Abstract
Walk Score: The Significance of 8 and 80 for Mortgage Default Risk in Multifamily Properties A u t h o r Gary Pivo A b s t r a c t In this paper, I use logistic regression to study the relationship between walkability and mortgage default risk in multifamily housing in a pool of nearly 37,000 Fannie Mae loans. Walkability is measured with Walk Score, a widely available metric. Controls were introduced for loan terms, property characteristics, neighborhood conditions, and macroeconomics. Walkability reduced default risk but the relationship was nonlinear with thresholds. Default risk significantly increased where walkability was very low and significantly decreased where it was very high. The implication is that walkability and its possible benefits to health and the environment could be fostered by relaxing lending terms without adding default risk. In this paper, I examine the relationship between Walk Score, a widely available indicator of walkability, and mortgage default risk in multifamily rental housing. The findings show that very high and very low Walk Scores significantly affect default risk. Where Walk Score is 80 or more out of 100, the relative risk of default is 60% lower than where Walk Score is less than 80, controlling for other factors that impact risk. Where Walk Score is 8 or less, default risk is 121% higher. This is the first paper that shows Walk Score affects default risk in multifamily rental housing. It builds on prior work showing that higher Walk Scores are related to lower default risk in single-family housing (Rauterkus and Miller, 2011) and higher values in office, retail, and apartment buildings (Pivo and Fisher, 2011; Kok and Jennen, 2012; Kok, Miller, and Morris, 2012). For lenders and developers, the findings reported here indicate that Walk Score could be used to help evaluate and underwrite properties and investment risk. For researchers in real estate and urban economics, the findings deepen our knowledge of investment risk correlates and the role of local accessibility in urban economic geography. And for practicing urban planners, developers, policy-makers and others interested in fostering healthier, more sustainable cities, it strengthens the case for walkable urban development. B a c k g r o u n d Walkability is the degree to which an area within walking distance of a property encourages walking trips for functional and recreational purposes (Pivo and Fisher, J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 1 8 8 P i v o 2011). Several physical and social attributes of an area can affect walkability including street connectivity, traffic volumes, sidewalk width and continuity, topography, block size, safety, and aesthetics (Frank and Pivo, 1994; Hoehner et al., 2005; Cao, Handy, and Mokhtarian, 2006; Lee and Moudon, 2006; Parks and Schofer, 2006; Freeman et al., 2012). However, research indicates that the presence of desired destinations, such as stores, parks and transit stops, is the most significant driver of walkability (Hoehner et al., 2005; Lee and Moudon, 2006; Sugiyama et al., 2012). Handy (1993) refers to this dimension of urban space as ‘‘local accessibility.’’ More than 30 years ago, Li and Brown (1980) noted that local accessibility was an important aspect of overall accessibility in urban areas even though accessibility was more commonly measured in relation to urban centers. Local accessibility is the particular dimension of walkability that is measured by Walk Score, although Walk Score is correlated with other walkability correlates, such as intersection, residential, and retail destination density (Duncan, Aldstadt, Whalen, and Melly, 2011). Studies have shown Walk Score to be a reliable and valid estimator of neighborhood features linked to walking (Carr, Dunsiger, and Marcus, 2010, 2011; Duncan, Aldstadt, Whalen, and Melly, 2011; Duncan et al., 2013). It is also a better predictor of walking for non-work trips than other related indices (Manaugh and El-Geneidy, 2011). Walk Score rates the walkability of an address by determining the distance from a location to educational (schools), retail (groceries, books, clothes, hardware, drugs, music), food (coffee shops, restaurants, bars), recreational (parks, libraries, fitness centers), and entertainment (movie theaters) destinations. Points are assigned to the location based on distance to the nearest destination of each type. If the closest establishment of a certain type is within a quarter mile, Walk Score assigns the maximum points for that type. No points are given for destinations beyond a mile. Each type of destination is weighted equally. Points for each category are summed and scores are normalized to produce a total from 0 to 100. Pivo and Fisher (2011) discuss some of the limitations and other caveats related to Walk Score. A newer version that addresses certain concerns is currently in development. Walk Score has advantages over other systems for measuring walkability (Moudon and Lee, 2003; Parks and Schofer, 2006). One advantage is that it measures the best predictor of walking proximity to desired destinations. Another is that it is available for all addresses nationwide. Weidema and Wesnæs (1996) developed data quality indicators including reliability, completeness, temporal, and geographical correlation with the time and place being assessed, and further technical correlation, including whether the data actually represent the process of concern. Walk Score scores well on such metrics. Increasing urban walkability is increasingly viewed as a major goal by urban planners, sustainability scientists, and public health experts for social and environmental reasons. The expected benefits remain an ongoing research topic, though a considerable body of evidence is emerging from well-controlled studies. Environmental benefits may include less air pollution, auto use, and gasoline W a l k S c o r e 1 8 9 consumption (Frank, Stone, and Bachman, 2000; Ewing and Cervero, 2001; Frank and Engelke, 2005; Handy, Cao, and Mokhtarian, 2005; Cao, Handy, and Mokhtarian, 2006). In fact, walking has been recognized as one of the main options for mitigating climate change in the transport sector (Chapman, 2007; Bosch and Metz, 2011). Social benefits may include better public health as a result of more physical activity (Lee and Buchner, 2008; World Cancer Research Fund / American Institute for Cancer Research, 2009; Berrigan et al., 2012) and increased social capital including more community cohesion, political participation, trust, and social activity (Leyden, 2003; du Toit, Cerin, Leslie, and Owen, 2007; Rogers, Halstead, Gardner, and Carlson, 2009; Wood, Frank, and Giles-Corti, 2010). Social capital has in turn been linked to the capacity of cities to transition toward greater sustainability (Portney, 2005; Geels, 2012). Walkability can be created by developing larger scale mixed-use development projects or by infilling development in currently walkable locations. There is evidence that it is more difficult to finance walkable projects because they are perceived to be riskier, leading to more expensive financing. Financiers could be concerned about disamenities from non-residential uses, uncertainty about the performance of mixed-use buildings, entitlement risk for infill projects, or weaker economic conditions in walkable, mixed-use neighborhoods. One study focused on residential developments that were planned to be compact, scaled for pedestrians, and designed to include activities of daily living within walking distance of homes (Gyourko and Rybczynski, 2000). It found that developers, financiers, and investors perceived such projects to be ‘‘inherently riskier and more costly. . . arising from the multiple-use nature of the developments.’’ On the other hand, the study also found that urban infill risk premiums could be quite small where communities were willing to accept high densities. More recently, Leinberger and Alfonzo (2012) pointed out that ‘‘walkable urban places remain complex developments that still carry high risk and, as such, costly capital (both equity and debt financing).’’ Of course, not all projects in walkable locations are mixed use or complex and the Urban Land Institute recently reported that ‘‘demand and interest in apartments in ‘American infill’ locations remain hot’’ (PwC and the Urban Land Institute, 2012). Thus, while experts have noted that more walkable projects are more difficult to finance because of their riskier reputation, the degree to which this is true for all walkable projects is unclear because they can vary in location, scale, and complexity. It is also unclear exactly what it is about the projects that are cause for concern. According to Grovenstein et al. (2005), mortgage lenders often respond to perceived risk by limiting how much they will lend. They point out that lenders could also increase interest rates on riskier projects, but that approach is constrained because higher rates can increase default risk. Assuming a given cash flow and value, limiting the amount loaned reduces the loan-to-value (LTV) ratio and increases the debt service coverage ratio (DSCR). For borrowers, a lower LTV ratio means that more walkable projects would produce a lower return on equity compared to what could be earned on more conventional projects with higher loan ratios, all else being equal, as long as positive leverage is possible (i.e., when the cost of debt financing is lower than the overall return generated by the property J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 1 9 0 P i v o Exhibit 1 u Loan Ratios by Walk Score return on assets). A lower return on equity could cause investors to disfavor walkable investments, decrease capital flows to walkable properties, and slow the movement toward more walkable cities. In the pool of nearly 37,000 multifamily mortgages examined in this study (see Methods below for details), there is evidence that lenders treated projects in more walkable locations as if they were perceived to be riskier loans. As shown in Exhibit 1, in the study sample, as Walk Score increased, LTV fell and DSCR increased. These trends in LTV and DSCR relative to Walk Score are consistent with lenders reducing the size of loans relative to property value and income in more walkable locations in response to perceived risk. As suggested above, less favorable loan terms for more walkable locations may not be caused by lenders’ views about walkability per se but rather by concern about other features of the properties or their location such as disamenities, entitlement risk, or economic conditions. This may seem counterintuitive if one simply assumes that places with higher Walk Scores are correlated with more supply-constrained markets. It is true that in the sample used in this study there was a very weak correlation between higher Walk Score and higher supply constraint as measured by vacancy rates and price change. However, higher Walk Scores were also correlated with more poverty and lower income households in the neighborhood and with smaller loans and building size, all of which can raise the level of expected risk. It goes beyond the scope of this paper to determine precisely why loan terms appear to have been less favorable in more walkable neighborhoods. The reasons, however, probably result from a number of social and economic conditions that distinguish more and less walkable locations. In the modeling presented below, however, the effect of factors beyond Walk Score W a l k S c o r e 1 9 1 that may affect default risk are statistically controlled so as to determine how walkability itself is related to default risk, all else being equal. I take a closer look at this risk issue by comparing default risk in more and less walkable properties (i.e., properties in more and less walkable locations). The findings show that default risk for multifamily properties in highly walkable neighborhoods is lower, not higher, than the default risk for projects in less walkable locations. The hypothesis for this paper is as follows: Greater walkability, as measured by higher Walk Scores, reduces mortgage default risk in multifamily housing. Studies have shown that walkability improves property values (Pivo and Fisher, 2011; Kok and Jennen, 2012; Kok, Miller, and Morris, 2012; Pivo, 2013). The higher values appear to result from both stronger cash flows and lower capitalization rates, suggesting that walkable properties are favored in both space (i.e., rental) and capital markets (Pivo and Fisher, 2010). This relationship between walkability and value should be expected, given the long known understanding that accessibility, in this case local accessibility, plays in the formation of property value. Pivo and Fisher (2011) discuss this in the context of a recent summary of the literature on the determinants of urban land and property values. Studies also show that the major risk factors for multifamily loan default are cash flow and property value. Default risk increases if declining cash flow prevents loan repayment or if falling property value produces negative net equity (Vandell, 1984, 1992; Titman and Torous, 1989; Kau, Keenan, Muller, and Epperson, 1990; Vandell et al., 1993; Goldberg and Capone 1998, Goldberg and Capone 2002, Archer et al. 2002). In these studies, cash flow and equity are commonly measured in terms of debt service coverage ratio (DSCR), or the ratio of income to required loan payments, and loan to value ratio (LTV), or the ratio of loan amount to property value. A lower DSCR and a higher LTV, both at origination and over the life of the loan, have been linked to greater default risk. If more walkable properties produce better cash flows and property values, then they should also exhibit lower default risk because default risk is inversely related to cash flow and value (Titman and Torous 1989, Kau et al. 1990, Vandell 1984, Vandell 1992, Vandell et al. 1993, Goldberg and Capone, 1998, 2002; Archer, Elmer, Harrison, and Ling, 2002; Pivo, 2013). However, as Pivo (2013) noted, adding information on walkability to the loan origination process would only be helpful if its impact on cash flow and value was not already fully accounted for in the loan origination process. The assumption here is that the walkability premium was not fully considered in past lending decisions. That is not to say it was completely ignored, just not recognized as important in property markets as it appears to be today. Indeed, loan proposal documents regularly address locational advantages such as access to public transportation and other amenities. M e t h o d s Logistic regression models were used to test the effects of Walk Score on default risk. This approach has been used in several studies to estimate the effects of J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 1 9 2 P i v o explanatory variables on the probability of mortgage default (Vandell et al., 1993; Goldberg and Capone, 1998, 2002; Archer, Elmer, Harrison, and Ling, 2002; Rauterkus, Thrall, and Hangen, 2010). Logistic regression is a statistical method for predicting the value of a bivariate dependent variable (Menard, 1995) or a variable with two possible values (e.g., default / not default in the present study). The value of the dependent variable predicted by a logistic regression is the probability that a case will fall into the higher of the two categories of the dependent variable, which normally indicates