In my paper I analyzed the articles "Education, earnings, and the Canadian G.I. Bill" by Lemieux and Card, "Estimating the returns to schooling: Econometric problems" by Tobais, and "Are Returns to Schooling concentrated Among the Most? A Semiparametric Analysis of the Ability-earnings Relationships" By Griliches. I examined the different approaches used in estimating the relationship between earning, schooling, and "ability."
In "Education, earnings, and the Canadian G.I. Bill" by Lemieux and Crad, a natural experiment was created when Canada established a wide-ranging program, the Veterans Rehabilitation Act, of benefits for returning World War Two veterans in order to advance their education. A natural experiment was created because of differences in military enlistments rates and education systems between two provinces, Ontario and Quebec. In Quebec less than twenty percent of French speaking men between the ages of 18-24 served in the military and were eligible for the VRA, but the Quebec university system made no accommodations for the returning veterans. On the other hand, in Ontario more than half of the English-speaking men served in the military and the university took up an "open door policy" for any returning veteran. In Quebec a smaller fraction of French-speaking men served in the military and the strict university system made it difficult for them to enroll in universities. As a result VRA had remarkable impacts in Ontario, and virtually no effect on university attendance rates in Quebec. Lemieux and Card use data from the 1971 Census data to compare "inter-cohort" differences in education and earnings Of English-speaking from Ontario relative to French-speaking men from Quebec. The data reveals that men were better educated in Ontario, had higher employment rates, and earned 25-30 percent higher wages. By contrast, the data for Quebec showed no shifts in the number of men enrolled in universities, employment rates and wages. Therefore, the data suggests that the VRA program affected Veteran's education and consequently earnings.
The ordinary least squares method according to Lemieux and Card is:
Si=Xiï¡ + ïµi
Yi=Siï¢ + Xiï§ +ï®i
The beta coefficient represents the change in average earnings for an additional unit of schooling. The problem with this equation is the positive correlation between ïµi and ï®i, which are the unobserved components of schooling and earnings, such as "ability". Therefore it leads to a positive "ability bias" which overestimates the average return to schooling. One of the solutions to problem of the "ability bias" is to use an instrumental variable that directly effects schooling, but has no direct effect on earnings. VRA is used as the instrumental variable(Zi), because VRA has a direct effect on schooling and not on earnings. But schooling is the variable that affects earnings directly and not the VRA. In the next equation schooling (Si) is regressed on the observed vectors (Xi) and the instrumental variable (Zi). Si= Xi ïsx + Zi ïsz +ï¨i. Then the estimated Xi and Zi are regressed on earnings, Yi= Xi yx + Ziyz + Ei. This regression model shows changes in earnings due to VRA benefits. The 1971 Census data is used and results of estimates of the ordinary least squares and the ï‰V represented the return to education. To control for endogeneity, they include experience and age that account for unobservable errors. Therefore, the earnings model used is a function of education and experience. Results showed that the VRA had a strong impact on the educational attainment and earning of Ontario men. The VRA had no impact on education and earning of French-speaking men from Quebec from the same age group. The 1971 data indicate that Ontario men in this cohort acquired 0.2 to 0.4 years of additional education and earned significantly higher wages relative to what would have happened without the VRA benefits. Using the ï‰V estimate the rise in earning is 15% rate of return. The OLS gives 7% return to education for the same sample.
In the second article "Are Returns to schooling Concentrated among the Most Able", Tobias emphasizes the use of the Ability variable to estimate the average wage premium of college graduates compared to non-college gradates. Tobias says "According to previous measures, Ability is strongly correlated with the quantity of schooling, therefore, not accounting for Ability in the regression equation, will have a positive effect on wages." In this paper data from the NLSY in 1979 is used. Test scores from the Armed Service Aptitude Battery are used to examine the role of Ability in explaining the college wage premium. The data is separated into people with a college education, and people without. Then a regression equation is used with the Ability variable entered into the equation. The college wage premium would be the mean of the difference between "college" and "non-college" log wages and this premium is monitored over the Ability support.
The ordinary least square model according to Tobias is:
Y1=Xï¢1 +m1 (A) +ï…1
Y0=Xï¢1+m0 (A) +ï…0
This model is constructed in order to find whether a linear relationship between Ability and the log of earnings exists. But findings show that no linear relationship between Ability and log wages exist and the relationship varies across college states. Yet Tobias ran a quadratic equation of ability for college and non-college graduates. The results show that the coefficient on the quadratic ability variable in the no-college state is always negative and is statistically significant at the 1% level in ten to eleven years. In the college state the coefficient on the quadratic variable is positive in nine to eleven years and statistically significant at the 10% level. When the results are graphed, the results show that returns to education have been concentrated among the most able, and the most able are continually being compensated for their ability in the college state, while they are not compensated in the non-college state. In turn this is interpreted, as people with a college degree are more able, and thus have the higher returns to the log of wages. A linear semi parametric estimate of log of earnings was used, another approach to confirm his findings. This model was limited to an ability support which was "interior" to both college and non college states, which also suggested that returns to schooling is concentrated among the most able.
