Home » 2015 Categories » 2015 Durham Paper » Do People Pay to Live Closer to Duke University? by Victor Yifan Ye

Do People Pay to Live Closer to Duke University? by Victor Yifan Ye

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[1]

Table 1 - Victor

 

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.[2] 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%

Figure 1 - Victor

 

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[3]

Table 2 - Victor

 

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.

 

[1] * = P<0.1, ** = P<0.05

[2] 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.

[3] 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.


12 Comments

  1. Victor,

    I thoroughly enjoyed reading your paper. Especially since I am personally transitioning into my senior year when many of my peers have been searching for housing near campus, I see the topic as highly relevant. The methods that you used in your research are also very clear and easy to follow. The graph that you included to show the price difference between apartments within and outside radii 2-16 kilometers is particularly compelling, as it clearly indicates the steep decline in apartment prices experienced as you move away from campus.

    In addition for what you explained were way you could improve the your model, I think that an interesting extension to your project would be to use your model framework to analyze the apartment/housing values during different periods of time. In this way, you could explore how distributions have changed over the years with the growth of Duke University and the Downtown Durham area.

    Again, great job with the report!

    In-Young

  2. I really enjoyed reading your paper. This is an interesting topic because many Duke students decide to live in apartments off campus. Your paper could help students determine how far away from Duke they should search for apartments. As someone who is not a statistics or economics major, I appreciate how clearly you explained your findings and statistical analysis. Also, I found your visual representations helpful and effective.

    I am surprised that you did not find the same link for triple apartments as you did with doubles and singles. You did offer reasonable explanations for why you did not see the same link. However, I would have thought that students would want to have roommates.

  3. Victor-
    Fascinating results, great work.
    As someone who looked at a similar topic for my Durham paper, I’m curious how demographic information would effect your (and my) findings. Specifically, though this would be hard to determine, I wonder how much of the direct surrounding housing environment is affected by people who are affiliated with Duke (as undergrads, grad students, administrators, professors and so forth) and how much is simply affected by people unaffiliated who have other reasons for wanting to live near campus. The correlation itself is of course telling in many ways, but I would be curious to understand more about the demographic of people and what specifically might be drawing non Duke-affiliated people to this area.
    Best,
    Marc

  4. Victor,

    I very much enjoyed reading your paper and hearing your presentation last week as well. I appreciate your thoroughness in addressing the results of your statistical analysis – I particularly liked how you parsed the finding that the correlation between the price of triple apartments and distance to campus is much weaker than that of double and single apartments.

    For further analysis, I would be interested in exploring a bit more the idea of the interaction between distance from Duke and distance from downtown Durham. Given the rapid development of the city’s downtown area (or, at least, my perceived notion that downtown has been very rapidly developing over the past four years I’ve been here), I think it would be helpful to look at the ways prices of homes near Duke, near downtown Durham, and near both have developed over the time of downtown Durham’s and Duke campus’s development. The historical data could then be compared to relatively-newer prices that are now coming from the influx of apartment complexes near East campus (including the 605 West, 300 Swift, and Crescent complexes, among others).

  5. Victor,

    Great work, this is a really interesting topic and one that may be relevant to a lot of college towns around the country. I love how you used the Bing Maps API to acquire a great dataset. It seems rather intuitive that rooms would be more expensive around Duke but I was rather surprised at your findings that triples didn’t fit the same trend as singles or doubles. I find your explanations reasonable and think that it would be interesting to have the data for the number of students who live on campus in triples as well as a proxy for how desirable triples are to Duke students.

    I think you also did a great job identifying the effect that distance might have on apartment prices. Based on my anecdotal knowledge, many students will opt to live further off campus when they have a car, whereas students without cars are bounded by a much stricter radius to campus. I think it would have been interesting to bucket the apartments into walking distance (<1 mile), immediate driving distance (2-10 mi), and longer commutes (10+ miles).

    Really substantial and interesting read overall!

    Best,

    Alan

  6. I learned many interesting points from reading your analysis! I also appreciate your use of SI units, reminding me again the intriguing choice to use feet and miles by the U.S. In the beginning of the paper, I like how you set up the analysis and make the insightful connection between the observation that triple apartments are less correlated with distance and the economic theory of inferior goods.

