasons behind these

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discontinuities. To the best of our knowledge, earlier eorts do not test the latter hypothesis and

implicitly assume that the eect of an interruption is the same regardless of the reason that has

caused it.

The rest of the dissertation is organized as follows. Section 1 presents the rst chapter,

while sections 2 and 3 respectively present the second and third chapters.

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Chapter 1

Whither the Progressive Tax?

Abstract

The progressive wage tax is the instrument commonly used by democracies to fund public expen-ditures. Yet it still divides opinions about its impact on skill formation. We develop a general equilibrium model to analyze this impact, in the context of uncertain return on higher educa-tion. We show that the quantitative impact on skill formation of switching from the at to the progressive tax varies with the level of eciency with which higher education imparts graduates with suitable skills. This impact is negative when the level of eciency of higher education is

low and positive when it is high.1

JEL: F21, F22, H20, J60.

Keywords: Tax progressivity, higher education, skilled formation, capital inows, general equi-librium.

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1.1 Introduction

There is a consensus that higher education graduates must bear the cost of their education since there

are private returns to the beneciaries.

2

There is also a consensus that society must share the cost of

investing in higher education because enrollment yields social returns that transcend the individuals

who directly benet from it (Moretti 2004). This double consensus explains the pervasiveness, in

advanced democracies, of cost-sharing models for funding higher education whereby the cost of

education is shared between the beneciaries and society at large (Barro and Sala-i-Martin 1995;

Barro 1998; Garcia-Penalosa and Wälde 2000; Lochner and Moretti 2004; Bassanini and Scarpenta

2001; Greenaway and Haynes 2003; Barr, 2004; Riddell, 2005). However, for a number of these

advanced democracies, including Canada and the United States, the general consensus ends there.

It does not extend to the thorny issue of how the state should collect the revenue needed to nance

its share of the cost of higher education. Instead, there are divided opinions over which, of the

progressive wage tax system, or the at wage tax system, is more likely to create an economy with

abundance of skilled workers.

On the one hand, there is the presumption that unlike the at tax, the progressive tax

sys-tem cannot create the abundance of skills that underlies economic prosperity, because the higher tax

rate levied on the skill-premium in wage acts as a disincentive to invest in skills (Heckman, Lochner

and Taber 1998). On the other hand, there is the view that the alternative at tax system would

lead to a regressive income distribution whereby low-income families that cannot aord to send their

children to college subsidize middle-income and higher-income families who can (Garcia-Penalosa

and Wälde, 2000). These dierences of opinions underscore the importance of the requirement that

the choice of a tax system for funding public expenditures be based on a clear understanding of its

impact. Yet missing in the existing literature on public nancing of higher education has been a

systematic assessment of how the tax system aects participation in higher education when (i) the

skills graduates gain are imperfectly aligned with those employers need, and (ii) there is international

mobility of (physical) capital. This article lls this gap, by contrasting the impacts of various tax

proposals indexed by their degree of tax progressivity.

Under the at wage tax system (i.e., one with tax progressivity of degree zero), the burden

of nancing access to a higher education is equally shared by all wage earners, as this has to do

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with the tax rate. In contrast, under tax systems with a positive degree of progressivity, graduates

who get a greater nancial return from their higher education see the increment in their earning

taxed at a higher rate depending upon the chosen degree of progressivity, thereby raising their share

of the burden relative to the other wage earners. We develop a simple general equilibrium model

of enrollment in higher education and labor supply, with uncertain return on higher education to

contrast the performances of these wage tax proposals. In our model, prospective students are aware

of the risk that the skills they gain through the higher education system are misaligned with those

employers need. This is the only source of uncertainty for the return on higher education.

3

We model an individual decision to pursue higher education as one that is determined

jointly by education-related costs, family wealth, and the nancial return on the skills gained.

In the absence of tuition subsidies, enrollment in higher education tracks family wealth, thereby

undermining the principle of equal opportunities. What is more, uncertainty about the return on

higher education raises the opportunity cost of education for risk-averse individuals, and thus may

increase inequality, as only individuals from rich family backgrounds can draw on family wealth to

mitigate the eects of risk-aversion. Poor, risk-averse individuals would miss out, as they fear that

participation in higher education would leave them saddled with debt.

