Use all 630 observations in dataset CORNWELL.dta (from Cornwell and Trumball, 1994) to estimate a model of county level crime rates.
(a) Using the data for all seven years, and using the logarithms of all variables, estimate both a random effects and a fixed effects model relating the crime rate (crmrte) to the deterrent variables prbarr , prbconv , prbpris , avgsen , and polpc . Also include a full set of year dummies.
(i) For the fixed effects estimation, which of the following variables is not significant at the 5% level? Answer: _______________ ( log(prbarr) , log(prbconv) , log(prbpris) , log(avgsen) or log(polpc) )
(ii) For the random effects estimation, which of the following variables has the highest test statistic (in absolute value)? Answer: _____________ ( log(prbarr) , log(prbconv) , log(prbpris) , log(avgsen) or log(polpc) )
(b) Add to the above model the nine wage variables (in logarithmic form) as additional regressors, and test for joint significance of these nine variables after estimation by fixed effects. The (original) wage variables are: wcon , wtuc , wtrd , wfir , wser , wmfg , wfed , wsta , and wloc .
(i) Report the F statistic of the test: ___________________
(ii) According to the test result:
____ All nine wage variables should be removed from the model
____ One or more of the wage variables deserve to be kept in the model
(c) Estimate the equation in part (b) by first differencing and test the residuals for AR(1) serial correlation.
(i) Report the t statistic of the test: ______________________
(ii) There is evidence of _________________ (negative / positive) serial correlation in _________________________ (idiosyncratic erros / differenced idiosyncratic errors)
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