«Moving to opportunity voluMe 14, nuMber 2 • 2012 U.S. Department of Housing and Urban Development | Office of Policy Development and Research ...»
Thus, the measure does not reflect the degree of homogeneity of smaller neighborhood units sharing the same ZIP Code. A higher degree of spatial autocorrelation likely would be observed with a narrower definition of neighborhood, such as the census tract level.18 Appendix B reports the mean and skewness statistics and the Moran’s I spatial autocorrelation measure for each of the 91 MSAs. Although we do not use it in classifying metropolitan-area delinquency patterns, appendix B also includes the Gini coefficient, a measure of inequality in the spatial distribution of delinquent loans.19 It is calculated using the following formula, where X is the cumulated portion of active loans and Y is the cumulated portion of delinquent loans across
ZIP Codes, ordered by number of delinquent loans:
A Gini coefficient equal to 0 indicates that delinquent loans in the MSA are distributed exactly in proportion to active loans. The greater the Gini coefficient, the more likely some ZIP Codes contain a disproportionate share of delinquent loans relative to active loans.20 Principal Component Analysis The multidimensionality associated with the full set of descriptive statistics introduced in the previous sections would confound an effort to analyze delinquency patterns or to draw intuitively meaningful comparisons across metropolitan areas. Moreover, a high correlation exists among these measures, especially among those that quantify related, but not identical, aspects of the Moreover, the spatial autocorrelation measures indicate the overall degree of spatial autocorrelation, not specifically the degree to which neighborhoods in the high-delinquency tail of a distribution are clustered. Nonetheless, they may be useful as relative measures for comparing spatial patterns across metropolitan areas.
The Gini coefficient is commonly used along with the Lorenz Curve to measure income distribution inequality (Litchfield, 1999).
Among the 91 selected MSAs, the Gini coefficient has a mean value of 0.20 and a standard deviation of 0.09. San Francisco has the highest Gini coefficient (0.47).
distribution (exhibit 2). These correlations complicate the description of delinquency patterns and impart redundancy to an analysis conducted using the full set of descriptive measures.
For example, the mean and standard deviation have a 0.72 correlation, whereas skewness and kurtosis are 92-percent correlated. The variables associated with the spatial aspects of the distribution also are highly correlated with each other and with the standard distribution moments. At the 5-percent significance level, 11 pairings of the 8 focus variables have significant Pearson correlation measures.
Therefore, in anticipation of conducting classification (cluster) and regression analyses of geographic delinquency patterns, we reduce dimensionality by applying principal component analysis (PCA).
PCA is often applied in the economic geography literature to reduce the number of variables used to describe and group cities or places along a number of socioeconomic dimensions without losing all the information contained in the numerous variables of interest (Vicino, Hanlon, and Short, 2007).21 In this application, we use PCA to reduce the number of variables used to describe a metropolitan area from eight measures to four principal components. The principal components essentially are indices that enable us to describe delinquency rate patterns that vary across metropolitan areas, reducing the dimensions of analysis without significant loss of information contained in the original set of analysis variables.
Researchers have also used PCA, for example, to develop neighborhood quality indices as a function of neighborhood characteristics (Can, 1992) and to include a composite measure of neighborhood quality in house price index construction (Can and Megbolugbe, 1997).
252 Refereed Papers Geographic Patterns of Serious Mortgage Delinquency: Cross-MSA Comparisons Exhibit 3 reports the eigenvalues associated with each component. An inspection of the eigenvalues shows that the first four components have eigenvalues greater than 1.00 and the fifth component’s eigenvalue is only 0.59.
Exhibit 3 also shows the proportion of the variance in the data that each component captures. The first two components account for more than one-half of the variation, and the third and fourth components account for nearly one-third of the variation. Each remaining component accounts for less than 10 percent of the total variation in the data, and omitting them is consistent with the analysis of the eigenvalues.
