Stat 521 Homework 3

This homework is due Friday, March 20th by 5 p.m. You can put in my mailbox in the statistics department on the fourth floor of Huntsman Hall if you do not hand it in during class on Wednesday.

1. In this problem, we will examine a differences-in-differences design. The data is in hprice.raw on the course web site (www-stat.wharton.upenn.edu/~dsmall/stat521-s09 ). The data is described in hprice.des on the course web site and comes from Kiel and MccAin, 1995, “House Prices During Sitting Decision Stages: The Case of an Incinerator from Rumor Through Operation.” The data contains housing prices and characteristics from two years, 1978 and 1981, for homes sold in North Andover, Massachusetts. In 1981, construction on a garbage incinerator began. Rumors about the incinerator being built were circulating in 1979, and it is for this reason that 1978 is used as the base year. By 1981, it was clear that the incinerator would be operating soon.

(a) Using the 1981 cross section, estimate a bivariate constant elasticity model relating housing price to distance from the incinerator, i.e.,

E[log( price ) | log( dist )]=b0 + b 1 log( dist ) for the 1981 data.

Does b1 likely measure the causal effect of the incinerator on housing prices? Explain.

(b) Pooling the two years of data, consider the model

E[log( price ) | log( dist ), year ]=d0 + d 1 y 81 + d 2 log( dist ) + d 3 y 81*log( dist ) where y81 is a dummy variable for year 1981. If the incinerator has a negative causal effect on housing prices for homes closer to the incinerator, what sign is d3 ? Estimate this model and test the null hypothesis that building the incinerator has no effect on housing prices.

(c) Add the variables log(intst ),[log( intst )]2 ,log( area ),log( land ), age , age 2 , rooms , baths to the model in part (b) and test for whether building the incinerator has an effect on housing prices. What do you conclude?

2. The data in wagepan.raw on the course web site (www- stat.wharton.upenn.edu/~dsmall/stat521-s09 ) is from the National Longitudinal Survey (Youth Sample); the data comprises a sample of full-time working males who have completed their schooling by 1980 and are then followed over the period 1980 to 1987. The variables in the data set are described in the file wagepan.des on the course web site.

Consider the wage equation log(wage )it=q t + b1 educ i + b 2 black i + b 3 hispan i + b 4 exper it + 2 b5experit+ b 6 married it + b 7 union it + c i + u it Note that education does not change over time.

(a) Estimate the coefficients in the wage equation by pooled OLS. Are the usual OLS standard errors reliable, even if ci is uncorrelated with all explanatory variables? Explain. Compute appropriate standard errors.

(b) Estimate the coefficients in the wage equation by random effects. Compute robust standard errors and compare the standard errors with the robust standard errors from pooled OLS.

(c) Now estimate b6 (the marriage premium) and b7 (the union premium) by fixed effects and compute 95% confidence intervals. How do the estimates of the marriage premium and the union premium from fixed effects compare to those from the random effects model?

(d) Is there strong evidence that ci is correlated with marriage status or union status? Explain your answer.

(e) Explain why you cannot estimate the effect of experience on earnings using the fixed effects model even though experience changes over time.

(f) Add a lead of the union variable, unioni, t+ 1 , to the fixed effects model. Note that you will need to drop the data from 1987 since the lead cannot be defined for t=1987. Is unioni, t+ 1 significant? What does this result say about the strict exogeneity of union membership?