Opportunity Costs •••
Opportunity Costs Exploring Rental Costs in the Baltimore Region and the Spatial Relationship to Opportunity Ashley Sampson URSP601 Research Methods Interim Report 3 May 13, 2014 Introduction 1
Opportunity Costs •••
Opportunity Costs Exploring Rental Costs in the Baltimore Region and the Spatial Relationship to Opportunity
Introduction Having previously mapped opportunity in the Baltimore Metropolitan Council (BMC) region and subsequently identified some key differences between households in areas of high and low opportunity, this report will focus on estimating the cost of rental housing in the region. I will then be able to draw some conclusions about the spatial distribution of housing affordability in relation to areas of high and low opportunity. I use a hedonic pricing model to estimate the cost of rental housing in each of the 22 Public Use Microdata Areas (PUMAs) in the region, controlling for housing characteristics available in the 2007 – 2011 American Community Survey Public Use Microdata Sample (PUMS).
Hedonic Model Specification The dependent variable for the model is monthly rent. The average monthly rent for the sample of 12,906 housing units is $896 with a standard deviation of $495, suggesting a large amount of variability in the sample. I selected nine control variables for the specification, as shown in Table 1. I created five dummy variables to describe the type of rental unit. These include single family detached, single family attached, small apartment buildings, large apartment buildings, and the category that includes boats, RVs, or vans. The omitted category is mobile homes and trailers. In recoding the variable PUMS variable to create the dummy variables, I collapsed the apartment categories of 2, 3 - 4,
Introduction 2
Opportunity Costs ••• 5 - 9, and 10 – 19 units into the “Small Apartment Building” variable and collapsed the apartment categories of 20 - 49 and 50 or more units into the “Large Apartment Building” variable. The mean in Table 1: Descriptive Statistics Variable Rent Single Family Detached Home Single Family Attached Home Small Apartment Building (2-19 units) Large Apartment Building (20+ units) Boat, RV, or Van Electric Included in Rent Gas Included in Rent Number of Bedrooms Number of Other Rooms Puma400 Puma501 Puma502 Puma503 Puma504 Puma505 Puma506 Puma507 Puma601 Puma602 Puma801 Puma802 Puma803 Puma804 Puma806 Puma901 Puma902 Puma1201 Puma1202 Puma1203 Puma1204
Table 1 represents the frequency of each of Mean 896.43 .1080 .2596 .4346
Std. Dev. 494.821 .31041 .43842 .49572
.1924
.39419
.0002 .1475 .6969 1.98 2.6064 .0331 .0250 .0519 .0520 .0566 .0367 .0495 .0446 .0150 .0341 .0500 .0621 .0405 .1080 .0614 .0247 .0487 .0432 .0297 .0221 .0410
.01245 .35465 .45962 .978 1.06468 .17887 .15621 .22186 .22202 .23101 .18810 .21694 .20633 .12137 .18147 .21791 .24142 .19719 .31041 .24001 .15527 .21533 .20340 .16970 .14696 .19827
the unit types. A majority of the units are in apartment buildings, with a total of 62.7 % of units. Single-family attached homes, such as row homes and townhouses, make up 26.0% of the sample, while single-family detached homes account for only 10.8%. Also included in the model are two dummy variables that indicate if electricity and gas charges are included in the rent or if the response was “no charge or electricity/gas not used.” Electricity is paid separately from the rent in 85.2% of cases and gas is paid separately in 30.3% of cases. Two continuous variables describe the number of rooms in the housing unit. “Number of Bedrooms” is the number of
bedrooms reported. It is capped at five bedrooms. Since the size of the unit and number of bathrooms
Hedonic Model Specification 3
Opportunity Costs ••• is not available in the PUMS dataset, the variable “Number of Other Rooms” was included to capture some of the same effects. The variable was created by subtracting the number of bedrooms for the total number of rooms in the unit. Other rooms would therefore include the bathrooms, living room, dining room, and kitchen among other possibilities. Lastly, the specification includes dummy variables for 21 of the 22 PUMAs in BMC region. The coefficients of these variables will indicate the relative cost of each PUMA holding constant the control variables. I chose PUMA 805 as the omitted case because it is located centrally within the study area and is small in terms of land area.
Results The linear regression results are presented in Table 2. The adjusted R2 is .288, meaning that 28.8% of the variation in rental costs in the Baltimore region are explained by housing type, rental terms of gas and electricity payments, the number of bedrooms, the number of rooms other than bedrooms, and the PUMA in which the housing unit is located. This is not an unexpected result due to the limited number of unit characteristics included in the model. The coefficients for the attached single family, detached single family, small apartment, and large apartment structure types were positive and significant at the .01 level. Units in large apartment buildings rent for $463.36 more than mobile homes and trailers, which were the base case, and $42.66 more than single-family homes. This may be because most large apartment buildings are located in the central business district in Baltimore City, where they can command higher rents, or they are new apartment buildings in densifying, higher income suburban areas. The coefficients for boats, RVs or vans; electric included in the rent; and gas included in the rent are not significant. Both number of bedrooms and number of other rooms are
Results 4
Opportunity Costs ••• positive and significant at the .01 level. The number of bedrooms, however, has a much larger effect on rent, which is expected. The hedonic price of an additional bedroom is $155.88, while the hedonic price of another type of room is $26.47. Coincidentally all of the PUMA coefficients are positive and significant. This is because the omitted PUMA had the lowest rental index. Table 2: Regression Results Variables (Constant) Single Family Detached Home Single Family Attached Home Small Apartment Building (2-19 units) Large Apartment Building (20+ units) Boat, RV, or Van Electric Included in Rent Gas Included in Rent Number of Bedrooms Number of Other Rooms Puma400 Puma501 Puma502 Puma503 Puma504 Puma505 Puma506 Puma507 Puma601 Puma602 Puma801 Puma802 Puma803 Puma804 Puma806 Puma901 Puma902 Puma1201 Puma1202 Puma1203 Puma1204
Unstandardized Coefficients
Standardized Coefficients
B
Std. Error
Beta
t
Sig.
