Please submit your answers electronically to Carmen in a single PDF le. I will accept answers that are (i) handwritten on paper and scanned, (ii) handwritten on tablet or (iii) typed. If you are submitting your answers handwritten on paper, try best to make a clean scan. You may discuss with your classmates how to approach problems or how to code for computer exercises. However, your submitted answers must be your own that you fully understand. Problem 1. Consider the following hypothetical crosssectional data of police size and crime rates in Ohio and its five neighboring states in year 2019. The variable Police Size is the number of police ofcers per 1,000 people. The variable Crime Rate is the number of violent crimes per 1,000 people. Election. is a dummy variable that takes value 1 if the state held a gubernatorial election in 2019 and takes 0 otherwise. Table 1. Police Size and Crime Rates State Police Size Crime Rate Election Indiana 10 12 0 Kentucky 2 3 0 Michigan 12 10 1 Ohio 4 1 Pennsylvania 1 West Virginia 3 0 Suppose that the underlying population model for the above data set is crimemte = g + lpalicesz'ze + u. where ,8] is the causal e"ect of police size on the {expected} crime rates and is the error term that contains the effects of all other factors that determine the crime rate. Note that the error term a may be arbitrarily correlated with the police size. Estimate the causal effect ,8] using simple Ordinary Least Squares (0L3) regression of the above equation. Assuming that gubernatorial elections are relevant and exogenous instrumental variable for police size with respect to crime rates. That is. elections affect crime rates only through affecting police size but through nothing else. estimate 81 using Instrumental Variables (IV) regression. Interpret the estimated coefficients. Why are the estimates so different