    In the next part, you find that triple apartments tend to be closer to Duke than the single/double groups, and on average most apartments are 9-10 kilometers away from Duke. One thing that comes to mind is that may some of the single/doubles apartments you included serve populations other than Duke students. Perhaps certain apartments that to the southeast or southwest of Duke are being rented by those who commute to Duke or to Chapel Hill for work, because an apartment that is 15 kilometers, or around 9 miles linear distance from Duke, is about right in between Chapel Hill and Durham. So that’s just an interesting thing I was thinking about.

    Finally, your graph for the price premium on apartments in each range of radii illustrates your results very clearly. It has a lot of impact and is very memorable to me, showing that apartments within 4 kilometers of Duke all have high price premiums, while those that are farther than 4 kilometers do not. So it seems like the presence of Duke is not a huge factor on the rental price of apartments that are more than 4 kilometers away. Still, the premiums of the apartments that are close to Duke are pretty shocking, but I feel like most Duke students don’t seem too bothered to pay that premium for the convenience and nice environment.

  7. Hi Victor, this is a fascinating topic and I enjoyed being able to go through your work. I thought a lot of your statistics work was very strong revealed some though provoking findings. I found it interesting that the correlation between the price of triple apartments and distance to Duke is weaker than double apartments and single apartments.

    I think this would be a great topic to expand to other schools. Maybe try it with a bigger state school with more of a “college town” environment. This could show how these towns are truly valued by students. Additionally, I think it would be interesting to compare these results to results from a school that has a similar college town as Durham. Maybe Winston Salem?

    Great work overall and hopefully your research was able to help some people out when it comes time to find a place to live off of campus.

  8. For someone who has hardly any statistics, upper-level math, or economics background, I found your paper very well researched and clearly articulated. Both your analysis of the regression models and your diagrams helped convey your findings, and I appreciate your attention to detail throughout your explanations.

    Your topic itself I found to be very interesting, since I am a rising senior and considered living off-campus. I’ve lived in Duke’s Central Campus apartments for the past two years, and one of the biggest lures to live off campus was because the quality of off-campus apartments nearby is far nicer than Duke’s central campus apartments. However, one of the biggest factors that ultimately made me decide to live on central for my senior year is the proximity and convenience to campus. Students might pay a premium to live closer to Duke’s campus, but they’re also paying a premium not to live directly on campus — the line between the two is an interesting consideration.

    Like many other students, I also found it surprising that the correlation between the price of triple apartments and distance to campus is significantly weaker than that of double and single apartments. You mentioned that part of this could be explained by the relatively few number of apartment buildings that offer triple rooms or that triple rooms represent an inferior good compared to single or double rooms, causing Duke students with high average spending power to not want to live in them. However, from my personal experience in the search for off-campus housing, I found that 3-bedroom apartments are becoming more and more popular among students. One of the reasons so many students want to live in the Erwin Mills apartments (which are located extremely close to campus) is because they are one of the few apartment complexes that offer triples. The wait list, I believe, for the triples is longer than any other list they have.

    One final point I’d like to make is the fact that the new supply of student-living apartment complexes near campus is a very new trend for Durham. It would be interesting to compare this to previous time periods. While the supply of off-campus housing has dramatically increased, the number of students eligible to live off campus (according to Duke rules, only seniors can live off campus, with a few exceptions for juniors and student-athletes) has remained more or less the same.

  9. Hi Victor, I am impressed that you examined the association between apartment rents and linear distance to Duke University both (1) using a method that regressed prices on distance estimates directly and (2) employing a second approach that recognized the potential binary nature of apartment rental prices’ response to distance from campus. The latter point is essential to include because once students or employees acquire a car and thus do not have to rely on walking or public transportation to reach Duke, distance would logically not make as much of a difference past a certain point. I also commend you for estimating the price discrepancies for zones of varying radii rather than arbitrarily choosing a border; this provides much richer information– in particular, I find the first figure (i.e., graph illustrating price differences within and outside circular areas of increasing radii from 2 km to 16 km) to be very clear in showing the drop-off in the apartment rents gap within the first couple kilometers of radii, followed by a more stabilized, gradual decline. If you control for other factors (e.g., economic conditions, demographics of neighborhoods), this pattern could motivate your intuition about distance mattering less as linear distance to campus increases since those who live farther are more likely to own automobiles.

