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C1 Use the data in RENTAL for this exercise. The data on rental prices and other variables for collegetowns are for the years 1980 and $1990 .$ The idea is to see whether a stronger presence of studentsaffects rental rates. The unobserved effects model is$\begin{aligned} \log \left(\text {rent}_{i t}\right)=& \beta_{0}+\delta_{0} y 90_{t}+\beta_{1} \log \left(p o p_{i t}\right)+\beta_{2} \log \left(a v g i n c_{i t}\right) \\ &+\beta_{3} p c t s t u_{i t}+a_{i}+u_{i t} \end{aligned}$where pop is city population, avginc is average income, and pctstu is student population as a percent-age of city population (during the school year).(i) Estimate the equation by pooled OLS and report the results in standard form. What do youmake of the estimate on the 1990 dummy variable? What do you get for $\hat{\beta}_{p c s t u}$ ?(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 $\beta_{\text {pctstu}}$ with thatfrom 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 errorsto those in part (iii).

Yes, the relative size of the student population pctstuappears to affect rental prices log(rent)as it is a statistically significant explanatory variable at 5$\%$ level of significance.

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Chapter 14

Advanced Panel Data Methods

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the first three parts we have done in computer exercise 13.5. So it's problems. Five. Chapter 13 Hartz four is the only new part. This is the regression result. We don't have an intercept because it is eliminated by the time demeaning. There are 64 cities and two years. You can confirm that the slope coefficients and the standard Iran's are identical to what we get from first difference ng estimation, yeah.

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