Estimating Marginal Returns to Education
Jenna Stearns
Department of Economics
University of California, Santa Barbara
1
Introduction
Estimating returns to education is an essential part of determining optimal schooling
decisions, both on an individual and social level. Because education is costly, individuals
make choices about how much time to spend in school based on the difference between the
marginal return to an additional year of schooling and the cost. From a policy perspective,
average marginal returns to education across the population drive investment decisions in
education as well as laws regarding mandatory schooling. However, the causal effects of
education on earnings are difficult to measure. Although economists have been estimating
returns to education for decades, the variation in empirical results along with the continuous
activity in this area both suggest that there is no clear consensus on how best to measure
marginal returns to education, or even how big they are.
In reality, people are heterogeneous and make decisions based on differences in individual characteristics that are both observed and unobserved by the economist. Because of this,
people react to policies, standards, and choices in different ways. Economists would like to
know, on average, how the marginal return to schooling changes as the number of years of
education increases, and would also like to be able to evaluate policies that change the probability of attaining a certain level of schooling. Estimating the marginal returns to education
can help do both of these things.
The purpose of this literature review is not to list the various empirical estimates of
marginal returns to education found in studies using different methods and different data.
Instead, I aim to provide an overview of the influential methods and papers in the field,
and to identify and explain some of the primary challenges in estimating marginal returns
to schooling. These issues likely explain a lot of the variation in reported returns. I also explore potential avenues for future research that can help better identify marginal returns to
education.
The remainder of this paper is organized as follows. Section 2 describes two distinct
ways of thinking about marginal returns to education. Section 3 discusses the estimation
techniques and problems with a more traditional definition. Section 4 describes the marginal
treatment effect, another way of interpreting marginal returns. The fifth section compares
the estimated parameters from these different methods in two empirical papers that estimate
1
the marginal returns to college. Finally, section 5 discusses areas for future research.
2
What are Marginal Returns to Education?
There are two related but fundamentally different ways of defining marginal returns to
education, and both are used in the literature to answer different types of questions. This
section identifies and explains these two concepts; subsequent sections relate each back to
some of the influential literature in which they are used.
The first way to think about marginal returns to education is in line with the traditional
idea of marginal benefits: each additional unit of a good provides some additional utility.
People want to consume more of the good until the benefits from the last unit are equal to
the cost of obtaining it. The same concept is true of education. Individuals should choose to
stay in school until the marginal return is no longer greater than the marginal cost.1 Thus, we
are interested in how the marginal return to schooling changes as the amount of schooling
increases. In other words, holding constant the individual, economists are interested in how
the marginal return changes over time.
Of course, the obvious problem with estimating an individual’s marginal return to education is that only one outcome per individual is realized. That is, if Tom completes twelve
years of schooling, only his return to twelve years of schooling can be estimated from his observed earnings. Economists do not observe the counterfactual: his earnings had he gotten
a college degree or had he dropped out of school in eleventh grade. To estimate individual
level marginal returns in this context, economists must make the assumption that all individuals have the same returns to education, and attempt to control for the differences driving
schooling decisions. More commonly, the average marginal return is what is actually estimated.
The second way to define a marginal return to education is to hold constant the level of
schooling and look at returns across individuals. To distinguish it from the above definition,
this marginal return will be called the marginal treatment effect (MTE), which is consistent
1
Empirically, returns to education are generally estimated using a measure of earnings. However, theoretically, returns to education are often defined more broadly to include components of utility that are more difficult
to measure in the data. For example, some people (e.g., Ph.D. students) enjoy learning and derive some intrinsic
benefit from knowledge; for others education is simply a means to an end or a signal in the labor market.
2
with the definition of the MTE used in the literature.2 The MTE measures how, as the fraction
of the population with a fixed level of schooling increases, the return to education for the
individuals who are indifferent to staying in school or not staying in school changes. In other
words, holding constant the level of schooling, we want to know how returns vary over
individuals. More specifically, we want to know the return of the person on the margin.
