You would like to estimate the effect of police size on city-level crime on a cross-section of cities. A regression of crime rate on police
size (per population) gives an estimate of 0. Suppose that people make their city increase police size if crime increases for some other
reason.
(a) Does that lead to a bias the OLS estimates for the causal effect of police size on crime? Explain.
(b) Does the estimated 0 coefficient mean that police size has no effect on crime?
(c) What assumptions should a valid IV satisfy in this case?
(d) Do you think electoral cycles can serve as a valid instrument (assuming incumbent city governments spend more on police in election years, ceteris paribus)? Why or why not?