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This paper investigates the association between apartment rental prices in Durham and their linear distance to Duke University. Considering the substantial role Duke plays in the economic activity and housing demand, in particular that of apartments, in the city of Durham, one would expect a positive relationship between proximity to campus and the rental price of apartments. This paper aims to quantitatively examine whether or not such a relationship exists.
While not impossible, a comprehensive quality-adjusted approach to apartment prices for Durham apartments involves the matching of several datasets and is not utilized in this paper. An alternative is found in online ratings of apartments provided by review sites. Ideally, these reviews are proxies for the relative quality of accommodations and services of each given apartment. Once matched for distributions of ratings on different websites, average scores can be seen as directly comparable between apartments. Potential correlation caused by a bias towards higher quality closer to Duke’s campus because of the higher endowed wealth of Duke students, or lower quality caused by their bad behavior, can be accounted for using an interaction term.
An initial model is established using only apartment distance to Duke University as the dependent variable. Apartment listing prices are collected from Apartmentguide.com and separated by room class: one, two and three-bedroom offerings are counted separately, with maximum, minimum and average listing price for each room type provided. A mean price for each room type is calculated by taking the average of the maximum and minimum prices – note that this may not be an accurate estimate, since the composition of apartments by price for each room type is unknown. Distance values are estimated using a linear point-to-point approach. Apartment locations are obtained using the Bing Map geocoding API, and the East/West campus bus stops are used as point proxies for the two campuses, respectively. A third estimate uses the shorter of the two distances to the campuses. This allows for the possibility that because of the extensive public transit options between East and West, individuals may not have a particular preference for one campus but simply desire to live closer to one of the C1 bus stops.
For the regression model, natural log transformations are applied both to listing prices and distance estimates. A fairly strong association has been found between the prices of most of the room types and all three distance estimates. The strongest association occurs between the price of double apartments and their distance to West Campus, with a doubling of distance translating into a price decrease of 5.1%. All three regressions using the price of double apartments reports significance over 95% when regressed against distance estimates. The association between price of single apartments and distance is significant at the 90% level for both the distance to West Campus and the minimum distance estimate to both East and West Campus. One could speculate that single rooms, being not only more expensive but also less conductive to a social lifestyle, are not as preferable to Duke students as double rooms, leading to the weaker price association.
Coefficients for single-variable regressions between distance estimates and average price
Interestingly, the link between price of triple apartments and distance to campus is much weaker than that of double and single apartments. No distance estimate seems to be even slightly correlated with the price of triple apartments. Part of this could be explained by the relatively few number of apartment buildings that offer triple rooms. However, it is also possible that since triple room represent an inferior good compared to single or double rooms, Duke students with high average spending power would typically not choose to live in them. Some students might move off campus to escape a triple or double dormitory and have little interest in similar living conditions. It could also be possible that local families unaffiliated with Duke University are more likely to occupy the large units, in particular three-bedroom apartments.
A possible way to indirectly check the validity of this explanation is to see if triple room-offering apartments are, on the average, further away from Duke than single or double apartments. If students don’t care for triple-room apartment, they ought to be distributed more randomly in Durham and be, on average, further away from the Campuses. However, this does not seem to be the case for the apartment sample in the dataset. The average distance to West Campus for all apartments offering triple rooms is 9.01 kilometers, closer than the figures for apartments offering single and double rooms (9.07 and 9.35 kilometers, respectively). The average distance to East Campus displays a similar trend, at 8.33 kilometers on average for apartments that offer triple rooms, 8.58 kilometers for apartments that offer single rooms, and 8.87 kilometers for apartments that offer double rooms.
It is also possible that the price response of distance is not only non-linear but also somewhat binary in nature. Intuitively, apartments beyond a reasonable walking range will only be marginally affected by extra distance: the extra mile should matter very little if one has to drive to school anyways. To test this, dummy variables indicator certain levels of proximity to West Campus, starting from closer than two kilometers, were regressed against prices of double apartments. Indicators at the 2,3 and 4-kilometer level report significance at greater than 95% levels, while all coefficients of indicators until 14 kilometers show significance at greater than 90% levels. Double apartments that are closer than 2 kilometers to campus show a substantial, 28.9% price premium over those that are further than 2 kilometers away from campus. Double apartments that are closer than 3 kilometers to campus have a 16.3% premium. However, there is also a premium of 4-7% (6.2% on average) of apartments closer to campus than a range of distances from 5km to 15km.
Price difference between apartments within and outside radii 2-16 kilometers, 1 = 100%
A potential explanation for this behavior is that apartments very far away from campus are so grossly inferior in quality terms that everything else offered seems better in comparison. This does not seem likely, but a positive association between quality and distance might exist simply because the presence of Duke raises surrounding land prices and makes low-quality, low-margin apartments less profitable. Being far from Duke may also mean being far away from downtown Durham, which in itself implies a number of other negative influences on price. A third explanation is that even if an apartment is beyond walking distance to Duke’s campus, there can still be indirect benefits from being somewhat close to Duke. Better policing, the coverage of Duke transit systems, short driving distances to the Duke Hospital might all be factors that play a role in prices of apartments beyond the walkable range.