the event (e.g., default) occurred, given the values for the case on the independent variables. In other words, it is the probability that an event will occur under various conditions characterized by the independent variables. The predicted value of the dependent variable is based on observed relationships between it and the independent variable or variables used in the study. The most common alternative to the logistic regression model in mortgage default research is the proportional hazard model. Hazard models can be used to explain the time that passes before some event occurs in terms of covariates associated with that quantity of time. They have been used to estimate the probability that a mortgage with certain characteristics will default in a given period if there has been no default up until that period (Vandell et al., 1993; Ciochetti, Deng, Gao, and Yao, 2002). A common view of the hazard model is that it is less sensitive to bias from database censuring than logistic regression. Censoring occurs when cases are removed from the database prior to observation (e.g., when a loan is paid off or foreclosed and sold prior to observation) or when the event of interest happens after observation occurs (e.g., when a loan defaults after the study observation date). However, as pointed out by Archer, Elmer, Harrison, and Ling (2002), bias is only an issue in logistic regression when the explanatory variables have a different effect on the censored and uncensored cases. In the present study, there is no reason to expect that walkability affected the odds of default differently in censored and uncensored cases. Hazard models also require a time series dataset that reports the occurrence of defaults over time and such a dataset was unavailable for the present study. One effort to predict mortgage pre-payment using both logistic regression and hazard models found that the logistic regression model made better predictions (Pericili, Hu, and Masri, 1996), while in another study on insolvency among insurers, the two models produced equally accurate predictions (Lee and Urrutia, 1996). So, while it would be interesting to repeat this study using a hazard model, there is no a priori reason to assume that the logistic regression method used here produced results that are inferior to those that would have come from another method. To build logistic regression models for the present study, data were provided by Fannie Mae on all the loans in its multifamily portfolio at the end of 2011:Q3. The sample included mortgages with fixed and adjustable rates and with a wide variety of seasoning, originating anywhere from September, 1971 through W a l k S c o r e 1 9 3 September, 2011. In the study, each loan was treated as a separate case or observation. For each case, data were available on the loan age, type, terms, and lender, on various financial, physical, and locational attributes of the property, and on the number of days the loan was delinquent, if any. In addition to these data on the loans, Walk Score data and other data on neighborhood and regional attributes were collected from other sources for use in the model. Further details on the variables are given below. Following Archer, Elmer, Harrison, and Ling (2002), cases in the Fannie Mae database with extreme values on certain variables were excluded from the study in order to filter out possible measurement error. The extreme value filters ensured that all the cases used had an original note interest rate greater than the 10-year constant maturity risk-free rate at their origination date, an original LTV ratio of 100% or less, an original DSCR greater than 0.9 and less than 5, and an original note interest rate greater than 3% and less than 15%. After these filters were applied, 36,922 loans remained in the sample out of the 42,474 loans originally provided. As noted, default status was observed as of 2011:Q3, making the study cross- sectional rather than longitudinal. The cross-sectional study design raises some concern about the external validity of the findings (i.e., how far the findings can be generalized beyond the study sample) because the relationships between the regressors and default risk could change over time. For example, walkability could reduce default rates by a greater amount when gas prices are peaking and demand is higher for apartments in more accessible locations. Since longitudinal data were not available for this study, it would be useful to confirm the results reported here in a follow-up study using longitudinal data. Another external validity issue comes from the fact that the Fannie Mae mortgage pool had an average default rate that was about one-fourth the rate found for mortgages held by depository institutions at the time the study was completed. It would be important to know whether the effects found in this study apply to those mortgages as well. The effects of Walk Score on default could be different for riskier loan pools if, for example, the properties were located where high Walk Scores were not such an attractive feature either because of different neighborhood conditions or tenant characteristics associated with the riskier pool of loans. V a r i a b l e s Dependent and Explanatory Variables DEFAULT was the dependent variable used in the study. It was binary, indicating whether (1) or not (0) a loan was in default as of 2011:Q3. A loan was classified as in default if it was delinquent on its payments by 90 days or more. This is an industry standard definition and matches that used by Archer, Elmer, Harrison, and Ling (2002), who pointed out that such a broad definition is useful because other resolutions in addition to foreclosure can be used to resolve defaults and they all involve delinquency-related costs to the lender. J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 1 9 4 P i v o WALK SCORE was the explanatory variable of interest. It captures the walkability of the area where each apartment building was located. As noted above, it has been found to be a reliable and valid estimator of neighborhood features linked to walking and a better predictor of walking for non-work trips than other similar indices. Control Variables The expectation was that WALK SCORE was related to default risk because it affects cash flow and value to a degree that was unaccounted for in the DSCR or LTV ratios at loan origination. However, it could also be the case that WALK SCORE is correlated with other factors that affect financial outcomes, such as other loan, property, neighborhood or macroeconomic variables. In that case, WALK SCORE could simply be a proxy for other drivers of cash flow and value, such as neighborhood vacancy rate. Therefore, in order to separate the effects of WALK SCORE on DEFAULT from other possible drivers, several control variables suggested by prior research were used in the models. The controls fall into four groups including loan, property, neighborhood, and economic characteristics. Loan Characteristics OLTV and ODSCR measured the LTV and debt service coverage ratios at loan origination. Higher OLTV and lower ODSCR were expected to be associated with greater default risk. LOAN AGE MONTHS was the number of months from the loan origination date to the observation date (2011:Q3). Previous researchers have shown that default risk declines with age, though the pattern is nonlinear, increasing rapidly in the first few years and then declining (Snyderman, 1991; Esaki, L’Heureux, and Snyderman, 1999; Archer, Elmer, Harrison, and Ling, 2002). The same pattern was observed in this study sample. Consequently, some degree of non-linearity in the logit (i.e., a nonlinear relationship with the logit form of DEFAULT ) was detected for