Economics 420 (sections 2 and 3) Fall Semester 2015 Problem Set #4

QUESTION

Economics 420 (sections 2 and 3) Fall Semester 2015Problem Set #4Directions: Following each question, type or handwrite your answers and copy/paste the Stataoutput (use the ‘copy as picture’ option). Staple all pages together — assignments turned inunstapled will be returned with a grade of zero. (Only stapling is acceptable — paper clips andother methods of binding are not acceptable.) Also, if we cannot discern the meaning of yourwork, your response will be assumed wrong.This problem set introduces you to regression with dummy variables and interaction terms, andhypotheses tests involving more than one parameter. It uses Stata file BEAUTY.dta, whichcontains the following variables used by Hamermesh and Biddle (American Economic Review1994):wage hourly wageexper years of workforce experiencelooks physical attractiveness score ranging from 1 to 5black =1 if blackfemale =1 if femaleeduc years of schoolingProblem 1 (5 points total)1.1. (1 point) Estimate the simple linear regression model:lwage = ?0 + ?1female + uInterpret the OLS estimates of the intercept and the slope on female.1.2. (3 points) Now estimate the multiple linear regression model:lwage = ?0 + ?1female + ?2educ + u.What are the OLS estimates of the slope on female and educ and how do you interpret them?(You do not need to comment on the intercept.)1.3 (1 point) Based on your estimates in part 1.2, draw a graph with educ on the X-axis andlwage on the Y-axis showing the regression lines for females and males. Hint: We solved a similarproblem in class.Problem 2 (6 points total)Consider the following three population models for log-earnings:log(wage) = ?0 + ?1educ + uf (for men only)log(wage) = ?0 + ?1educ + um (for women only)log(wage) = ?0 + ?1educ + ?2female + ?3educ•female + ub (for both women and men)2.1. (2 points) Write each of the four ? coefficients in terms of ?0, ?1, ?0, and ?1. That is, showhow ?0 , ?1, ?2, and ?3 are related to ?0, ?1, ?0, and ?1. You need to write down four equations:?0 = …, ?1 = …, ?2 = …, and ?3 = …. (Notes: The first equation is ?0 = ?0. This question is askingabout the population parameters, not the OLS estimates. We did something similar to this inclass.)2.2. (3 points) Now use dataset BEAUTY.dta to estimate these three regressions and interpretall of the estimated parameters (?0, ?1, ?2, and ?3) of the third model. Which of thesecoefficients are statistically significant at a significance level of 0.01?Hints: You will need to generate the log-wage variable. To estimate the first two models, type inStata:reg lwage educ if female==0reg lwage educ if male==1To estimate the third model, first generate a variable equal to the product of variables educ andfemale (the interaction term) by typing:gen educ•female = educ*femaleThen estimate the regression:reg lwage educ educ•female2.3 (1 point) Based on your estimates in 2.2, draw a graph with educ on the X-axis and lwage onthe Y-axis showing the regression lines for males and females.Problem 3 (9 points in total)The variable looks from dataset BEAUTY.dta contains each persons’s score on their physicalattractiveness, as ranked by an interviewer. Attractiveness was coded in five categories_1=homely, 2=quite plain, 3=average, 4=good looking, and 5=strikingly beautiful/handsome.3.1. Create three dummy variables that represent a person’s looks as follows: the first variable(belowaverage) equals 1 if looks is less than 3, 0 otherwise; the second (average) equals 1 if looks =3, 0 otherwise; and the third (aboveaverage) equals 1 if looks is greater than 3, 0 otherwise. Note:no submission for this part is required.Hint: All you need to do for this part is type in Stata:gen belowaverage = (looks<3)gen average = (looks==3)gen aboveaverage =(looks>3)3.2. (3 points) Now estimate the following model for log-earnings (lwage) for women:lwage = ?0 + ?1belowaverage + ?2aboveaverage + uInterpret the OLS estimates of ?0, ?1, and ?2. (Hint: To estimate the model for women, type inStata:reg lwage belowaverage aboveaverage if female==1Note that you cannot include all the dummies in the regression — in this case we excludedaverage.)2Now use the regression results to test the following hypotheses. To get full credit write downthe null hypothesis, the t-statistic, the p-value, whether you reject the null, and why. Include yourStata output.3.3. (2 points) Test the hypothesis that women with below average looks earn the same logwageas women with average looks. Use a significance level of 10%.3.4. (2 points) Test the hypothesis that women with above average looks earn the same log-wageas women with below average looks. Use a significance level of 5%.3.5. (2 points) Test the hypothesis that how a woman looks does not affect her log-earnings.

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