Our general equilibrium model highlights two channels through which distortionary

taxa-tion impacts individuals' decision on whether or not to pursue higher educataxa-tion. On the one hand,

a wage tax reduces the reward from being skilled, and thus tends to create a disincentive to pursue

costly higher education as a skill-imparting mechanism. A progressive wage tax system reinforces

this disincentive in two related ways. First, because the increase in earnings induced by these skills

pushes individuals into higher tax brackets, it tends to reduce the return on skills gained through

higher education, which creates a disincentive for participation. Second, it tends to raise the

im-portance of family wealth for participation in higher education because the induced reduction in

earnings tends to restrict gains from participation only to prospective students who require a

mini-mal level of debt for participation. On the basis of this channel alone, a at wage tax system would

3Our assumption that the misalignment between skills gained through a higher education system and those

employers need creates a risk for prospective students is consistent with reality. The higher education system in Canada is a case in point. See Margaret Wente, "Access or quality  our universities can't have both", published in The Globe and mail, October 31st, 2012; Tavia Grant, "Canada's labour pain: 1.3 million jobless, but not enough skills", published in The Globe and Mail , April 1, 2013; and Gwyn Morgan, "Radical re-nancing proposal would ease skills shortage", The Globe and Mail, Monday, April 15, 2013). Indeed, despite having one of the highest rates of university enrollment in the world, in 2011 Canada ranked second to last among OECD countries in producing graduates with suitable skills for the labor market, suggesting that the qualications obtained do not always match the needs of the labor market (OECD 2011).

(23)

dominate a progressive wage tax system on eciency grounds, as in Heckman, Lochner and Taber

(1998). But on the other hand, when a fraction of the tax revenue collected through wage taxation

is invested in enhancing access to higher education, for example, through tuition subsidies, a

sec-ond channel for the impact of wage taxation on the decision to pursue higher education opens up,

working through the level of tax revenue collected. To the extent that the progressive tax dominates

the at tax from the view point of revenue generation, it may be better at extending access to

prospective students from poor family backgrounds. Yet tax revenue does not only depend on the

tax rate; it also depends on the allocation of taxpayers across wage brackets, and its impacts (both

direct and indirect) on wages. Because wage taxes are distortionary, they impact the allocation of

workers across wage brackets through the decision on whether or not to pursue higher education.

These complex feedback between taxation, the allocation of workers across wage brackets, wages,

and tax revenue justify our use of a general equilibrium model.

We structure the interactions between the two channels of the impacts of wage taxation

around three key features. First, we consider an aggregate production function such that abundance

of capital raises the productivity of both skilled and unskilled workers. Second, capital is

interna-tionally mobile, and its productivity rises with the abundance of labor inputs. Third, the structure

of this aggregate production function is selected to ensure that the earnings of skilled workers are

always higher than those of unskilled workers. This has two eects. On the one hand, because

skilled workers are more productive than their unskilled counterparts, their availability becomes a

lever of capital inows. On the other hand, because skilled workers earn more, they become key

contributors to tax revenue. The more there are skilled workers, the higher the tax revenue. We

show that a progressive wage tax reinforces this revenue eect. We supplement our analysis with a

quantitative assessment of a tax reform underlaid by a switch from a at to a progressive tax. To

do so we use numerical methods to compute the degree of wage tax progressivity that maximizes

the size of the skilled labor force and the level of capital inows. We show that the quantitative

impact on skill formation and capital inows of switching from the at to the progressive tax varies

with the level of eciency with which higher education imparts graduates with suitable skills. This

impact is negative when the level of eciency of the higher education system is low and positive

when it is high. In other words, when the level of eciency of the higher education system is low,

the at tax dominates the progressive tax as a mechanism for enhancing skill formation and capital

inows. The reverse is true, however, when this level of eciency is suciently high.

