Estimating User Accessibility Benefits with a Housing Sales Hedonic Model Michael Reilly Metropolitan Transportation Commission mreilly@mtc.ca.gov March 31, 2016 Words: 1500 Tables: 2 @ 250 words each Figures: 2 @ 250 words each Effective Words: 1500 + 500 + 500 = 2500 (limit 3000) 1
Motivation The assessment of user benefits from a proposed transportation project or policy requires an estimate of the value of the improvement to each traveler. It is common in practice to use a monetized version of travel time savings to estimate user benefits. Here, we attempt to empirically monetize a measure of accessibility. One way to value accessibility is to estimate how much more households are willing to pay for a home as its generalized regional accessibility increases. A hedonic regression model can be used to decompose a housing unit's market price into the various non-market factors that influence price (Rosen 1974). While most of these factors relate to the unit or the unit's context, the role of accessibility can be separated out. We build a hedonic model with recent San Francisco Bay Area housing transaction data to estimate accessibility's contribution to housing prices. Model results are briefly explained and a method for monetizing the accessibility-related portion of a housing unit's value is described. Back of the envelope calculations result in a monetized version of travel time savings that is approximately twice the asserted value of time in MTC's current methodology. While, additional refinement is needed to improve and support this estimate, the value of an empirical approach is clear. Approach Spatially explicit Bay Area housing unit sales data was collected from Redfin for 2013 and 2014. These records were spatially joined to jurisdictional boundaries and a variety of neighborhood factors represented in a raster GIS. This combined dataset contains recent sales prices and information on most of the unit, neighborhood, and public service characteristics that affect housing prices. Accessibility, another important driver of prices and the focus here, is represented using simplified mandatory trip destination-choice model logsums from MTC's Travel Model One. Destination-choice logsums are calculated for twelve household categories based on income and auto-sufficiency 1 for each of the region's 2832 geographic units. 2 The logsum values are transformed from utils to typical weekday minutes of in-vehicle time by subtracting out the minimum value for each household category. This transformation is necessary in order to compare or combine values across the household categories. Then the values for each household category are combined into a single metric, the Combined Mandatory Logsum or CML, by averaging each zone s values using weights to represent each household group s regional share. Each housing unit is spatially joined to a geographic unit and assigned a CML representing its generalized mandatory regional accessibility. 1 Auto-sufficiency bins households into three categories: those with no access to cars, those with fewer cars than workers, and those with an equal number or greater of cars than workers. 2 Travel Analysis Zone Sub-Zones, or TAZ-SZs. (These are a geography that divides each TAZ into area within 1/3 of a mile of a transit stop, 1/3-2/3 of a mile of a stop, and more than 2/3 of a mile from a stop.) 2
When limited to records for single family homes, townhouses, and condos for which all variables tested were present and within a reasonable range, 21,323 observations are available. Correlations between most variables range from modest to high. After testing various combination of dependent and independent variables, a relatively simple model structure was chosen. The nine independent variables shown in Table 2 are regressed on Log Unit Sales Price. Log Unit Sales Price is the log of the revealed value of the housing unit as indicated by the price agreed upon during the sale transaction. Square Feet measures unit size. Post-War is a dummy variable indicating the unit was built between 1940 and 2010, while New indicates a post-2010 home. Housing Density (units per acre) and Median Income are both calculated using Census data within a one-kilometer straight-line distance. Ocean View is a dummy calculated in a GIS that indicates the unit is likely to a have a view of the ocean. Units are assigned their School District s Average Academic Performance Index (API) for reading and math combined. Finally, units receive a Crime Rate value based on their jurisdiction s combined violent and non-violent crime rate as provided by the FBI. Table 1: Variables Variables Mean Standard Deviation Median Min Max Units Sales Price 676,890 824,957 540,000 50,500 9,900,000 Log Units Sales Price 13.17 0.707 13.20 10.83 16.11 Square Feet 1706 2196 1505 243 12,405 Bedrooms 3.108 2.697 3.000 0 11 Bathrooms 2.133 2.486 2.000 1 12.5 Year Built 1970 20.7 1972 1866 2014 Housing Density within 1km 13.992 20.04 10.090 0 365.071 Median Income within 1km 71.88 27.16 68.00 0 200 School District Average API 800 43.2 791 688 967 Crime Rate 0.0349 0.0212 0.0324 0.00616 0.185 Combined Mandatory Logsum 277.06 48.147 287.55 80.09 384.03 3
Hedonic Results The selected hedonic regression model produces an adjusted R-squared of 0.60. As presented in Table 2, most variables are significant at a level of 0.0001 and New is significant at 0.001. Fundamental characteristics of the unit, neighborhood, and jurisdiction are the main drivers of price. All else equal, an additional square foot of living space is worth around $390. The presence of an additional bathroom is worth an additional $250 beyond its size. Compared to pre-1940 homes, homes built between 1940 and 2010 are worth $170,000 less. Homes built after 2010 are worth $3000 more. Higher neighborhood densities and incomes are associated with higher values. The average ocean view is worth around $3000. A one standard deviation increase in school quality increases value by over $45,000, while a one standard deviation drop in the overall crime rate increase value by almost $35,000. A minute change