-239.911 420.698 344.564 354.648 463.361 -449.491 17.183 6.363 155.883 26.478 318.299 462.147 443.865 477.411 510.256 467.606 198.504 416.736 367.535 274.209 168.401 281.250 220.344 283.661 213.465 754.753 666.446 778.081 377.976 576.173 660.212
54.821 52.496 51.905 51.648 52.280 300.223 11.211 8.373 5.041 3.866 24.876 27.328 21.506 21.570 20.991 23.838 21.687 22.394 33.654 24.453 21.647 20.339 23.124 17.889 20.438 27.393 21.930 22.652 25.863 28.704 23.241
.264 .305 .355 .369 -.011 .012 .006 .308 .057 .115 .146 .199 .214 .238 .178 .087 .174 .090 .101 .074 .137 .088 .178 .104 .237 .290 .320 .130 .171 .265
-4.376 8.014 6.638 6.867 8.863 -1.497 1.533 .760 30.925 6.849 12.795 16.911 20.639 22.133 24.309 19.616 9.153 18.610 10.921 11.214 7.779 13.828 9.529 15.856 10.444 27.553 30.389 34.349 14.615 20.073 28.407
.000** .000** .000** .000** .000** .134 .125 .447 .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000** .000**
Dependent Variable: RNTP
R2 = .288
N = 12,906
Adjusted R2 = .286
Results 5
Opportunity Costs •••
Model Limitations As I touched on earlier, the model is limited in its ability to explain rental values because it lacks many variables that are important factors to a rental unit’s desirability. The model does not include a variable for age of the structure, despite its availability in the dataset, because I found that it reduced the sample size to an unacceptably low number. Other variables that should be included in a hedonic rental pricing model to increase the explanatory power and reduce omitted variables bias are number of bathrooms, presence of an elevator, central air conditioning, central heat, parking included in rent, and building material (brick versus wood construction), age of kitchen appliances, and flooring material. Because these variables are not included, and they are likely to be correlated with one or more of the included variables, the OLS estimator is biased. The plot of the residuals indicates that there is a negative covariance between the population error term and the predicted values, suggesting that the coefficients in my model are smaller than the true value of the coefficients (see Table 3 in the Appendix). An additional limitation of my hedonic model is that it assumes the functional form of the relationship is linear. Coulson argues that because housing characteristics are tied together and cannot be sold separately and repackaged, one should never assume linearity in a hedonic housing function. Instead, the semilog functional form is commonly used.
Spatial Patterns To observe spatial patterns in the hedonic rental price of different PUMAs, I calculated the predicted housing value for a three-bedroom townhome that has five other rooms and no gas or electric included in the rent. Figure 1 shows the estimated rental price for such a unit in each of the
Model Limitations 6
Opportunity Costs ••• PUMAs. The PUMAs are classified by quantile. The highest rents are in Howard and Anne Arundel Counties, while the lowest rents are concentrated in Baltimore City. Parts of Baltimore County near the Chesapeake Bay are also in the lowest quantile. Carroll County also has low rental costs. Unfortunately, PUMAs are quite large geographic units and mask a lot of spatial variation in rental cost.
Policy Implications
Figure 1: Model-Estimated Rental Price for a Townhouse
Now that we have a general map of the cost of rental housing in the Baltimore region holding some key housing traits constant, we can compare this spatial distribution with that of opportunity in the region. Opportunity was measured using a series of neighborhood-level variables at the Census-tract level. The variables included in the index are primarily indicators of opportunity for lowincome, working-age adults. The resulting opportunity map is shown in Figure 4 in the Appendix. By overlaying the affordability designations from Figure 1 onto the opportunity map, we can get a general idea of the areas of high opportunity that have highly and moderately affordable rental prices (see Figure 2).
Policy Implications 7
Opportunity Costs ••• Figure 2: Overlay of Estimated Rental Cost and Opportunity Index Score
Policy Implications 8
Opportunity Costs ••• These are areas that provide high levels of opportunity for working-age adults because of their access to transit, jobs, workforce training, and social capital, while also offering rental housing at rates that are more affordable for low income households than other parts of the region. The lightest green represents Census tracts of high opportunity, while the most affordable PUMAs are shown with diagonal hatch marks. We can see that in Baltimore City, the most affordable areas generally coincide with the lowest opportunity neighborhoods; however, the high opportunity corridor that runs north-south through the city and east along the harbor is in the second lowest rental price quantile. Incentivizing low-income workers from very low-opportunity neighborhoods to live in this area would increase their access to opportunity while keeping subsidy costs low. In essence, housing assistance agencies can get more “bang for their buck” by focusing programs on neighborhoods with high opportunity and low housing costs.
Policy Implications 9
Opportunity Costs •••
References Coulson, Edward. 2008. Monograph on Hedonic Estimation and Housing Markets, Department of Economics, Penn State University. http://www.econ.psu.edu/~ecoulson/hedonicmonograph/chapter2.pdf, accessed 12 May 2014.
Policy Implications 10
Opportunity Costs •••
Appendix Figure 3: Plot of Residuals versus Predicted Values
Policy Implications 11