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Higher education nancing is a highly debated issue in advanced democracies such as

Canada and the United States, and both empirical and theoretical studies of this issue exist (e.g.,

Coelli 2009; Caponi and Plesca 2009; Burbidge, Collins, Davies, and Magee 2012). However, we

view our work as complementary to existing theoretical works that rely on the discipline of a general

equilibrium model to analyze the eect of public policy on enrollment in higher education and labor

supply. Examples of such works include Heckman, Lochner, and Taber (1998), Garcia-Penalosa and

Wälde (2000), Caucutt and Kumar (2003), and Hanushek et al. (2003). Heckman, Lochner, and

Taber (1998) build a dynamic general equilibrium model to explore the impact of alternative tax

systems on human capital formation. In particular, they contrast the performances of three dierent

tax policy proposals namely, a progressive wage tax, a at wage tax, and a at consumption tax. In

their model, a wage tax reduces marginal returns on schooling, but has no eects on the marginal

costs of schooling. Unlike the two other tax systems considered, the progressive wage tax reinforces

the negative eects on the marginal returns to education, because the increase in earnings induced

by schooling pushes individuals into higher tax brackets. In their model, this is the only channel

through which tax policy aects human capital formation. We complement Heckman, Lochner, and

Taber (1998), through the addition of a second channel for the eect of wage taxes on the decision

to pursue higher education, and the level of eciency with which higher education system imparts

graduates with skills suitable for the labor market. In particular, we allow tax revenue to be invested

in higher education system in the form of tuition subsidies, based upon documented evidence that

governments in advanced democracies use tax revenue to fund access to education.

4

Garcia-Penalosa and Wälde (2000) contrast the performances of a at tax, loan schemes,

and a graduate tax in a general equilibrium model of investment in higher education and labor

supply. They show that a at tax is dominated by the other funding mechanisms on the basis of

equity-eciency trade-os. They also show that when the return on higher education is uncertain,

and prospective students are risk-averse, a graduate tax out-performs the loan schemes, making it

the best funding mechanism for public nancing of higher education. It is not clear, however, how

this graduate tax will be implemented in reality. In addition, Garcia-Penalosa and Wälde (2000)

abstract away from international capital mobility, so that unskilled workers in their model do not

benet from the abundance of skilled workers, which explain why in their model, these workers are

exempted from contributing to education nancing. In our model, unskilled workers benet from

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capital inows because abundance of capital raises labor productivity. Yet, as we show in our model,

it is abundance of workers with suitable skills which enhances capital inows. This combines with

the positive eect of capital inows on unskilled labor wage to justify taxing the unskilled wage.

Caucutt and Kumar (2003) develop a dynamic general equilibrium model of college

atten-dance and labor supply to contrast the performances of three alternative higher education policies,

including (i) a tax and subsidy scheme reecting equality of opportunities, (ii) a policy of

maxi-mizing the fraction of people with a college education, (iii) the provision of merit-based aid to the

poor. As in Garcia-Penalosa and Wälde (2000), higher education in Caucutt and Kumar (2003)

only benets those who successfully pursue it and there is no international capital mobility. They

show that the tax-subsidy scheme underpinning the equal opportunities policy is dominated by the

other two higher education policies because the former maximizes the equity-eciency trade-o. In

particular, they argue that increased subsidies end up attracting inframarginal students (those with

lower abilities) to college, thereby causing an increase in the dropout rate a waste of education

resources. Our article, however, is not primarily about how to best use public funds; instead, it

is more about how to best raise such funds to nance access to higher education when taxes are

distortionary.

Hanushek et al. (2003) also use a general equilibrium model of college attendance and labor

supply to compare three redistribution schemes, including (i) tuition subsidies for higher education,

(ii) a negative wage tax, (iii) a wage subsidy. Like Garcia-Penalosa and Wälde (2000), and Caucutt

and Kumar (2003), Hanushek et al.(2003) emphasize heterogeneous abilities and tie the level of

uncertainty underlying returns to education to agents' innate abilities.