LOAN AGE MONTHS using the Box- Tidwell transformation (Menard, 1995). Transformations of LOAN AGE MONTHS were tried in the models but they did not improve the results and were discarded to simplify interpretation of the findings. ARM FLAG was a dummy indicating whether the loan was adjustable (1) or fixed (0). Property Characteristics NO CONCERNS was a dummy indicating whether or not there were no substantial concerns about the property condition at the time of loan origination. This should reduce default risk by decreasing the need to divert cash flow to deferred maintenance. BUILT YR was the year the property was built. Archer, Elmer, Harrison, and Ling (2002) found that default rates increased with building age, so BUILT YR was expected to be inversely related to default risk (i.e., older buildings would default more often). This was the expectation for the nation as a whole, although it could be true that in some areas the historic or design qualities associated with older buildings may be preferred, which could influence how age is related to default risk by increasing demand, cash flow, and value for older W a l k S c o r e 1 9 5 buildings. TOT UNTS CNT was the total number of units in the property. Smaller properties have been reported to experience more financial distress (Bradley, Cutts, and Follain, 2000). Perhaps this is because of the characteristics of borrowers on smaller properties who may have less experience, less access to capital, and less of a tendency to use professional property managers. Archer, Elmer, Harrison, and Ling (2002), however, looked at unit count in a multivariate analysis and found that size (and value) was unrelated to default, even though their univariate analysis showed that smaller properties had less default risk, contrary to Bradley, Cutts, and Follain (2000). So the expected effect in this study was ambiguous. Neighborhood- and City-Scale Geographic Characteristics Researchers have found that stress on properties is related to geographical effects. In fact, Archer, Elmer, Harrison, and Ling (2000) found geographical effects to be one of the most important dimensions for predicting multifamily mortgage default. More recently, An, Deng, Nichols, and Sanders (2013) found that local economic conditions affect commercial mortgage-backed security (CMBS) loans significantly and improve predictive power. Five control variables were created to control for these sorts of effects at the city and neighborhood level. MEDHHINC000 was the median household income in the census tract from the 2000 census. Higher income was expected to be linked with lower default rates. PROP CRIME MIL was the annual number of property crimes per million persons at the city scale, reported by the U.S. Department of Justice. Higher crime in the city was expected to increase default risk. VACANCY RATE was the vacancy rate for housing in the census block group as determined by the 2007– 11 U.S. Census American Community Survey. Vacancy rate was used to control for the effect of housing supply constraint on default rates in order to rule out the possibility that WALK SCORE was a proxy for constrained supply. PRINCIPAL CITY indicated whether the property was located in a Principal City, defined by the U.S. Census as the largest incorporated or census designated place in a core- based statistical area. Its purpose was to control for whether or not a property was centrally located within a metro- or micropolitan area because central areas have outperformed suburban locations over the past decade and Walk Score tends to be higher in central cities. Properties in Principal Cities were expected to have lower default risk. URB RUR was also used to measure regional centrality. It was based on the 11 Urbanization Summary Groups defined in the ESRI Tapestry Segmentation System, which groups locations along an urban-rural continuum from Principal Urban Centers to Small Towns and Rural places. Finally, TOP25CITY was a dummy variable indicating whether the property was in one of the 25 largest U.S. cities. Regional and National Economy Regional and national variables were used to control for difference in the economic context experienced by properties since loan origination. Dummies were created for each of the nine census divisions as proxies for regional economic conditions. Vandell et al. (1993) used a similar variable. Additional variables designed to capture regional effects were dummies for whether the property was J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 1 9 6 P i v o located in New York City (NYC) or Washington, DC (DC), and changes in vacancy rates and prices in the metropolitan area in the most recent six-year period. AVG PRICE 6 and AVG OCC 6 were computed using the NCREIF Apartment Index for metro areas. They described the average increase in apartment prices and the average occupancy rate in the metro area for each property over the last six years prior to the study observation date. Prior researchers have used updates of LTV and DSCR over time to predict default on the theory that negative equity or cash flow will trigger default. Both are affected by the property’s net operating income, which is in turn affected by vacancy rates and rental price indices. Therefore, changes in vacancy rates and rental price indices at the metro scale can be used to capture changes in market conditions that strengthen or weaken mortgages over time, following Goldberg and Capone (1998, 2002). Borrower Characteristics Lenders consider borrower characteristics to be crucial to predicting default rates. Relevant variables include borrower character, experience, financial strength, and credit history. In their ‘‘simple model of default probability,’’ Archer, Elmer, Harrison, and Ling (2002) theorize that losses from loans depend upon the risk characteristics of the borrower, among other things, though such variables were not included in their models. Vandell et al. (1993) used borrower type (individual, partnership, corporation, other) in their analysis of commercial mortgage defaults, as did Ciochetti, Deng, Gao, and Yao (2003), who expected individuals to represent a lower risk to lenders, though neither study found these variables to be significant. Unfortunately, due to privacy rules, data on borrowers were not provided by Fannie Mae for this study. It is likely, however, that lenders adjusted the original loan terms based in part on their assessment of borrower characteristics. Therefore, OLTV, ODSCR, and ARM FLAG may be proxies for borrower characteristics. TOT UNTS CNT may also be correlated with borrower characteristics, as mentioned above. It is inappropriate, however, to make assumptions about the effects of omitting variables in logistic regression. It is known that omitting relevant variables introduces bias in linear regression, but less is known about how it may bias logistic regression (Dietrich, 2003). One study showed that omitted orthogonal variables (i.e. variables that are uncorrelated with other independent variables) can depress the estimated parameters of the remaining regressors toward zero (Cramer, 2007). That would make the findings about Walk Score in this study appear to be weaker than they actually are. It would be helpful to include borrower characteristics in future work that builds on the present study. Collinearity Correlation among the independent variables is indicative of collinearity. Collinearity can create modeling problems including insignificant variables, unreasonably high coefficients, and incorrect coefficient signs (e.g., negatives that should be positive). Collinearity will not affect the accuracy of a model as a whole, but it can produce incorrect results for individual