    Additionally, your paper focuses primarily on Duke students as the clientele of the apartments surrounding the university. But since the university (main campus plus Duke Med) is the top employer in Durham, I can imagine a fair share of non-students also live in nearby apartments. Thus, as Marc mentioned in an earlier post, it could be insightful to control for demographic characteristics when examining the relationship between apartment prices and distance. However, once demographics are accounted for, it is crucial to recognize that segments of the population may have limited access to the Internet and are thereby less likely to frequent or post on an apartment ratings website. This could skew the extent of which representative online ratings are representative of actual apartment quality.

  10. Victor,

    Your paper was well written and and structurally sound. I enjoyed how thorough your empirical analysis was in relation to the multi-family market around campus. Several of your insights are extremely note worthy. The fact that walk-ability plays such a factor in price is very indicative of what the actual services are that the University provides to its students and surrounding residents. I also found the differences in responsiveness between price and number of bedrooms interesting. After just going through an apartment search myself for a different city, I would have expected 1 bedrooms to be the most responsive in price, followed by 2 and 3 bedrooms. This insight could be specific to the University life style and culture that you were talking about.

    I found two small issues with your analysis: You often discuss the rationale behind the renters of these complexes as students and their relationship to Duke. I think more often than not, a lot of these complexes close to campus are not rented by students, but by locals. This should be expanded upon and noted in further revisions, to help gain a better grasp of who exactly wants to be around universities and for what reasons. The other option is to only take data from “student housing.” Coupled with this, you stated briefly that the apartments closest to Duke are biased to higher quality due to the wealth of Duke students. I’m not sure if this is entirely accurate. I also understand that you were just speculating reasons in that section, but I think the question of “why are there higher quality options nearest to campus?” demands a more hedonic approach in order to figure out exactly why these properties vary so much on the upper end of your gradient. You could even compare hedonics to other universities to see if the reasons for Duke’s specific price layout differ to those of other institutions.

    Finally, I think it would be very interesting to have your empirical analysis reconstructed in 10 years. As Durham changes, the quality of apartments and the premiums attached to Downtown and the suburbs will change drastically. I hypothesize that your gradient will become more hyperbolic, and students themselves will have less of an impact on pricing. At this point in time, the premiums attached to being around Duke’s campus could be due more to the research opportunities, hospital, and aesthetics, rather then job opportunities and wealth.

  11. Victor,

    I definitely enjoyed reading your paper. It was an interesting topic to which I, as a Duke student, could personally relate. It was so interesting that I happened to write my Durham paper and term paper on the same topic. Even the approach of using regression analysis is similar so that I was actually paying much more attention on finding differences between your paper and mine.

    While reading your paper, there were some questions that came up in my mind. First of all, I understand that you used the shorter of the two distances to the campuses, because it allows for the possibility that individuals may not have a particular preference for one campus but simply desire to live closer to one of the C1 bus stops. However, I expect that most of the students living off-campus would commute to West campus, because most of the buildings for classes and meetings are located in West campus. Also, you assumed that students from Duke generally have high spending power, but in my paper, I assumed otherwise. It is possible that Duke students have higher spending power compared to students from other universities, but it seems unlikely that students would have higher spending power compared to residents who live around Duke University and are likely to be Duke-affiliated.

    I really liked your method of separating the effect of single, double, and triple rooms. It was another good measure that shows how college students behave in apartment market around universities. The results of doing so were also very interesting. I didn’t expect them to be too different, but it was clear that residents have different feelings about triple room, because the correlation was much weaker than the other two. You mentioned that the reason might be that there are relatively few apartment buildings that offer triple rooms and that triple rooms represent an inferior good compared to single or double rooms, causing Duke students with high average spending power to not want to live in them. I agree that there are few complexes that offer triples, but I am not too sure that triples are inferior goods, given that majority of the residents are actually not students.

  12. I really enjoyed your research on housing prices near Duke, especially since it is a topic that is extremely relevent for us students. The two methodologies for examining the price response of distance to Duke were definitely a good idea. Personally, I think that the binary model makes the most sense intuitively for the Duke community. I would say that most housing is either “walkable” to Duke or it is not, and that rents reflect that. With the other regression model that examined prices and distances to campus, you could also consider estimating the commute time instead of distance (which I’m guessing would be measured “as the crow flies”).

    Overall, I thought this was a great paper on an especially interesting topic, and one that would definitely be worth examining even further.

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