Economics 515 Final Exam Professor Thornton

Economics 515 Final Exam Professor Thornton Econometrics 100 Points Winter 2014

This assignment is a take-home final exam. It is due no later than Wednesday, April 23 at 6:30 pm. Exams submitted late will not be accepted. Each student should do his/her own work and not consult with other students. Any questions related to the assignment should be directed at me. Question #1 can be answered using the results of the duration models you estimated for the last in-class Stata assignment.

QUESTION #1

You have been hired by the Michigan Department of Corrections (MDOC) to conduct a study of the factors that affect criminal recidivism.

Objective of Study

MDOC is interested in the effect of an inmate’s marital status, education, and time served in prison on recidivism. It wants you to address the following questions. 1) How strong is the evidence that the amount of time served in prison and education have an effect on the amount of time that elapses until a typical inmate is arrested after being released from prison? 2) What is the direction and size of the effects of these two variables? 3) Is an inmate more likely, less likely, or equally likely to be arrested the longer he has been out of prison? 4) Does marital status affect this hazard rate? If so, how does it affect the hazard rate? 5) What is the probability that a married inmate with 12 years of education that served 18 months in prison will not be arrested for at least 24 months after being released from prison?

Data

The dataset you will use for the study contains data on the time in months until an inmate is arrested after being released from prison, as well as variables that may affect this duration. The sample size is 1,445 inmates. Of these, 893 were not arrested during the period they were followed, and therefore these observations are censored. The censoring times differed among inmates, ranging from 70 to 81 months. The variables are as follows. durat is the amount of time until arrested after release from prison, or until the inmate was no longer followed, in months. cens is a dummy variable that takes a value of 1 if durat is right censored, and zero otherwise. tserved is time served in prison in months. educ is years of schooling. married is a dummy variable that takes a value of 1 if an inmate is married when sent to prison, and 0 otherwise.

Statistical Model

To answer MDOCs questions, you must choose a statistical model, estimate the parameters of this statistical model, and use the parameter estimates to obtain the information you require. Your model will have four variables: durat, tserved, educ, and married.

1. Choose one of the following models: Weibull duration model, Cox proportional hazards model. Carefully explain why you select this model. Write down the specification for the model you select. Discuss the specification. What is the dependent variable? What are the explanatory variables? What are the parameters? Do the parameters of the model have a useful interpretation? If so, what is the interpretation?

Empirical Strategy

1 2. Explain the empirical strategy you will use to address each of the five the questions of interest to MDOC.

Estimation of the Model

3. Report the estimates of the parameters of your model. What estimator did you use to obtain your parameter estimates?

Conclusions

4. Use the estimation results to answer the five questions in which MDOC is interested. Show any work that is necessary to answer these questions.

QUESTION #2

You have a sample of 2,000 newly built homes for a large metropolitan area for the years 2008, 2009, 2010, and 2011. You estimate the following hedonic price equation using the OLS estimator.

Pt = α0 + α1D(2009)t + α2D(2010)t + α3D(2011)t + β1SQFTt + β2BEDt + β3BATHt + β4DISTt + μt ; t = 1,.., 2000

P is the market price of a home measured in thousands of dollars; SQFT is the number of square feet; BED is the number of bedrooms; BATH is the number of bathrooms; DIST is the distance in miles the home is located from the city center; D(2009) is a dummy variable that takes a value of 1 if the home was built in 2009 and zero otherwise; D(2010) is a dummy variable that takes a value of 1 if the home was built in 2010 and zero otherwise; D(2011) is a dummy variable that takes a value of 1 if the home was built in 2011 and zero otherwise. Estimation of this equation using the OLS estimator yields the following results.

Variable Coefficient Estimate t-statistic

INTERCEPT 100 2.5

D(2009) 4 6.4 D(2010) 10 3.3 D(2011) 8 4.2 SQFT 0.10 4.7 BED 12 2.3 BATH 28 3.9 DIST 1.5 1.2

Given this information, answer the following questions.

1. Using hedonic price theory as your guide, what is the economic interpretation of the variables SQFT, BED, BATH, and DIST, and the parameters β1, β2, β3, β4?

2. Interpret the estimate of β1. What information does it give you about home buyers and home builders? What is necessary for these estimates to provide information about home buyers but not home builders?

3. Are any of the estimates of the slope coefficients insignificant at the 5% level? If so, what does this tell you? Explain.

2 4. Construct a quality-adjusted price index for new homes for this metropolitan area for the period 2008 to 2011. Interpret you index. What does it tell you about the behavior of the average price of a new home over this period of time?