Econ 4400, Elementary Econometrics

HOMEWORK 6

Econ   4400,   Elementary Econometrics

Directions: Please follow the instructions closely. Completion of this assignment re- quires the data set gpa2.dta available on Carmen. Due: All problem sets have to be turned in at the beginning of the  class.

Due Dates:

April 21, 2016

1.(20 points)Estimate the following equations and report the results in a table: (a)GPA as a function of SAT score, total hours, athlete, high school  percentile

rank, sex, race, high school size, and school size squared

(b)Add an interaction term between SAT and athlete to regression (a) (c)Add high school rank to regression (b)

(d)Estimate High school rank as a function of all of the regressors in (b)

2.(15 points)Which model do you prefer and why?(There is not necessarily a correct answer. As long as you use the criteria that we discussed in class correctly, you will get credit.)

3.(15 points)Interpret the coefficient on the interaction term between athlete and SAT.

4.(25 points)Calculate a variance inflation factor for high school rank.  What does   a high VIF indicate? Is the estimate cause for concern? (pages 259-260 in text) Report the necessary regression results.

5.(25 points)Use a new regression and a t-test to test whether sat scores differently predict gpa for men and women. Report regression results in a  table.

Table 1:  Regression Results

 (1) GPA (2) GPA (3) GPA (4) high school rank (5) GPA combined SAT score 0.00153∗∗∗ (0.0000679) 0.00158∗∗∗ (0.0000695) 0.00156∗∗∗ (0.0000695) -0.0150∗∗∗ (0.00391) 0.00158∗∗∗ (0.0000881) total hours 0.00175∗∗∗ (0.000243) 0.00174∗∗∗ (0.000242) 0.00171∗∗∗ (0.000242) -0.0231∗ (0.0136) 0.00174∗∗∗ (0.000242) =1 if athlete 0.210∗∗∗ (0.0423) 0.909∗∗∗ (0.225) 0.946∗∗∗ (0.225) 28.46∗∗ (12.67) 0.912∗∗∗ (0.227) high school percentile -0.0135∗∗∗ (0.000574) -0.0136∗∗∗ (0.000575) -0.0104∗∗∗ (0.000879) 2.413∗∗∗ (0.0323) -0.0136∗∗∗ (0.000576) =1 if female 0.148∗∗∗ 0.150∗∗∗ 0.148∗∗∗ -1.991∗∗ 0.162 (0.0178) (0.0178) (0.0177) (0.999) (0.133) =1 if white -0.0388 -0.0319 -0.0248 5.363 -0.0318 (0.0623) (0.0622) (0.0621) (3.500) (0.0623) =1 if black -0.349∗∗∗ (0.0720) -0.359∗∗∗ (0.0720) -0.342∗∗∗ (0.0719) 12.47∗∗∗ (4.048) -0.358∗∗∗ (0.0720) size grad. class, 100s -0.0548∗∗∗ -0.0564∗∗∗ -0.0252 23.79∗∗∗ -0.0564∗∗∗ (0.0161) (0.0161) (0.0174) (0.907) (0.0161) hsize2 0.00430∗ 0.00452∗∗ 0.00448∗∗ -0.0337 0.00452∗∗ (0.00222) (0.00222) (0.00221) (0.125) (0.00222) asat -0.000753∗∗∗ (0.000238) -0.000785∗∗∗ (0.000238) -0.0247∗ (0.0134) -0.000755∗∗∗ (0.000240) rank in grad.  class -0.00131∗∗∗ (0.000276) femsat -0.0000114 (0.000128) Constant 1.331∗∗∗ (0.102) 1.278∗∗∗ (0.103) 1.215∗∗∗ (0.103) -48.14∗∗∗ (5.786) 1.273∗∗∗ (0.119) Observations 4137 4137 4137 4137 4137

R2                                          0.312               0.314                0.318                   0.775                   0.314

Adjusted R2                           0.311               0.312                0.316                   0.775                   0.312

Standard errors in parentheses

p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01