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PS5--Answers - Econ 141 Problem Set 5Answers Fall 2007 Due...

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Econ 141: Problem Set 5–Answers Fall 2007 Due Monday, November 5th in Class 1. (Requires SAS) This question uses data from “wage1.sas7bdat”. In that dataset, lwage is the natural log of hourly wage, exper is experience in years, and female is equal to 1 if female and 0 if male. You do not need to turn in a SAS output or editor unless you think there are problems and you want feedback. i. Run the regression of log hourly wage on experience (and an intercept) for men and women separately. Report your regression equations with standard errors. SAS code: proc reg data=wage1; model lwage=exper; where female=1; run; proc reg data=wage1; model lwage=exper; where female=0; run; Results: For women: lwage=1.40424 (0.04391)+0.00073727 (0.00206)*exper (standard errors in parentheses) For men: lwage=1.69767 (0.05242)+0.00660 (0.00237)*exper ii. Show algebraically (NOT IN SAS) how you would combine these two equations into one equation that you could run in SAS. 1
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lwage i = β f 0 + β f 1 exper i + u f i if female lwage i = β m 0 + β m 1 exper i + u m i if male Let δ i equal 1 if female and 0 if male lwage i = ( β f 0 + β f 1 exper i + u f i ) δ i + ( β m 0 + β m 1 exper i + u m i )(1 - δ i ) = β m 0 + ( β f 0 - β m 0 ) δ i + β m 1 exper i + ( β f 1 - β m 1 ) exper i δ i + u m i + ( u f i - u m i ) δ i = β m 0 + ( β f 0 - β m 0 ) δ i + β m 1 exper i + ( β f 1 - β m 1 ) exper i δ i + v i where v i = u m i + ( u f i - u m i ) δ i . Note that this regression is fine as long as we think that the variance of the error term is the same for men and women. This is an assumption you might want to test in real- ity, and you would want to correct for heteroskedasticity if you reject homoskedasticity. This question does not ask you to do that however. iii. In SAS, run the single regression you derived in part (ii). Report the regres- sion equation and standard errors. Are the coefficients you get in this regression what you would expect from the algebra in part (ii)?
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