variables. Tolerance statistics, which check for a relationship between each independent variable and all other independent variables, were used as an initial check for collinearity and they raised W a l k S c o r e 1 9 7 no concerns (Menard, 1995). A pairwise correlation matrix among the independent variables also uncovered no issues. R e s u l t s Univariable Analysis The process of building the logistic regressions began with a univariable analysis of each variable as recommended by Hosmer and Lemeshow (2000). For the dummy and ordinal variables, this was done by using a contingency table to compare outcomes for properties that did and did not default. The significance of the differences was determined with the likelihood ratio and Pearson chi-squared tests. For the continuous variables, means for the default and not-default groups were compared using the two-sample t-test. The results are shown in Exhibit 2 along with descriptive statistics for the total sample. Other than TOP25CITY and a few of the regional dummies, all of the variables, including WALK SCORE, were significantly related to DEFAULT. Logistic Regressions Following the univariable analysis, several different models were produced; each model has a specific purpose. The statistics for each model are given in Exhibit 3. Particular attention was paid to changes in the WALK SCORE coefficients across the various models. Model 1 included all of the scientifically relevant variables. This allowed the effect of removing insignificant variables on the variables that remained in subsequent models to be observed. The size and direction of the relationships are indicated by the unstandardized coefficients (b). b gives the change in the risk of default associated with a one- unit change in the variable while other variables are held constant. If b is positive, then default risk increases with a one-unit increase in the variable. If b is negative, the relationship is inversed. For example, in Model 1, the B coefficient for WALK SCORE (20.018) indicates that as WALK SCORE rises, the risk of DEFAULT falls, holding the other variables constant. All of the variables in Model 1 were related to DEFAULT in the expected direction even though some of the relationships were statistically insignificant. The Exp(b) statistic is the odds ratio or the number by which one would multiply the odds of default for each one-unit increase in the independent variable. An Exp(b) greater than one indicates the odds increase when the independent variable increases and an Exp(b) less than one indicates the odds decrease when the independent variable increases. For WALK SCORE in Model 1, Exp(b) indicate that a one-unit increase resulted in a 1.8% decrease in the odds of default (i.e., the odds of DEFAULT are multiplied by 0.018, which is 0.982 less than 1). Odd ratios can also be interpreted as relative risk when the outcome occurs less than J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 1 9 8 P i v o Exhibit 2 u Descriptive Statistics Difference Tests All Loans Defaulted Loans Non-defaulted Loans Likelihood Pearson Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. t-test Ratio Chi-Square Dependent Variable Fraction of loans defaulting 0.86% 100% 0% Walkability Variable Walk Score 66.0 21.8 61.6 21.0 66.1 21.8 0.000 Loan Characteristics Loan-to-value ratio at origination 61.20% 16.30% 70.40% 11.50% 61.20% 16.30% 0.000 Debt coverage ratio at origination 1.5 0.6 1.3 0.3 1.5 0.6 0.000 Loan age in months 73.2 52.9 67.9 33.1 73.2 53.0 0.005 ARM flag 0.31 0.462 0.39 0.49 0.31 0.46 Property Characteristics No concerns 0.29 0.45 0.12 0.32 0.29 0.45 0.000 0.000 Year built 1968.0 26.3 1955.0 32.1 1968.0 26.2 0.000 Total units 94.6 125.0 64.2 99.5 94.9 125.2 0.000 Neighborhood and City Characteristics Median household income in 2000 census 42,694 16,957 34,085 13,483 42,768 16,965 0.000 tract Property crime per million capita in city 407.5 165.3 474.5 161.6 406.9 165.2 0.000 Housing vacancy rate 2011 block group 6.58 5.87 9.85 7.45 6.56 5.85 0.000 (%) Urban/Rural Continuum 1.92 1.16 2.00 1.08 1.92 1.16 0.001 0.000 Principal City 0.60 0.49 0.68 0.47 0.60 0.49 0.002 0.002 Top 25 City 0.23 0.42 0.19 0.39 0.23 0.42 0.069 0.076 W a l k S c o r e 1 9 9 J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u Exhibit 2 u (continued) Descriptive Statistics Difference Tests All Loans Defaulted Loans Non-defaulted Loans Likelihood Pearson Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. t-test Ratio Chi-Square Geographic Variables New England 0.03 0.17 0.13 0.34 0.03 0.47 0.000 0.000 Mid Atlantic 0.14 0.35 0.15 0.36 0.14 0.35 0.590 0.586 East North Central 0.08 0.26 0.15 0.36 0.08 0.26 0.000 0.000 East South Central 0.02 0.14 0.02 0.14 0.02 0.15 0.906 0.906 West North Central 0.04 0.19 0.02 0.15 0.04 0.19 0.102 0.131 South Atlantic 0.09 0.29 0.22 0.42 0.09 0.29 0.000 0.000 West South Central 0.08 0.27 0.06 0.24 0.08 0.27 0.287 0.303 Mountain 0.05 0.22 0.06 0.24 0.05 0.22 0.397 0.382 Pacific 0.47 0.50 0.17 0.38 0.47 0.50 0.000 0.000 New York City 0.03 0.16 0.01 0.10 0.03 0.16 0.021 0.045 Washington, D.C. 0.01 0.08 0.01 0.08 0.01 0.08 0.895 0.893 Avg. pct. price change in MSA, past 6 yrs. 21.3 3.5 21.6 2.7 21.3 3.7 0.266 Avg. pct. leased in MSA, past 6 yrs. 91.0 3.9 90.9 3.7 91.0 3.9 0.127 2 0 0 P i v o Exhibit 3 u Logistic Regression Results for DEFAULT Model 2: Insignificant Model 3: Walk Score Model 4: Without Model 1: All Variables Variables Removed 80 plus or 8 minus Walk Score b (sig.) Exp(b) b (sig.) Exp(b) b (sig.) Exp(b) b (sig.) Exp(b) WALK SCORE 20.018 (.000) 0.982 20.018 (0.000) 0.982 WALK SCORE * ln(WALK SCORE) WALK SCORE801 20.924 (0.000) 0.397 WALK SCORE82 0.792 (0.046) 2.208 Loan OLTV 0.029 (0.000) 1.029 0.028 (0.000) 1.028 0.027 (0.000) 1.028 0.032 (0.000) 1.033 ODSCR 21.120 (0.000) 0.326 21.133 (0.000) 0.322 21.100 (0.000) 0.333 21.072 (0.000) ARM FLAG 0.719 (0.000) 2.053 0.758 (0.000) 2.135 0.657 (0.000) 1.929 0.775 (0.000) 2.170 LOAN AGE MONTHS 20.001 (0.301) 0.999 Property NOCONCERNS 20.892 (0.000) 0.410 20.907 (0.000) 0.404 20.879 (0.000) 0.415 20.952 (0.000) 0.386 BUILT YR 20.016 (0.000) 0.984 20.015 (0.000) 0.985 20.018 (0.000) 0.982 20.013 (0.000) 0.987 TOT UNTS CNT 20.005 (0.000) 0.995 20.005 (0.000) 0.995 20.005 (.000) 0.995 20.005 (0.000) 0.995 Neighborhood and City MEDHHINC000 20.027 (0.000) 0.974 20.029 (0.000) 0.972 20.030 (0.000) 0.971 20.027 (0.000) 0.974 PROP CRIME MIL 0.001 (0.011) 1.001 0.001 (0.001) 1.001 0.001 (0.000) 1.001 0.001 (0.002) 1.001 VACANCY RATE 0.023 (0.008) 1.023 0.022 (0.006) 1.023 0.022 (0.008) 1.022 0.024 (0.004) 1.025 PRINCIPAL CITY 0.313 (0.033) 1.368 URBAN RURAL 20.154 (0.015) 0.858 20.139 (0.024) 0.870 W a l k S c o r e 2 0 1 J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u Exhibit 3 u (continued) Logistic Regression Results for DEFAULT Model 2: Insignificant Model 3: Walk Score Model 4: Without Model 1: All Variables Variables Removed 80 plus or 8 minus Walk Score b (sig.) Exp(b) b (sig.) Exp(b) b (sig.) Exp(b) b (sig.) Exp(b) Regional Economy TOP25CITY 20.203 (0.239) 0.816 DC 21.057 (0.151) 0.347 NYC 20.731 (0.212) 0.457 REGION unreported unreported unreported unreported AVG PRICE 6 0.003 (0.857) 1.003 AVG PCT LEASED 6 0.021 (0.185) 1.021 Constant 25.926 (0.000) 1.82E111 26.909 (0.000) 4.86E111 32.318 (.000) 1.09E114 20.288 (0.000) 6.47E108 Notes: The number of observations is 36,922. For Model 1, model chi-square 5 621.714, 22 log likelihood 5 3,063.855, Nagelkerke R 5 0.176, and under ROC curve 5 0.845. For Model 2, model chi-square 5 606.523, 22 log likelihood 5 3,079.046, Nagelkerke R 5 0.172, and under ROC curve 5 0.841. For Model 3, model chi-square 5 617.482, 22 log likelihood 5 3,068.087, Nagelkerke R 5 0.175, and under ROC curve 5 0.844. For Model 4, model chi-square 5 582.323, 22 log likelihood 5 3111.265, Nagelkerke R 5 0.164, and under ROC curve 5 0.837. 2 0 2 P i v o 10% of the time, which is the case for DEFAULT in the study sample (Hosmer and Lemeshow, 2000). So, we can say that for every one-unit increase in WALK SCORE, the relative risk of default declines by 1.8%. If, for example, the default rate for properties with a particular WALK SCORE was 0.9% (the mean for the sample), then according to Model 1, a one-point increase in Walk Score would decrease the risk of default from 0.90% to 0.88% (i.e., 0.90 3 (1 2 0.018)). Model 2 is the reduced version of Model 1. Insignificant variables are dropped to produce a more parsimonious model that achieves the best fit with the fewest parameters. Using irrelevant variables increases the standard error of the parameter estimates and reduces significance (Menard, 1995). Removing controls did not alter the coefficient or significance of WALK SCORE, indicating that its relationship with DEFAULT was unaffected by any relationships between DEFAULT and the variables that were eliminated for Model 2. The goodness-of-fit statistics in Exhibit 3—model chi-square, 22 log likelihood, Nagelkerke R , and under ROC curve—measure how well all the explanatory variables in each model, taken together, predict DEFAULT. The higher the chi- square and the lower the 22 log likelihood, the better the model predicts DEFAULT. Comparing these statistics for Models 1 and 2 indicates that goodness- of-fit declines slightly as variables are removed, which normally occurs when variables are eliminated. Goodness-of-fit was also tested using the area under the receiver operating characteristic (ROC) curve. It measures a model’s ability to discriminate between loans that do and do not default. It represents the likelihood that a loan that defaults will have a higher predicted probability than a loan that does not. If the result is equal to 0.5, the model is no better than flipping a coin. For all the models, ROCs were 0.83 to 0.85, indicating excellent discrimination (Hosmer and Lemeshow, 2000). In other words, all the models did an excellent job distinguishing between loans that did and did not default. A degree of non-linearity in the logit was detected for WALK SCORE using the Box-Tidwell transformation. Following that approach, a multiplicative term in the form of WALK SCORE times the log-normal form of WALK SCORE was added to Model 2. Statistically significant interaction terms indicated that linearity may not be a reasonable assumption for WALK SCORE. Two graphical methods were used to further investigate the shape of the nonlinear relationship between WALK SCORE and DEFAULT. In the first approach, 20 groups of cases were created using five-point increments of WALK SCORE. The average WALK SCORE for each group was then plotted against the average DEFAULT for each group. The result is shown in Exhibit 4, along with a third- order polynomial fitted line. The patterns showed two thresholds; one at a Walk Score of about 8, below which there was a marked increase in default risk, and one at a Walk Score of about 80, above which there was a marked decrease in default relative to the normal default rate of about 0.9%. This first graphical method for investigating nonlinearity did not use control variables. In order to take the controls into consideration, the grouped smooth method suggested by Hosmer and Lemeshow (2000) was employed. First, the W a l k S c o r e 2 0 3 Exhibit 4 u Default Rate vs. Walk Score Exhibit 5 u Estimated Logistic Regression Coefficients vs. Quartile Midpoints Range Midpoints b (sig.) 0–8 3 0.966 (0.019) 52–69 62 0.020 (0.888) 69–83 75 20.222 (0.173) 83–100 91 21.063 (0.000) quartiles of the distribution of WALK SCORE were determined. Next, a categorical variable with four levels was created using the three cut-points based on the quartiles. An additional categorical variable was also created using 8 on WALK SCORE as the cut-point, in order to investigate the threshold of 8 found in the prior graphic analysis. Then, the multivariable model (Model 2) was refitted, replacing the continuous WALK SCORE variable with the four-level categorical variable and the dummy for 8 or less, using the lowest quartile as the reference group. The coefficients for each of the three categorical variables were then plotted against the midpoints for WALK SCORE in each of the groups. A coefficient equal to zero was also plotted at the midpoint of the first quartile. The resulting data and plot are given in Exhibits 5 and 6. The grouped smooth method confirmed that the relationship between WALK SCORE and DEFAULT was nonlinear while holding control variables constant. It also showed the existence of the previously discovered thresholds. As shown in Exhibit 5 and as indicated by the shape of the J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 2 0 4 P i v o Exhibit 6 u Grouped Smooth Method Chart line in Exhibit 6, in the middle range of WALK SCORE, the coefficients were small and insignificant. This indicates that the middle range of WALK SCORE is unhelpful for predicting DEFAULT. However, at the lowest and highest levels the coefficients were larger and significant. In an applied setting, cut-points can be more useful than continuous indicators because they allow a simple risk classification of cases into ‘‘high’’ and ‘‘low’’ and they communicate clearly the threshold above (or below) which risk will consistently be above (or below) average (Williams et al., 2006). In this case, thresholds could identify the cut-points for WALK SCORE above which default risk is consistently below average and below which it is consistently above average. Using a method for finding optimal cut-points recommended by Williams et al. (2006), candidate cut-points were evaluated by comparing the default rates above and below each candidate WALK SCORE value and computing a p-value for the difference using the chi-square test. This method indicated that 80 was the most significant WALK SCORE cut-point at the upper level and 8 was the most significant at the lower level. Based on this analysis, Model 3 was produced using dummy variables indicating whether or not a property had a Walk Score of 80 or more (WALK SCORE801) or 8 or less (WALK SCORE802). Model 3 had better goodness-of-fit statistics than Model 2, meaning that it did a better job predicting DEFAULT than the prior model that treated WALK SCORE as a continuous variable. (Recall that the lower b W a l k S c o r e 2 0 5 J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u Exhibit 7 u Trade-off Experiments Model 3 Mean Case Walk Score 801 Case Walk Score 82 Case Variables b Value b 3 Value Value b 3 Value Value b 3 Value WALK SCORE801 20.924 0.000 0.000 1.000 20.924 0.000 0.000 WALK SCORE82 0.792 0.000 0.000 0.000 0.000 1.000 0.792 OLTV 0.027 61.296 1.679 83.000 2.274 51.000 1.397 ODSCR 21.100 1.518 21.669 1.230 21.353 2.010 22.210 ARM FLAG 0.657 0.309 0.203 0.309 0.203 0.309 0.203 NOCONCERNS 20.879 0.286 20.252 0.286 20.252 0.286 20.252 BUILT YR 20.018 1967.834 235.421 1967.834 235.421 1967.834 235.421 TOT UNTS CNT 20.005 94.643 20.469 94.643 20.469 94.643 20.469 MEDHHINC000 20.030 42.694 21.276 42.694 21.276 42.694 21.276 PROP CRIME MIL 0.001 407.479 0.411 407.479 0.411 407.479 0.411 VACANCY RATE 0.022 6.573 0.142 6.573 0.142 6.573 0.142 New England 0.836 0.031 0.026 0.031 0.026 0.031 0.026 ENCENT 0.612 0.076 0.046 0.076 0.046 0.076 0.046 SoAtlantic 0.924 0.093 0.086 0.093 0.086 0.093 0.086 Pacific 21.045 0.469 20.490 0.469 20.490 0.469 20.490 Constant 32.318 32.318 32.318 32.318 Sum of b 3 value 24.665 24.677 24.696 Exp(sum) 0.009 0.009 0.009 11 Exp(sum) 1.009 1.009 1.009 Predicted Probability