An alternative to the Mincer model of education
John Humphreys1
Education is widely regarded as one of the most important variables in determining the prosperity of
individuals and the wealth of nations. Many eloquent stories can be told about the various virtues of
schooling, which has given rise to a large and ever-growing literature – nearly all of it based on the
famous Mincer model of education.
In the basic Mincer model, wages are determined by years of education and years of experience. The
basic model has been challenged on a number of grounds, including (a) the problem of ability
endogeneity and omitted variable bias; (b) the non-linearity of the relationship between wages and
education; and (c) the potential for different experience premiums for people with different levels of
education.
This paper will explore these limitations in more detail, applying a serious of modified models to a
new set of data gathered in Cambodia in 2012. More information on the data set is available in
Appendix A.
The approach of this paper is to start with the basic Mincer model to set a benchmark against which
to compare the modified models. The first two modifications (extra controls and non-linear
education) are already popular within the literature, and the results from this new data conform to
expectations.
In contrast, there is little existing literature on how to address the third issue of divergent experience
premiums. The final sections of this paper will suggest a new model that allows for experience
heterogeneity, and provides results that fundamentally challenge the standard perception regarding
the return on education. Traditional models have assumed that education provides an immediate
wage premium but does not change the future wage growth profile. The results from this model
suggest that higher education may give little or no immediate wage premium, and instead it shifts
the graduate onto a faster wage growth profile.
If true, then standard models of education economics have fundamentally miss-specified the nature
of the relationship between education and wages, and there is a need for new models (such as the
one presented in this paper) that explicitly factor in the relationship between education and the
experience coefficient.
The basic Mincer model
There is a very thorough literature covering the link between education and earnings that goes back
at least to Friedman and Kuznets (1954). Since Jacob Mincer (1974), the dominant approach to
measure the benefit from education has been to use ordinary least squares (OLS) regression based
on the Mincerian equation (Card 1999, 2001):
1
University of Queensland, [email protected]
1
ln(w) = a + bS + cE + dE^2 + error
Where:
ln = national logarithm
w = wages
S = schooling (education)
E = experience
For a detailed explanation of the theoretical foundations of the Mincer equation, see Heckman et al.
(2003). The simplest form of the Mincer equation has (the log of) wages depending only on years of
schooling and years of experience, with a linear relationship between schooling and wages.
Despite the many legitimate concerns about using the “basic Mincer” approach, that is still a
common starting point (and sometimes end point) in much of the literature. To provide a reference
case, we apply the basic Mincer model to the 2012 Cambodian data, using OLS estimation. The
confidence level shows the likelihood that the coefficient is not zero (one-tailed test).
TABLE A: Basic Mincer model
Value
Constant
-1.965
Education
0.086
Experience
0.024
Experience squared
-0.000
Sample size
R squared (adjusted)
F-stat
Standard error
0.173
0.010
0.020
0.001
Confidence level
99%
99%
Not significant (89%)
Not significant
530
0.133
28.1
These results indicate that an additional year of education will increase income by 8.6%, while an
additional year of experience will increase income by 2.4%, though due to a relatively high standard
error, we cannot be confident that the experience coefficient is statistically significantly different to
zero. While all of these values are consistent with expectations, this model and these results are
provided only as a reference case.
The basic Mincer model has been hugely popular and offers a good starting point. However, there
have been many valid critiques made, and suggested improvements offered. The accuracy of the
basic Mincer approach rests on a series of assumptions that are often violated. The following
sections will consider some objections to the Mincer model and will explore various solutions, and
how those solutions change the results.
Controlling for ability and other factors
One of the most common concerns with education economics has been the degree to which
schooling is endogenous due to an “ability bias”, which is described by Harmon et al. (2003) as “the
2
preoccupation of the empirical literature since the earliest contributions” (p119). Students with
greater abilities (or some other hidden advantage) are likely to receive more schooling and also
receive higher incomes, which could result in a correlation between schooling and wages that does
not describe a causal link. If ability related to both schooling and wages, then the basic Mincer
equation will give an upward biased result, and will also cause a convex relationship between
education and (log of) wages.
One way to respond to this problem is to include other explanatory variables in the regression that
are assumed to capture natural ability, such as performance on an IQ test or school grades (Harmon
et al. 2003; Maluccio 1998).
Another common approach is to use an instrumental variable (IV) that correlates closely with
schooling but is not correlated with ability or wages. Two common examples are “distance to
school” and “spouse’s education”. Lall and Sakallariou (2010) used “education of spouse” as well as
“early age smoking”, with the theoretical rationale that smoking indicates a high time value of
money (high discount rate) while education generally requires a relatively lower time value of
money (low discount rate).
