A Researcher Investigating the Determinants of Crime in the United$\sqrt{\ln (c m r t)_{i t}}=0.063 \times \text { unrtm }_{\mathrm{it}}+3.739 \times \text { proyth }_{\mathrm{it}}-0.588 \times \ln (p p)_{\mathrm{it}} ; R^{2}=0.904$

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The Answer is (a)Since there is no constant in addition to the entity and time fixed effects, setting φ_t to one in year t and zero for all other years for t = 1, …, 22 would result in perfect multicollinearity. α picks up omitted variables that are specific to police regions and do not vary over time. φ picks up effects that are common to all police regions in a given year. Attitudes toward crime may vary between rural regions and metropolitan areas. These would be hard to capture through measurable variables. Common macroeconomic shocks that affect all regions equally will be captured by the time fixed effects. Although some of these variables could be explicitly introduced, the list of possible variables is long. By introducing time fixed effects, the effect is captured all in one variable.
(b)A higher male unemployment rate and a higher proportion of youths increase the crime rate, while a higher probability of punishment decreases the crime rate. The coefficients on the probability of punishment and the proportion of youths is statistically significant, while the male unemployment rate is not. The regression explains roughly 90 percent of the variation in crime rates in the sample. A ten percent increase in the number of convictions over the number of crimes reported decreases the crime rate by roughly six percent.
(c)The coefficients of the three regressors other than the entity coefficients would have been unaffected, had there been a constant in the regression and (n-1)police region specific entity variables. In this case, the entity coefficients on the police regions would have indicated deviations from the constant for the first police region. Hence there are 41 restrictions imposed by eliminating the entity fixed effects and adding a constant. Since there are over 100 observations (900 degrees of freedom), the critical value for F_41,_∞ ≈ F_30,_∞ = 1.70 at the 1% level. Hence the restrictions are rejected.
(d)This result would make the male unemployment rate coefficient significant. It suggests that male unemployment rates change slowly over the years in a given police district and that this effect is picked up by the entity fixed effects. Of course, there are other slowly changing variables, such as attitudes towards crime, that are captured by these fixed effects.

A Researcher Investigating the Determinants of Crime in the United

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