5

In this context, they show

that tuition subsidies are dominated by other redistribution schemes on the basis of the

equity-eciency trade-o criterion. They abstract away from physical capital as an input in the aggregate

production function, as well as from international capital movements. Therefore, as in Heckman,

Lochner, and Taber (1998), Garcia-Penalosa and Wälde (2000) and Caucutt and Kumar (2003),

there is no role for the abundance of workers with suitable skills to benet unskilled workers.

5By abstracting from heterogeneous abilities among prospective students, in our model, we do not at all pretend

that abilities do not matter for college performance. Instead, our modelling strategy relies on two important facts. First, most colleges have admission criteria emphasizing abilities to pursue college studies. To restrict admission of low ability-students, the government can simply mandate a threshold test score below which an individual is not admissible to college, as is the case in France and England. Second, average college tuition diers from one country to another. Some countries like Canada and Germany have relatively low average tuitions when compared to the United States. However, there is no evidence that the average college student in Germany or Canada has lower ability than the average college student in the United States.

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The remainder of this paper is structured as follows. Section

3.2

presents the model, which

is solved numerically in section

3.3

. Finally, section

3.4

concludes the paper.

1.2 Preliminaries

The model emphasizes the role played by the tax system on individuals' decisions to participate

in higher education (hereafter, HE for short). The basic structure of the model is a one-period

general equilibrium with competitive markets, inspired by Hanushek et al. (2003). Workers, in total

size normalized to unity, have all completed secondary education and all have the ability to pursue

higher education. There is no learning-by-doing. Participation in HE is the only mechanism for

acquiring productive skills. A worker may decide to invest in skills by pursuing HE or she may

decide to look for a job as an unskilled worker, when the labor market opens. Training through

HE is instantaneous in this one-period economy, and takes place prior to the opening of the labor

market. We introduce a cost-sharing model whereby the beneciaries of HE bear the costs of their

education, albeit with the help of taxpayers' contributions. We draw from McPherson and Shapiro

(1991), Garcia-Penalosa and Wälde (2000), Keane and Wolpin (2001), Caucutt and Kumar (2003),

and Lochner, Belley, and Frenette (forthcoming) in recognizing that higher education nancing has

a strong intergenerational connection to it. To capture this feature of high education nancing, we

assume that each worker has access to a family fund of size b (for bequest), on which she can draw

to help defray HE costs (including tuition, fees, school supplies, lodging, and other living expenses),

but only if she decides to pursue HE.

Prior to entering the labor market, workers make an optimizing choice about the pursuit

of HE for skill-acquisition based upon the tuition charged, their endowment of family fund, and

expected wages. The decision on whether or not to pursue HE involves uncertainty because the

skills gained through HE may or may not be aligned with those employers need, something which,

in our model, is outside the control of prospective students. More formally, with an exogenous

probability q ∈ (0, 1), a worker who participates in HE prior to entering the labor market gains

skills that are aligned with those employers need, and thus gets a skilled job. But with the converse

probability 1 − q, the education received is misaligned, in which case she joins the unskilled labor

force. We assume that the market to insure against the misalignment risk is missing. We interpret

the probability q as the level of eciency with which the HE system imparts workers with skills

suitable for the labor market.

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1.2.1 HE Cost and Student Debt

For each worker, and in the absence of subsidies, the cost of education is e ∈ R

+

. We analyze workers'

aggregate decisions on the pursuit of risky HE under various alternative tax systems indexed by their

degree of progressivity θ ∈ 0, ¯θ. By convention, we denote as tax system θ, the tax system whose

degree of progressivity is θ. When θ = 0, we have the at wage tax system. For simplicity, we limit

heterogeneity of labor income to two types only, skilled and unskilled.

Assume that the government subsidizes tuition at a rate z ∈ [0, 1], as is the case in most

advanced democracies such as Canadian Provinces. Therefore given the tax system θ chosen by the

government, for an agent who decides to pursue HE, the subsidized cost of HE is given as follows:

E

θ

:= (1 − z

θ

) e.

(1.1)

The subsidy rate z

θ

is determined endogenously by the size of tax revenue under a balanced budget

legislation, and given the degree of progressivity of the tax system, θ.