There are several problems with the IV approach. Using IV analysis it is not possible to relax the
assumption of linearity between education and log of wages (as discussed below). If the nonlinearity were entirely explained by the ability bias then this would not be a major concern.
However, studies by Belzil and Hansen (2002) and Belzil (2006) show that the non-linearity is “not
solely a reflection of omitted skill heterogeneity” (Belzil, 2006, 17). Another problem is that the IV
approach produces somewhat of a paradox. If ability endogeneity were a significant problem, then
we would expect the education premium using the IV approach to be lower than the education
premium found using the OLS approach. Strangely, the reverse is often the case, with IV estimates
often being higher than OLS estimates (Lall and Sakallariou 2010; Blundell, et al. 2001; Maluccio
1998; Harmon et al. 2003). This may simply be an issue of measurement error. However, it may be a
problem with the choice of instrumental variables. For example, while “distance to school” may be
uncorrelated with ability and wages (and so avoid that endogeneity problem), it may instead be
correlated with socio-economic status, which could create additional biases in the estimate. This is
one of several concerns raised by Heckman and Urzua (2009) in their critique of the IV approach. As
explained by Card (1999):
“the validity of a particular IV estimator depends crucially on the assumption that the
instruments are uncorrelated with other latent characteristics of individuals that may affect
their earnings.” (p1821).
Several authors have tried to explain the low IV estimates. Card (2001) suggests that the normal OLS
estimates are for an average person but IV estimates are for a marginal person, and if marginal
returns exceed average returns then that would explain relatively higher IV estimates. However,
Carneiro and Heckman (2002) and Carneiro et al. (2005) show with US data that the marginal return
is below the average return for college goers, which is consistent with the standard assumption of
decreasing marginal returns to investment. As an alternative explanation, they suggest that
unobserved abilities of those who acquire more schooling and those who do not are negatively
correlated. In other words, there are lots of different types of ability, and not all of them are relevant
3
to higher education. This means that despite much concern to the contrary, there may not be a large
endogeneity problem.
In his comprehensive analysis of education economics, Griliches (1977) argued that endogeneity was
not a large issue, a position also supported by the findings of Angrist and Krueger (1991). The
decade-old words of Heckman et al (2003) are probably still appropriate today: “the current
empirical debate on the importance of accounting for the endogeneity of schooling is far from
settled” (p3).
Putting aside the debate about whether there is an endogeneity problem, it is highly questionable
whether the IV approach provides an effective solution since it is not able to relax the linearity
assumption, the instrumental variable used may raise other endogeneity problems, and the IV
approach has historically provided anomalous results. A more robust approach is to stay with OLS,
while including an “ability” related explanatory variable.
While the “ability bias” problem discussed above is the most prominent example of an omitted
variable, there are many other issues that may have an important impact on wages that are not
included in the basic Mincer equation. For example, Topel (1991) and Altonji & Williams (1997) both
found significant positive relationships between tenure and wages. In contrast, Kifle (2007) found a
negative relationship in Ethiopia, which he interpreted as a cost of lack of job mobility. In his
examination of the relationship, Williams (1991) found that tenure was positively related to wages
only for the first few years of employment, suggesting a non-linear relationship.
There is also some literature that suggests the importance of socio-economic factors in determining
wages. For example, Lam & Schoeni (1993) reported that having a father with a university degree
instead of being illiterate would provide a 20% wage premium to the child, ceteris paribus. The
transmission mechanism of socio-economic factors may be through an improved learning
environment, or it may be through more effective family connections to the job market. While the
latter is difficult to measure, the former can be controlled for by including parents’ education and/or
income levels.
Another potential factor is public/private sector of employment. Mann & Kapoor (1988) have
suggested that public sector workers can be paid more than their private sector counterparts. This
was explained by Rees & Shah (1995) as potentially a result of public wages not being limited by
economic constraints. However, Lall & Sakellariou (2007) found a negative premium on public sector
employment, which suggests a more complicated relationship between employment sector and
wages.
Other variables that have been suggested include gender, marital status, hours worked, type of
industry, and other personal details. One control that would especially helpful but is often difficult to
measure is “quality” of schooling. Adding these additional variables extends the Mincer equation:
ln(w) = a + bS + cE + dE^2 +eX + error
Where:
w = wages
S = schooling
4
E = experience
X = vector of other variables
By adding in some key control variables it is possible to improve on the basic Mincer model. In the
below model, control variables are included for ability (grades), socio-economic status (parents’
income), gender and urbanity. For the sake of clarity, the coefficient for grades shows the
percentage change in expected wages based on a 10-point change in grades (out of a 100 point
scoring system) while the coefficient for parents’ income shows the percentage change in expected
wages based on a change of parents’ income of $100/month.
