Read the box “the Return to Education and the Gender Gap” in Section 8.3.a) Consider a male with 16 years of education and 2 years of experience. Use the results from column (4) of Table 8.1 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. b) Explain why your answer to (a) does not depend on the region he is from.c) Repeat (a), assuming 10 years of experience.d) Explain why the answers to (a) and (b) are different.e) Is the difference in the answers to (a) and (b) statistically significant at the 5% level? Explain. f) Would your answers to (a) through (d) change if the person were female? Explain. g) How would you change the regression if you suspected that the effect of experience on earnings was different for men than for women? The Return to Education and the Gender Gapn addition to its intellectual pleasures, educationhas economic rewards. As the boxes in Chapters 3and 5 show, workers with more education tend toearn 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 forother determinants of earnings that might be cor-related with educational achievement, so the OLSestimator of the coefficient on education could haveomitted variable bias. Second, the functional formused in Chapter 5-a simple linear relation-impliesthat earnings change by a constant dollar amount foreach additional year of education, whereas one mightsuspect that the dollar change in earnings is actuallylarger at higher levels of education. Third, the boxin Chapter 5 ignores the sex differences in earningshighlighted in the box in Chapter 3.These limitations can be addressed by a multipleregression analysis that controls for determinants ofearnings that, if omitted, could cause omitted vari-able bias and that uses a nonlinear functional formrelating education and earnings. Table 8.1 summa-rizes regressions estimated using data on full-timeworkers, ages 30 through 64, from the Current Popu-lation Survey (the CPS data are described in Appen-dix 3.1). The dependent variable is the logarithmof hourly earnings, so another year of education isassociated with a constant percentage increase (nota dollar increase) in earnings.Table 8.1 has four salient results. First, the omissionof sex in regression (1) does not result in substantialomitted variable bias: Even though sex enters regres-sion (2) significantly and with a large coefficient, sexand years of education are nearly uncorrelated: Onaverage, men and women have nearly the same lev-els of education. Second, the returns to education areeconomically and statistically significantly differentfor men and women: In regression (3), the t-statistictesting the hypothesis that they are the same is 3.42(= 0.006/0.0018). As the tight confidence intervalsattest, the return to education is precisely estimatedboth for men and for women. Third, regression (4)controls for the region of the country in which theindividual lives, thereby addressing potential omittedvariable bias that might arise if years of educationdiffer systematically by region. Controlling for regionmakes a small difference to the estimated coefficientson the education terms relative to those reported inregression (3). Fourth, regression (4) controls for thepotential experience of the worker, as measured byyears since completion of schooling. The estimatedcoefficients imply a declining marginal value for eachyear of potential experience.200The estimated economic return to education inregression (4) is 11.14% for each year of educationfor men and 11.96% (= 0.1114 + 0.0082, in percent)for women. Because the regression functions formen and women have different slopes, the gendergap depends on the years of education. For 12years of education, the gender gap is estimated tobe 27.0% (= 0.0082 x 12 0.368, in percent);for 16 years of education, the gender gap is less inpercentage terms, 23.7%.These estimates of the return to education andthe gender gap still have limitations, including thepossibility of other omitted variables, notably thenative ability of the worker, and potential problemsassociated with the way variables are measured inthe CPS. Nevertheless, the estimates in Table 8.1 areconsistent with those obtained by economists whocarefully address these limitations. A survey by theeconometrician David Card (1999) of dozens ofempirical studies concludes that labor economists'best estimates of the return to education gener-ally fall between 8% and 11% and that the returndepends on the quality of the education. If you areinterested in learning more about the economicreturn to education, see Card (1999). TABLE 8.1Dependent variable: logarithm of Hourly earnings.Regressor(1)Years of educationFemaleFemale X Years of educationPotential experienceThe Return to Education and the Gender Gap: Regression Resultsfor the United States in 2015Potential experience²R²a. Regional control variables?No95% confidence interval for return to educationCombined men & womenFor menFor women0.1056(0.0009)[0.104, 0.107]0.209(2)0.1089(0.0009)-0.252(0.005)No[0.107, 0.111]0.251(3)0.1063(0.0018)The Expected Change in Y from a Change in X₁in the Nonlinear Regression Model [Equation (8.3)]-0.342(0.026)0.0063(0.0018)No[0.104, 0.109][0.110, 0.115]0.251(4)0.1114(0.0013)The expected change in Y, AY, associated with the change in X₁, AX₁, holdingX₂,..., X constant, is the difference between the value of the population regres-sion function before and after changing X₁, holding X₂, ..., X constant. That is,the expected change in Y is the difference:ΔΥ = f(X + ΔΧ, Χ2, Xk) − f(Xí, X2, ..., X).(8.4)The estimator of this unknown population difference is the difference betweenthe predicted values for these two cases. Let (X₁, X₂, ..., X) be the predictedvalue of Y based on the estimator f of the population regression function. Thenthe predicted change in Y isAŶ = Ĵ(X₁ + AX₁, X₂, ..., Xk) - Ĵ(X₁, X₂,..., Xk). (8.5)-0.368(0.026)0.0082(0.0018)0.0147(0.0013)-0.000183(0.000024)Yes[0.109, 0.114][0.117, 0.122]The data are from the March 2016 Current Population Survey (see Appendix 3.1). The sample size is n = 47,233 obser-vations for each regression. Female is an indicator variable that equals 1 for women and 0 for men. Potential experienceequals the number of years since completion of schooling. The regional control variables included in regression (4) areMidwest, South, and West which are indicator variables denoting the region of the United States in which the workerlives (the omitted region is Northeast). Heteroskedasticity-robust standard errors are reported in parentheses belowthe estimated coefficients.0.262KEY CONCEPT8.1

Introduction: From the fourth column of Table 8.1, the regression equation is:

Answered: Read the box “the Return to Education…

6th Edition

ISBN:9781119256830

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Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P