1 Part I: Nonlinearities and SEMs(50 points) 1. (20 points) Cities often want to determine how much additional law enforcement will decrease their murder rates. A simple model with cross-section data at the provincial level to address this question is murdpe = 3.+ 8 polpe + Beinepe + Bapety + (1) where murdpc is murders per capita, polpe is number of police officers per capita, incpc is income per capita and puty is the percent of people in the city that are below a poverty line. Assume that polpe is endogenous, due to possible simultaneity, while the others explanatory variables are exogenous. a. (3 points) What would economic theory suggest for the signs of 8, 8, and 83? What type of decision maker would be described by the previous structural equation? (Hint: consider potential criminals and city officials as possible decision makers) b. (3 points) Why would there be simultaneity btween polpc and murdpe? Explain. c. (3 points) Suppose that the supply of polpc is a function of murdpc described by the following equation polpe = 60 + 61 murdpc +62 incpc + 83 stax +v (2) where stat is the percent of sales tax in the province in which the city is located. Assume murdpc is endogenous while incpc and stax are exogenous variables. What sign would economic theory suggest for 81, 82 and 83? What type of decision maker would be described by the previous equation? (Hint: consider potential criminals and city officials as possible decision makers) Explain. d. (6 points) Consider equations (1) and (2) as a SEM. What assumptions are needed to identify 8, and 8,? (Hint: think about assumptions required for poty and stax to be valid IVs). Explain. f. (5 points) What would be the reduced form equations for the SEM? In these equations what would be the condition that is required for the corresponding IVs to be valid? Explain. PE