2. Suppose you are interested in the effect of police on crime. You download dat

Question

2. Suppose you are interested in the effect of police on crime. You download data for an i.i.d. sample of n cities, [pi, ci), where ci is the crime rate in city i (total number of crimes per 1000 people) and p, is the total number of police in city i. Now, suppose we run the regression: (a) Suppose we wish to adopt the causal interpretation of 31. (For instance, suppose you run OLS on your sample and find =-01, what does-01 mean if we adopt the causal interpretation.) (b) Do you think EUPl = 0 here?

Explanation / Answer

a) Here, B1^= -0.01. So, a unit increase in log(p) decreases the mean crime rate by 0.01.

b) We know the in the OLS, E(C)= Bo+B1log(P)

Therefore, E[U|P] =E[C-Bo-B1log(P)]=E[C]-E[Bo + B1log(P)]= 0.

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