Estimating Returns to Education in the UK - BSc Economics

This dissertation explores the returns to education in the UK, drawing upon human capital theory and econometric analysis. It examines the impact of factors like school leaving age (RoSLA) and the sheepskin effect on earnings, referencing Mincer's equation and related studies. The literature review covers both pecuniary and non-pecuniary benefits of education, while acknowledging limitations of existing research. The study also compares marginal and infra-marginal students, and questions the intergenerational mobility of RoSLA. It references studies using Stata for data analysis. Desklib provides access to similar dissertations and AI study tools for students.

2.1 Introduction
Human Capital is often measured in terms of levels of attainment at school. School education or
the levels of attainment at school is the most commonly used proxy to understand human capital
(Edwards, 2004). In the 1950s, Gary Becker demonstrated that the returns to educational
attainment showed significant variability even among people with similar IQs . In the years to
follow, Becker highlighted the need for investment in education in order to achieve higher levels
of investment. (Teixeira, 2014)
In many ways, productivity of a person can be very enhanced sue to school attainment. Mincer
has described “level of schooling” in such a way that schools provide endowment to students in
the form of “ability” which then, in turn, improves their productivity, thereby, indirectly
improving their earnings, thus explaining the causality between educational attainment and
increased productivity. (Edwards, 2004)
In order to develop Human Capital, more than just physical strength of labour is required. In
order to make the physical strength or physical more productive, investment in human capital is
required. This investment is not just in the form of knowledge or skills but also, in the form of
better overall well being. Gary Becker described this as general human capital. Schooling helps
improve the general human capital i.e. development of skills and knowledge in a generic sense
that would allow the person to be more productive in any area, instead of having a specific skill
in a particular area. For example, if a country has plenty of farmer who have a great knowledge
of farming, then according to Becker’s theory, then it can be described as specified human
capital. However, if a country has farmers who have the ability to read and write well, then those
farmers can use those skills to do their farming with greater efficiency. Similarly, a person with
knowledge of specific computer programming skills (Teixeira, 2014)
Hence, in the context of Mincer’s theory, schooling is a investment which has a rate of return.
The investment made in terms of schooling is made in terms of financial investment made in the
achieving a desired level of schooling as well as the time foregone , in order to achieve
schooling , which could be used in directly productive work. Oreopoulos and Petronijevic (2013)
described this decision as borrowing from the future income. Thus, Mincer’s equation provides
as estimation of the “average monetary returns of one additional year of education” .

The earning potential of a person can be increased due to schooling as schooling does provide
once with skills like “critical thinking”, understanding of language, basic ability to read and write
and much more. These, however, are skills provided by primary education. Generally, a large
percentage of populations invest in beyond the mandatory and necessary levels of educational
attainment and invest in tertiary education. In many cases, tertiary education provides with
“specified knowledge” and may make a person more efficient and armed with a level of skills as
soon as they enter college. Thus, tertiary education can act as a foundation to increase the
efficiency of a person. A degree can signal the proficiency and skills and can provide a
prospective employer or contractor detailed information about one’s “ability” in a specified field
or in general. Hence, a degree is a signal to prospective employers and contractors.(Teixeira,
2014)
College transcripts, scores from competitive tests etc. are some of the tools that persons with
tertiary college attainment signal their ability. Additionally, college degrees often provide with
“specified knowledge” which may be useful as a signal to prospective employers about the skills,
proficiency and productivity of a person in an objective manner. In an imperfect market, signals
such these can help a college student be more competitive. In context of Spence’s signaling
process, a college degree itself may be an endowment , instead of being a medium to achieve
endowment or productivity.(Oreopoulos & Petronijevic, 2013) Some may call this the
“Sheepskin Effect”
The logical question that follows is whether the returns on such an investment are worth the
investment made and whether the investment in a degree is a bad investment. In order to evaluate
the validity of an investment the rates of return must be evaluated. Mincer proposed an equation
to evaluation the Internal Rate of Return on schooling. The rates to return on schooling were
measured by the average increase in earnings that would be accrued for every increase in a
schooling year. The equation can be used at all levels of schooling primary, secondary as well as
tertiary. However, it must be noted that a vast majority of these studies simply estimate the
relationship between the earnings and additional schooling. This, does not imply that there is a
causality between the two variables. Moreover, as the economy of the world becomes more
digital, the way in which education is consumed and delivered may render Mincer’s equation
obsolete. (Patrinos, 2016)