in the CML variable increases unit value by $3586, all else equal. As noted above, the CML variable emerges from the travel model in units of destination choice utils. Prior to entering the variable into the regression, we transform the variable to express it in units of typical weekday in-vehicle time minutes, i.e. one minute spent driving in a car or riding in a transit vehicle on a typical weekday. As seen in Figure 1, the coefficient of $3586 per minute suggests, for example, that similar homes in Downtown Berkeley (A) and suburban Walnut Creek (B) would be expected to have a price difference of nearly $240,000 on account of Berkeley s superior accessibility. (This may seem counterintuitive but, for a variety of reasons, many units with lower accessibility have higher overall prices on account of the other variables in Table 2.) Table 2: Coefficients Estimate Standard Error t-value Intercept 9.286e+00 Square Feet 3.533e-02 5.735e-06 53.551 Bathrooms 5.051e-02 3.652e-03 7.903 Post-War -1.715e-01 5.683e-03-17.501 New 6.934e-02 1.082e-02 2.598 Housing Density within 1km 2.164e-03 1.733e-04 10.395 Median Income within 1km 6.518e-03 1.232e-02 43.751 Ocean View 7.992e-02 2.102e-02 3.802 School District Average API 1.762-03 5.521e-05 26.513 Jurisdiction Crime Rate -3.287+00 1.657e-01-16.272 Combined Mandatory Logsum 5.490e-03 7.024e-05 64.751 4
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User Benefit Results The next step is to monetize the accessibility measure so that is can be used in user benefit analysis. Here this is attempted by comparing median incomes and median housing prices in the Bay Area. According to Zillow (Hopkins 2013), the Bay Area 2012 median home price was 6.8 times the region's median income. 3 As shown in Figure 2, starting with $3586 per minute change in unit sales prices, multiply by 0.75 to reflect the fact that home value deriving from accessibility is related to both mandatory and non-mandatory trip-making and only the former is considered here. For Bay Area workers, 10-30% of time and a greater share of trips is spent on non-mandatory purposes. For now, it is assumed that ¾ of the value is related to commuting. Then divide by 6.8 to get to each minute difference being worth $396 in annual household income. Dividing this by the 260 workdays in a year results $1.52 per day. Dividing this by the two commute directions arrives at a typical weekday minute of in-vehicle time being worth $0.76 per household commute set. Bay Area households average 1.3 workers and dividing by this results in a typical weekday minute of invehicle time of $0.59. This approach values accessibility at around twice as much as the current MTC method of assuming it's worth half the region's median income, or $0.22 per minute (Metropolitan Transportation Commission 2013). Figure 2: Translating the Value of Typical Weekday Minute of In-Vehicle Time Value from a Housing Unit Price Representation into a User Representation Value of 1 typical weekday minute of in-vehicle time from hedonic $3586 Scale down to reflect value of correlated non-commute accessibility x 0.75 Value of 1 typical weekday minute of in-vehicle commute time from hedonic $2690 Divide by the ratio of Bay Area housing unit price by household income 6.8 Value of a minute in annual household income $396 Divide by number of workdays in a year 260 Value of a minute in week-daily household income $1.52 Divide by two commutes per day 2 Value of a minute in household income per commute $0.76 Divide by mean Bay Area workers per household 1.3 Value of a minute in worker s income per commute $0.59 Compare to current method s assertion $0.22 3 Historically the region's ratio was 4.9 and the U.S. ratio has been around 2.6 or a bit lower for many decades. However, it seems most appropriate to use the higher value for the work here because it is things unrelated to the value of accessibility that are driving regional housing prices up. 6
Caveats This alternate means of estimating the value of accessibility (and policies and projects that change it) produces results that are somewhat higher but of the same order of magnitude as the current methodology. In refining this approach, a number of issues should be kept in mind: Hedonic specifications are notoriously unstable due to high correlation between variables. Sensitivity analysis should be performed to achieve a more robust estimate of value of accessibility. Only mandatory travel is considered in this analysis. Non-mandatory logsum were examined but their high correlation with mandatory logsums made model specification and interpretation difficult. For now, a simplistic ratio was used to portion value into a share associated with mandatory travel. Future work could combine the two via a single index. This analysis covers only owner-occupied units. Renters may value accessibility differently. Theory suggests they may place more value on high accessibility. Additional refinement could improve the translation of the accessibility-related portion of unit price into the value of time for average or sub-markets of owner-occupied residents. Contribution and Innovation Monetized accessibility metrics are a fundamental component of user benefit estimation in transportation policy analysis. While most steps in user benefit assessment are rigorously calculated, the value of accessibility is often asserted as a rule-of-thumb. The work here applies hedonic regression to a database of housing transactions to estimate accessibility s contribution to the value of a housing unit. Translating this into the value to each user provides a novel method for the empirical estimation of user valuation of accessibility. 7
References Hopkins, C. (2013). Low Mortgage Interest Rates Masking High Home Price to Income Ratios on Zillow Blog. http://www.zillow.com/blog/low-mortgage-interest-rates-masking-high-homeprice-to-income-ratios-116868/ Metropolitan Transportation Commission (2013) Final Performance Assessment Report Plan Bay Area. Rosen, S. (1974) Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition Journal of Political Economy 82:1. 8