One issue to consider is that positive price effects of larger radii are much weaker with regard to single apartments and virtually nonexistent for triple apartments. Single apartments closer than 2km and 3km to West Campus enjoy a 22% and 14% respective price premium, which is comparable in absolute terms with those of double apartments. However, when the indicator search radius is expanded the positive price effect quickly disappears. Using search radii of 11 and 12 kilometers, double apartments within the radius enjoy a 7% and 5.1% price premium compared to those that are outside, both significant at the 90% level. Single apartments within the same radii, on the other hand, only enjoy a 3.3% and 0.8% price premium. Neither of these relationships are statistically significant. No regression model with triple apartment prices reports statistical significance at the 90% level, although the 2-kilometer indicator represents a 10.4% price premium (P=0.47) for triple apartments.
Concluding the results thus far, all three apartment types show some level of response to difference distance gradients. Prices of double apartments are the most responsive, while evidence for price responses of triple apartments is somewhat weak. If we take the average price premium level for double apartments between 5-16 kilometers as reasonable expectations for price of a resident not living within walking distance to campus, then the model suggests that compared to not being able to walk to school at all, living closer than two kilometers to west campus comes with a price premium of 22.7%. Living closer than three kilometers has a relative premium of 10.1%. The same respective rates for single apartments are 18.5% and 10.5%, and for triples 9.5% and 6.2%. However, the triple apartment figures are not statistically significant.
Frequency Plot of Ratings of Sample Apartments
To further develop the model, online ratings of apartments are added in as a control variable. Ratings are collected from several websites and matched by average value and standard deviation. Ratings from different websites are aligned not by absolute score but by standard deviations from the mean, capped at 0 and 100. Apartments with fewer than five ratings for all websites aggregated are not considered in the dataset to avoid misrepresentation. Apartments with ratings from multiple websites have a composite score derived by first matching scores by mean and SD and then averaging over all scores. Unfortunately, not all apartment groups in the dataset have at least five ratings. Out of the 238 total observations with price data and 119 total observations with at least five reviews, only 89 observations have both price data and the minimum number of rating scores. Scores are tallied at a maximum of 100 and minimum of 0, with an adjusted average score of 55.7 out of 100 for the 89 usable observations. The 25th percentile score is 35 and the 75th percentile score 84.3.
With the inclusion of ratings as a control, no distance gradient terms in any of the regression models report statistical significance above 90%. This is the case for all three distance estimations, three apartment types and radii 2 – 6 kilometers. Distances terms remain below the 90% level of significance after adding in an interaction term between distance and ratings. However, the coefficient of the ratings term is highly significant for all regression models. Regressing only the ratings term against price of single, double and triple rooms results in strongly positive connections. For 10 extra points in the rating score, there is a price premium of 1.82%, 1.81% and 1.13% for the three room types, respectively. Note that these effects are weaker than those associated with distance to campus.
Influence of distance estimates/indicators on apartment ratings and respective significance
The reduction of statistical significance in distance gradient coefficients after introducing ratings as a control suggests a relationship between distance to campus and ratings. This can be demonstrated by a variety of metrics. Using the full, 119-observation dataset of apartments with ratings, the correlation coefficient between average review score and log-distance to West campus and East campus is -0.206 and -0.207, respectively. Modelling distance preferences using a natural log transformation, a doubling of distance to West Campus results in an average expected rating decrease of about 8.2 points. However, it must be noted that this association is rather weak considering the large spread of apartment ratings, which reports a standard deviation of 30.6 points.
The association between distance gradients and ratings can be explained in several ways. The obvious rationale is that raters are taking distance into account when giving scores, boosting the scores of apartments closer to campus. It is also possible that there is an inherent bias in apartment quality, with higher quality apartments generally being built closer to campus. If Duke students do actually have higher spending power than the average apartment resident in Durham, developers could be selectively offering high-quality, expensive apartments at locations closer to school in response greater demand. Even if apartment quality is not inherently associated with distance, students could be on average less responsive to quality differences. This could be the case either because most students know that they will be moving out in the near future (upon graduation) and have little concern for quality factors, or because their social lives are centered on Duke’s campus regardless of how far away they live. If apartments closer to Duke have larger student populations that only view the apartment as a place to shower and sleep, scores of bad apartments close to Duke could be buoyed even if such groups do not care about distance.
It is not difficult, at least in principle, to test for these explanations. However, currently available data do not offer a straightforward way to introduce controls beyond rating scores. Several websites do offer extra information about size and amenities, but the total number of observations in the dataset that have such information is small. Future research on such issues could focus on the obtaining of apartment quality data and geospatial quality variables such as crime rates and distances to public utilities. The distance estimate itself could also be improved, for example using actual walking/driving distance estimates instead of linear distance to campus. It might also be useful to model Duke Campuses as shapes with different points of priority (bus stops, Bryan Center, etc.) instead of a single point.
In conclusion, this paper has provided evidence of distance gradient effects on apartment prices in Durham. On average, a 100% increase in linear distance to west campus results in a 3.6% price decrease for single apartments and a 5.1% price decrease for double apartments. Using distance indicators, being within 2 kilometers of the west campus bus stop translates to a substantial, 22.7% price premium for double apartments and an 18.5% price premium for single apartments. The same figures derived with a 3-kilometer radius estimate are 10.1% and 10.5%. There is also evidence of a negative association between rating scores of apartments and their distance to campus. For a doubling of distance to West Campus, ratings scores decrease by approximately 8.2 out of 100 or 0.27 standard deviations.
 * = P<0.1, ** = P<0.05
 Only 142 apartments out of the 238 listings in the dataset offered triple rooms. In contrast, 228 apartments offered double rooms and 212 apartments offered single rooms.
 The 2km-radius indicator is not used here because only 2 apartments out of the 16 observation within the 2km radius have at least five reviews.