The issue is further explored by (Grenet, 2013) who carried out a comparative analysis of two
important schooling reforms related to School Leaving Age which were adopted in Europe.
France introduced in 1967 Berthoin a legistation that raised the minimum School Leaving Age
for students from age 14 years to 16 years. In 1972, England extended the minimum School
Leaving age from the age of 15 years to 16 years for the regions of England and Wales. The
legislation known as “Raising of School Leaving Age” (here onwards known as RoSLA) seems
to have has an impact on the earnings of the English population, in general. Acoording to Grenet,
the effect of RoLSA on the English population was greater than the effect that its counterpart
legislation had in France. There could be a number of reasons for this. Grenet however, proposed
that these were differences were simply due to the fact that the likelihood of French students
staying in school, even without the legislation, was greater than the likelihood of the English
population staying in school. Thus, the legislation seeks to understand the impact of RoSLA on
earnings in UK.
2.2 Literature Review
The issue of the School Leaving Age and it’s impact on the earning in UK has been reasearched
widely.
Oreopoulos and Petronijevic, 2013 measured the returns to schooling in a more secular way than
just , in terms of money. They calculated the cost benefit of attaining a tertiary degree. They also
proposed to account for the benefit of “better signaling” as one of the attainment of tertiary
effect of attainment of an additional schooling as way of providing to prospective employers or
other people that one has a attained a certain level of intelligence. The authors, also, described
the “Non-pecuniary Benefits” of attending college. These include experiences that would not be
possible to achieve while a person is engaged in competition for better earnings. As such,
colleges act as incubators for students have the time and the freedom to make themselves more
efficient by engaging in various extra curricular activities. This also, provides them , if possible ,
the time to accumulate intellectual capital that may make them more creative. Thus, according to
Oreopoulos, college students may enter the work force as more efficient and more creative
human capital which may increase their productivity and consequently their earnings.
(Oreopoulos & Petronijevic, 2013) The study however, fails to take into account the role of

vocational education. Students who take degree primarily from the point of view of
consumption, such as Bachelors in Anthropology do not necessarily gain higher earnings due to
the degree but due to their own ability to find jobs. Similarly, students who gain vocational
degrees do not seem to have been included in the study, even though the impact on earnings in
those cases would be higher.
Several studies conducted to understand the relationship between “earnings” and “School Level
Attainment”, try to use the Mercer’s Equation(Patrinos, 2016). Mincer’s equation suggests that
earnings are a function of school years and the labour market experience. According to some
studies such as Crespo and Reis (2009) have found that the returns are higher for an additional
year, if that year signifies the attainment of some qualification or some degree. This is known as
the sheepskin effect. If the sheepskin effect comes into the picture, then the impact of an
additional year would be higher.
The equation reads as follows:
lny = lny0 + rS + β1X + where
Lny = the earnings from an additional year or marginal earnings
lny0 = earnings without any education
S = Total number of years of schooling attained
X - total number of years of experience in the labour market
In this case, earnings are not just dependent on schooling alone but also labour market
experience. Schooling is an endogenous variable to earnings. There is also, a case of a minimum
earning potential, regardless of whether an individual has attained schooling or not. This
equation accounts for schooling but also for work experience. For example, if one were to be an
entrepreneur, then the earning potential would have a very weak co-relation with schooling but
the earning potential would still be high due to work experience. (Rodel & Arvin, 2017)
The equation can be used at all levels of schooling primary, secondary as well as tertiary.
However, it must be noted that a vast majority of these studies simply estimate the relationship
between the earnings and additional schooling. This, does not imply that there is a causality

