Economics 515 Assignment #3 Professor Thornton

Econometrics 100 Points Winter 2019

This homework is due no later than Wednesday, April 17. When answering each question, copy the question on your answer sheet and then provide the answer.

QUESTION #1 (75 points)

The U.S. Department of Health and Human Services (HHS) believes that increasing taxes on cigarettes would be an effective policy tool to decrease cigarette consumption, and therefore reduce illness and death from smoking. However, HHS wants to know precisely how much the price of cigarettes must increase to induce a substantial reduction in cigarette consumption. For example, by how much would the price of cigarettes need to increase to reduce cigarette consumption by 25%? To answer this question, HHS hires you as a consultant to obtain a good estimate of the price elasticity of demand for cigarettes.

Data

The data you will use for your study are contained in the data file cigarettes. This dataset consists of annual data for each of the 48 continental states for the years 1985 to 1995. Cigs is annual per capita cigarette sales in packs; price is the average price of a pack of cigarettes in cents; inc is state personal income in dollars; taxe is the federal, state, and local excise tax per pack of cigarettes in cents; taxs is the sales tax per pack of cigarettes in cents; state is state; sindex is a state index; year is year.All prices, income, and taxes are adjusted for inflation using the consumer price index, and therefore are in real terms.

Statistical Model

Given the data available to you, to analyze the relationship between the price of cigarettes and cigarette consumption, you specify the following demand and supply equations for cigarettes.

Demand Equation: lcigsit = β1 + β2 lpriceit + β3 lincit + μit

Supply Equation:lcigsit = α1 + α2 lpriceit + α3 taxeit + α4 taxsit + εit

where the letter “l” before a variable designates natural logarithm, and the subscripts i and t designate state and year. Note that inc, cigs, and price are in logarithmic form and taxe and taxs are not in logarithmic form.

Variables

1. For each of the following variables, create a new variable which is the logarithm of the variable: inc, cigs, price. Designate each of these variables by the first letter l. (No written answer required).

2. What coefficient measures the price elasticity of demand for cigarettes? If the objective of your study is to estimate the price elasticity of demand for cigarettes, then why does your model have a cigarette supply equation? Carefully explain.

3. Is the demand equation exactly identified or overidentified? Explain how you determined this? Do you believe the exclusion restrictions for the demand equation are valid? That is, do you believe the exogenous variable(s) that have been excluded from the demand equation to identify it can be validly excluded? Yes/no. Explain.

Estimation

4. Estimate the demand equation (1) using the OLS estimator and cluster robust standard errors. Report the results. Estimate the demand equation (1) using the 2SLS estimator and cluster robust standard errors. Report the results. What variable(s) are identifying instruments for the 2SLS estimator? Do you believe the identifying instruments are relevant and exogenous? Yes or no. Explain.

5. Compare the OLS and 2SLS estimates of β2. Does the OLS estimate appear to be biased up or down relative to the 2SLS estimate? Does the bias appear to be relatively large or small? Now test the hypothesis that lprice is exogenous in demand equation (1) using a Hausman test. Interpret the result. What does this tell you about the bias in the OLS estimate relative to the 2SLS estimate of β2?

6. Estimate the first-stage regression for lprice using the OLS estimator and cluster robust standard errors. Do the estimates of the coefficients of the identifying instruments have expected signs? Yes or no. Explain. Check for instrument relevance (the strength of the instruments). Do you believe the instruments are relatively weak or strong? What does this tell you about the bias in the 2SLS estimate relative to the OLS estimate ofβ2 ?

7. Estimate the demand equation (1) using the GMM estimator and cluster robust standard errors. Report the results. Given the results, do you believe the GMM estimator is more appropriate than the 2SLS estimator? Yes or no. Explain.

8. Choose an appropriate test, and test the overidentifying restrictions for the demand equation (1). Explain why the test you selected is the most appropriate test. Interpret the result. What does this tell you about the validity of your instruments? Does the result of your test provide evidence that the instruments are exogenous or endogenous? What does the result of the test suggest about the 2SLS and GMM estimates of β2?