TABLE B: Modified Mincer with control variables
Value
Constant
-2.010
Education
0.066
Experience
0.024
Experience squared
-0.000
Female
-0.217
Parents’ income
0.087
Grades
0.036
Urban
0.166
Sample size
R squared (adjusted)
F-stat
Standard error
0.195
0.012
0.019
0.001
0.074
0.037
0.023
0.090
Confidence level
99%
99%
Not significant (89%)
Not significant
99%
99%
90%
95%
530
0.160
15.4
As expected, by including control variables (including ability) the calculated education premium
drops from 8.6% down to 6.6%. The coefficients for gender, parents’ income, urbanity and grades
are all statistically and economically significant. These results confirm the suspicion (outlined above)
that the basic Mincer model over-estimates education premiums due to omitted variable bias.
Non-linear education premium
In addition to the problems of ability endogeneity and other omitted variables, the basic Mincer
model assumes a linear relationship between (log of) wages and schooling. Over two decades ago,
Card and Krueger (1992) concluded that the relationship was essentially linear, with the exception of
the first few years and last few years. However, since that time the majority of evidence has
suggested that education premiums are becoming increasingly convex (Mincer 1997, Deschenes
2001, Lemieux 2003, Belzil 2006).
Mincer (1997) argued that this is a logical response to a relative increase in the demand for human
capital. Another potential reason for non-linearity may be “sheepskin” effects, where achieving the
final credential (e.g. a high school certificate or university degree) is more important than noncredentialed education. For example, completing four out of four years of a University degree may
5
well result in a large wage premium, but a person who completes only three out of four years of the
same degree may receive a much smaller wage premium.
The most common response to these concerns has been to split education into different levels
(none, primary, secondary, tertiary) and use dummy variables to estimate different premiums for
the different levels. This approach is used in nearly every comprehensive study of education
economics. Adding in the education level dummy variables gives the results shown in Table C.
TABLE C: Modified Mincer with dummy variables for education level
Value
Standard error
Constant
-1.550
0.179
Finish primary
0.073
0.112
Finish secondary
0.277
0.119
Graduate university
0.747
0.147
Experience
0.011
0.019
Experience squared
-0.000
0.001
Female
-0.239
0.075
Parents’ income
0.073
0.037
Grades
0.042
0.023
Urban
0.227
0.089
Sample size
R-squared (adjusted)
F-stat
Confidence level
99%
Not significant
99%
99%
Not significant
Not significant
99%
95%
95%
99%
530
0.153
11.63
To convert the education dummy coefficients into a measure of annualised education premium for
that education level it is necessary to make a few adjustments. First, we need to adjust the
coefficients by calculating [exp(b)-1]2, then find the difference between the relevant coefficients
(e.g. university coefficient minus secondary school coefficient), then divide that number by the
average years of school spent at that level of education. Based on the above model, the annualised
education premium for each education level are given in Table D.
TABLE D: Annualised education premium at each level
Annualised education premium at level
Complete primary school
1.9%
Complete secondary school
6.0%
Graduate university
21.0%
These results show that the wage-education relationship in the current data is highly non-linear,
with students receiving a relatively low benefit from each year of primary schooling but a much
higher benefit from each year of university study. This is consistent with the recent literature and
2
For further discussion on this adjustment, see Conlon and Patrignani (2011) and Kifle (2010).
6
lends further weight to the emerging view that “the non-linear (convex) shape of the wage schooling
relationship is acute” (Belzil 2006, 14).
Another way to factor in non-linearity is to include “schooling squared” as an explanatory variable
(Lemieux 2003, Kifle 2007, Diagne and Diene 2011). A positive coefficient would show that education
premiums are convex (higher premiums for higher education) while a negative coefficient would
show that education premiums are concave (lower premiums for higher education).
TABLE E: Modified Mincer with schooling squared
Value
Constant
-1.743
Education
0.007
Education squared
0.003
Experience
0.024
Experience squared
-0.000
Female
-0.222
Parents’ income
0.088
Grades
0.033
Urban
0.171
Sample size
R-squared (adjusted)
F-stat
Standard error
0.259
0.040
0.002
0.019
0.001
0.074
0.037
0.023
0.090
Confidence level
99%
Not significant
90%
Not significant (89%)
Not significant
99%
99%
90%
95%
530
0.162
13.8
As expected, the coefficient for schooling squared is positive and statistically significant. Based on
the above coefficients, it is possible to calculate an equivalent annualised education premium to
compare with the results from the dummy variable approach discussed earlier.
