I am looking answers to the following three questions for some students. I study psychology and this in depth statistics is out of my league and more economics based to be working this out. Any advice is helpful so that I can see how someone works their way around these questions.....

You are a Behavioural Public Policy researcher investigating the determinants of crime in the United Kingdom. You have data for 42 police regions over 22 years, and you estimate the following OLS regression:

ln(cmrt)it=i+t+1unrtmit+2proythit+3ln(pp)it+uit;i= 1,...,t= 1,..., 22

• wherecmrtis the crime rate per head of population
• unrtmis the unemployment rate of males
• proythis the proportion of youths,ppis the probability of punishment measured as (number of convictions)/(number of crimes reported).
• andare area and year fixed effects, whereiequals one for areaiand is zero otherwise for alli, andtis one in yeartand zero for all other years fort= 2, ..., 22.
• 1is not included.

(a) What is the purpose of excluding1? What are the termsandlikely to pick up? Discuss the advantages of using panel data for this type of investigation. (150)

(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:

= 0.063 unrtmit+ 3.739 proythit- 0.588 ln(pp)it;R2= 0.904

(0.109) (0.179) (0.024)

Comment on the results. In particular, what is the effect of a ten percent increase in the probability of punishment? (150)

(c) 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,anddo not change by much, although their standard errors roughly double. However,is now 1.340 with a standard error of 0.234. Why do you think that is? (150)