Posted: November 17th, 2015

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

Economics 420 (sections 2 and 3) Professor Woodbury Fall Semester 2015 Problem Set #4 (Due: Tuesday, November 17) Directions: Following each question, type or handwrite your answers and copy/paste the Stata output (use the ‘copy as picture’ option). Staple all pages together — assignments turned in unstapled will be returned with a grade of zero. (Only stapling is acceptable — paper clips and other methods of binding are not acceptable.) Also, if we cannot discern the meaning of your work, your response will be assumed wrong. This problem set introduces you to regression with dummy variables and interaction terms, and hypotheses tests involving more than one parameter. It uses Stata file BEAUTY.dta, which contains the following variables used by Hamermesh and Biddle (American Economic Review 1994): wage hourly wage exper years of workforce experience looks physical attractiveness score ranging from 1 to 5 black =1 if black female =1 if female educ years of schooling Problem 1 (5 points total) 1.1. (1 point) Estimate the simple linear regression model: lwage = β0 + β1female + u Interpret the OLS estimates of the intercept and the slope on female. 1.2. (3 points) Now estimate the multiple linear regression model: lwage = β0 + β1female + β2educ + 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 and lwage on the Y-axis showing the regression lines for females and males. Hint: We solved a similar problem in class. Problem 2 (6 points total) Consider the following three population models for log-earnings: log(wage) = α0 + α1educ + uf (for men only) log(wage) = β0 + β1educ + um (for women only) log(wage) = γ0 + γ1educ + γ2female + γ3educ•female + ub (for both women and men) 2.1. (2 points) Write each of the four γ coefficients in terms of α0, α1, β0, and β1. That is, show how γ0 , γ1, γ2, and γ3 are related to α0, α1, β0, and β1. You need to write down four equations: γ0 = …, γ1 = …, γ2 = …, and γ3 = …. (Notes: The first equation is γ0 = α0. This question is asking about the population parameters, not the OLS estimates. We did something similar to this in class.) 2.2. (3 points) Now use dataset BEAUTY.dta to estimate these three regressions and interpret all of the estimated parameters (γ0, γ1, γ2, and γ3) of the third model. Which of these coefficients 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 in Stata: reg lwage educ if female==0 reg lwage educ if female==1 To estimate the third model, first generate a variable equal to the product of variables educ and female (the interaction term) by typing: gen educ•female = educ*female Then estimate the regression: reg lwage educ female educ•female 2.3 (1 point) Based on your estimates in 2.2, draw a graph with educ on the X-axis and lwage on the 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 physical attractiveness, 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 = β0 + β1belowaverage + β2aboveaverage + u Interpret the OLS estimates of β0, β1, and β2. (Hint: To estimate the model for women, type in Stata: reg lwage belowaverage aboveaverage if female==1 Note that you cannot include all the dummies in the regression — in this case we excluded average.) 2 Now use the regression results to test the following hypotheses. To get full credit write down the null hypothesis, the appropriate test statistic, the p-value of that statistic , whether you reject the null, and why. Include your Stata output. 3.3. (2 points) Test the hypothesis that women with below average looks earn the same logwage as 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-wage as 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. 3