To cover her education costs, a typical student relies on two dierent sources. The rst

source is the family fund, b ≥ 0, and, if not sucient, a second source is a student loan, extended

interest free (just for simplicity) by the government, and repayable after graduation. For each tax

system θ implemented by the government, we dene the level of student debt, d

θ

∈ R, as the

dierence between the (subsidized) level of education costs, E

θ

, and the nancial resources provided

by the family, b:

d

θ

= E

θ

− b.

The level of this student debt is a determining factor of an individual's decision whether or not to

pursue risky HE.

1.2.2 Individual Actions and Payos

A worker b is one who has an endowment of family fund, b. Initially, individuals dier only with

respect to these endowments. They are distributed across levels of family fund according to a

cu-mulative probability distribution function, Ψ, with strictly positive density, ψ (b) := Ψ

0

(b)

, over a

compact support [0, e], where e is the per capita cost of education. That e is the upper bound of the

compact support for family funds means that no worker in this environment has an endowment of

family fund bigger than the pre-subsidy per capita cost of education, e. Workers have identical

pref-erences over the quantity consumed of the numeraire, c. The common utility function representing

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these preferences is given by:

U (c) := ln c.

(1.2)

At the opening of the labor market, after workers' skill-investment decisions are made, an individual

is either a skilled worker (i = s) or an unskilled worker (i = u). A worker's after-tax income depends

on her skill-investment decision, a ∈ {0, 1}, and the tax system, θ, implemented by the government

to raise tax revenue.

Denote as R (a, b, i, θ), the realized after-tax income of worker b who, having made the

skill-investment decision a ∈ {0, 1} prior to entering the labor market, ends up with a skill-status

i ∈ {s, u}

, when the government's chosen degree of tax progressivity is θ ∈ 0, ¯θ. A worker b who

makes the decision a = 0 has skill-status i = u with certainty, and thus earns an after-tax wage

given by:

R (0, b, i, θ) := (1 − τ ) ω

θu

,

where ω

u

θ

denotes the unskilled labor wage under the tax system θ. In contrast, a worker who makes

the decision a = 1 has skill-status i = u, with probability 1 − q, in which case her realized labor

income is

R (1, b, u, θ) := (1 − τ ) ω

θu

;

but with the converse probability, q, she has skill-status i = s, in which case her after-tax wage is

R (1, b, s, θ) := (1 − τ ) ω

θu

+ [1 − (1 + θ) τ ] (ω

θs

− ω

u

θ

) ,

(1.3)

where ω

s

θ

denotes the skilled labor wage, and ω

−ω

, the incremental wage from having suitable skills

under the tax system θ. Expression (

1.3

) states that, under the at wage tax (i.e., θ = 0) the

after-tax wage of skilled workers is simply R (1, b, s, 0) := (1 − τ) ω

s

0

. As long as θ > 0, the incremental

wage from having suitable skills is taxed at a higher rate, (1 + θ) τ, reecting a marginal tax rate of

θ

.

A worker's after-tax income, which we specify fully further below, determines her budget

constraint:

c ≤ R (a, b, i, θ) − ad

θ

,

(1.4)

where d

θ

denotes the level of student debt under the tax system θ,

R (a, b, i, θ) :=

(1 − τ ) ω

u θ

if a = 0

R (1, b, i, θ)

if a = 1

.

(1.5)

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A worker b thus has essentially one important decision to make namely, whether or not to pursue

HE prior to entering the labor market. Combining (

1.2

), (

1.3

), (

1.5

), and (

1.4

) yields worker b's

realized payo from taking the decision a as follows:

¯

U (a, b, i, θ) =

ln (1 − τ ) ω

θu

≡ B

θ

if a = 0

ln [(1 − τ ) ω

θu

− d

θ

] ≡ C

θ

if a = 1 and i = u

ln [(1 − τ ) ω

θu

+ [1 − (1 + θ) τ ] ∆

θ

− d

θ

] ≡ A

θ

if a = 1 and i = s

,

(1.6)

where

θ

:= ω

− ω

θu

(1.7)

is interpreted as the skill premium in wage under the tax system θ.

