What is the relationship between crime and punishment? This important question has been examined by Cornwell and Trumbull \({ }^{18}\) using a panel of data from North Carolina. The cross sections are 90 counties, and the data are annual for the years 1981-1987. The data are in the data file crime. In these models, the crime rate is explained by variables describing the deterrence effect of the legal system, wages in the private sector (which represents returns to legal activities), socioeconomic conditions such as population density and the percentage of young males in the population, and annual dummy variables to control for time effects. The authors argue that there may be heterogeneity across counties (unobservable county-specific characteristics).

a. What do you expect will happen to the crime rate if (i) deterrence increases, (ii) wages in the private sector increase, (iii) population density increases, and (iv) the percentage of young males increases?

b. Consider a model in which the log of crime rate (LCRMRTE) is a function of the log of the probability of arrest (LPRBARR), the log of probability of conviction ( \(\angle P R B C O N V)\), the log of the probability of a prison sentence (LPRBPRIS), the log of average prison sentence (LAVGSEN), and the log of average weekly wage in the manufacturing sector (LWMFG). Estimate this model by OLS. (i) Discuss the signs of the estimated coefficients and their significance. Are they as you expected? (ii) Interpret the coefficient on LPRBARR.

c. Estimate the model in (b) using a fixed effects estimator. (i) Discuss the signs of the estimated coefficients and their significance. Are they as you expected? (ii) Interpret the coefficient on LPRBARR and compare it to the estimate in (b). What do you conclude about the deterrent effect of the probability of arrest? (iii) Interpret the coefficient on LAVGSEN. What do you conclude about the severity of punishment as a deterrent?

d. In the fixed effects estimation from part (c), test whether the county level effects are all equal.

e. Based on these results, what public policies would you advocate to deal with crime in the community?