Question 23 On next page there are three regressions related to a simple model o

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Question 23 On next page there are three regressions related to a simple model of crime on the US. Your college campus. You are interested in a number of crime. Use the effectiveness of campus police in knowledge of econometrics, program and output next page (and your a. of course) to answer the questions below. How many observations are there in the data set? What is the average number of crimes per campus? What is the value of a in What is the OLS estimate of the error variance g 2 in equation (2) b. egression (2) employs OLS to estimate a model of crime. Note the high R2 and high t statistic on police and enrol. Apparently regression results provide evidence that police cause crime. Assuming that campus police are not engaged in some criminal conspiracy, explain the sign and significance of the coefficient on police in regression (2). Which of the classical assumptions is most likely violated here? What are the statistical properties of estimator for D when this assumption is violated? (No proofs c. In common sense terms that a layman with no statistical training could understand, explain why the coefficient on police in regression (2 is positive. d. Regression (3) uses an instrumental variables approach to re-estimate the model. It uses the variable "priv" (explained at the top of the next page) as an instrument for "police." Explain, both in statistical and layman's terms, what the desirable properties of an instrumental variable might be. Evaluate whether or not priv is a good instrument for police, using all the evidence you can muster from the output on the next page, including the results of regression (i). Be sure to be specific about what you mean by "good instrument."

Explanation / Answer

Part-a

Number of observations=96+1=97

Average number of crimes per campus=394.45361

The value of ehatehat’ in equation 2 is =SSE=5425757

OLS estimate of error variance in equation 2=MSE=58341

Square root of (3,3) element of shat2(x’x)-1 in equation 2 is=ROOT MSE=241.53980

Part-b

Coefficient of police is significant with p-value=0.0009<0.05.

The value is 7.78662 which means that corresponding to number of place employee increase of 1, there is on an average an increase of 7.78662 crimes in campus.

This absurd results is due to the fact that dummy variable pricv and police has strong relationship and hence issue of multicollinearity arose which though do not affect the OLS properties of regression models yet inflates the standard errors and make the sign of coefficients reversed.

Part-c

Coefficient of police is positive because there is low police and marginal increase in police force do not control the crime

Part-d

In order priv to be a good instrumental variable it should be uncorrelated with error term and correlated with the police.

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