A worker b with a realized payo ¯

U (0, b, i, θ) ≡ B

θ

is one who elected to pass on the

opportunity to pursue HE prior to entering the labor market. There are 1 − n

θ

such workers, where

n

θ

denotes the measure of HE graduates, under the tax system θ. A worker b with a realized payo

¯

U (1, b, s, θ) ≡ A

θ

is one who elected to pursue HE prior to entering the labor market and eectively

became a skilled worker upon graduation. By the application of the law of large numbers, there

are ¯

S

θ

:= qn

θ

such workers. In contrast, a worker b with a realized payo ¯

U (1, b, u, θ) ≡ C

θ

is one

who chose to pursue HE prior to entering the labor market, but was unfortunate not to acquire

suitable skills upon graduation, and thus had to settle for an unskilled job. The total measure of

such workers is (1 − q) n

θ

, again by the application of the law of large numbers. Therefore, the size

of the unskilled labor force under the tax system θ is 1 − n

θ

+ (1 − q) n

θ

= 1 − qn

θ

. A worker b's

decision process on the pursuit of HE is summarized in Figure

1.1

below:

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1.2.3 Tax Progressivity and Gains from Participation in HE

In this sub-section, we explore the determinants of a worker's gain from pursuing risky HE. Dene

a real-valued function V : {0, 1} × Θ × b, ¯b by (a, θ, b) 7→ V (a, θ, b), where

V (a, θ, b) := a [qA

θ

+ (1 − q) C

θ

] + (1 − a) B

θ

,

denotes the expected payo of worker b from taking the decision a ∈ {0, 1}, prior to entering the

labor market, when the tax system implemented by the government is θ, and there are, in total,

n

θ

∈ [0, 1]

workers who made the decision a = 1. Making use of (

1.6

), we obtain a reformulation of

this expected payo function as follows:

V (a, θ, b) =

ln [(1 − τ ) ω

θu

]

if a = 0

ln

 (1 − τ ) ω

u θ

+ [1 − (1 + θ) τ ] ∆

θ

− d

θ

(1 − τ ) ω

uθ

− d

θ



q

+ ln [(1 − τ ) ω

u θ

− d

θ

]

if a = 1

.

(1.8)

The decision on whether or not to participate in HE is made by comparing the expected payo from

participating, V (1, θ, b), with the payo from not participating, V (0, θ, b).

Let ϑ (θ, b, q) := V (1, θ, b) − V (0, θ, b) denote the net expected payo gain to a worker b

from participating in HE prior to entering the labor market. Given θ, using (

1.8

), rearranging, yields

this net expected payo gain as follows:

ϑ (θ, b, q) = ln

 (1 − τ ) ω

u θ

− d

θ

+ [1 − (1 + θ) τ ] ∆

θ

(1 − τ ) ω

uθ

− d

θ



q

− ln



(1 − τ ) ω

θu

(1 − τ ) ω

θu

− d

θ



.

(1.9)

Therefore a worker b will choose to participate in HE if and only if her level of family fund satises

ϑ (θ, b, q) > 0

. She will elect to pass on it if and only if ϑ (θ, b, q) < 0. She is indierent between the

two options if and only ϑ (θ, b, q) = 0. A number of important remarks can be derived from (

1.9

) to

give us preliminary insights about the impact of tax progressivity on skill formation.

Remark 1 There is no incentive to leverage HE for one's social promotion if there is no skill

premium in wage. In other words, given θ, the condition

θ

> 0,

(1.10)

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Remark 2 The net expected payo gain from participating in HE prior to entering the labor market

is strictly increasing in a worker's level of endowment of family fund, b:

∂b

ϑ (b, θ, q) > 0.

This remark suggests that workers who gain from participating in HE are those with a

suciently high endowment of family fund, b. By subsidizing HE, the government therefore can

expand access to it to include individuals from poorer backgrounds.