Because you have panel data, you decide to estimate a demand equation with fixed-effects and time effects. You specify the following model.

(2) lcigsit = β1 + β2 lpriceit + β3 lincit+ vi+ λt + μit

You decide to estimate demand equation (2) using the 2SLS estimator with cluster robust standard errors. The command is,

ivregress 2SLS lcigs (lprice= taxe taxs) linc i.sindex i.year, vce(cluster sindex)

9. Estimate this demand equation. Report the results for lprice and linc (Do not report the estimates of the coefficients of the state and year dummy variables). Compare the estimate of β2 for the 2SLS model with fixed and time effects and the 2SLS model without fixed and time effects that you reported previously. Are the estimates similar or are they noticeably different?

10. You have estimated the following models: OLS, 2SLS, GMM, and 2SLS with fixed and time effects. Choose the model that you believe gives you the best estimate of the price elasticity of demand for cigarettes. Carefully explain why you chose this model. Do you believe that this estimate of the price elasticity of demand for cigarettes is a relatively good or relatively poor estimate? Explain.

11. The average price of a pack of cigarettes in the U.S. is $6.00. Use the estimate of the price elasticity of demand from the model you selected in part 10 to answer the following policy question. By how much would the average price of cigarettes have to increase to reduce cigarette consumption by 25%? Explain how you obtained your answer.

QUESTION #2(25 points)

You have been hired as a consultant by the U.S. Department of Health and Human Services (HHS) to conduct a study of the length of first marriage of young and middle age women. HHS is particularly interested in the effect of education on length of marriage.

Data

The dataset you will use for the study is a sample of 1,500 women between the ages of 18 and 40 who are married for the first time. These women were followed from date of marriage for 120 months (10 years) or time of divorce. Of these 1,500 women, 550 were divorced and 950 remained married after 120 months. The variables are as follows. dur is the amount of time that elapses until a woman is divorced or the woman is no longer followed after 120 months. inc is household income. It is measured as the combined annual income of husband and wife on date of marriage in thousands of dollars. edu is the woman’s education. It is a dummy variable that takes a value of one if she has a college degree and zero if she does not have a college degree on date of marriage. age is the woman’s age. It is measured as her age in years on date of marriage.

Statistical Model and Results

To analyze the data, you estimate the following Weibull duration model.

S(dur) = exp[-(dur)] where  = exp[-(0 + 1inc + 2edu + 3age)]

The results are given below.

. streg inc edu age, d(weibull) time

No. of subjects = 1500 Number of obs = 1500

No. of failures = 550

LR chi2(3) = 26.09

Log likelihood = -1702.727 Prob > chi2 = 0.0000

------

_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]

------+------

inc | .0454086 .0238689 1.90 0.057 -.0013737 .0921909

edu | .3410084 .1394471 2.45 0.014 .067697 .6143198

age | .022803 .006453 3.53 0.000 .0101554 .0354505

_cons | 4.050045 .3269784 12.39 0.000 3.409179 4.690911

------+------

/ln_p | -.2564357 .0396047 -6.47 0.000 -.3340594 -.178812

------+------

p | .7738048 .0306463 .7160113 .8362631

1/p | 1.292316 .0511817 1.195796 1.396626

Questions

HHS wants you to address the following questions.

1. Does education have an effect on the average duration of marriage? If so, what is the direction and size of the effect? Make sure you interpret your measure of size.

2. What is the hazard rate? Provide an estimate of the hazard rate for education. Show how you obtained this estimate. Interpret the estimate. Why might HHS be interested in the effect of education on the hazard rate?

3. Is a young or middle age woman more likely, less likely, or equally likely to get divorced the longer she has been married? Explain how you arrived at the answer to this question.

4. Predict the probability that a woman age 30 with a college degree and a household income of $50,000 at date of marriage will remain married for more than 5 years. Show your work.