Political Methodology Comprehensive Examination
Department of Political Science
The George Washington University
September 2005
Part I. To be completed in 5 hours (open book)
1.Assume that you have estimated the following equation on yearly data ranging from 1950 to 2000:
You have reason to suspect that your disturbances may be autocorrelated. How can you test for autocorrelation, and what can be done if you conclude that your errors are autocorrelated? What are the relative merits of the different “solutions” to autocorrelation?
Now assume that you include a lagged dependent variable in your model:
Given this specification, how can you test for autocorrelation, and what can be done if you conclude that your errors are autocorrelated?
2.Given the following specification, which models the percentage of the two party vote received by the incumbent (Inc%) as a function of incumbent spending (Inc$), challenger spending (Challenger$), the strength of the incumbent’s party (partystrength), and an interaction of the challenger spending and party strength (Challenger$*partystrength):
What is the total effect of challenger spending (Challenger$) on the dependent variable? What is the standard error of the total effect of challenger spending when party strength equals .60?
3.X is normally distributed, with a value of 15 for the 10th percentile and a value of 25 for the 60th percentile. What are the mean and variance of X?
4.A recent article reported on a study concluding that there was no evidence of a link between a woman having had an abortion and her risk of breast cancer. (There were medical theories/hunches that suggested the possibility of a link.) 1.5 million women were in the study altogether. The concluding paragraph of the article states:
“Among the 280,965 women in the study who had 370,715 abortions, 1,338 cases of breast cancer were diagnosed by 1992. In the remaining group of women who had not had an abortion, 8,908 cases of breast cancer occurred, according to the study.”
Test the hypothesis that the mean rate of cancer occurrence is the same regardless of having had an abortion or not. In particular:
a) What assumption(s), if any, do you need to make to test the hypothesis?
b) At what p-level could you just reject the hypothesis? (show your work; make whatever assumptions necessary)
c) Does the conclusion of “no evidence of any difference” seem warranted to you given this evidence?
5.Data question
The file named comp0905.dta contains data on the filibusters in the U.S. Senate. The descriptions of the variables are contained below. Observations are sessions of congress. The number of filibusters is contained in the numfilib variable, with lagged filibusters contained in the labfilib variable. The “strength” of the majority and minority parties (defined as party cohesion times party size) are in the majstr and minstr variables. The final substantive variable, lastsess, is a dummy variable indicating whether or not the Senate is in the final session for a given congress. Given these data, answer the questions below.
storage display value
variable name type format label variable label
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congress int %9.0g Congress number
seqnum byte %9.0g sequence ID
numfilib byte %9.0g Number of filibusters
lagfilib byte %9.0g Lagged number of filibusters
majstr float %9.0g Majority party strength
minstr float %9.0g Minority party strength
lastsess byte %9.0g Last session of a Congress
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(a) Graphically, summarize the number of filibusters variable (numfilib). Given the properties of the measure, what would be an appropriate model to use when explaining variation in the number of filibusters? Why?
(b) Given your answer to the previous question, estimate a model with numfilib as the dependent variable and lagfilib, majstr, and minstr as the independent variables. Interpret the statistical significance of each of the independent variables.
(c) Do majority strength and minority strength have the same impact on the number of filibusters? Justify your answer with a statistical test.
(d) What is the substantive impact of being in the last session of a Congress versus not being in the last session?
6.Game theory:
Part I
(a) Using backward induction, find and report both the Sub-Game Perfect Equilibrium/Equilibria for this game and the payoffs associated with this equilibrium/equilibria.
(b) Does this equilibrium/equilibria seem intuitively “right” to you as a description of how people behave in real life? Write a short paragraph on this topic.
Part II
Player 1/Player 2 / a / BA / 0,0 / -1,3
B / 3,-1 / -2,-2
Find the Nash equilibria in both pure and mixed strategies for this game.
Part II. Submit an empirical research paper along with the exam.
Good Luck!