In a competitive environment, rents are determined by the intersection of supply and demand. This post will analyze how, after controlling for average income and population in a city, the percentage of colleges students in a city impact rental rates. There are several ways one can think about how the relationship between college students and can manifest itself. College students tend to be tough on the housing stock, you can imagine how maintenance can differ in a apartment with college students relative to retirees. The potential is that this higher level of maintenance can be partially passed down to the students themselves in the form of higher rent or absorbed by the property owner in the form of lower profit. On the other hand, college students tend to be out of the labor force, and thus have lower earnings. This analysis will control for that by using the average income per city as a control variable. Low income can still manifest itself in another form, through the political process. Students can join together and use the political process to enact rent control provisions in their city’s regulations. This has happened in several college towns, including UC Berkeley and UCLA, and is another way in which college students can influence rental rates in a city. One can think of several other arguments for the direction of the relationship between college students and rental rates in a city, so the question’s answer departs from a theoretical stanpoint and lends itself to empirical analysis. The analysis conducted here suggest that a 10% increase in the percentage of college students increases rent in a city by about 11%.

The first regression that was estimated was a simple pooled OLS regression. The model was improved by removing serial autocorrelation in the error term by taking the first difference of all variables then running OLS. After first differencing, there was an opportunity to remove heteroskedasticity by using heteroskedasticity robust standard errors in the first differenced OLS model.

Pooling independent cross sections is data from different time periods placed in the same data set and used to analyze a problem. A cross sectional data set is a sample from the population and if there are several of these pooled together then we have **Pooled Cross Sections over Time**. The figure below shows how pooled cross sections should be organized for analysis on STATA from a data set on rental rates found in Introductory Econometrics: A Modern Approach.

The variable “city” indicates the number of a city under observation. The variable “year” indicates the year the observation was made and the variable pop, for example, shows the population in during the observation. One can see that the population in city one went from 75,211 in 1980 to 77,759 in 1990. This way of organizing the data is typical and allows most statistical packages to handle calculations fairly easily.

**Simple Panel Data Regression Methods**

**The regression above suggest that the relationship between college students and rental rates is positive. A 10% increase in colleges students is expected to increase the rents in a city by about 5% even after controlling for average income, population, and a time trend in rents between 1980 and 1990. There can be a problem with this regression in the form or auto-correlation in the error term, thus first differencing the data would eliminate this issue, and results in the regression result below.**

Notice that after using regressing using first differences one can see that the OLS on the level data underestimated how large the relationship between college students and rents are. In our new model, after controlling for income and population, a 10% increase in college students increases rent by about 10% in a city. The final issue could be heteroskedasticity in the regression, so the final model uses heteroskedasticity robust standard errors, and finds that the a 10% increase in the percentage of college students increases rental rates by about 11%. These results are shown in the final regression below: