Week 8 - Problem Set
1.
Economists are often concerned about using survey data-i.e., what individuals say they would do rather than what those individuals actually do because survey respondents can be overly optimistic or pessimistic when the truth is complex ("How much more would your business invest under the tax plan of Candidate A?"), or deliberately untruthful when the truth is embarrassing ("When was the last time you cheated on your spouse?"). Consider the simple population model y;= Po + B1 i; +u, where zi, is unobserved and 1;= ;+r; is a measure of z generated from survey data. Under what circumstances would you find the Classical Errors-in-Variables (CEV) assumption cov[,,r] = 0 to be reasonable?
2.
Kiel and McClain (1995) used the pooled cross section data set hprice.txt-which contains the prices and characteristics of homes sold in North Andover, Massachusetts in 1978 and 1981-to measure the relationship between price and the distance to a newly-built garbage incinerator. An extensive public conversation concerning the incinerator began in 1979 and its construction began in 1981. The variables are listed on the following page.
(a) Are these data independent and identically distributed (i.i.d.)? Why or why not? (b) Using the data for year-1981 only, estimate the linear equation
log(price, 1981) Bo+ B1 log(disti, 1981) + 4,1981
and explain whether it is appropriate for determining the causal effects of proximity to the incinerator on housing prices.
(c) Using both years of data, estimate the difference-in-differences regression
log(price it)=80+81 1[year 1981] +82 log(distit) + 83 1[year = 1981].log(distit) + uit
where 1[year 1981] is a dummy equal to 1 if year 1981. Perform a robust test of the null hypothesis that the building incinerator had no effect on home prices. Discuss results.
(d) Is the equation in (c) a structural model? Why or why not? Why would it matter?
(e) Repeat the test in (b) adding the variables log(int st), (log(intst))2, log(area), log(land), age, age, rooms, and baths to the regression. Does the addition of these regressors change your interpretation of the economic meaning of 83?
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