In the third article," Estimating the returns to schooling: Some Econometric Problems", Griliches incorporates the Ability measure (A) in the equation, Y=ï¡ + ï¢S + ï§A +ï, which has been ignored in Liuemx and Crad's study. Therefore, Ebys= ï¢ + ï§cov (AS)/var S, this leads to an upward bias on the coefficient of S. Griliches uses test scores and IQ as measures of Ability in the Equation to measure the magnitude of the ability bias. Griliches says, "The results showed that the overall contribution of ability as measured by test scores to the explanation of the variance of individual expected earnings is quite small, around 0.01." He tries to optimize his model by adding ability and observable variables that effect ability such as family background, level of schooling, father earnings in the original equation, to reduce the correlation between ï and schooling. But the problem is the more background variables he added to the equation the smaller the schooling coefficient would be, until the schooling coefficient goes to zero, making the bias worse. Consequently, he concluded that there is no important reason to expect that the coefficient of ability in the earnings function to be positive and he believed that the ability bias turns out to be negative or zero. Even when the problem is treated "asymmetrically" and direct measures of ability are included in the earnings function, it indicates a relatively small contribution of ability to the expected actual earnings. The upward bias is about 0.01. And when schooling was treated "symmetrically" with ability measures, by allowing the ability measure to be subject to errors of measurement and to correlate to the disturbance in the earnings function, the net bias was zero or negative.
In the first study liuemx and Card totally ignored the ability variable, and used a natural experiment to determine the return to education, and they concluded that an additional year of schooling leads to an increase of about seven to fifteen percent in wages. But the study by Griliches states that there is no need to add the ability measure, because it underestimates the ï¢ coefficient of schooling. Under this assumption Liuemx and Card's estimates would be accurate. Since, Girliches states "The ability measure does not have an upward bias on returns to schooling." In his model he adds variables that are correlated with ability, such as family background. But the problem is ability varies cross individuals, therefore a formalization to account for ability is hard to obtain. The author even says, "Studies done by twins, with same genetic endowment show difference in ability." Conversely, I am convinced with Tobias's interpretation of the correlation between ability and the log of earning. Tobias illustrates a positive return to earnings for people with higher education and a negative effect for people with low levels of education.
Tobias's analysis of the effect of ability is more the extent to which an individual can benefit form extended education. It shows that the higher levels of ability, on average people receive higher returns from longer education, than the individual with lesser ability. Tobias captures the relationship between ability and the log of earning as a quadratic relationship to allow more flexibility between the dependent and in the independent variables, because the slope is not forced to be constant. On the same lines, I think a quadratic relationship between schooling and average wages better capture the data, because the slope of the equation would be a function of schooling, thus is more flexible. This curve would start steep and then flattens out. To be precise, this curve would show that at low levels of schooling (high school), and additional year of schooling, has greater returns on wages, than higher levels of schooling. Because the model is quadratic, for low levels of education the slope is steep, the returns are higher. But at the flat part of the curve where individuals have high levels of education, returns still increase but at a decreasing rate, and eventually reaches zero.
In conclusion, there are different views of ability among different economists; some interpret ability as IQ, motivation, or energy that is correlated with schooling. As a result ability drives people to get more schooling and earn more. Obviously, better educated people receive higher wages on average, and this is proved by the four authors, Lieumx and Card, Griliches and Tobias. They gave evidence that an additional unit of schooling leads to a seven to fifteen percent increase in wages. The problem is that data does not allow separating the effect of ability on earnings in a regression model. So is the wage increase a reflection of both extra schooling and innate abilities of individuals? The correlation among schooling, earning and ability remains controversial.
Work cited
Thomas Lemieux and David Crad(2001) "Education, Earnings, and the 'Canadian G.I Bill" Canadian Journal of Economics.
Justin L. Tobias "Are Returns to Schooling concentrated Among the Most? A Semi parametric Analysis of the Ability-earnings Relationships."journal of political economy.
Zevi Griliches (1997) Estimating the Returns to Schooling: Some Econometric Problems. (Econometrica, Vol. 45, No. 1)1-22