These two definitions are equivalent if returns to education are the same for everyone.
However, as discussed in detail below, marginal returns to schooling are not homogeneous.
Therefore, each of these concepts helps answer a specific question. If economists are interested in how individuals make schooling decisions, the first definition is more useful. If
instead economists want to assess the impact of a policy aimed at changing the number of
people who complete a certain level of education, then the second is preferred.
3
Marginal Return to Education
3.1
Estimation
Any analysis of marginal returns to education starts with the assumption that individuals
decide on their optimal amount of education by comparing the benefits to the costs. Benefits
include improvements in earnings over the course of the lifetime, as well as non-monetary
gains such as access to more desirable jobs, self-worth, and the joy of learning (“psychic earnings”). Costs usually are thought of as a combination of money spent directly on education,
the forgone value of the time spent obtaining education, and disutility of studying.
Becker and Chiswick (1966) play an important role in developing the literature on estimating marginal returns to education. Their canonical model of human capital views education as an investment decision, where the costs are compared to the discounted stream of
expected future benefits. Thus, schooling is an endogenous decision. The simple model says
that total earnings over the lifetime are the sum of the returns to investments in education
plus the earnings from any original human capital:
2
The concept of the MTE was first introduced by Bjorklund and Moffitt (1987) as a way to estimate marginal
returns, and was more formally defined by Heckman (1997).
3
Ei = Xi +
m
X
rij Cij ,
j=1
where Ei is the lifetime earnings of person i, Cij is the amount spent by person i on the j th
unit of investment in education, rij is the marginal rate of return on the j th unit of investment,
and Xi is the return from any original human capital. Becker and Chiswick point out that
each individual invests in education until the marginal rate of return on a dollar of investment is equal to the marginal “interest” cost of that dollar. If the rate of return is assumed to
be constant across units of schooling, then the marginal return is equal to the average return.
Becker (1967) extends this analysis. In a slightly more detailed model, he lays out how to
solve for a condition for the optimal amount of schooling. Again, this is the point at which
the marginal benefits equal the marginal costs. He also suggests that individual heterogeneity in this optimal choice can arise from one of two sources. Individuals can differ in their
marginal returns to schooling, or they can face different marginal costs of schooling. However, if individuals all face the same costs (what he calls “equality of opportunity”) or have
the same benefits (“equality of ability”) then the marginal return to a given level of schooling
is the same for everyone.
A main limitation of the Becker model is that schooling is the only specified source of
human capital. If schooling and the error are uncorrelated, then an Ordinary Least Squares
(OLS) regression will produce an unbiased estimate of the return to a year of education.
However, if they are correlated, the estimate will be biased. Becker identifies two obvious
reasons why schooling is likely correlated with the error in this model. First, human capital can also be accumulated through on-the-job training (experience). Years of schooling and
years of experience, conditional on age, are highly correlated. Second, if ability is unobserved
and the return to education varies by ability, then estimates of the marginal return to education will also be biased. If more able individuals make greater investments in education, then
the estimated marginal rate of return to schooling is actually the return to schooling plus the
returns to ability and other unobserved forms of human capital.
Mincer (1974) extends Becker’s work to try to address part of this problem. He includes
in his model a measure of on-the-job training and experience. Importantly, he also shows that
percent changes in earnings are strictly proportional to the absolute differences in schooling.
4
In other words, log earnings are a linear function of years of education:
ln Yi = ln Y0 + rSi + ui ,
where Yi is the level of earnings of individual i, and Y0 is the mean level of earnings of
someone with zero years of schooling. The coefficient r is the marginal return to a year of education, which Mincer assumes to be constant in the simplest model, but can be subscripted
by S and allowed to vary.
In this framework of log earnings, Mincer argues, years of work experience should enter
additively and not multiplicatively. Additionally, the experience term is concave, resulting
in the following earnings equation for an individual with t years of experience:
ln Yi = ln Y0 + rSi + β1 ti − β2 t2i + εi .