TABLE F: Annualised education premium using dummy variables v schooling squared
Education level model
Schooling squared model
Complete primary school
1.9%
4.2%
Complete secondary school
6.0%
8.5%
Graduate university
21.0%
15.7%
Both non-linear models show that the education returns are acutely convex, with a much higher
annualised education premium for university graduates than school graduates. The non-linearity is
particularly obvious in the “education level” model.
While the education level approach is more common in the literature, for the present data the
schooling squared model recorded a marginally higher R^2, suggesting that it has more explanatory
power. In addition, the schooling squared model is more robust in that it allows the estimation of
education premiums for any education level; for example, using the schooling squared model, the
annualised education premium for a two-year masters degree is estimated at 24.5%.
7
Heterogeneous experience
By adding control variables and allowing for a non-linear education premium, the above models
have been able to address some common critiques of the Mincer framework, and the results of
those modified models have been consistent with much of the recent literature. However, there
remains one other significant problem: the Mincer model assumes that the experience premium is
constant for everybody, irrespective of their education level.
In Heckman et al. (2003) this issue was explored by observing whether the earnings-experience
profiles for different education levels in the United States were parallel, which was rejected. Belzil
(2006) and Card and Lemeiux (2001) found the same results. The problem of heterogeneous
experience premiums leading to divergent wage growth paths is often noted in the literature, but
most studies provide no solution.
Andini (2008) explains the divergent wage growth paths by suggesting that observed earnings may
not be equal to net potential earnings due to wage bargaining imbalances and asymmetric
information, but that observed earnings will approach potential earnings over time. One
interpretation of his approach is that highly educated individuals will see a relatively high experience
premium as delayed compensation for their high education level.
Another potential reason for non-parallel wage growth paths is that experience returns may in part
represent general productivity improvements, and that productivity growth may be different at
different skill levels. For example, if there was little productivity improvement in unskilled work but
strong productivity growth in highly skilled work, and these productivity improvements were
captured in the experience coefficient, then it would be expected that the experience profiles would
diverge.
A third potential reason for different experience profiles is that high-skilled jobs may include a
significant amount of “on the job” training and greater opportunities for professional advancement.
If the benefits of a high-skilled job accrue slowly over time, then they will be captured in the
experience coefficient instead of the schooling coefficient.
To address the issue of experience heterogeneity, this paper presents a model that explicitly allows
for different wage growth profiles. In this model there is not just a single experience variable, but
instead there are a series of different experience variables for each different education level. For the
current model, with four education levels (none, primary, secondary, university), there would be
four different experience coefficients. The functional form of the model would be:
ln(w) = a + b.Education + c1.Ed1.Ex + c2.Ed2.Ex + c3.Ed3.Ex + c4.(1-sum(Ed1:Ed3)).Ex + d1.Ed1.Ex^2 +
d2.Ed2. Ex^2 + d3.Ed3.Ex^2 + d4.(1-sum(Ed1:Ed3)).Ex^2 + error
Where:
c1-c4 represent four different experience coefficients; and
d1-d4 represent four different exp^2 coefficients.
8
Using the heterogeneous experience model (but with a linear education premium) gives the results
shown in Table G below. It can be seen that the experience premium for university graduates is
11.2%, which is significantly higher than the estimates from the above models and much higher than
normally reported in the literature.
Of the other three experience premiums, two were not statistically significantly different from zero
and the third (the experience premium for people with no schooling) was 3.6% and significant at the
90% level. This shows a structural break in the experience premium, where non-graduates receive a
low (or no) premium from their experience while university graduates see their incomes increase
dramatically with experience. This result lends further weight to the growing theoretical and
empirical arguments against the Mincer assumption that experience and education premiums are
unrelated.
TABLE G: Heterogeneous experience with linear education premium
Value
Standard error
Constant
-2.023
0.260
Education
0.066
0.018
Experience (no school) 0.036
0.026
Experience (primary)
0.023
0.033
Experience (secondary) 0.016
0.037
Experience (university) 0.112
0.058
Exp^2 (no school)
0.000
0.001
Exp^2 (primary)
0.000
0.002
Exp^2 (secondary)
0.000
0.002
Exp^2 (university)
-0.007
0.004
Female
-0.225
0.075
Parents’ income
0.077
0.038
Grades
0.034
0.023
Urban
0.174
0.090
Sample size
R-squared (adjusted)
F-stat
530
0.159
8.71
Confidence level
99%
99%
90%
Not significant
Not significant
95%
Not significant
Not significant
Not significant
95%
99%
95%
90%
95%
(174+111+166+79)
(no + prim + sec + uni)
Heterogeneous experience and non-linear education premiums
The final model considered in this paper simultaneously relaxes all of the strict Mincer assumptions
discussed above. By including control variables, using schooling squared to consider the non-linearity
of education premiums, and including different experience premiums for different education levels,
the resulting model is significantly different from the Mincer model. The results are on Table H.
