A researcher investigating the determinants of crime in the United Kingdom has data for 42 police regions over 22 years. She estimates by OLS the following regression
ln(cmrt)_it = ?_i + ?_t + ?₁unrtm_it + ?₂proyth_it + ?₃ln(pp)_it + u_it; i = 1,..., t = 1,..., 22
where cmrt is the crime rate per head of population, unrtm is the unemployment rate of males, proyth is the proportion of youths, pp is the probability of punishment measured as (number of convictions)/(number of crimes reported). ? and ? are area and year fixed effects, where ?_i equals one for area i and is zero otherwise for all i, and ?_t is one in year t and zero for all other years for t = 2, …, 22. ?₁is not included.
(a)What is the purpose of excluding ?₁? What are the terms ? and ? likely to pick up? Discuss the advantages of using panel data for this type of investigation.
(b)Estimation by OLS using heteroskedasticity and autocorrelation-consistent standard errors results in the following output, where the coefficients of the fixed effects are not reported: $\sqrt{\ln (c m r t)_{i t}}=0.063 \times \text { unrtm }_{\mathrm{it}}+3.739 \times \text { proyth }_{\mathrm{it}}-0.588 \times \ln (p p)_{\mathrm{it}} ; R^{2}=0.904$
$\begin{array}{lll}(0.109) & (0.179)&(0.024)\end{array}$
Comment on the results. In particular, what is the effect of a ten percent increase in the probability of punishment?
(c)To test for the relevance of the area fixed effects, your restrict the regression by dropping all entity fixed effects and add single constant is added. The relevant F-statistic is 135.28. What are the degrees of freedom? What is the critical value from your F table?
(d)Although the test rejects the hypothesis of eliminating the fixed effects from the regression, you want to analyze what happens to the coefficients and their standard errors when the equation is re-estimated without fixed effects. In the resulting regression, $\hat\beta _ { 2 }$ and $\hat \beta _ { 3 }$ do not change by much, although their standard errors roughly double. However, $\hat { \beta } _ { 1 }$ is now 1.340 with a standard error of 0.234. Why do you think that is?

Question

A researcher investigating the determinants of crime in the United Kingdom has data for 42 police regions over 22 years. She estimates by OLS the following regression
ln(cmrt)_it = ?_i + ?_t + ?₁unrtm_it + ?₂proyth_it + ?₃ln(pp)_it + u_it; i = 1,..., t = 1,..., 22
where cmrt is the crime rate per head of population, unrtm is the unemployment rate of males, proyth is the proportion of youths, pp is the probability of punishment measured as (number of convictions)/(number of crimes reported). ? and ? are area and year fixed effects, where ?_i equals one for area i and is zero otherwise for all i, and ?_t is one in year t and zero for all other years for t = 2, …, 22. ?₁is not included.
(a)What is the purpose of excluding ?₁? What are the terms ? and ? likely to pick up? Discuss the advantages of using panel data for this type of investigation.
(b)Estimation by OLS using heteroskedasticity and autocorrelation-consistent standard errors results in the following output, where the coefficients of the fixed effects are not reported:

\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

\begin{array}{lll}(0.109) & (0.179)&(0.024)\end{array}

Comment on the results. In particular, what is the effect of a ten percent increase in the probability of punishment?
(c)To test for the relevance of the area fixed effects, your restrict the regression by dropping all entity fixed effects and add single constant is added. The relevant F-statistic is 135.28. What are the degrees of freedom? What is the critical value from your F table?
(d)Although the test rejects the hypothesis of eliminating the fixed effects from the regression, you want to analyze what happens to the coefficients and their standard errors when the equation is re-estimated without fixed effects. In the resulting regression,

\hat\beta _ { 2 }

and

\hat \beta _ { 3 }

do not change by much, although their standard errors roughly double. However,

\hat { \beta } _ { 1 }

is now 1.340 with a standard error of 0.234. Why do you think that is?

Quizplus · Accepted Answer

The Answer of A researcher investigating the determinants of crime in the United Kingdom has data for 42 police regions over 22 years. She estimates by OLS the following regression ln(cmrt)_it = ?_i + ?_t + ?₁unrtm_it + ?₂proyth_it + ?₃ln(pp)_it + u_it; i = 1,..., t = 1,..., 22 where cmrt is the crime rate per head of population, unrtm is the unemployment rate of males, proyth is the proportion of youths, pp is the probability of punishment measured as (number of convictions)/(number of crimes reported). ? and ? are area and year fixed effects, where ?_i equals one for area i and is zero otherwise for all i, and ?_t is one in year t and zero for all other years for t = 2, …, 22. ?₁is not included. (a)What is the purpose of excluding ?₁? What are the terms ? and ? likely to pick up? Discuss the advantages of using panel data for this type of investigation. (b)Estimation by OLS using heteroskedasticity and autocorrelation-consistent standard errors results in the following output, where the coefficients of the fixed effects are not reported: $\sqrt{\ln (c m r t)_{i t}}=0.063 \times \text { unrtm }_{\mathrm{it}}+3.739 \times \text { proyth }_{\mathrm{it}}-0.588 \times \ln (p p)_{\mathrm{it}} ; R^{2}=0.904$ $\begin{array}{lll} (0.109) & (0.179)&(0.024) \end{array}$ Comment on the results. In particular, what is the effect of a ten percent increase in the probability of punishment? (c)To test for the relevance of the area fixed effects, your restrict the regression by dropping all entity fixed effects and add single constant is added. The relevant F-statistic is 135.28. What are the degrees of freedom? What is the critical value from your F table? (d)Although the test rejects the hypothesis of eliminating the fixed effects from the regression, you want to analyze what happens to the coefficients and their standard errors when the equation is re-estimated without fixed effects. In the resulting regression, $\hat\beta _ { 2 }$ and $\hat \beta _ { 3 }$ do not change by much, although their standard errors roughly double. However, $\hat { \beta } _ { 1 }$ is now 1.340 with a standard error of 0.234. Why do you think that is?

A Researcher Investigating the Determinants of Crime in the United