Remark 3 A higher degree of wage tax progressivity tends to lower the net expected gain from

participating in HE:

∂θ

ϑ (θ, b, q) < 0,

This remark highlights the main criticism of the progressive tax: it tends to create a

disincentive to invest in skills. Furthermore:

Remark 4 The function ϑ (.) is supermodular in (b, θ): given q,

2

∂b∂θ

ϑ (b, θ, q) > 0,

implying that the incremental net expected payo gain from having a higher endowment of family

fund is larger, the higher the degree of progressivity of the tax system.

This fourth remark states that the progressive tax reinforces the role family income plays in

inuencing the decision to participate in HE: the higher the degree of progressivity of taxation, the

richer the prospective student must be in order to gain from participating in HE. Overall, Remarks

2-4 suggest that tax progressivity may actually be regressive because it tends to bias the gain

from participation in HE towards prospective students from richer family background. However,

as can also be seen from (

1.9

), the above eects are only a partial equilibrium eects due to the

fact that tax revenue collected partially feedback into higher education, thus opening up additional

(indirect) channels for the impact of the progressive tax on the incentive to participate in HE. Indeed,

tuition subsidies lower the cost of education, thus providing prospective students from poorer family

background with the incentive to participate in HE. Workers' aggregate decisions on participation

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in HE yield the measure of skill-investors, n

θ

∈ [0, 1]

, of which qn

θ

have skills that match those

employers need. We are interested in the impact of tax progressivity on qn

θ

, the aggregate supply

of skilled workers.

1.2.4 Production

As is standard in the macroeconomics literature (e.g., Heckman, Lochner, and Taber 1998; Caucutt

and Kumar, 2003), we assume that the institutional environment in this economy is characterized by

perfectly competitive markets, implying that the prices of labor and capital services are determined

as derivatives of an aggregate production function. Under the tax system θ, and at the aggregate

level, the numeraire is produced using capital K, unskilled labor, U, and skilled labor, S, according

to a constant return to scale technology:

Y := A (K)

α

[φ (S + γU )

ρ

+ (1 − φ) (U + εS)

ρ

]

1−αρ

,

(1.11)

where α ∈ (0, 1) denotes the capital income share, A > 0 is a measure of total factor productivity,

φ > 0

, a measure of the relative number of skill tasks created at the aggregate level, ρ < 1, a factor

determining the level of the elasticity of substitution between the low-tech process and the high-tech

process, γ > 0, the relative productivity of unskilled labor in the high-tech process and ε > 0, the

relative productivity of skilled labor in the low-tech process. We make the following assumption, as

in Caucutt and Kumar (2003):

A.1. 0 < γ < ε < 1.

Assumption A.1 means the following. First, because ε < 1, it implies that skilled workers

are not as good as unskilled workers at operating the low-tech production process. Second, because

γ < 1, it also implies that unskilled workers are not as good as skilled workers at operating the

high-tech process. Finally, because γ < ε, Assumption A.1 implies that it is relatively easier for skilled

workers to operate the low-tech process, than it is for unskilled workers to operate the high-tech

process. This assumption may be justied by the fact that the operation of a high-tech production

process usually has high technical requirements that only suitably skilled workers can fulll, while

the operation of low-tech process requires more manual abilities for which unskilled individuals may

be relatively more suited (Caucutt and Kumar 2003).

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S

S

¯

θ

:= qn

θ

U

≤ 1 − ¯

S

θ

:= 1 − qn

θ

K

K

¯

where ¯

K

denotes the global stock of capital, as capital is perfectly internationally mobile in this

environment.

We express market-clearing factor prices and input levels in terms of the chosen degree of

progressivity of the wage tax θ, under perfect competition:

ω

θs

=

(1 − α) A (K

θ

)

α

(H

θ

)

1−α

"

φ λ ¯

S

θ

+ γ



ρ−1

+ ε (1 − φ) 1 − δ ¯

S

θ



ρ−1

φ λ ¯

S

θ

+ γ



ρ

+ (1 − φ) 1 − δ ¯

S

θ



ρ

#

(1.12)

ω

uθ

=

(1 − α) A (K

θ

)

α

(H

θ

)

1−α

"

