Use the data in RENTAL.RAW for this exercise. The data on rental prices and other variable...

Use the data in RENTAL.RAW for this exercise. The data on rental prices and other variables for college towns are for the years 1980 and 1990. The idea is to see whether a stronger presence of students affects rental rates. The unobserved effects model is

log(rentt) = β0+ δ0y90t + β1log(popit) + β2log(avgincit) + β3 pctstuit + ai + uit ,

where pop is city population, avginc is average income, and pctstu is student population as a percentage of city population (during the school year).

(i) Estimate the equation by pooled OLS and report the results in standard form. What do you make of the estimate on the 1990 dummy variable? What do you get for

(ii) Are the standard errors you report in part (i) valid? Explain.

(iii) Now, difference the equation and estimate by OLS. Compare your estimate of fipcmu with that from part (i). Does the relative size of the student population appear to affect rental prices?

(iv) Estimate the model by fixed effects to verify that you get identical estimates and standard errors to those in part (iii).