Exp(sum)/11 Exp(sum)) 0.93% 0.92% 0.90% 2 0 6 P i v o the 22 log likelihood, the better the goodness-of-fit.) In Model 3, the Exp(b) for WALK SCORE801 was 0.397, indicating that when a property had a WALK SCORE of 80 or more, it had a 60.3% decrease in the odds of default (i.e., 0.397 less than 1). In terms of relative risk, we can say that the relative risk of default was 60.3% lower for the properties with a Walk Score above 80 than those below 80. Similarly, Exp(b) for WALK SCORE82 was 2.208, indicating that properties with Walk Scores of 8 or less had a 121% increase in the odds of default (i.e., the odds of default for properties with Walk Scores greater than 8 are multiplied by 2.208). Model 4 was the final model produced in order to show that using WALK SCORE in the default model improved its goodness-of-fit. It includes the same variables as Model 3, except for WALK SCORE801 and WALK SCORE82. Comparison of the goodness-of-fit statistics for Models 3 and 4 shows that goodness-of-fit was better for Model 3, when the Walk Score variables were in the model. That indicates that Walk Score can be used to improve our ability to predict default and discriminate between loans that do and do not default. C o n c l u s i o n The hypothesis was that greater walkability, as measured by higher Walk Scores, reduces mortgage default risk. The results supported the hypothesis; however, the relationship was not linear. Instead, there were thresholds at Walk Scores of 8 and 80. Below 8, there was a significant increase in default risk and above 80 the risk significantly declined. A key implication of this study is that walkability could be fostered by relaxing lending terms without increasing default risk. For example, in terms of the impact on default rate, Model 3 predicts that the risk of default would be 0.9% for a property with a WALK SCORE between 9 and 79 and average values on the other model variables. This includes an OLTV of 0.61 and an ODSCR of 1.52, which are the sample means. However, if WALK SCORE was 80 or more, the OLTV for the same average property could be increased to 0.83, the ODSCR could be reduced to 1.23 and the property would still have a predicted default risk of 0.9%, according to Model 3. Inversely, with a WALK SCORE of 8 or less, the loan terms would need to be tightened to an OLTV of .51 and an ODSCR of 2.01, according to Model 3, in order to produce a default risk of 0.9%. Figures for these scenarios are given in Exhibit 7. If higher LTV ratios at origination could be obtained by borrowers on more walkable properties, they could achieve a higher return on their equity as long as positive leverage is possible (i.e., when the cost of debt financing as indicated by the mortgage constant is lower than the overall return generated by the property as indicated by the return on assets). They could also use the unused portion of their equity funds for other projects that could diversify their investment portfolios. All else being equal, more attractive loan terms could make walkable property investments more attractive to investors, increase capital flow to more sustainable buildings, and foster a transition toward more sustainable cities. W a l k S c o r e 2 0 7 Walkability has several potential social and environmental benefits, not the least of which include improved public health and mitigation of global climate change and other environmental impacts linked to motorized transportation. Fortunately, as this paper shows, properties in highly walkable locations, as indicated by a Walk Score of 80 or more, can also reduce mortgage default risk by more than 60%. This means that lenders could be willing partners in the promotion of more walkable cities by offering better terms for walkable property investments without increasing the exposure by lenders to default risk. Socially responsible property investing has been described as maximizing the positive effects and minimizing the negative effects of property investment on society and the natural environment in a way that is consistent with investor goals and fiduciary responsibilities (Pivo and McNamara, 2005). If it is possible to promote, as this study shows, social and environmental goals through greater walkability without increasing default risk, then it seems that ethical, responsible lenders should offer better terms for more walkable properties. It may even be possible to promote walkability while improving business outcomes. In that case, investment in walkable places is simply a smarter way of doing business. R e f e r e n c e s An, X., Y. Deng, J.B. Nichols, and A.B. Sanders. Local Traits and Securitized Commercial Mortgage Default. Journal of Real Estate Finance and Economics, 2013, 47:4, 787–813. Archer, W.R., P.J. Elmer, D.M. Harrison, and D.C. Ling. Determinants of Multifamily Mortgage Default. Real Estate Economics, 2002, 30:3, 445–73. Berrigan, D., D.D. Carroll, J.E. Fulton, D.A. Galuska, D.R. Brown, J.M. Dorn, B. Armour, and P. Paul. Vital Signs: Walking Among Adults—United States, 2005 and 2010. Morbidity and Mortality Weekly Report, 2012, 61:31, 595–601. Bosch, P. and B. Metz. Options for Mitigating Climate Change: Results of Working Group III of the Fourth Assessment Report of the IPCC. In H.G. Brauch et al. (eds.), Coping with Global Environmental Change, Disasters and Security. Berlin: Springer-Verlag, 2011. Bradley, D.S., A.C. Cutts, and J.R. Follain. An Examination of Mortgage Debt Characteristics and Financial Risk among Multifamily Properties. Journal of Housing Economics, 2001, 10, 482–506. Cao, X., S.L. Handy, and P.L. Mokhtarian. The Influences of the Built Environment and Residential Self-Selection on Pedestrian Behavior: Evidence from Austin, TX. Transportation, 2006, 33, 1–20. Carr, L.J., S.I. Dunsiger, and B.H. Marcus. Walk Scoree As a Global Estimate of Neighborhood Walkability. American Journal of Preventative Medicine, 2010, 39:5, 460– ——. Validation of Walk Scoree for Estimating Access to Walkable Amenities. British Journal of Sports Medicine, 2011, 45, 1144–48. Chapman, L. Transport and Climate Change: A Review. Journal of Transport Geography, 2007, 15, 354–367. Ciochetti, B.A., Y. Deng, B. Gao, and R. Yao. The Termination of Commercial Mortgage Contracts through Prepayment and Default: A Proportional Hazard Approach with Competing Risks. Real Estate Economics, 2002, 30:4, 595–633. J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 2 0 8 P i v o Cramer, J.S. Robustness of Logit Analysis: Unobserved Heterogeneity and Mis-specified Disturbances. Oxford Bulletin of Economics and Statistics, 2007, 69:4, 545–55. du Toit, L., E. Cerin, E. Leslie, and N. Owen. Does Walking in the Neighborhood Enhance Local Sociability? Urban Studies, 2007, 44:9, 1677–95. Dietrich, J. Under-specified Models and Detection of Discrimination in Mortgage Lending. Office of the Comptroller of the Currency. Economic and Policy Analysis Working Paper 2003-02, 2003. Duncan, D.T., J. Aldstadt, J. Whalen, and S.J. Melly. Validation of Walk Scores and Transit Scores for Estimating Neighborhood Walkability and Transit Availability: A Small-area Analysis. GeoJournal, 2013, 78:407–416. Duncan, D.T., J. Aldstadt, J. Whalen, S.J. Melly, and S.L. Gortmaker. Validation of Walk Scoret for Estimating Neighborhood Walkability: An Analysis of Four U.S. Metropolitan Areas. International Journal of Environmental Research and Public Health, 2011, 8, 4160– Esaki, H., S. L’Heureux, and M. Snyderman. Commercial Mortgage Defaults: An Update. Real Estate Finance, 1999, 16:1, 80–6. Ewing, R. and R. Cervero. Travel and the Built Environment: A Synthesis. Transportation Research Record, 2011, 1780, 87–114. Frank, L.D. and P. Engelke. Multiple Impacts of the Built Environment