#### Question Details

EC 420, Spring 2016

Problem Set 4

Due Thursday, March 24th in class

NOTE: ?For questions using Stata, please type your answers into a word processing document (using MS Word or something similar).? Insert the relevant part of your Stata log file into your document, and clearly explain how your Stata output answers the question.?

Estimate the following three regressions using the NLSY dataset:

1. Interpret all of the estimated coefficients (slopes and intercept) for the third model, being as specific as possible.? Which of these coefficients are statistically significant, at a significance level of 0.05?? (Note: you will hav1.e to generate lwage = log(wage) and also generate the interaction variable.) (2 points)

1. Show how the coefficients in the third model can be used to exactly recover the coefficients in the first two models. ?For example, how are the ? coefficients related to the ? and ? coefficients? (Note: to get the coefficients in the first two models, type reg lwage school if male= and reg lwage school if male=) (2 points).?

1. Draw a picture to scale (by hand) based on the estimates for the third model, with log(wage) on the y-axis and school on the x-axis. (1 point)

1. Previous studies have found that a year of education increases average wages by approximately 8 percent.? Using the second regression model, test the hypothesis that the coefficient on school for men differs from 0.08.? Perform the test using the regression output and issuing a Stata command (hint:? type help test if you don?t remember how to do this?not ttest but test).? Do you reject the hypothesis?? Why or why not?? Choose a significance level of 0.05. (2 points)

1. Test the same hypothesis for women. ?Do you reject the hypothesis?? Why or why not?? Choose a significance level of 0.05. (2 points)

This problem is intended to examine the relationship between education and wages.

1. Run a regression of the log of wages on education (type reg lwage school).? Draw a picture that represents the regression line (again, just draw your graphs by hand). (2 points)

1. Create 3 dummy variables that represent education categories.? The first equals 1 if education is less than 12 years and zero otherwise (you could call it dropout and code it ?gen dropout = (school<12)?, the next equals 1 if education is exactly 12 years and zero otherwise (you could name it hsgrad and type ?gen hsgrad = (school=)?), and the last equals 1 if education is greater than 12 (you could call it college).? Run a regression of lwage on these dummy variables, remembering to exclude one (it would probably be easiest if you excluded dropout).? Add the estimated regression line to the same picture from part (a).? (2 points)

1. Calculate the mean of log wages for individuals in these 3 education categories (for example, ?sum lwage if dropout==1?).? How do these compare to the predicted values from the regression that you ran in part (b)? (2 points)

EC 420, Spring 2016

Problem Set 4

Due Thursday, March 24th in class

(using MS Word or something similar). Insert the relevant part of your Stata log file into your

1. Estimate the following three regressions using the NLSY dataset:

log(wage) 0 1 school u

(for women)

log(wage) 0 1 school u

(for men)

log(wage) 0 1 school 2 male 3 ( school male) u

(for both)

a. Interpret all of the estimated coefficients (slopes and intercept) for the third

model, being as specific as possible. Which of these coefficients are statistically

significant, at a significance level of 0.05? (Note: you will have to generate

lwage = log(wage) and also generate the interaction variable.) (2 points)

b. Show how the coefficients in the third model can be used to exactly recover the

coefficients in the first two models. For example, how are the ? coefficients

related to the ? and ? coefficients? (Note: to get the coefficients in the first two

models, type reg lwage school if male==1 and reg lwage school if male==0) (2

points).

c. Draw a picture to scale (by hand) based on the estimates for the third model, with

log(wage) on the y-axis and school on the x-axis. (1 point)

d. Previous studies have found that a year of education increases average wages by

approximately 8 percent. Using the second regression model, test the hypothesis

that the coefficient on school for men differs from 0.08. Perform the test using

the regression output and issuing a Stata command (hint: type help test if you

don?t remember how to do this?not ttest but test). Do you reject the hypothesis?

Why or why not? Choose a significance level of 0.05. (2 points)

e. Test the same hypothesis for women. Do you reject the hypothesis? Why or why

not? Choose a significance level of 0.05. (2 points)

2. This problem is intended to examine the relationship between education and wages.

a. Run a regression of the log of wages on education (type reg lwage school). Draw

a picture that represents the regression line (again, just draw your graphs by

hand). (2 points)

b. Create 3 dummy variables that represent education categories. The first equals 1

if education is less than 12 years and zero otherwise (you could call it dropout and

code it ?gen dropout = (school&lt;12)?, the next equals 1 if education is exactly 12

years and zero otherwise (you could name it hsgrad and type ?gen hsgrad =

(school==12)?), and the last equals 1 if education is greater than 12 (you could

call it college). Run a regression of lwage on these dummy variables,

remembering to exclude one (it would probably be easiest if you excluded

dropout). Add the estimated regression line to the same picture from part (a). (2

points)

c. Calculate the mean of log wages for individuals in these 3 education categories

(for example, ?sum lwage if dropout==1?). How do these compare to the

predicted values from the regression that you ran in part (b)? (2 points)

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