Read the box “The Return to Education and the Gender Gap.”
The Return to Education and the Gender Gap Dependent variable: logarithm of Hourly Earnings. Regressor (1 ) (2) (3) (4)
Years of education 0.1035″ 0.1050″ 0.1001 ** 0.1 192M
(0.0009) (0.0009) (0.0011) (0.0012)
Female – 0.263″ – 0.432″ – 0.451 ”
(0.004) (0.024) (0.024)
Female >< Years of education 0-0121" 0-0134"
(0.0017) (0.0017)
Potential experience 0.0133″
(0.001 2)
Potential experience2 ‘ 0000207"
(0.000022)
Midwest – 0.095"
(0.006)
South – 0.092″
(0.006)
West — 0.021 ** m nn-1\ VIVIILIUI VANVIIVIIVY
(0.000022)
Midwest
– 0.095**
(0.006)
South
– 0.092**
(0.006)
West
– 0.021**
(0.007)
Intercept
1.533**
1.629**
1.697**
1.519**
(0.012)
(0.012)
(0.016)
(0.023)
0.208
0.258
0.258
0.267
The sample size is 52,970 observations for each regression. Female is an indicator variable that equals 1 for
women and 0 for men. Midwest, South, and West are indicator variables denoting the region of the United States
in which the worker lives: For example, Midwest equals 1 if the worker lives in the Midwest and equals 0
otherwise (the omitted region is Northeast). Standard errors are reported in parentheses below the estimated
coefficients. Individual coefficients are statistically significant at the *5% or **1% significance level.
Scenario A
Consider a man with 16 years of education and 2 years of experience who is from a western state. Use the results from column (4) of the table and the method in Key Concept 8.1 to estimate the
expected change in the logarithm of average hourly earnings (AHE) associated with an additional year of experience.
The expected change in the logarithm of average hourly earnings (AHE) associated with an additional year of experience is |%. (Round your response to two decimal places.) The Return to Education and the Gender Gap In addition to its intellectual pleasures, education has economic rewards. As the boxes in Chapters 3 and 5 show, workers with
more education tend to earn more than their counterparts with less education. The analysis in those boxes was incomplete,
however, for at least three reasons. First, it failed to control for other determinants of earnings that might be correlated with
educational achievement, so the OLS estimator of the coefficient on education could have omitted variable bias. Second, the
functional form used in Chapter 5—a simple linear relation—implies that earnings change by a constant dollar amount for each
additional year of education, whereas one might suspect that the dollar change in earnings is actually larger at higher levels of
education. Third, the box in Chapter 5 ignores the gender differences in earnings highlighted in the box in Chapter 3. All these limitations can be addressed by a multiple regression analysis that controls for determinants of earnings that, if
omitted, could cause omitted variable bias and that uses a nonlinear functional form relating education and earnings. The
Return to Education and the Gender Gap table summarizes regressions estimated using data on full-time workers, ages 30
through 64, from the Current Population Survey (the CPS data are described in Appendix 3.1 ). The dependent variable is the
logarithm of hourly earnings, so another year of education is associated with a constant percentage increase (not dollar
increase) in earnings. The Return to Education and the Gender Gap table has four salient results. First, the omission of gender in regression (1) does
not result in substantial omitted variable bias: Even though gender enters regression (2) significantly and with a large
coefficient, gender and years of education are uncorrelated; that is, on average men and women have nearly the same levels of
education. Second, the returns to education are economically and statistically significantly different for men and women: In
regression (3), the t—statistic testing the hypothesis that they are the same is 7.02. Third, regression (4) controls for the region of
the country in which the individual lives, thereby addressing potential omitted variable bias that might arise if years of education
differ systematically by region. Controlling for region makes a small difference to the estimated coefficients on the education
terms, relative to those reported in regression (3). Fourth, regression (4) controls for the potential experience of the worker, as
measured by years since completion of schooling. The estimated coefficients imply a declining marginal value for each year of
potential experience. The estimated economic return to education in regression (4) is 10.32% for each year of education for men and 11.66% for
women. Because the regression functions for men and women have different slopes, the gender gap depends on the years of
education. For 12 years of education, the gender gap is estimated to be 29.0%; for 16 years of education, the gender gap is
less in percentage terms, 23.7%. These estimates of the return to education and the gender gap still have limitations, including the possibility of other omitted
variables, notably the native ability of the worker, and potential problems associated with the way variables are measured in the
CPS. Nevertheless, the estimates in the Return to Education and the Gender Gap table are consistent with those obtained by
economists who carefully address these limitations. A survey by the econometrician David Card (1999) of dozens of empirical
studies concludes that labor economists’ best estimates of the return to education generally fall between 8% and 11%, and that
the return depends on the quality of the education. If you are interested in learning more about the economic retum to
education, see Card (1999). Key concept 8.1
The Expected Effect on Y of a Change in X, in the Nonlinear Regression Model
The expected change in Y, AY, associated with the change in X1, AX, , holding X2,…, Xx constant, is the difference between
the value of the population regression function before and after changing X,, holding X,,…, Xx constant. That is, the
expected change in Y is the difference:
AY = f(X1 + AX1, X2,…, XK) – f(X1, X2 ,…, XK).
The estimator of this unknown population difference is the difference between the predicted values for these two cases. Let
f(X1, X2,.., XK) be the predicted value of Y based on the estimator f of the population regression function. Then the predicted
change in Y is
A Y = f ( X , + 4 X 1 , X 2 . . . . X K ) – f ( X 1 , X 2 . . .. . XK ) .
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