Examining the factor coefficients (loadings) can yield a high-level interpretation for each of the first four components. The fact that each component has at least two significant loading variables, whereby the variables with the largest coefficients are conceptually related, facilitates interpretation. In the first component, the skewness and kurtosis—both measures related to the tails of the delinquency distribution—have coefficients near 0.50. Thus, this component is viewed as a skewness/kurtosis component. With the second component, the mean and standard deviation are the most relevant coefficients; they contribute 0.52 and 0.59, respectively. The third component is most related to the spatial gradient measure, with our two variations of the gradient having the largest coefficients, about 0.55 each. The fourth component is the measure of autocorrelation captured by Moran’s I and Geary’s C. The coefficients of C and I have opposite signs, consistent with the negative and statistically significant correlation between the two measures.
Exhibit 3 Principal Component Analysis Results Component Eigenvalue Percent of Variance Cumulative Percent 1 2.59 32 32 2 1.85 23 55 3 1.18 15 70 4 1.08 14 84 5 0.59 7 91 6 0.41 5 96 7 0.22 3 99 8 0.07 1 100 Cluster Analysis Each of the four principal components from the PCA has a specific value, or “component score,” that equals the weighted sum of the original eight distributional measures, whereby the weights are the factor loadings. To classify MSAs based on delinquency patterns, we conduct a k-means cluster analysis of these component scores (Derudder et al., 2003).
Examining the clusters obtained under alternative specifications of number of groupings, we find that six clusters are most satisfactory. Appendix C lists the metropolitan areas by cluster.
Broadly speaking, the groupings suggested by the cluster analysis reflect the degree to which an MSA’s delinquent mortgages are concentrated in high-foreclosure neighborhoods and the spatial pattern of those neighborhoods: congregated, dispersed throughout the MSA, or relatively few and isolated.
To help characterize the clusters and enable us to visualize how delinquency patterns vary across metropolitan areas in relation to component scores, we create density plots selected as examples for each cluster. The density plots presented in exhibit 4 show how delinquent mortgages in each MSA are distributed in relation to the ZIP Code delinquency rate. They provide a visual reference for components 1 and 2, which are closely associated with this distribution.
The bars in each chart represent the proportion of delinquent loans associated with each neighborhood delinquency rate band, whereby we apply a 1-percentage-point bandwidth. For example, about 5 percent of the delinquent loans in Miami are located in ZIP Codes with a delinquency rate of between 9 and 10 percent, whereas about 10 percent are associated with a neighborhood delinquency rate between 17 and 18 percent.
We also created and examined density maps highlighting the range of ZIP Code delinquency rates through color coding. These maps provide a visual reference for spatial autocorrelation and gradient (closely associated with components 3 and 4). We are unable to reproduce them here, but note some of our observations in the following discussion.22
20% 20% 10% 10% 0% 0%
20% 20% 10% 10% 0% 0%
10% 10% 0% 0%
10% 10% 0% 0%
20% 20% 10% 10% 0% 0%
20% 20% 10% 10% 0% 0% MSA = metropolitan statistical area.
Group 1 The first cluster analysis grouping consists of MSAs with high spatial autocorrelations and low or moderate delinquency rate means. These MSAs contain a modest number of high- or moderately high-delinquency neighborhoods that are clustered together or comprise a distinct pocket of neighborhoods within the MSA. Examples include Austin, Raleigh, and (as of the third quarter of 2008 analysis date) Seattle.23 The density plots associated with this group, as illustrated by those of Bridgeport and Seattle, are relatively compact, with most of the mass in low-delinquency neighborhoods. The distinguishing characteristic of this group, spatial clustering of the higher delinquency neighborhoods, is not evident from the density plots but is observable in density maps. For example, for the Bridgeport metropolitan area, we observe a distinct, concentrated pocket of high delinquency in the urban core. Throughout the remainder of the MSA, we observe lower delinquency rates.
