Kinsley Chen, Yatian Xie, Vy Vo
HW 5 Econometrics
In order to determine the effects of collegiate athletic performance on applicants, you
collect data on applications for a sample of Division I colleges for 1985, 1990, and 1995.
(i) What measures of athletic success would you include in an equation? What are
some of the timing issues?
Measures of athletic success that you should include the win rate of the games and if those wins
lead to going to the championships and winning at the national level. For example, there are
many types of sports championships for basketball and volleyball and we can determine if they
won them at that level. We need to collect those measurements about athletic success before the
final deadline to apply to college. Depending on when the season ends for the specific sport, we
may have to consider extending the timing of the collection because some game seasons start
later in the year after the application deadline for college.
(ii) What other factors might you control for in the equation?
You must control for the tuition because it is a relevant factor for the applicants because not
many of applicants can afford to pay a high cost for the tuition so their choices in the college
they apply to are more limited. There are also other factors that influence performance such as
the quality of education provided, the class sizes being big or small, the scholarships and the
amount of grant money received.
(iii) Write an equation that allows you to estimate the effects of athletic success on
the percentage change in applications. How would you estimate this equation?
Why would you choose this method?
log(appsit) = δ1d90t + δ2d95t + β1athlsuccit + β2log(tuitionit) + K + ai + uit, t = 1,2,3
athlsuccit refers to the measurement of athletic success. For example, if athletic success is the
winning percentage, then 100* β1 is the percent change in application if there is a 1% increase in
the winning percentage. The ai may be correlated with the athletic success and other variables
such as tuition so we should use the fixed effect estimate.
For this exercise, we use JTRAIN.RAW to determine the effect of the job training grant on
hours of job training per employee. The basic model for the three years is
) + a1 + uit
Kinsley Chen, Yatian Xie, Vy Vo
i) Estimate the equation using fixed effects. How many firms are used in the FE
estimation? How many total observations would be used if each firm had data on all
variables (in particular, hrsemp) for all three years?
F test that all u_i=0: F(134, 250) = 5.12 Prob > F = 0.0000
rho .64942011 (fraction of variance due to u_i)
_cons 9.324956 14.92757 0.62 0.533 -20.07487 38.72478
lemploy -.1762661 4.287935 -0.04 0.967 -8.621347 8.268815
grant_1 .5040804 4.127325 0.12 0.903 -7.62468 8.632841
grant 34.22818 2.858438 11.97 0.000 28.59849 39.85787
d89 4.090049 2.481125 1.65 0.101 -.7965232 8.97662
d88 -1.098678 1.983157 -0.55 0.580 -5.004503 2.807148
hrsemp Coef. Std. Err. t P>|t| [95% Conf. Interval]
corr(u_i, Xb) = -0.0270 Prob > F = 0.0000
F(5,250) = 48.21
overall = 0.2206 max = 3
between = 0.0514 avg = 2.9
R-sq: within = 0.4909 Obs per group: min = 1
Group variable: fcode Number of groups = 135
Fixed-effects (within) regression Number of obs = 390
. xtreg hrsemp d88 d89 grant grant_1 lemploy, fe
According to the Stata output for the fixed effect technique of linear regress, the equation for the
effect of Job training grant on hours of job training per employee is:
it= -1.10*d88t + 4.09*d89t + 34.23grantit + 0.504granti,t-1 -0.176*lemployit
with n = 390, N = 135, t = 3
The number of firms used in the equation is 135 firms. If the firm had data for all three years, the
number observations should increase to 405 but because we are missing some data, we can only
include the total of 390 estimation
ii) Interpret the coefficient on grant and comment on its significance
The coefficient on the grant tells you that if the firm received one grant in the year, it will train a
worker on average of 34.22 hours more than if they had no received the grant. The effect is
significant and the t value is very large as well