γφ λ ¯

S

θ

+ γ



ρ−1

+ (1 − φ) 1 − δ ¯

S

θ



ρ−1

φ λ ¯

S

θ

+ γ



ρ

+ (1 − φ) 1 − δ ¯

S

θ



ρ

#

(1.13)

r

θ

=

αA

φ λ ¯

S

θ

+ γ



ρ

+ (1 − φ) 1 − δ ¯

S

θ



ρ



1ρ

K

θ

1−α

,

(1.14)

where

H

θ

:

=

φ λ ¯

S

θ

+ γ



ρ

+ (1 − φ) 1 − δ ¯

S

θ



ρ



1ρ

(1.15)

δ

:

= 1 − ε

λ

:

= 1 − γ,

and ¯

S

θ

:= qn

θ

. Expressions (

1.12

) and (

1.13

) implies that a skill premium exists (i.e., ∆

θ

> 0

) if

and only if

φλ

δ (1 − φ)

>

 λ ¯

S

θ

+ γ

1 − δ ¯

S

θ



1−ρ

.

(1.16)

Observe that the right-hand side of the inequality (

1.16

) is strictly increasing in ¯

S

θ

. We once again

draw from Caucutt and Kumar (2003) to make the following assumption which guarantees that a

skilled worker always earns a higher wage than an unskilled worker in this environment:

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A.2. The parameters γ, ε, φ, and ρ satisfy

ε >

 δ (1 − φ)

λφ



1−ρ1

.

(1.17)

Assumption A.2 gives a sucient condition for inequality (

1.16

) to hold. It guarantees that

skilled workers are always paid a higher wage than their unskilled counterparts in this environment.

In other words, a skill premium always exists.

1.2.5 Abundance of Skilled labor and Capital Inows

Consider expression (

1.14

). Since capital is internationally mobile, this expression implies that

capital will continue to ow in until the after-tax domestic rental rate of capital, (1 − τ

k

) r

θ

, equals

the international rate, r

: (1 − τ

k

) r

θ

= r

, where τ

k

∈ (0, 1)

denotes the at tax rate levied on

capital gains. Solving this equation for K

θ

yields the level of capital inows under the tax system θ

as follows:

K

θ

=

 αA (1 − τ

k

)

r



1−α1

φ λ ¯

S

θ

+ γ



ρ

+ (1 − φ) 1 − δ ¯

S

θ



ρ



1ρ

≡ χ ¯

S

θ

 ,

(1.18)

where ¯

S

θ

denotes the endogenous supply of skilled workers. We then can obtain the partial derivative

of (

1.18

) with respect to ¯

S

θ

as follows:

∂K

θ

∂ ¯

S

θ

=

"

λφ λ ¯

S

θ

+ γ



ρ−1

− δ (1 − φ) 1 − δ ¯

S

θ



ρ−1

φ λ ¯

S

θ

+ γ



ρ

+ (1 − φ) 1 − δ ¯

S

θ



ρ

#

 α (1 − τ

k

) A

r



1−α1

H

θ

,

where H

θ

is as dened in (

1.15

). The above partial derivative is strictly positive if and only if

φλ

δ (1 − φ)

>

 λ ¯

S

θ

+ γ

1 − δ ¯

S

θ



1−ρ

,

which is guaranteed to hold under Assumption A.2. Hence the following result:

Proposition 1 Under Assumptions A.1 and A.2, an exogenous increase in the supply of skilled

workers, ¯

S

θ

, causes the volume of capital inows, K

θ

, to increase.

Assumption A.2 is sucient for the skill premium in wage to exist (i.e., condition (

1.16

)

holds) under the tax system θ. It also gives a necessary and sucient condition for abundance of

suitable skills to become a driver of capital inows. Therefore, Proposition 1 can be interpreted as

suggesting that as long as there is a productivity premium for skills, and to the extent that HE

Figure

Figure 1.1: Worker b 's Decision Tree
Table 1.1: Parameter Values
Figure 1.2 below contains 4 graphs. In each of them, the horizontal axis represents the degree of progressivity of the wage tax system, θ
Figure 1.3 below plots the equilibrium level of K θ against the degree of progressivity of the wage tax system, θ, for four dierent levels of q.
+7

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