Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percentage of the total population. One model to test for a relationship is: log(rent) = ?0 + ?1 log(pop) + ?2 log(avginc) + ?3 pctstu + u Assume that you have estimated the above equation using the OLS and got the following estimation result: log(rent) = 0.043 (0.844) + 0.066 (0.039) log(pop) + 0.507 (0.081) log(avginc) + 0.0056 (0.0017) pctstu N = 64 R^2 = 0.458 Numbers between the brackets are the standard error. Answer the following questions: a) What signs do you expect for all slope coefficients? b) Interpret all of the estimated coefficients. c) Comment on the value of the R-squared. d) Perform a 1%, 5% and 10% individual significance test for all slope coefficients. Comment on your results. State the null and the alternative hypotheses for each one. e) Calculate the 95% confidence interval for all slope coefficients. f) Perform a 5% joint significance test. Comment on your results. State the null and the alternative hypotheses.
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Larger populations may increase demand for housing, raising rent. - **log(avginc)**: Positive. Higher average income suggests greater ability to pay higher rent. - **pctstu**: Positive. A higher student population may increase demand for rental units, raising Show moreā¦
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Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percentage of the total population. One model to test for a relationship is ln(rent) = ĆĀ²0 + ĆĀ²1ln(pop) + ĆĀ²2ln(avginc) + ĆĀ²3pctstu + u. a. Use rental.dta to estimate the model by OLS using data for 1990 only and report the results. Use non-robust standard errors. b. Difference the equation by calculating the difference between 1990 and 1980 for each city and estimate by OLS. Report the estimates. Use non-robust standard errors. c. Interpret the estimate for ĆĀ²3. Does the relative size of the student population appear to affect rental prices? d. Estimate the model by fixed effects using city and time fixed effects and report your estimates. Use non-robust standard errors. Compare these results to those in question (b) and comment.
Sri K.
Use the data in RENTAL for this exercise. The data for the years 1980 and 1990 include rental prices and other variables for college towns. The idea is to see whether a stronger presence of students affects rental 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 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 $\hat{\beta}_{\text { perstit }} ?$ (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 in part (iii). Does this change your conclusions?
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