«Urban Problems and sPatial methods VolUme 17, nUmber 1 • 2015 U.S. Department of Housing and Urban Development | Office of Policy Development and ...»
Property values were assigned to each lot for each year between 1999 and 2007 based on inverse distance weighting of the price per square foot of the closest 15 properties sold in that year within 500 feet of the lot. This approach essentially calculates a weighted average of those sale prices, with the weightings assigned so that closer properties have higher weights. When fewer than 15 properties sold within 500 feet of a lot, the number of properties included in the calculation was reduced to 10. If fewer than 10 properties sold, the search radius was increased to ensure that at least 10 sales were included.
With sale price per lot as the dependent variable, the specification of the difference-in-differences model was
where lnVit is the natural log of the average price per square foot of residential real estate near vacant lot i at time t; Pi is a dummy variable set to 1 if lot i is part of PLC or 0 if it is not; Git is a dummy variable set to 1 if time t is post-greening for lot i (for a control lot, this value is set to 1 when the associated treated lot is greened); PiGit (that is, the interaction term defined as P times G) is a dummy variable set to 1 if lot i is in PLC and time t is post-greening; Mi is a variable encoding the real estate market index value of lot i; Si is a fixed-effects variable for the Neighborhood Planning District of the city of lot i; Yt is a fixed-effects variable for year to account for temporal effects; εit is an error term; and b terms are the coefficients to be estimated by the model.
This model provides an overall assessment of whether property values changed near greened lots in a manner that was different from changes near nongreened lots, but, as previously noted, it calculates a single equation that is assumed to represent the relationship between PLC and property values for the entire study area. I was, however, keenly interested in thinking about whether the PLC program behaved differently in different areas. One way of answering this question would be to split up the observations based on neighborhoods that might be expected to behave differently and to calculate model coefficients for each group separately. I attempted to assess neighborhood differences by running the model in two ways—first, by splitting the lots into planning neighborhoods and, second, by splitting lots into different real estate typology categories. That approach, however, requires some decision to be made in advance about the appropriate means for defining areas that might be expected to behave differently from each other. An alternative to the prescribed approach to splitting observations into neighborhoods is to use geographically weighted regression (GWR) instead of ordinary least squares regression in the specification of the difference-in-differences model.
The GWR model essentially calculates a separate regression equation for each observation in the dataset by calculating coefficients using only a subset of “nearby” observations, which are weighted based on proximity so that nearer observations have higher weights than those that are farther away (Fotheringham, Brunsdon, and Charlton, 2002).
The equation for the GWR model can be specified as
with (ui, vi) representing the coordinates of point i, and xk representing the kth independent variable in the model. All variables from the original global difference-in-differences model were included in the GWR variant. This model weights observations based on their distance to point i so that it creates a Gaussian weight surface in which closer locations are weighted closer to 1 and farther locations’ weights decrease ultimately to 0. The GWR model was run with bandwidths specifying neighborhoods of ½ mile, 1 mile, and 2 miles in radius.
One final step taken after the models were run was the calculation for each lot of the percentage of surrounding lots that had been greened. For each greened lot in the study, the number of lots within 500 feet was counted and the percentage of lots that were greened through PLC was calculated. This measure was then averaged for each neighborhood to create a measure of “concentration of greening” within that area. These values were mapped against the model results as a purely visual assessment of a possible relationship between effects of the program and the structure of its implementation.
Results The global difference-in-differences model coefficients (exhibit 1) showed that property values surrounding greened lots did increase more than property values surrounding control lots, but much more information was gleaned from the geographically focused models, which showed that this relationship varied considerably over space. In the neighborhood-specific models, only three of seven neighborhoods—Eastern North Philadelphia, West Philadelphia, and Southwest
Philadelphia—actually showed the pattern of increased property values surrounding greened lots, while the other four neighborhoods had coefficients that were not significantly different from 0.
The real estate market-based model also showed variations across the city, with distressed markets showing increased property values as a result of the PLC program but transitional and steady neighborhoods showing no effect.
Both of these patterns were further illuminated by the GWR model, which similarly demonstrated wide variation in the effects of the PLC program. Exhibit 2 indicates the results of the GWR model with a 1-mile bandwidth, although the results were consistent at all bandwidths tested. Note that
GWR = geographically weighted regression. PG = the PG term in the model equation.