In general, these metropolitan areas have relatively stable housing market and economic environments overall; foreclosure rates in the higher delinquency neighborhoods may or may not rise to a level of concern. Neighborhood effects of delinquency and foreclosure, to the extent they are a concern, would be limited to the higher delinquency pockets, which should then receive particular attention.
We would advise first assessing the potential for effects on house values in adjacent neighborhoods that could cause the foreclosure problem to expand, and taking countermeasures as needed.24 Targeted use of Neighborhood Stabilization Program (NSP) funds to acquire and rehabilitate properties close to the boundaries of the high-foreclosure area is a possible containment strategy.
In many, if not most, cases, the high-foreclosure pocket will consist of neighborhoods where subprime lending was concentrated (the regression analysis in the following section provides some empirical support for this statement). Thus, strategies to prevent foreclosure, such as loan modification to reduce the payment burden on households with high-cost subprime loans, could help stem neighborhood decline. The high-delinquency pocket may also need to be the focus of efforts to mitigate adverse neighborhood effects of REO and vacant properties, applying the kinds of strategies discussed at length in Fleischman (2010), Ryan (2010), and others in the same volume.25 Housing values in Seattle declined substantially and unemployment rose after the third quarter of 2008. As a result, the current delinquency distribution for Seattle likely is different from that in our data, with mean delinquency higher.
Negative externalities associated with foreclosures include lower prices for nearby properties, reduced local property tax base, and high crime rates. Kingsley, Smith, and Price (2009) include a survey of the literature regarding the effect of foreclosures on families and communities.
These strategies include (1) use of public- and nonprofit-sector resources to acquire and rehabilitate foreclosed properties, including bulk acquisitions; (2) partnerships of public-sector and nonprofit agencies with mortgage lenders and servicers to facilitate the sale of REO properties to owner occupants, particularly first-time homebuyers, or to existing occupants (tenants or former owners); (3) partnerships of public-sector and nonprofit agencies with mortgage lenders, servicers, and investors to develop viable REO rental or rent-to-own options for former owners or for existing or new tenants; (4) property code enforcement to mitigate the adverse neighborhood effects of vacancy and abandonment, and legal strategies to facilitate lien transfers to parties willing to perform maintenance or rehabilitation; and (5) demolition of vacant properties and planning for long-term reuse and redevelopment of vacant lots.
256 Refereed Papers Geographic Patterns of Serious Mortgage Delinquency: Cross-MSA Comparisons In some cases, particularly if the high-foreclosure pocket is an area where overdevelopment led to severe home value declines, market-driven recovery may be the best option. Home value declines may suffice to bring homebuyers back into the community as owner occupants, or to attract private investors who see an opportunity to rehabilitate properties for rental or resale.26 Group 2 The second grouping from the cluster analysis exhibits a high mean and standard deviation for delinquency rates. These cities have wide variation across neighborhoods, with most delinquencies occurring in distressed neighborhoods.
Metropolitan areas in this group include Cape Coral, Detroit, Memphis, Palm Beach, and Stockton.
Although they may have some spatial concentrations, high means and very high-delinquency-rate areas in the right tail of the distribution are their most prominent features, as illustrated by the density plots for Cape Coral and Detroit. Widespread occurrence of moderate-to-high delinquency rates characterizes the density maps for these metropolitan areas.
The large number and broad swath of neighborhoods affected by high and very high delinquency necessitate a citywide or regional planning perspective, in contrast with the neighborhood focus associated with Group 1. Strategies to address foreclosure and REO, such as developing viable REO rental or rent-to-own options for former owners or for existing or new tenants, will have to be scalable. Using public- and nonprofit-sector resources directly to acquire and rehabilitate foreclosed properties is unlikely to be an effective strategy, given the scale and scope of the problem.
Redevelopment plans may need to incorporate demolition of vacant and abandoned properties and planning for long-term reuse and redevelopment of vacant lots, a strategy that is being used effectively in Cleveland, for example.