Economics 371
Introductory Econometrics
Fall 2005
Problem Set 7
1. It is sometimes argued that a university can expect to receive increased alumni
contributions as a reward for more a more successful football team, all else equal.
To evaluate this hypothesis and estimate the effects of more football wins on
alumni contributions, consider the following econometric model:
ACit = β0 + β1Wit + uit
i = 1,…,n and t = 2000,2001
where ACit denotes the alumni contributions to university i in year t, Wit denotes
the number of football games won in year t by university i, and uit is an error
term.
i.
Specify two variables that you think might be 1) university specific and
fixed between 2000 and 2001, and 2) the source of omitted variable bias in
the estimate of β1 obtained from the regression of AC on W. Explain why
you think each of these variables meet these two conditions.
Show how to use the panel data on AC and W in a “before and after”
analysis (i.e., using a regression involving changes in variables) to obtain
an estimate of β1 that would not suffer from omitted variable bias as a
result of the problems you identified in part (i). Explain how this
procedure eliminates this source of omitted variable bias.
Specify a variable that you think might change over time and be a source
of omitted variable bias in the estimate of β1 obtained from the regression
of AC on W, explaining your choice. Does the “before and after” analysis
you outlined in part (ii) resolve this problem? Explain.
ii.
iii.
2. Now suppose that the data set in problem 1 has been expanded to include data
from 2000, 2001, 2002, and 2003.
i.
ii.
iii.
Explain how you would use “binary regressors” to estimate β1 and
why that procedure would eliminate any bias due to university fixed
effects.
Explain how you would use an “entity-demeaned” regression to
estimate β1 and why that procedure would eliminate any bias due to
university fixed effects.
Show how you would use the results from (i) and (ii) to predict the
amount of alumni contributions Iowa State would receive if a) the
football team wins 9 games this year versus b) the football team wins 7
games this year. Can you say anything about the predictions obtained
from (i) and (ii) would compare to one another? Explain.
3. Referring to problems 1 and 2, with data for 2000, 2001, 2002, and 2003:
i.
ii.
iii.
Specify a variable that might be the source of omitted
variable bias due to time fixed effects in the estimate of β1 obtained
from the regression of AC on W. Explain the reasoning behind your
choice.
Explain how you would use “binary regressors” to estimate β1 and
why that procedure would eliminate any bias due to time fixed effects.
Explain how you would use a “year-demeaned” regression to estimate
β1 and why that procedure would eliminate any bias due to time fixed
effects.
4. Now assume that there are both university and time fixed effects that can create
omitted variable bias in the regression of AC on W.
i.
ii.
Explain how you would use “binary regressors” to estimate β1 and
why that procedure would eliminate any bias due to these fixed effects.
Explain how you would use an “entity and year-demeaned” regression
to estimate β1 and why that procedure would eliminate any bias due to
these fixed effects.
5. Suppose that in the formulation of the regression model including the university
and time fixed effects, the error term is correlated across time for each university.
That is, for example, the error term for Iowa State University in 2000 is correlated
with the error term for Iowa State University in 2001,… Assuming that these
error terms are uncorrelated with the regressors, i) what problem(s) does this
create in the estimation/inference process and ii) how can this problem(s) be
resolved?