By relaxing education linearity and experience uniformity at the same time, it is notable that the
education premium loses statistical significance while the high-skilled experience premium is large
9
and significant. This result is economically important, and has the potential to fundamentally change
the way the education premium is measured and understood.
TABLE H: Heterogeneous experience with non-linear education
Value
Standard error
Constant
-1.954
0.339
Education
0.050
0.055
Education^2
0.001
0.003
Experience (no school) 0.034
0.026
Experience (primary)
0.026
0.033
Experience (secondary) 0.018
0.037
Experience (university) 0.106
0.061
Exp^2 (no school)
0.000
0.001
Exp^2 (primary)
0.000
0.002
Exp^2 (secondary)
0.000
0.002
Exp^2 (university)
-0.007
0.005
Female
-0.226
0.075
Parents’ income
0.078
0.038
Grades
0.034
0.023
Urban
0.174
0.091
Sample size
R-squared (adjusted)
F-stat
530
0.158
8.09
Confidence level
99%
Not significant
Not significant
90%
Not significant
Not significant
95%
Not significant
Not significant
Not significant
90%
99%
95%
90%
95%
(174+111+166+79)
(no + prim + sec + uni)
When the model has the maximum amount of flexibility, it suggests that a highly educated person
should not expect an immediate premium from their schooling, but instead their benefit will come
over the course of their career in the form of faster wage growth. If this is an accurate reflection of
how education impacts wages, then most previous studies of education economics are likely to give
misleading results.
Any model that requires a fixed experience premium (which is most models in the literature) will
artificially inflate the education premium for high-skilled people to compensate for having an
artificially low experience premium. Such models will distort the wage profile of high-skilled workers
by overestimating their early-career income and underestimate their late-career income. By bringing
forward the estimated income of university graduates, standard Mincer models will artificially
increase the measured rate of return and the net present value from university education.
Conclusion
The implication of the above result is more important than simply over-estimating the benefit from
university education; it suggests that the standard approach to education economics fundamentally
mis-characterises the nature of the benefit. The standard Mincer model suggests that education
gives you a wage premium and then wages grow at a constant rate according to experience. A more
10
accurate reflection of reality would seem to be that higher education gives little or no immediate
wage benefit, and instead that most of the benefit comes in the form of faster wages growth over
the course of a graduate’s working life.
The implications for education economics are significant. If the benefits of education show up
primarily through a faster wages growth profile then the standard approach actually hides the main
story. Further, this requires a re-thinking of the so-called “experience” coefficient, since it is no
longer simply a measure of experience but also represents (in part) the mechanism through which
education impacts on wages.
To understand the true benefits from education, economists will need to shift their focus away from
directly measuring the education premium and instead investigate the relationship between
education and the wages growth profile. This requires that models with a single experience
coefficient should be rejected, and replaced with heterogeneous experience models as described
this paper.
Previous critiques of the Mincer model have resulted in modifications that have improved education
economics by accounting for ability bias and other omitted variables and the non-linearity of (log of)
wages to education. Such modifications have been appropriate and have improved our
understanding of the returns on education.
However, the growing body of evidence regarding the divergent experience premiums needs to be
more adequately incorporated into new models of education economics. Doing so will give a more
accurate account of education economics, and has the potential to fundamentally change the way
we think about education economics. The above analysis supports the thesis that high-educated
people benefit from faster wage growth profile, and goes further to suggest that this wage growth
may indeed be the main mechanism through which education impacts on wages.
It is no longer feasible for economists to ignore the relationship between education and experience
premiums, and the above approach provides a potential template for exploring that link.
11
Appendix A:
The data used for these regressions was gathered in regional Cambodia in early 2012. In total, 530
surveys were returned, of which 43% were from women and 61% from urban (non-farming) areas. A
brief data summary is provided in Table AA below, and original data is available from the author.
TABLE AA: Data summary
Variable
Income (USD)
Hours worked per month
Income/hour (USD)
Education (years)
University graduate
Experience (years)
Parents income (USD)
School grades (out of 100)
Public sector
Average
104.4/month
213.6
0.52/hour
9.4
0.149 (14.9%)
7.9
57.3/month
49.1
0.098 (9.8%)
12
Standard Deviation
81.4
62.8
0.50
4.7
0.356
6.1
98.9
16.6
0.30
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