#5. What is the relationship between crime and punishment? This important question has been examined by Cornwell and Trumbull using a panel of a 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 file crimesas. In these models the crime rate is explained by variables describing the deterrence effect of the legal system, wages in the private sector (which presents 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 if (i) deterrence increases, (ii) wages in the private sector increase, (iii) population density increases, (iv) the percentage of young males increases? (b) Consider a model in which the crime rate (LCRMRTE) is a function of the probability of arrest (LPRBARR), the probability of conviction (LPRCONV), the probability of a prison sentence (LPRBPRIS), the average prison sentence (LAVGSEN), and the average weekly wage in the manufacturing sector (LWMFG). Note that the logarithms of the variables are used in each case. Estimate this model by least squares. (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 (time demeaning) 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) To test specification in part (b) add the population density (LDENSITY) and the percentage of young males (LPCTYMLE), as well as dummy variables for the years 1982-1987 (D82-D87). (1) Compare the results obtained by using least squares (with no county effects) and the fixed effects estimator. (ii) Test the joint significance of the year dummy variables. Does there appear to be a trend effect? (iii) Interpret the coefficient of LWMFG in both estimations. (f) Based on these results, what public policies would you advocate to deal with crime in the community
