Exercise 9

(1)         Use the data in RENTAL.dta 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

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 pctstu?

(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  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).


(2)   Suppose that, for one semester, you can collect the following data on a random sample

of college juniors and seniors for each class taken: a standardized final exam score, percentage of
lectures attended, a dummy variable indicating whether the class is within the student’s major,
cumulative grade point average prior to the start of the semester, and SAT score

(i) Why would you classify this data set as a cluster sample? Roughly, how many observations would
you expect for the typical student?

(ii) Write a model, that explains final exam performance in terms of attendance and the other
characteristics. Use s to subscript student and c to subscript class. Which variables do not change
within a student?

(iii) If you pool all of the data and use OLS, what are you assuming about unobserved student
characteristics that affect performance and attendance rate? What roles do SAT score and prior GPA
play in this regard?

(iv) If you think SAT score and prior GPA do not adequately capture student ability, how would you
estimate the effect of attendance on final exam performance?