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Use the data in RENTAL for this exercise. The data for the years 1980 and 1990 include rental pricesand other variables for college towns. The idea is to see whether a stronger presence of students affectsrental rates. The unobserved effects model is$\log \left(r e n t_{i t}\right)=\beta_{0}+\delta_{0} y 90_{t}+\beta_{1} \log \left(p o p_{i t}\right)+\beta_{2} \log \left(\operatorname{avginc}_{i i}\right)+\beta_{3} p c t s t u_{i t}+a_{i}+u_{i l}$where pop is city population, avginc is average income, and pctstu is student population as a percentageof 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 $\hat{\beta}_{\text { perstit }} ?$(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 $\beta_{p c i s r u}$ with that from part (ii). Does the relative size of the student population appear to affect rental prices?(iv) Obtain the heteroskedasticity-robust standard errors for the first-differenced equation inpart (iii). Does this change your conclusions?

(i) see video (ii) not valid (iii) see video (iv) smaller standard error

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Chapter 13

Pooling Cross Sections Across Time: Simple Panel Data Methods

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part one. We obtain these results using pulled old L s. Oh, the coefficient on D 90 is positive and very significant. It's coefficient implies that nominal rents grew by over 26% over the 10 year period. All else equal the coefficient on percent s to you means that a 1% point increase in PCT stu increases rent by half a percent. This variable has a T statistic of five, meaning at least based on the usual analysis PCT. Stu is very statistically significant. Hard to the standard errands we got from part one are not valid unless we think a sub I the heterogeneity component, does not really appear in the equation. If a supply is in the error term, the Iran's across the two time periods for each city are positively correlated. And this invalidates the usual L as standard. Iran's and T statistic part three. This is the result from first difference ing the left hand side becomes the change in the lock of rent or the person he changed in rent. So before we get 128 observations and after difference thing, we have Onley half of that. We have 64 observations and we have a smaller are square. What we care about is there estimate on PCT. Stu, we find that the effect of PCT Stu is over twice as large as we estimated in the Poland O L s equation now a 1% point increase in PCT. Stu is estimated to increase rental rates by about 1.1%. It is not surprising that we get a much less precise estimate when we difference when we difference away a sub I there may be other and observable that change over time and are correlated with the change in PCTs D'You Yeah, so let me write it down. We have okay, we have larger beta hat for this variable, but also a larger standard error. And the reason is a sub. I is eliminated part four hetero statistics city robots standard. They're all on the change of PCT. Stu is about 0.2 eight, which is actually much smaller than the usual old l s centered error. This makes PCT as to you. More significant, the robust T statistic is roughly four. Okay, serial correlation is not an issue anymore because we have no time component in the first different equation

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