Three Essays on the Economics of Higher Education
Thèse
Safa Ragued
Doctorat en économique
Philosophiæ doctor (Ph.D.)
Québec, Canada
© Safa Ragued, 2017
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
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.
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.
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.
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.
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
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
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
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
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.
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.
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
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.
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
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
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
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
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.
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.
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.
2There 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
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.
3We 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).
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.
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.
4Garcia-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
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.
5In 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.
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.
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
θis 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
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
uθ
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
uθ
) ,
(1.3)
where ω
sθ
denotes the skilled labor wage, and ω
sθ−ω
uθ, 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
s0
. 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
θdenotes the level of student debt under the tax system θ,
R (a, b, i, θ) :=
(1 − τ ) ω
u θif a = 0
R (1, b, i, θ)
if a = 1
.
(1.5)
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
θif a = 0
ln [(1 − τ ) ω
θu− d
θ] ≡ C
θif a = 1 and i = u
ln [(1 − τ ) ω
θu+ [1 − (1 + θ) τ ] ∆
θ− d
θ] ≡ A
θif a = 1 and i = s
,
(1.6)
where
∆
θ:= ω
sθ− 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
θis one who elected to pass on the
opportunity to pursue HE prior to entering the labor market. There are 1 − n
θsuch workers, where
n
θdenotes the measure of HE graduates, under the tax system θ. A worker b with a realized payo
¯
U (1, b, s, θ) ≡ A
θis 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
θsuch workers. In contrast, a worker b with a realized payo ¯
U (1, b, u, θ) ≡ C
θis 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:
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)
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
in HE yield the measure of skill-investors, n
θ∈ [0, 1]
, of which qn
θhave 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).
S
≤
S
¯
θ:= qn
θU
≤ 1 − ¯
S
θ:= 1 − qn
θK
≤
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−1φ 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−1φ 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 ρ1ρK
θ
1−α,
(1.14)
where
H
θ:
=
φ λ ¯
S
θ+ γ
ρ+ (1 − φ) 1 − δ ¯
S
θ ρ1ρ(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:
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