(1)
The above equation is the basis for many studies estimating the returns to schooling. It
can be extended in several ways. There is no reason to assume that marginal returns to
education are constant; for example adding in a nonlinear schooling term (Si2 ) captures how
marginal returns are changing as the level of schooling changes. An interaction term between
schooling and experience may help predict marginal returns as well. Mincer specifies the
following equation to estimate the marginal effects of education on log earnings using a
cross-sectional distribution of annual earnings in 1959 for white men:
ln Yi = α + r1 Si − r2 Si2 − γti ∗ Si + β1 ti − β2 t2i + i .
He estimates
ln Yi = 4.87 + 0.255Si − 0.0029Si2 − 0.0043ti ∗ Si + 0.148ti − 0.0018t2i .
Then the marginal returns at different levels of schooling can be approximated. The marginal
return to the S th year of education is given by:
rS =
d(ln Y )
= 0.255 − 0.0058 ∗ S − 0.0043t.
dS
5
Clearly, the marginal returns are decreasing in the level of schooling. For someone with eight
years of experience (t = 8), the marginal return to the eighth year of education in this sample
is 17.4 percent. The marginal return is 15.1 percent for the twelfth year of schooling, and is
12.8 percent for the sixteenth year.
Although this specification is a good illustration of a simple way to estimate non-constant
marginal returns empirically, Mincer notes that both the nonlinear schooling term and the interaction term become insignificant when other covariates (namely number of weeks worked
in 1959) are controlled for. Ignoring possible sources of bias, which are discussed in the
following section, Mincer’s simple model in (1) seems to do a good job of estimating the
marginal return to schooling.
In his 2001 survey, Card extends the Mincer model described above. He shows that one
can allow for individual heterogeneity to affect both the intercept of the log earnings equation as well as the slope, through the coefficient on schooling. Individual intercepts are estimated by including an individual level fixed effect in the regression equation, and the average marginal return to education is just the expectation of the individual marginal return.
3.2
Problems with OLS Estimation
There is significant cause for concern that OLS estimates of marginal returns to education
are biased. Bias means that the difference between the probability limit of the estimator and
the average marginal return to schooling in the true population is not equal to zero. The
issue of bias is well-acknowledged throughout the literature using OLS to estimate returns
to education, and Card (2001) has a particularly nice discussion about some of the main
problems.
First, suppose that log earnings are linear in years of education, and that there is no individual heterogeneity in returns. Even if these assumptions are true, OLS is biased if there is
correlation between an individual’s unobserved ability and the marginal cost of schooling. If
the marginal costs are lower for people who are more able (i.e., those who would earn more
at any level of schooling than those of lower ability would), then OLS is biased upward. This
is known as ability bias.
If we allow for heterogeneity in returns, then there are even more issues. People with
6
higher returns to education have incentive to acquire more education, all else equal. Even assuming there is no ability bias, cross-sectional estimates likely yield upward biased estimates
of the average marginal return to education. This endogeneity, or comparative advantage,
bias arises from the fact that differences in the earnings-education relationship result from
differences in returns as opposed to differences in preferences for education, costs, or ability.
More simply stated, OLS estimates are upward biased if an individual’s return to schooling
is positively correlated with the amount of education chosen. If there is ability bias on top of
this, the upward bias in OLS is even larger.
Education can also be mismeasured or misreported. Empirically, economists only observe information on rounded years of schooling rather than a continuous measure, and
self-reported schooling information is not always accurate. Measurement error is a form
of attenuation bias in OLS. Because returns to schooling are generally assumed to be positive, this is a downward bias. Griliches (1977) argues that measurement error is enough of
a problem to at least partially offset any upward bias from the sources mentioned above.
Angrist and Krueger (1999) conclude that the reliability of self-reported schooling is about
85-90 percent, which implies that the resulting measurement error is enough to offset modest
ability bias. However, Card (2001) points out that measurement error in schooling is meanregressive. People with the highest levels of education cannot over-report, and those with the
lowest levels cannot under-report. This means that conventional estimates of measurement
error are likely overstated and the true attenuation bias in OLS estimates of marginal returns
to education is smaller than previously thought.
