Econometrics
Fall 2012
Midterm Exam 3 – Solutions
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The question is asking about an interaction effect – whether the effect of athletic participation on grades is different for men and for women. The correct model is
( )
The EViews output is:
Dependent Variable: COLGPA Method: Least Squares Date: 12/11/12 Time: 16:19 Sample: 1 4137
Included observations: 4137
White heteroskedasticity-consistent standard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
C 2.608557 0.014846 175.7064 0.0000 ATHLETE -0.301577 0.048729 -6.188822 0.0000 FEMALE 0.124853 0.020795 6.003888 0.0000 ATHLETE*FEMALE 0.196389 0.106363 1.846398 0.0649
R-squared 0.018842 Mean dependent var 2.652686 Adjusted R-squared 0.018129 S.D. dependent var 0.658635 S.E. of regression 0.652637 Akaike info criterion 1.985375 Sum squared resid 1760.390 Schwarz criterion 1.991494 Log likelihood -4102.749 Hannan-Quinn criter. 1.987540 F-statistic 26.45599 Durbin-Watson stat 1.946987 Prob(F-statistic) 0.000000
The coefficient on ATHLETE is negative, but the coefficient on the interaction term is positive. This means that being on an athletic team is associated with a lower GPA, but that the effect is smaller for women than for men. Specifically, athletic performance is associated with a decline in GPA for men, but a decline of for women.
a. should be positive because of inflation – 1989 prices are higher than 1980 prices in general.
b. Using period fixed effects, but no cross-section fixed effects, the estimated coefficient is
̂ . Each 1% increase in the percentage of students in a town’s population is associated with a 0.5% increase in rent.
c. Using both period and cross-section fixed effects, the estimated coefficient is ̂
. Each 1% increase in the percentage of students in a town’s population is associated with a 1.12% increase in rent.
d. The marginal effect of adding students to a town is to increase the rents charged by a fairly large amount. However, if such towns are less pleasant places to live in general, then comparing between towns will dampen the effect (i.e. no town fixed effects).
However, within the town, we see a larger effect on the rent (i.e. with town fixed effects).
Problem 3
a. Parental support clearly affects a student’s school performance since students who get more support at home do better in school. It could be correlated with GIRLHS since parents who support their children academically are more likely to be willing to pay private school tuition. Thus, GIRLHS could “pick up” the effect of having supportive and interested parents rather than the effect of the girls’ high school itself.
b. ̂ would be too large, since it would “pick up” the effect both of supportive and interested parents and the effect of attending a girls’ high school.
a. ( )
b. ( )
c.
d.
e.
f.
g. ( ) . Evidently, the coefficient on a dummy variable in a logit regression is the natural log of the odds ratio.
a. Using OLS, the estimated coefficient is ̂ . Each 1% increase in the fare is associated with a 0.39% decline in the number of passengers. This is the estimate for price elasticity of demand.
b. Regressing ( ) on and the other two exogenous regressor ( ) and
[ ( )] gives an F-statistic . This is the first-stage regression and thus the instrument is relevant. The economic interpretation is just that a higher level of
concentration by a single large firm allows the firm to exercise market power and raise the price.
c. Yes – Market concentration is exogenous to the factors creating error in the demand
equation. Consumers don’t care about market concentration as such, only to the extent to which it affects price.
d. Using TSLS, the estimated coefficient is ̂ . Each 1% increase in the fare is associated with a 1.17% decline in the number of passengers.