on Public Health: Walkable Places and the Exposure to Air Pollution. International Regional Science Review, 2005, 28:2, 193–216. Frank, L. and G. Pivo. The Impacts of Mixed Use and Density on the Utilization of Three Modes of Travel: The Single Occupant Vehicle, Transit, and Walking. Transportation Research Record, 1994, 1466, 44–52. Frank, L.D., B. Stone, and W. Bachman. Linking Land Use with Household Vehicle Emissions in the Central Puget Sound: Methodological Framework and Findings. Transportation Research Part D, 2000, 5, 173–96. Freeman, L., K. Neckerman, O. Schwartz-Soicher, J. Quinn, C. Richards, M.D.M. Bader, G. Lovasi, D. Jack, C. Weiss, K. Konty, P. Arno, D. Viola, B. Kerker, and A.G. Rundle. Neighborhood Walkability and Active Travel (Walking and Cycling) in New York City. Journal of Urban Health: Bulletin of the New York Academy of Medicine, doi:10.1007 / s11524-012-9758-7, 2012. Geels, F.W. A Socio-technical Analysis of Low-carbon Transitions: Introducing the Multi- level Perspective into Transport Studies. Journal of Transport Geography, 2012, 24, 471– Goldberg, L. and C.A. Capone. Multifamily Mortgage Credit Risk: Lessons from Recent History. Cityscape, 1998, 4:1, 93–113. ——. A Dynamic Double-Trigger Model of Multifamily Mortgage Default. Real Estate Economics, 2002, 30:1, 85–113. Grovenstein, R.A., J.P. Harding, C.F. Sirmans, S. Thebpanya, and G.K. Turnbull. Commercial Mortgage Underwriting: How Well Do Lenders Manage the Risks? Journal of Housing Economics, 2005, 14, 355–83. Gyourko, J.E. and W. Rybczynski. Financing New Urbanism Projects: Obstacles and Solutions. Housing Policy Debate, 2000, 11:3, 733–50. Handy, S. Regional versus Local Accessibility: Implications for Nonwork Travel. Transportation Research Record, 1993, 1400, 58–66. Handy, S., X. Cao, and P. Mokhtarian. Correlation or Causality between the Built Environment and Travel Behavior? Evidence from Northern California. Transportation Research Part D, 2005, 10, 427–44. W a l k S c o r e 2 0 9 Hoehner, C.M., L.K.B. Ramirez, M.B. Elliott, S.L. Handy, and S.C. Brownson. Perceived and Objective Environmental Measures and Physical Activity among Urban Adults. American Journal of Preventative Medicine, 2005, 28:2S2, 105–16. Hosmer, D.W. and S. Lemeshow. Applied Logistic Regression. Second Edition. New York: John Wiley & Sons, Inc., 2000. Kau, J.B., D.C. Keenan, W.J. Muller III, and J.F. Epperson. Pricing Commercial Mortgages and Their Mortgage-backed Securities. The Journal of Real Estate Finance and Economics, 1990, 3:4, 333–56. Kok, N. and M. Jennen. The Impact of Energy Labels and Accessibility on Office Rents. Energy Policy, 2012, 46, 489–97. Kok, N., N.G. Miller, and P. Morris. The Economics of Green Retrofits. Journal of Sustainable Real Estate, 2012, 4:1, 4–22. Lee, I.M. and D.M. Buchner. The Importance of Walking to Public Health. Medicine and Science in Sports and Exercise, 2008, 40, S512–S518. Lee, C. and A.V. Moudon. The 3Ds 1 R: Quantifying Land Use and Urban Form Correlates of Walking. Transportation Research Part D, 2006, 11, 204–15. Lee, S.H. and J.L. Urrutia. Analysis and Prediction of Insolvency in the Property-Liability Insurance Industry: A Comparison of Logit and Hazard Models. Journal of Risk and Insurance, 1996, 63:1, 121–30. Leinberger, C.B. and M. Alfonso. Walk this Way: The Economic Promise of Walkable Places in Metropolitan Washington, D.C. The Brookings Institution, Washington, DC, 2012. Leyden, K.M. Social Capital and the Built Environment: The Importance of Walkable Neighborhoods. American Journal of Public Health, 2003, 93:9, 1546–51. Li, M.M. and H.J. Brown. Micro-Neighborhood Externalities and Hedonic Housing Prices. Land Economics, 1980, 56:2, 125–41. Manaugh, K. and A. El-Geneidy. Validating Walkability Indices: How Do Different Households Respond to the Walkability of Their Neighborhood? Transportation Research Part D, 2011, 16, 309–15. Menard, S. Applied Logistic Regression. Sage University Paper Series on Quantitative Applications in the Social Sciences, 07-106. Thousand Oaks, CA: Sage, 1995. Parks, J.R. and J.L. Schofer. Characterizing Neighborhood Pedestrian Environments with Secondary Data. Transportation Research Part D, 2006, 11, 250–63. Pericli, A., J. Hu, and J. Masri. The Prepayment of Fixed-Rate Mortgages: A Comparison of Logit with Proportional Hazard Models (June 25, 1996). Available at SSRN: http: / / ssrn.com.ezproxy2.library.arizona.edu / abstract57982. Pivo, G. The Effect of Sustainability Features on Mortgage Default Prediction and Risk in Multifamily Rental Housing. Journal of Sustainable Real Estate, 2013, 5, 152–73. Pivo, G. and J. Fisher. Income, Value, and Returns in Socially Responsible Office Properties. Journal of Real Estate Research, 2010, 32:3, 243–70. ——. The Walkability Premium in Commercial Real Estate Investments. Real Estate Economics, 2011, 39:2, 185–219. Pivo, G. and P. McNamara. Responsible Property Investing. International Real Estate Review, 2005, 8:1, 128–43. Portney, K. Civic Engagement and Sustainable Cities in the United States. Public Administration Review, 2005, 65:5, 579–91. PwC and the Urban Land Institute. Emerging Trends in Real Estate 2013. Washington, D.C.: PwC and the Urban Land Institute, 2012. J O S R E V o l . 6 N o . 1 – 2 0 1 4 u u 2 1 0 P i v o Rauterkus, S., G.I. Thrall, and E. Hangen. Location Efficiency and Mortgage Default. Journal of Sustainable Real Estate, 2010, 2:1, 117–41. Rauterkus, S. and N. Miller. Residential Land Values and Walkability. Journal of Sustainable Real Estate, 2011, 3:1, 23–43. Rogers, S.H., J.M. Halstead, K.H. Gardner, and C.H. Carlson. Examining Walkability and Social Capital as Indicators of Quality of Life at the Municipal and Neighborhood Scales. Applied Research in Quality Life, 2011, 6, 201–13. Snyderman, M. Commercial Mortgages: Default Occurrence and Estimated Yield Impact. Journal of Portfolio Management, 1991, 18:1, 6–11. Sugiyama, T., M. Neuhaus, R. Cole, B. Giles-Corti, and N. Owen. Destination and Route Attributes Associated with Adults’ Walking: A Review. Medicine & Science in Sports & Exercise, 2012, 44:7, 1275–86. Titman, S. and W. Torous. Valuing Commercial Mortgages: An Empirical Investigation of the Contingent-Claims Approach to Pricing Risky Debt. Journal of Finance, 1989, 59, 165–206. Vandell, K.D. On the Assessment of Default Risk in Commercial Mortgage Lending. Journal of the American Real Estate and Urban Economics Association, 1984, 12:3, 270– ——. Predicting Commercial Mortgage Foreclosure Experience. Real Estate Economics, 1992, 20:1, 55–88. Vandell, K., W. Barnes, D. Hartzell, D. Kraft, and W. Wendt. Commercial Mortgage Defaults: Proportional Hazards Estimation Using Individual Loan Histories. Real Estate Economics, 1993, 4:21, 451–80. Weidema, P. and M.S. Wesnaes. Data Quality Management for Life Cycle Inventories— An Example of Using Data Quality Indicators. Journal of Cleaner Production, 1996, 4:3 / 4, 167–74. Williams, B.A., J.N. Mandrekar, S.J. Mandrekar, S.S. Cha, and A.F. Furth. Finding Optimal Cutpoints for Continuous Covariates with Binary and Time-to-Event Outcomes. Technical Report Series No. 79. Department of Health Sciences Research, Mayo Clinic, Rochester, Minnesota, 2006. Wood, L., L.D. Frank, and B. Giles-Corti. Sense of Community and its Relationship with Walking and Neighborhood Design. Social Science & Medicine, 2010, 70, 1381–90. World Cancer Research Fund / American Institute for Cancer Research. Food, Nutrition, and Physical Activity: A Global Perspective. Washington, DC: American Institute for Cancer Research, 2009. Gary Pivo, University of Arizona, Tucson, AZ 85721 or gpivo@email.arizona. edu.
Journal
Journal of Sustainable Real Estate
– Taylor & Francis
Published: Jan 1, 2014