Theoretically, the direction of the overall bias in OLS estimates is ambiguous. However,
the literature concludes that it is most likely positive. Ability and endogeneity biases dominate measurement error. This means that many of the empirical estimates of the marginal
returns to education in the literature are probably overstating the true return.
3.3
Instrumental Variables and Marginal Returns to Education
The instrumental variables (IV) method is often used as an alternative to OLS estimation
of marginal returns to education in order to overcome the ability bias and measurement error
issues. In the absence of heterogeneity in returns, if there exists an observable instrument that
7
affects education choices but is uncorrelated with ability, then an IV estimator based on this
instrument will yield a consistent estimate of the average marginal return to schooling. When
marginal returns are the same for everyone, any valid instrument will identify the same
parameter. If there is heterogeneity in returns to schooling (endogeneity bias), however, a
stronger independence assumption between the instrument, individual ability, and the error
in the schooling equation is needed to produce a consistent estimate. Examples of common
instruments used to estimate returns to education include distance to college (Card, 1993),
tuition costs (Kane and Rouse, 1995), and minimum mandatory schooling laws (Angrist and
Krueger, 1991; Oreopoulos, 2006).
The stronger assumption is usually violated by these sorts of instruments. Different instruments thus measure different effects, depending on which individuals are induced to
change their optimal education choice by a change in the instrument. Imbens and Angrist
(1994) formalize the notion that when there is heterogeneity in returns, IV actually measures
a local average treatment effect (LATE). The LATE parameter is consistently estimated given
the instrument satisfies the standard assumptions, but it consistently estimates the marginal
return to education only for a select subset of the population: those whose schooling decision
is affected by a change in the instrument.
In comparison to OLS, IV estimates are unaffected by classical measurement error. This
is one reason why IV estimates are generally larger than OLS estimates. In the presence of
heterogeneity, when IV estimates the LATE parameter, it could produce a larger parameter
than OLS because of who the instrument affects. For example, if the individuals affected are
more credit constrained but have high returns to schooling, then IV will overestimate the
average marginal return to education of the sample population.
The validity of the IV estimator depends crucially on the assumption that the instrument
is uncorrelated with the error. Small violations of this assumption cause the estimated parameter to blow up. Carneiro and Heckman (2002) show that several commonly used instruments, including distance to college and tuition, are correlated with ability. If ability is not
controlled for as a covariate, than these instruments are ”bad” and result in upward biased
IV estimates. This is problematic because many commonly used data sources do not include
a measure of individual ability, and thus it cannot be controlled for.
8
4
Marginal Treatment Effects
4.1
Relationship between Marginal Returns and Marginal Treatment Effects
If the instrument is valid, the LATE parameter is a consistent estimate of the marginal
return to education for a specific subset of the population. However, because of the extreme
sensitivity to the choice of instrument, it is often difficult to establish exactly what the LATE
parameter is measuring. Furthermore, instruments such as the ones mentioned above tend
to affect a particular level of schooling: changing the compulsory schooling age from 16 to
17, for example, does not directly affect the returns of people who would have completed
sixteen years of education anyway.3 Because the LATE estimates the return to education
of those affected by the instrument, it is not measuring the return to an additional year of
education for the average individual. For these reasons, Heckman (1997) argues that LATE
does not necessarily produce a parameter that is economically interesting, nor does it capture
how marginal returns are changing over the level of education. It fits somewhere in between
the two definitions discussed in section 2.