Note: Open circles indicate lots where the PG coefficient is positive and significant (that is, locations where Philadelphia LandCare raised the nearby residential property values).
this pattern matches the results of the neighborhood-specific models, with batches of positive coefficients in each of the neighborhoods that showed positive effects of PLC in its own model. The GWR results actually add additional nuance, however, highlighting the potential for variation of effects even within a neighborhood. In particular, additional small clusters of positive coefficients are found in South Philadelphia, Western North Philadelphia, and Northwest Philadelphia, indicating that PLC did lead to increased property values in parts of those neighborhoods, although not consistently throughout them. The GWR results also indicate areas of no effect within the three neighborhoods where the neighborhood models indicated PLC to have positive effects.
Comparison of the various model results with the concentration of greening measure showed that neighborhoods with the most positive effects of greening on property values in both the neighborhood-specific models and the GWR results tended to be those with the higher scores for concentration of greening (exhibit 3), suggesting that areas in which a higher proportion of lots were treated were more likely to see gains in property values. For additional tables, figures, and discussion of the results of this study, see Heckert and Mennis (2012).
Exhibit 3 Results of Geographically Weighted Regression Compared With Neighborhood Greening
GWR = geographically weighted regression. PG = the PG term in the model equation. PLC = Philadelphia LandCare.
Note: GWR results compared with the concentration of greening in each neighborhood, meaning the percentage of lots surrounding greened lots that also were greened.
Discussion This analysis ultimately revealed that, although property values throughout the city increased during the study period, properties surrounding treated lots enjoyed a greater increase in value than properties surrounding controls, but it also showed that these effects were not felt evenly across the study area. The local models demonstrated that the effect was more pronounced in some parts of the city than others, a result that may have significant implications for continued implementation of the program.
This study further shows that the difference-in-differences method can be applied in understanding the spatial effects of an intervention—in this case, treatment of vacant lots by greening them—although special consideration must be given to spatial relationships in selecting appropriate controls. The additional use of a geographically weighted variant of the model was a key to generating meaningful results that can be used by program administrators and policymakers in future planning. The use of distinctly spatial methods was crucial throughout the study—first, for appropriate selection of control lots and specification of the initial aspatial model; second, for developing neighborhood and real estate market-specific variants of the model to begin to assess variations across the study area; and, third, in the development and specification of the GWR model, which ultimately provided the most nuanced results. Spatial methods were then able to be used to begin exploring how differences in program implementation in terms of the percentage of lots greened may have contributed to the differences in effects seen across neighborhoods.
The analysis provides direct, robust evidence for a positive change in nearby property values as a result of greening vacant lots while highlighting the importance of using spatial methods. The ability to compare local and global models to determine neighborhood factors that may influence program outcomes provides additional value in helping to target future initiatives to locations where they may be most likely to succeed.
Acknowledgments The author thanks Jeremy Mennis, the Pennsylvania Horticultural Society, and the Cartographic Modeling Lab at the University of Pennsylvania. This research was supported in part by a Doctoral Dissertation Research Grant from the U.S. Department of Housing and Urban Development and by a University Fellowship from Temple University.
Author Megan Heckert is an assistant professor in the Department of Geography and Planning at West Chester University.
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Abstract Multilevel models are important to use when data are nested. To demonstrate this point, an example is given where the probability of a house being abandoned is predicted using house- and neighborhood-level variables. The example illustrates the types of findings that are possible when different spatial scales are carefully considered. The final model indicates that for stable neighborhoods, house-level characteristics have a greater impact on the probability than do neighborhood-level characteristics; however, for more distressed neighborhoods, neighborhood characteristics matter more. Without the use of multilevel modeling techniques, this relationship might not have been found.
Introduction Prediction is a powerful public policy tool. By being able to anticipate phenomena, policymakers are better able to make informed decisions. Given the importance of prediction, researchers often use multivariate regression to predict an outcome (for example, poverty, illness, and foreclosure) based on several potential predictors or causes. Although this method is popular, few researchers have considered the influence that spatial scale might have on their results and model interpretations.
Thus, the primary objective of this article is to demonstrate why scale matters; the article does so using an example of abandoned housing prediction. The article will likewise add to the housing literature by providing new information about the spatial characteristics of abandonment. By considering two scales in the same model, one can identify the scale that has the greatest influence on the probability. Perhaps characteristics of a home matter more than the characteristics of the neighborhood where it is located. Some variables might be significant at one scale but not another.
There are many theories about the causes of abandonment. Because the focus of this article is methodological, a literature review on abandonment will not be provided. Nonetheless, the variables