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? ←(1) Wh M Inbox M Kotak | | Assign|||сPROBLHW7 KEconoA1 SoluWritterJames H. Stock, Mark W. Watson - Introduction to Econometrics [3rd ed. upd... 32 / 59edisciplinas.usp.br/pluginfile.php/4842747/mod_resource/content/1/Stock%20and%20Watson%20-%20Chapter%208.pdf90%3. Non JP Nobel AM HowdyThe Return to Education and the Gender Gapn addition to its intellectual pleasures, educationhas economic rewards. As the boxes in Chapters3 and 5 show, workers with more education tend toearn more than their counterparts with less educa-tion. The analysis in those boxes was incomplete,however, for at least three reasons. First, it failedto control for other determinants of earnings thatmight be correlated with educational achievement,so the OLS estimator of the coefficient on educa-tion could have omitted variable bias. Second, thefunctional form used in Chapter 5— a simple linearrelation-implies that earnings change by a constantdollar amount for each additional year of education,whereas one might suspect that the dollar change inearnings is actually larger at higher levels of educa-tion. Third, the box in Chapter 5 ignores the gen-der differences in earnings highlighted in the box inChapter 3.All these limitations can be addressed by amultiple regression analysis that controls fordeterminants of earnings that, if omitted, couldcause omitted variable bias and that uses a nonlin-ear functional form relating education and earn-ings. Table 8.1 summarizes regressions estimatedusing data on full-time workers, ages 30 through64, from the Current Population Survey (the CPSdata are described in Appendix 3.1). The depen-dent variable is the logarithm of hourly earnings,so another year of education is associated with aconstant percentage increase (not dollar increase)in earnings.Table 8.1 has four salient results. First, the omis-sion of gender in regression (1) does not result in sub-stantial omitted variable bias: Even though genderenters regression (2) significantly and with a largeParaph ATM Filescoefficient, gender and years of education are uncor-related; that is, on average men and women havenearly the same levels of education. Second, thereturns to education are economically and statisti-cally significantly different for men and women: Inregression (3), the t-statistic testing the hypothesisthat they are the same is 4.55 (= 0.008/0.0018).Third, regression (4) controls for the region ofthe country in which the individual lives, therebyaddressing potential omitted variable bias thatmight arise if years of education differ systematicallyby region. Controlling for region makes a small dif-ference to the estimated coefficients on the educa-tion terms, relative to those reported in regression(3). Fourth, regression (4) controls for the potentialexperience of the worker, as measured by yearssince completion of schooling. The estimated coeffi-cients imply a declining marginal value for each yearof potential experience.The estimated economic return to education inregression (4) is 11.26% for each year of educa-tion for men and 12.25% (= 0.1126 + 0.0099, inpercent) for women. Because the regression func-tions for men and women have different slopes, thegender gap depends on the years of education. For12 years of education, the gender gap is estimatedto be 27.3% (= 0.0099 × 12 -0.392, in percent);for 16 years of education, the gender gap is less inpercentage terms, 23.4%.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 8.1continued on next pageCAggieJar XHome +CUpdate: r~~HF∞AutoSave OFFHome Insert Draw Design LayoutA APastePage 1 of 1Calibri (Bo... V 12B92I0 wordsUV14Vab x₂x²221ATABLE 8.1Female✓ ✓ AReferencesAa ✓RegressorYears of educationMidwestSouthWest11Potential experienceInterceptFemale x Years of educationPotential experience²Dependent variable: logarithm of Hourly Earnings.English (Indonesia)2VMailings Review3EEE====4(1)0.1082**(0.0009)1.515**(0.013)50.221Vare consistent with those obtained by economistswho carefully address these limitations. A survey bythe econometrician David Card (1999) of dozens ofempirical studies concludes that labor economists'best estimates of the return to education generally fall6(2)0.1111**(0.0009)The Return to Education and the Gender Gap: Regression Resultsfor the United States in 2012-0.251**(0.005)View1.585**(0.013)0.263307VLī8A↓V(3)0.1078**(0.0012)-0.367**(0.026)0.0081***(0.0018)(0.016)1.632**0.264Tell me910Document1(4)0.1126**(0.0012)-0.392**(0.025)0.0099***(0.0018)0.0186**(0.0012)R²The data are from the March 2013 Current Population Survey (see Appendix 3.1). The sample size is n = 50,174 observa-tions for each regression. Female is an indicator variable that equals 1 for women and 0 for men. Midwest, South, and Westare indicator variables denoting the region of the United States in which the worker lives: For example, Midwest equals 1 ifthe worker lives in the Midwest and equals 0 otherwise (the omitted region is Northeast). Standard errors are reported inparentheses below the estimated coefficients. Individual coefficients are statistically significant at the *5% or **1% sig-nificance level.-0.000263**(0.000024)-0.080**(0.007)-0.083**(0.007)-0.018**(0.007)1121.335**(0.024)0.276between 8% and 11%, and that the return dependson the quality of the education. If you are interestedin learning more about the economic return to edu-cation, see Card (1999).AaBbCcDdEeNormal12H13Aa BbCcDdEeNo Spacing14T15Aa BbCcDc AaBb CcDdE AaBb AaBb CcDd EeHeading 1Heading 2TitleSubtitle161718419The Expected Change on Y of a Change in X₁in the Nonlinear Regression Model (8.3)2048.1 A General Strategy for Modeling Nonlinear Regression FunctionsAY = f(X₁ + AX₁, X2, ‚ Xk) — ƒ(X₁, X2, ..., Xk).-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:21X) − f(Xí, X2, …,X).D22The estimator of this unknown population difference is the difference betweenthe predicted values for these two cases. Let ƒ(X₁, X₂, ..., X₁) 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,Focus(8.4)23(8.5)24263KEY CONCEPT8.1EStylesPane25|||IShareDictateGCommentsEditorBOD+ 130%

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

Answered: Read the box “the Return to Education…

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