From a policy perspective, the second definition of a marginal return to education is often more relevant. Economists want to know what the marginal return to schooling is for
the people affected by a policy change, so that they can compare the benefits and costs of the
policy. In a series of papers, Heckman and Vytlacil (Heckman, 1997; Heckman and Vytlacil,
1999, 2001a) attempt to define such a parameter. The marginal treatment effect is the effect
of treatment for individuals indifferent to taking or not taking treatment. The MTE is the
limit form of the LATE. Unlike the LATE, however, the MTE parameter does not depend on
the choice of instrument. Additionally, because the MTE identifies the return to education
at every margin, it can be used to construct any treatment parameter of interest.4 In particular, Carneiro, Heckman, and Vytlacil (2010) show how the MTE can be used to identify
the marginal return to education of individuals affected by a specific educational policy. The
following section outlines the framework used to identify the MTE.
3
General equilibrium effects are ignored here, as in the majority of the literature. However, they are important
to consider. See Heckman, Lochner, and Taber (1998) for a discussion of general equilibrium effects in education.
4
In practice, the MTE may not be defined everywhere. This limitation is discussed below.
9
4.2
A Generalized Roy Model to Estimate the MTE
This section summarizes the generalized Roy Model used in much of the econometric
literature deriving treatment effect parameters (e.g., Imbens and Angrist, 1994; Heckman and
Vytlacil, 2001b; Heckman, Urzua, and Vytlacil, 2006). This framework is directly applicable
to estimating the marginal effects of schooling on earnings. For simplicity, suppose that there
are only two levels of education. Individuals can choose to go to college or not go to college.
Because this decision is likely correlated with unobserved ability, a valid instrument is used
to solve the selection bias issues. This instrument must affect the decision to go or not go to
college, but must not affect earnings in any other way.
For each individual i, assume there are two potential outcomes, (Y0i , Y1i ), corresponding to earnings if the individual does not go to college and does go to college, respectively.
Earnings in each state are a function of a vector of observable random variables Xi and an
unobserved random variable Ui :
Y0i = µ0 (Xi ) + U0i
Y1i = µ1 (Xi ) + U1i .
There is no reason to impose that µ(Xi ) is linearly seperable, but separability between the
observable and unobservable characteristics is assumed.
Further, the outcome of individual i depends upon the college decision, given by:
Di? = µD (Zi ) − UDi
where the instrument Zi is a vector of observed random variables and UDi is an unobserved
random variable. The vector of instruments can contain all of the Xi s and must include at
least one instrument that is excludable from the outcome equation. The value of Di? is not
observed by the economist, but an indicator of treatment, Di , is. The treatment indicator is
defined as:
Di =


 1
if Di? > 0

 0
if Di? ≤ 0
10
Although Di? is not observed, both the realized outcome of individual i and the treatment
indicator are observed:
Yi = Di Y1i + (1 − Di )Y0i .
(2)
This can be written as:
Yi = µ0 (Xi ) + Di [µ1 (Xi ) − µ0 (Xi ) + U1i − U0i ] + U0i .
The difference U1i − U0i can be interpreted as the idiosyncratic gain from education, and the
average gain from going to college is µ1 (Xi ) − µ0 (Xi ).
In this framework, Heckman and Vytlacil (2001a) define the conditional probability of
going to college as:
P (z) ≡ P r(Di = 1|Zi = z, Xi = x) = FUDi (µD (z))
where FUDi is the cumulative distribution function (CDF) of the random variable UDi with
realization u. Empirically, the selection probability can be estimated using a probit or a logit
model. Given the properties of a CDF and the assumptions above, it is possible to assume
UDi ∼ Uniform[0, 1] without loss of generality.5 One way to think about this is that the
transformed values of UDi represent the quantiles of the original values. This normalization
allows us to avoid making an assumption about the true distribution of the error. It also then
follows that µD (z) = P (z). Furthermore, because of the uniform distribution, we can define
UDi = FUDi (UDi ). Notice that Di = 1 if and only if P (Zi ) ≥ UDi .
The marginal treatment effect is the mean return to going to college for people who are
indifferent to going or not going, conditional on both the observed and unobserved characteristics that determine the college decision:
M T E(x, u) = E[Y1i − Y0i |Xi = x, UDi = u].
