Problem Set #7

Problem One.(This question was written by Jeffrey Wooldridge.) For this question, please write your STATA codes in a .do file, and upload your .do file along with your problem set. Use the data set PNTSPRD from Canvas. This dataset contains scores from 553 college basketball games, as well as the Las Vegas point spread. The point spread is a number used in gambling. When people bet on a team, there is often a clear favorite. To make the betting fair, the spreadis the amount of points that the favorite has to win by, for the bet to pay off. For example, if the spread is 10, then the favorite has to win by 10 points to win the bet.

1. Estimate a linear probability model of favwin on spread. Interpret the constant and the coefficient. (Note: favwin is the probability that the favorite wins the game, not that they win the bet or cover the spread. )

1. Is the coefficient on spread statistically significant?

1. What is the estimated probability that the favored team wins when spread =10?

1. Now estimate the same regression but with a probit. What is the coefficient on spread?

1. Use the margins command to find the average marginal effect of spread. Interpret the result.

1. Add the variables favhome and fav25 to the probit regression. What coefficients do you estimate for them? Are either statistically significant? [Notes: Fav25 is a dummy variable for whether the favored team is in the top 25, and favhome is a dummy variable for whether the home team is favored. This question is asking you to test the efficiency of betting markets.]

Problem Two.This problem was written by Steve Pischke (one of the authors of Mastering 'Metrics). Use Lakisha_aer.dta from Canvas. This contains data from an experiment conducted by Marianne Bertrand and Sendhil Mullainathan, who sent 4,870 fictitious resumes out to employers in response to job ads in Boston and Chicago in 2001. The resumes differ in various attributes including the skills, experience, and names of the applicants. Some of the names are distinctly white sounding and some distinctly black sounding, but the names were randomly assigned to different resumes. The researchers collecting these data were interested to learn whether black sounding names obtain fewer callbacks for interviews than white names.

1. The main outcome is call, a dummy variable for whether the resume received a call back. Regress callbackon black (a dummy variable for a candidate with a typically Black name). Report its coefficient and standard error, and interpret the coefficient.

1. Make dummy variables for high school drop out, high school graduate, some college, and college. Add these variables to your regression (omitting the category "education not reported") and also years of experience, and re-estimate. Now what do you find for the coefficient and its standard error?

Hint: You will need to generate new dummy variables from the variableeducation. This variable codes education as "0 not reported; 1 = high school dropout; 2 = high school graduate; 3 = some college; 4 = college or more." To create dummy variables, first create a variable that takes values of 0, and then replace the variable values to 1 where the dummy variable should be 1.

For example, if you want to create a dummy variable for high school dropout, you could do the following:

gen hsdropout=0

replace hsdropout=1 if education==1

1. Interpret the coefficients on high school drop out and high school. How much more likely is a high school graduate to get a callback than a drop out?

1. According to this regression, how many more years of experience would a black applicant need to have the same call back rate as a non-black applicant (for a given level of education)?