Returns to Education: An approach.
This essay shows the estimates of the rates of return to education for a sample of working-age men using the basic Mincerian equation while controlling the likely endogeneity of education. The results show a 39.2% difference between the estimates of returns to education of the ordinary least square regression and the instrumental variables regression. The instrument and instrumented variable respectively are rosla and anyqual.
There is a positive correlation between education and earnings. ‘The universality of this positive association between education and earnings is one of the most striking findings of modern social science’ (Blaug, 1972). Since the work of Becker (1964) and Mincer (1974), numerous contributions to the field of the economics of education have shown, in different countries and time periods, that an individual’s academic qualifications play a vital role in ascertaining their earnings. For instance, Psacharopoulos (1985) calculated the returns for sixty-one countries, grouping them by their level of development. He found that returns to any level of education were highest in the least developed countries and lowest in the advanced countries of the west.
Indeed, there is much literature regarding the estimation of education’s rate of return. The empirical tool used in most of this research is the traditional Mincerian earnings function proposed by Mincer (1974). This function is a semi-logarithmic function that shows that an individual’s earnings vary linearly with the time dedicated to education and in a quadratic manner with experience.
This study aims to estimate returns to education that is consistent for a sample of working-age men in England, taking into account the potential endogeneity of education and correcting for the possible bias arising using the instrumental variables method.
DATA DESCRPITION AND MODEL SPECIFICATION
All results computed in this article are based on a ten per cent (that is, fifty per cent of twenty per cent) random sample of working-age men in England during the period 1996 to 2006 taken from the UK Quarterly Labour Force Survey (QLFS).
In order to carry out an analysis of returns to education, the Mincerian function relating the logarithm of wages to education, age (used as a proxy for experience) and its square is employed. Pereira and Silva (2004) suggest that for a better perception of the direct and indirect effects of education on wages we use a simple specification of the Mincer equation and only dummy variables indicating the individuals’ region of residence. Thus, the final model specification is:
LogWage= β0 + β1 anyqual + β2 age + β3 age_sq + β4 married + β5 cohab + β6 lim-dis + β7 nonwhite + β8 london + β9 se + u
The log of real hourly wages is represented by . is a binary variable with a value of 1 if the respondent has any formal education, and zero for any other situation. is the age of the respondent (a proxy for experience) while captures the concavity of the age-earnings profile. , and are dummies for being married, cohabiting or disabled respectively. Also, is a dummy for being nonwhite while and are equal to one if the respondent lives in London or the rest of the Southeast Region respectively. The summary statistics for key variables are available in the Appendix.
ORDINARY LEAST SQUARE ESTIMATES
The regression results (as shown in Appendix 1) using the ordinary least square (OLS) method show that it can be predicted that a male worker with any formal education earns 21.2% more in real hourly wages than a male with no formal education, ceteris paribus. Also, as expected, age and its square have positive and negative coefficients respectively – additional experience time units lead to higher earnings of 4.1%. However, each extra year of experience has a lower effect on earnings than the previous year, ceteris paribus. Furthermore, being married will lead to a predicted 14.2% increase in real hourly while a decrease of 4.7% is predicted for being non-white, ceteris paribus. In addition, those who are disabled will have a 12.9% decrease in earnings, ceteris paribus. Finally, living in London, elsewhere in South East England, and cohabiting yields an increase in a real hourly wage of 20.4%, 14.01% and 7.6% respectively, ceteris paribus. All estimates are predicted at a 5% significant level.
The p-values of the control variables show that they are statistically significant (individually) and from the p-value of the F-stats, they are also jointly significant. The goodness-of-fit (R2) of 0.1185 shows that only 11.8% of the variation in the dependent variable is explained by the model. This implies that the regression line is not well fitted to the data.
From the diagnostic tests (all results at the 5% significant level), the model is well specified and has no omitted variable (but the Ramsey’s test has low power). The skewness/kurtosis tests show that the residual is not normally distributed. Moreover, there is evidence of heteroskedasticity in the model. This means that even though the estimates are unbiased and consistent, the standard errors are biased and thus the t and F statistics are invalid. Consequently, OLS is no longer the best linear unbiased estimator in the class of linear estimators.
INSTRUMENTAL VARIABLES REGRESSION MODEL and RESULTS
The instrumental variables (IV) regression is a method for obtaining a consistent estimator of the unknown coefficients of the population regression function when the control variable is correlated with the error term. Specifically, the IV regression partly replaces a defective explanatory variable with one that is not correlated with the error term. More importantly, the IV estimator is unbiased and consistent but it is less efficient compared to the OLS estimator. A valid instrument must be correlated with the regressor and uncorrelated with the error term.
