Problem
Use the data in CORNWELL.RAW (from Cornwell and Trumball, 1994) to estimate a model of county level crime rates, using the year 1987 only.
a. Using logarithms of all variables, estimate a model relating the crime rate to the deterrent variables prbarr, prbconv, prbpris, and avgsen.
b. Add logðcrmrteÞ for 1986 as an additional explanatory variable, and comment on how the estimated elasticities dier from b. How confident are you that the OLS estimates from part a are estimating the causal e¤ect of attendence? Explain.
c. As proxy variables for student ability, add to the regression priGPA (prior cumulative GPA) and ACT (achievement test score). Now what is the e¤ect of atndrte? Discuss how the e¤ect di¤ers from that in part a.
d. What happens to the significance of the dummy variables in part c as compared with part a? Explain.
e. Add the squares of priGPA and ACT to the equation. What happens to the coefficient on atndrte? Are the quadratics jointly significant?
f. To test for a nonlinear e¤ect of atndrte, add its square to the equation from part
g. What do you conclude? part a. c. Compute the F statistic for joint significance of all of the wage variables (again in logs), using the restricted model from part b.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.