between the two variables. Moreover, as the economy of the world becomes more digital, the
way in which education is consumed and delivered may render Mincer’s education obsolete.
(Patrinos, 2016)
Devereux and Hart (2010) tried to analyse the impact of RoSLA on the average earnings and
found no increase in retuns for women while the returns of additional year of schooling for men
has a modest return of 4% -7 % . This implies that RoSLA may have not been as impactful as it
is believed to be and put forth the prospect of other insitutions within the society that may
enhance the benefits of compulsory education.
Buscha and Dickson (2015) found that the returns could vary from 0% t 7% , varying based on
the method used for estimation. This puts a question mark on various studies conducted and
highlights the point that any study on returns cannot be taken at face value and must be viewed in
a certain context.
The gains of an investment in an additional year of schooling can be best understood by
comparing those who would have other wise not been able to enter another level at school versus
those who were able to get in only due to some intervention like a policy intervention, financial
support, etc. (Fack & Grenet, 2013)
Fack and Grenet (2013) compared the earnings difference between the “marginal students” and
“infra marginal students”. Marginal students who was the cohort of students would not have
been able to gain additional education without financial support and infra marginal student or
students who had the ability to pay and would have gained additional education regardless of
financial support. The analysis in the paper uses the same logic. The comparison is between the
students at the margins of the policy or right after the policy and the generations of the students
that followed.
Clark and Royer (2013)Another impact of the additional year of schooling that has been studied
is who explored the impact of RoSLA on health. Health could be an endogenous variable to
earnings . By avoiding getting to the work force earlier than required, the policy may help

workers prolong their life span as well improve their earnings. Thus, they questioned the idea of
returns beyond hourly wages.
Sturgis and Buscha (2015)went further ahead and questioned the intra-generational mobility that
such a policy would be able to bring about. However, it is difficult to identify whether a complex
phenomenon like inter generational mobility can be brought about by a very simple and basic
policy like RoSLA
Dickson and Smith (2011) have quesstioned the practicality of the policy and point out the
Easter Leaving Rule. Students who were of age 16 years by the end of the Easter tern tended to
drop out of the school after the Easter term instead of staying in school to complete the rest of
the term. Students who did not celebrate their birthdays before the beginning of the summer term
tended to end stay until the end of the year. Thus, the RoSLA policy only extends the school for
drop outs for a few months. Those students who were motivated to drop out or demotivated to
continue would not end up staying more than a few months that they normally would have. Thus,
the policy is not practical in the sense that it is based on the age of the student instead of being
based on the minimum number of years that a student must gain. It also raises a question about
the practicality for those people who started late or had to take a break during their schooling.
This is more true if the student has completed some kind of qualification such as a preparatory
test and gained some qualification.
Bono and Galindo-Rueda (2006) found results that supported the Easter Rule. However,m the
results of the study found that the Easter Rule was more true for women than for men in the UK.
3.1 Econometric Theory
We approach the analysis by trying to understand the problem by applying a treatment effect , or
the causal effects of “yes or no” or “binary differences. OLS estimates on their own present very
confounding results, results that are way off the base. Hence, a probit model would be a better
solution. According to (Harmon, et al., 2003), a probit model was found to have generated better
results than Ordinary Least Squares, since OLS estimate often give linear estimations while in
reality, linear and isolated relationships are rare.