Because P (z) = u for the person indifferent to selecting or not selecting treatment (Di? =
0), the MTE can be estimated by taking the derivative of the conditional expectation of the
5
See Heckman and Vytlacil (2001a) for a proof of this within the latent variable framework.
11
outcome with respect to the probability of treatment:6
M T E(x, P (z)) =
∂E[Yi |Xi = x, P (Zi ) = P (z)]
.
∂P (z)
Clearly, the MTE is only defined over the support of P (Zi ), but is otherwise not sensitive to
the instrument choice. This means that in regions of common support, two instruments will
yield identical estimates of the MTE.
4.3
Advantages and Disadvantages of the MTE
The marginal treatment effect has two primary advantages over other ways of estimating
marginal returns. First, it is a natural way to characterize heterogeneity in returns to education because it shows how returns vary with Xi and UDi . By estimating the MTE for all
values of UDi , it is possible to identify the returns to college at any relevant margin. In contrast, the LATE parameter estimates returns at unidentified intervals. The MTE aids in the
analysis of variation in returns to education across populations, and also allows a more accurate analysis of policy changes, as described below. Second, Heckman and Vytlacil (2001a)
show that all treatment effect parameters7 can be expressed as different weighted averages of
the MTE, where the weights all integrate to one. In this sense, the MTE unifies all of the treatment effect parameters. It can be used to estimate other treatment effects when endogeneity
bias prevents consistent estimation of these parameters directly.
However, there are some important limitations of the MTE. Most importantly, estimation
is empirically challenging. The MTE is identifiable only over the support of P (Zi ). If the
support is not the full unit interval, the MTE will not be defined everywhere. If the CDF is
not smooth enough (the conditional probability of going to college is not continuous), the
MTE cannot be estimated either.
Finally, the marginal treatment effect is in itself generally not the parameter of interest.
It identifies the average return at very specific margins. Usually, economists are interested
in the returns over a wider interval. This is not such an issue because it is relatively easy to
6
The derivative of a conditional expectation can be estimated using standard nonparametric regression techniques (see Heckman and Vytlacil, 2001b).
7
E.g., the average treatment effect, effect of treatment on the treated, LATE, and policy relevant treatment
effects.
12
construct other treatment parameters once the MTE is defined over the relevant range. The
next section describes how the MTE can be used to construct a parameter that estimates the
return to education of people affected by specific policies.
4.4
Policy Relevant Treatment Effects
The MTE can be used to derive treatment effect parameters that directly answer the pol-
icy questions at hand. The main problem with IV estimation in the presence of heterogeneity
in returns to schooling is that it is not always clear what effect the LATE parameter is identifying. However, using the MTE, economists can derive a treatment parameter that answers
a specific question.
Consider a policy that affects the probability of going to college, but that does not directly
affect earnings or unobservables in the decision process. Let Di∗ be the college choice made
under the alternative policy and P ∗ (Zi ) be the probability that Di∗ = 1 conditional on Zi .
Then the earnings outcome under the alternative policy is:
Yi∗ = Di∗ Y1i + (1 − Di∗ )Y0i
and the outcome under the baseline policy is as in (2). The mean effect of going from the
baseline policy to the alternative policy per person shifted is the policy relevant treatment
effect (PRTE), defined by Heckman and Vytlacil (2001b). It is defined wherever E[Di |Xi =
x] 6= E[Di∗ |Xi = x] as:
PRTE =
E[Yi |Alternative Policy, Xi = x] − E[Yi |Baseline Policy, Xi = x]
,
E[Di |Alternative Policy, Xi = x] − E[Di |Baseline Policy, Xi = x]
which can be alternatively expressed as a weighted average of the MTE.8 The PRTE depends
on the policy change only through the distribution of P ∗ (Zi ). Thus, the CDFs of P ∗ (Zi ) and
P (Zi ), along with the MTE, are sufficient to calculate the average return to education of the
people affected by the policy change. Unless the instrument used corresponds exactly to the
policy change, this parameter is different from the LATE estimate.