For this study, the regressor, is correlated with the error term and thus, the need for an IV regression. The viable instruments are rosla (Raising of School leaving Age) which increased the minimum school leaving age from 15 to 16 in the UK for people born after September 1957 and to a lesser extent, date of birth month (dobm).
According to Leigh and Ryan (2005), changes in school leaving laws is a valid instrument if increases in compulsory schooling boost schooling attendance, and if these increases are uncorrelated with the ability distribution of residents in that state. Harmon and Walker (1995), found a 15% rate of return to schooling using increases in compulsory school attendance laws. Oreopoulos (2003) used changes in school leaving laws in states/provinces in Britain, Canada and the USA. His estimates show that an additional year of schooling boosts earnings by 16%, 8% and 13% in the three countries respectively.
The use of an individual’s month of birth as an instrument was first employed by Angrist and Krueger (1991) who concluded that the rate of return to schooling in the US was 9%. The same methodology was applied by Webbink and Van Wassenberg (2004) who found a rate of return to schooling of 8% in the Netherlands. Del Bono and Galindo-Rueda (2004) use variation in the way that month of birth interacts with the school leaving age to show that increased schooling boosts the probability that an individual will be employed.
After using the rosla instrument in my IV regression (as shown in the Appendix), the F-stat of the first stage regression gives a value of 90.40 which is greater than 10. This value is consistent with the rule of thumb which says that for the case of a single endogenous variable, a first stage F-stat greater than 10 indicates a strong instrument. Moreover, the over-identifying restrictions test (at 5% significant level) with a p-value of 0.092 shows that all instruments are exogenous. Consequently, the rosla instrument is valid.
The estimates for the instrumented variable anyqual under the IV regression model show that there is a 60.5% increase in real hourly wage for those with any formal qualification. If a male employee is married, cohabiting or living in London the model predicts a 12.3%, 6.9% and 20.3% increase in real hourly wage, respectively. In addition, there is a predicted 12.5% increase in real hourly wage for those who live anywhere in the South East region of England. As expected, an additional age time leads to higher earnings of 3.8% but each extra year of aging or experience has a lower effect on earnings than the previous year as shown in the agesq coefficient. There is a predicted 12.6% decrease in real hourly wage for a male employer who is disabled and of 5.7% for a male employer who is non-white, respectively. All estimates were examined at ceteris paribus and a 5% significant level. Estimates are also statistically significant at a 5% level.
From the Hausman test (in the Appendix), we do not reject the H0 that differences between the IV and OLS estimates are not systematic. This discards the concern of the use of weak instruments in our IV estimation. It simply indicates that differences in coefficients are not systematic and hence we can infer the use of a valid instrument.
From the IV regression estimates, education has a significant positive effect on wages and thus policies should be directed at improving the quality of education. Also, because a limiting disability decreases wages by up to 12%, policies should focus on alleviating the effect of such disabilities. Further, policies should be aimed at abolishing the earnings differentials between whites and non-whites. Finally, if the square of age decreases real hourly wages as a result of outdated skills among older workers, re-training these workers should be encouraged. This would help remove this negative effect.
This study has been able to derive a consistent estimator, using the instrumental variables (IV) regression model, when a control variable is correlated with the error term. OLS estimates are biased and inconsistent due to measurement error in one of the regressors.
Angrist, J.D. and Krueger, A.B. (1991). Does compulsory school attendance affect schooling and earnings?, Quarterly Journal of Economics, 106, 979-1014
Becker, G.S. (1964).Human Capital. New York: National Bureau of Economic Research
Blaug, M. (1972). ‘The correlation between education and earnings: What does it signify?’ Higher Education 1, 53–76.
Del Bono, E. and Galindo-Rueda, F. (2004). “Do a few months of compulsory schooling matter? The education and labour market impact of school leaving rules’, mimeo, Centre for Labor Economics, University of California
Harmon, C. and Walker, I. (1995). “Estimates of the Economic Return to Schooling for the United Kingdom”, American Economic Review, 85: 1278-1286
Leigh, A. and Ryan, C. (2005). “Estimating Returns to Education: Three Natural Experiment Techniques Compared” Discussion Paper 493, Centre for Economic Policy Research, Australia National University
Mincer, J. (1974). “Schooling, Experience and Earnings” Columbia UP: New York
Oreopolous, P. (2003). “Do Dropouts Drop Out Too Soon? International Evidence from Changes in School-Leaving Laws” NBER Working Paper 10155, NBER, Cambridge, MA
Psacharopoulos, G. (1985). “Returns to Education: A Further International Update and Implications,” Journal of Human Resources, 20: 583-604.
Webbink, D. and van Wassenberg, J. (2004). “Born on the first of October: Estimating the returns to education using a school entry rule”, mimeo, University of Amsterdam