As identified earlier, education is an Instrumental Variable that determines earning. However, it
cannot be the only factor. As mentioned earlier, there are other institutions that play a role in the
determination of earnings. These covariates could be some of the conditional variables or
variables that act as catalysts in increasing the earnings of an individual Health is an example of
such a covariate. It is difficult to isolate the impact of the dependent variable from such co-
variates and it is not possible to conduct an experiment to understand the effect of education on
the earnings. Hence, a Regression Discontinuity Design (RDD) model is a good option to isolate
the effects of an additional year of education on earnings.
An RDD helps understand the effect of a treatment on a population. The causal effect of a ‘yes or
no’ variable can be understood using RDD. It helps compare the results between those who
received a certain “treatment” and those who did not receive the same treatment (or in this case,
the application of the RoSLA mandate).
The most common metric of the treatment effect is the estimatioon of the “average effect of
treatment”. The average effect for a localized or specified cohort among a larger population is
called a local average treatment effect (LATE). (Gelman & Imbens, 2014.)
Two assumptions are generally made while estimating the WALD estimator. It is assumed that
the impact of the Independent variable or the treatment (in this case the increase in minimum
SLA) is jointly distributed among various cohorts and that the impact is monotonic. However,
the impact of the treatment (RoSLA) is not smooth or monotonic. This implies that the impact of
the policy change may have encouraged all students in school for another year. In reality, this
cannot be true. Some students, who would have otherwise dropped out, may have been
encouraged to stay in school while some others who may have given up. As it is clear, the impact
of RoSLA was not consistent for every student. Hence, the RDD proposed in this analysis is a
Fuzzy Regression Discontinuity Design. (Gelman & Imbens, 2014.)(Imbens & Lemieux, 2008)
The Wald estimator consistently estimates LATE or the average effect as written formally as
E [Y1i − Y0i|W1i > W0i]

It is important to note that all the values estimated by Wald Estimators are expected values. They
can only define the likelihood of increased or decreased earnings and not reflect the actual
estimated earnings. (Gelman & Imbens, 2014.) (Imbens & Lemieux, 2008)
In general, the Average Treatment Effect is the most common measure used. The idea is that a
comparision between those just below the threshold date of birth and those just above the
threshold date of birth will help understand the effects of policy reform better. The Wald
Estimator is a predictor of a smooth curve. However, when the curve is not smooth there is an
indication of a cut off. This cut off indicates that there is a causality between the treatment or
RoSLA and the earnings. (Gelman & Imbens, 2014.) (Imbens & Lemieux, 2008)
This predictor may itself be associated with the potential outcomes, but this association is
assumed to be smooth, and so any discontinuity of the conditional distribution (or of a feature of
this conditional distribution such as the conditional expectation) of the outcome as a function of
this covariate at the cutoff value is interpreted as evidence of a causal effect of the treatment.
(Gelman & Imbens, 2014.) (Imbens & Lemieux, 2008)
3.2 Econometric Analysis
The data was taken from the British Household Survey Panel. Observations for this “Date of Birth Year”
or the running variable were taken from this panel. The variable “rosla” was created to encode the Date
of Birth in Binary terms.
The equation taken is as follows:
tf = {lim E x↓c (Y│X = x) - lim E x ↑c (Y│X = x) } / lim E x↓c (D│X = x) - lim E x ↑c (D│X = x)
where
Where
Y = actual earnings
X = variable date-of-birth as x takes the value of dob
c= RoSLA threshold or the cut off date of birth which defines the cohort

D is the years’ of schooling
The earnings estimates were taken from the pooled data of the Labour Force Survey. Hourly wages were
taken into consideration and the lo fog hourly wages was used as a variable. In order to understand the
effect on real wages and not just nominal wages, the The British Household Panel survey was used by
The Second Reform or the RoSLA Act is assumed to started to have an impact on students who entered
school from 1958 onwards.
The outcome variable or the dependent variable is taken as the log of the hourly wages. The RD
command was executed in order to gain the WALD estimators.
Given below are the WALD estimates of the “log of Hourly wages” at various bandwidths.
lhw Coef. Std. Err.z P>z [95% Conf. Interval]
lwald .0290028 .0294992 0.98 0.326 -.0288146 .0868202
lwald200 .0358885 .0509679 0.70 0.481 -.0640069 .1357838
lwald300 .0240047 .0370004 0.65 0.516 -.0485148 .0965242
lwald400 .0226849 .0304755 0.74 0.457 -.037046 .0824158
lwald500 .0389304 .0267853 1.45 0.146 -.0135679 .0914287
lwald600 .0297792 .0241037 1.24 0.217 -.0174632 .0770217
Wald Estimates: Log of Hourly Wages
As seen above the Wald estimates are positive, implying that the there is a positive relationship
between the policy treatment and hourly wages in Britain.
.