The PRTE can only be identified if the support of P ∗ (Zi ) is contained in the support of
8
PRTE =
R1
0
M T E(x, u)ωP RT E (x, u) du, where ωP RT E =
13
FP |X (u|x)−FP ∗ |X (u|x)
.
E[P (Zi )|Xi =x]−E[P ∗ (Zi )|Xi =x]
P (Zi ). This often means that the support must be the full unit interval, which again is a
requirement that is empirically challenging to satisfy. The marginal policy relevant treatment effect (MPRTE) corresponds to a marginal change from a baseline policy and does not
run into this problem. It still answers economically interesting questions and, according to
Carneiro, Heckman and Vytlacil (2010), is the appropriate parameter with which to conduct
cost-benefit analysis of policy changes. The MPRTE is expressed as a weighted average of the
MTE as well, and places positive weight on the MTE only for values of u where the density
of P (Zi ) is positive (fP (u) 6= 0) so it is identified under only the assumption that P (Zi ) is a
continuous random variable.
5
Empirical Estimation of Marginal Returns to Education
In a homogeneous world, the OLS, IV, and MTE methods of estimating returns to ed-
ucation would all produce the same parameter. However, in practice heterogeneity in returns, ability bias, and measurement error complicate the analysis in the ways previously
discussed. How much do these factors affect different estimation methods?
Carneiro, Heckman, and Vytlacil (2011) use data from the National Longitudinal Survey
of Youth (NLSY) of 1979 to show that returns to college vary across individuals. Furthermore, they provide evidence that the people in their sample act on the knowledge about
their idiosyncratic returns to education. By calculating the MTE, they compare marginal policy relevant treatment effects and the average treatment effect to the OLS and IV estimates of
the return to a year of college. Their findings suggest that both OLS and IV are substantially
upward biased compared to the average return to a year of college in the sample, as estimated by the average treatment effect. Just as importantly, they show that different policies
produce different marginal policy relevant treatment effect parameters. The average return
to a year of college of the people affected by a policy that changes the probability of going to
college by a fixed amount for everyone, for example, is similar in size to the average treatment effect. However, the people affected by a policy that changes the probability of going
to college by a small proportion have an average return only one third the size of the IV estimate. This suggests that the IV/LATE estimates may be wildly off the mark if they are used
to estimate the returns to individuals affected by a certain policy change and the instrument
14
does not correspond exactly to that policy.
Moffitt (2008) uses a similar approach to estimate the MTE. He uses data on the earnings
of 33 year old men in the United Kingdom in 1993 to estimate the returns to higher education.
Again, education is considered a binary choice. The OLS and IV estimates of the return to college are very similar in size to those found by Carneiro, Heckman, and Vytlacil (2011) despite
using different data and different instruments.9 He shows further evidence for heterogeneity
in returns to education, and that the marginal returns to college fall as the proportion of the
population with higher education rises. Encouragingly, he finds that the shape of the MTE
over different values of UD (for a given level of the observable characteristics) in his sample
is the same as Carneiro, Heckman, and Vytlacil estimate in their study. While Moffitt does
not calculate MPRTEs, his results imply that both OLS and IV overstate the return to college
in his sample.
6
Directions for Future Research
The existing empirical work on estimating marginal treatment effects (and thus policy
relevant treatment effects) is subject to several limitations. The current empirical literature
limits educational decisions to a binary choice of whether or not to go to college. From
this marginal return to college, economists can back out an approximate marginal return
to a year of college (as in Carneiro, Heckman, and Vytlacil (2011)). However, this analysis
is somewhat misleading. Empirically, we know that returns to schooling are not constant
across years. Specifically, returns are highest in degree years. More work is needed to be able
to apply this methodology to multiple schooling level outcomes. Heckman, Urzua, and Vytlacil (2006) extend their theoretical analysis of treatment effects to more than two outcomes
using an ordered choice model. Ordered choice is theoretically correct for education because
individuals must complete a grade before moving on to the next one. However, no one has
been able to empirically estimate marginal treatment effects with multiple schooling choices.
