Economics

Consider the two-way relationship between crime rate and number of police Crime = 0 + 0P olice + 0Density + u, P olice = 1 + 1Crime + 1Budget + v. The first equation models the determinant of crime rate given the number of police and the population density of the area. The second equation models the number of 1 police the government chooses to hire given the crime rate in the area and the budget of the government for the area.

(a) What do you expect the signs of 0 and 1 are? Explain.

(b) Explain why the OLS estimator for 0 and 1 are biased. If we use OLS estimator to estimate 0 and 1, what signs are the biases? Explain.

(c) The only variables available are crime, police, density, and budget. To estimate 0 and 1 by the two stage least squares estimator, which variables among the data you have should be used as instruments? Be specific, what IV is for 0 and which IV is for 1. Explain.

(d)To ensure these instruments are relevant, what are the requirements on the coefficients in two equations above?

(e) Explain the steps in the estimation of 0 by the two stage least squares estimator.

(f) Suppose now the two-way relationship between crime rate and number of police is given by Crime = 0 + 0P olice + 0Density + 2W eather + u, P olice = 1 + 1Crime + 1Budget + v. How will this change the estimation for 1? What is the advantage of having two exogenous variables in the first equation?