edage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwald | .6611186 .0939538 7.04 0.000 .4769726 .8452647
lwald200 | .8931519 .1664694 5.37 0.000 .5668779 1.219426
lwald300 | .8136544 .119519 6.81 0.000 .5794015 1.047907
lwald400 | .7849923 .0998491 7.86 0.000 .5892916 .9806929
lwald500 | .7325889 .0876089 8.36 0.000 .5608786 .9042993
lwald600 | .6421133 .0788039 8.15 0.000 .4876605 .7965661
Wald Estimates: School Leaving Age
As the table above shows, there is a positive relationship between the policy treatment and
School Leaving Age, implying that more people stayed in school sue to the RoSLA policy.
. The Wald Estimator for the two variables put together are given as below.
lhw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
numer | .0290028 .0294878 0.98 0.325 -.0287922 .0867978
denom | .5060028 .1284389 3.94 0.000 .2542672 .7577384
lwald | .0573175 .0527199 1.09 0.277 -.0460117 .1606466
numer200 | .0358885 .0509386 0.70 0.481 -.0639494 .1357264
denom200 | .5879629 .2311252 2.54 0.011 .1349659 1.04096
lwald200 | .0610387 .0784556 0.78 0.437 -.0927315 .2148089

numer300 | .0240047 .036986 0.65 0.516 -.0484866 .096496
denom300 | .6439495 .1648967 3.91 0.000 .3207579 .967141
lwald300 | .0372773 .0536113 0.70 0.487 -.0677989 .1423535
numer400 | .0226849 .0304669 0.74 0.457 -.0370291 .0823989
denom400 | .6351497 .1374297 4.62 0.000 .3657924 .9045069
lwald400 | .0357158 .04492 0.80 0.427 -.0523257 .1237574
numer500 | .0389304 .0267793 1.45 0.146 -.0135562 .0914169
denom500 | .6676602 .120514 5.54 0.000 .4314572 .9038633
lwald500 | .0583087 .0364533 1.60 0.110 -.0131384 .1297557
numer600 | .0300065 .024101 1.25 0.213 -.0172306 .0772435
denom600 | .5990884 .1076989 5.56 0.000 .3880024 .8101744
lwald600 | .0500869 .0369814 1.35 0.176 -.0223953 .122569
Wald Estimates: Combined
The WALD estimators are positive even for those who were born many years later than the
RoSLA legislation. This implies that there is a causal relationship between RoSLA and the
average earnings in Britain.
To check for the robustness of the regression, a simple local linear regression was conducted and
the R-square, although weak was positive
Linear regression Number of obs = 257,306

F(2, 257303) = 20924.71
Prob > F = 0.0000
R-squared = 0.2022
Root MSE = 6.2531
------------------------------------------------------------------------------
| Robust
realhw | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
MSLA16 | -1.5028 .0253502 -59.28 0.000 -1.552485 -1.453114
edage | 1.297617 .0063523 204.27 0.000 1.285166 1.310067
_cons | -8.801205 .1037108 -84.86 0.000 -9.004475 -8.597934
Robustness Check : Simple Linear Regression
.
.
4. Conclusion
There is causal relationship between spending an “additional year in school” and earnings in
Britain. However, this relationship wanes and waxes as the Year of Birth gets further and further
away from the base or the year 1958. This implies that there may be more variables within the
economy that may be affecting the earnings. The qualifications of the participants were not
considered in these tests. There is room to improve the testing for more factors such as family
income, educational background and more. Moreover, this analysis only contains the effects the