This is primarily because of data concerns. To estimate the MTE at any point, the conditional
support of the probability to attaining that level of education must be the full unit interval.
9
The estimates reported in Carneiro, Heckman, and Vytlacil (2011) are the true parameters divided by four, so
that they can be interpreted as the return to one year of college. Moffitt reports estimates of the return to a college
education, and so are approximately four times as large.
15
Adding more choices significantly increases the demands on the data.
Nevertheless, the non-linear returns are important to think about, especially when estimating policy relevant treatment effects. A policy that increases the probability of starting
college will have a very different impact on earnings than a policy that increases the probability of graduating from college. A significant proportion of individuals who start college
never receive a degree. This implies that students are learning about their costs and returns to
education and updating their optimal schooling choices. While actual earnings data is used
to estimate returns to schooling, it is an individual’s perceived return that influences educational choices. In a world of imperfect information, Jensen (2010) points out that there is no
reason to expect the level of education chosen to be either individually or socially efficient.
Using data on eighth grade boys in the Dominican Republic, he finds that perceived returns
to secondary education are substantially lower than measured returns. Students who are
provided with information about the observed returns to schooling in the area stay in school
significantly longer than students who do not receive this information.
Stinebrickner and Stinebrickner (2012) use data from a college that serves mostly low income students to examine the role of learning in the college dropout decision. In contrast to
Jensen (2010), they find evidence that students overestimate returns to education. As they
learn about their academic ability and psychic costs to education, they update their beliefs
about their individual return to schooling. The authors find that in their sample, dropout
would be reduced by 40 percent if learning about ability did not occur. Because perceived
returns and perceived costs affect education decisions, it is important to understand these
perceptions. This is a very relevant area for future work. If low-income students are less
informed about the true costs and returns to education, then policies that disseminate information may be as important as policies that change the costs of schooling. Future research
that explores the relationship between perceived marginal returns and actual marginal returns to education will help guide educational policy.
Additionally, all of the empirical work on marginal treatment effects thus far has focused
on while males. This is because more data is available. In most surveys the sample of minorities is smaller, and the sample of females with wage data is smaller than that of males
because traditionally more women do not enter the labor market. Yet, evidence suggests
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that working women have a higher rate of return to college degrees than do working men
(Dwyer, Hodson, and McCloud, 2013). If the observed marginal returns to education differ
for different groups of people (men, women, minorities, etc.), then policies that change the
probability of getting a certain level of education are going to have different effects depending on which groups of people they primarily affect. In order to be able to do cost benefit
analysis of educational policies that are targeted at particular groups, it is important to be
able to estimate marginal returns for people other than white men. Further work on both
the theoretical and empirical sides of estimating marginal treatment effects will hopefully
result in techniques that can be applied more generally. This is especially relevant in terms
of analyzing the effectiveness of policies that promote education through affirmative action
or that aim to push women into STEM fields. Before economists can draw conclusions about
whether such programs are good or bad, more research needs to be dome in order to learn
how effective they are at improving outcomes.
Finally, marginal returns to education have mostly been analyzed in a partial equilibrium
setting. However, this is a simplistic view of the world. As the supply of workers with
a certain level of education changes, wages will adjust and the returns to education will
change as well. Consider a simple signaling model. If education is only a signal to employers
about ability, as the proportion of individuals who get a college degree rises, for example, the
conditional expectation of a college-educated person’s ability falls and the signal becomes
less valuable in the market. This drives observed returns to education down.
It is important to remember that economists cannot measure true returns to education.
Wages do not capture the intrinsic value that education provides. There are likely network
effects and other non-monetary benefits to education as well. When interpreting either the
marginal return to an extra year of education or the marginal treatment effect, it is important
to think carefully about what the parameter is measuring and what it is not. The enormous
amount of heterogeneity in returns highlights the need for continued discussion about how
to best estimate marginal returns to education.
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