ECMT6002: Econometric Applications - Statistics Assessment Answer

ECMT6002: Statistics Assessment Task

Answer all the following questions:
1. State the research question addressed in Levitt (1997) and explain the reason why the question is important.
2. List two papers cited in Levitt (1997) and explain how they are related to Levitt (1997).

3. State the type of crimes assigned for your group. Report the summary statistics for variables in the data set posted on Canvas. If you detect any issues with the data, state the issues and clean the data accordingly. Plot the data points of (Cit, Pit) and briefly discuss
the pattern. The main empirical model considered in Levitt (1997) is

ln (Cit) = β1 ln (Pit) + β2 ln (Pi,t−1) + Xitη + γt + λi + εit (1) where, for city i in year t, C is the number of criminal offense, P is the number of sworn police officers, γ is a time effect, λ captures unobservable city/state effects. X is a vector of covariates, including
? rincpc (real income per capita in state),
? unemp (state unemployment rates),
? citypop (city-population),
? sta educ (state and local spending per capita on education in 1992 dollars),
? st welf (state and local spending per capita on public welfare in 1992 dollars), and
? price (consumer price index).
4. Interpret β1 and β2 in model (1), and explain how they are related to the research question, such as the sign of β’s. Briefly explain why ln(Pi,t−1) is included in model (1). Also briefly explain why it is important to include other covariates (in X); list at least two reasons.
5. Estimate model (1) by the OLS and report the results (with robust standard errors) as a column along with other estimates in a table. Are the sign of β1 and β2 estimates expected? Explain briefly.
Note: you need to generate Pi,t−1 (the lag of P) and the log of C and the log of P. In Stata, you may use L.y for the first lag of y.
6. The unobservable city effects captured in λ may be correlated to the regressors in model (1). How could this affect the OLS estimation of model (1)? Explain briefly.
7. To address the problem related to λ, the model can be transformed by taking the first difference 4 ln (Cit) = β14 ln (Pit) + β24 ln (Pi,t−1) + 4Xitη + 4γt + 4εit (2) where 4 denotes the first difference, such as 4 ln(Cit) = ln(Cit) − ln(Ci,t−1). Note that λi is differenced away and the error term in equation (2) becomes 4εit. Estimate (2) by OLS and report the results (with robust standard errors) as a column in the table. Are the sign of β1 and β2 estimates expected? Are they different from the OLS estimates for (1)?
Explain briefly. In Stata, you may use D.y for the first difference of y.
8. Based on the OLS estimates of equation (2), test the joint significance of β1 and β2 and draw the conclusion accordingly.
9. We are concerned that the regressors in equation (2) may still be endogenous. Briefly explain the reason for endogeneity in (2).
10. Levitt (1997) proposed that the timing of elections could be used as an instrument for police hiring. There are two variable in the data set: Mit = 1 if t is a mayoral election year in city i, and zero otherwise; Git = 1 if t is a governor election year in city i, and zero otherwise. State the conditions for Mit and Git to be valid instruments.
11. Briefly explain the 2SLS estimation procedure for equation (2). Then estimate equation (2) by 2SLS, and report the results (with robust standard errors) as a column in the table.
12. Perform the Wu-Hausman test of endogeneity to see whether the regressors in equation (2) are indeed endogenous.
13. Based on the 2SLS estimates of equation (2), provide an answer to the research question and compare to the literature.
14. Based on your answer to all parts above, give comments (critical appraisal) of Levitt (1997). And if you think there are any issues with the original paper Levitt (1997), state the issues and explain briefly.

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