Refer to Example 13.9 and the data in CRIME4.RAW.
(i) Suppose that, after differencing to remove the unobserved effect, you think Δlog(polpc) is simultaneously determined with Δlog(crmrte); in particular, increases in crime are associated with increases in police officers. How does this help to explain the positive coefficient on Δlog(polpc) in equation (13.33)?
(ii) The variable taxpc is the taxes collected per person in the county. Does it seem reasonable to exclude this from the crime equation?
(iii) Estimate the reduced form for Δlog(polpc) using pooled OLS, including the potential IV, Δlog(taxpc). Does it look like Δlog(taxpc) is a good IV candidate? Explain.
(iv) Suppose that, in several of the years, the state of North Carolina awarded grants to some counties to increase the size of their county police force. How could you use this information to estimate the effect of additional police officers on the crime rate?