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«reNtal HousiNg Policy iN tHe uNited states Volume 13, Number 2 • 2011 U.S. Department of Housing and Urban Development | Office of Policy ...»

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Exhibit 4 contains several pieces of information that were not available in the original percentage map of the Black population in exhibit 1. The original percentage map in exhibit 1 showed a limited aspect of segregation, which was just a continuum of percentages of where the Black population was and was not located. That map also did not situate the Black population within a context of another population for comparison and account for local segregation. The final map now meets several elements of excellence in statistical graphics that are not in the single percentage map.7 The final map more accurately identifies core areas of segregation and reveals systemic and anomalous patterns that facilitate the exploration of factors associated with segregation such as regional poverty, education, or economic deprivation. Further, because the data have been standardized, a more direct comparison can be made with those factors in and between specific cities or counties. More informed questions can be developed about spatial connections with the local levels and the broader region in which they sit. The use of a diversity index, localized or not, is much more analytically robust and brings out several aspects often hidden in single percentage maps.

The main point of this article is to push thinking away from simple percentage maps of segregation at the national level. As the United States becomes a more diverse nation, the percentage maps become more misleading about segregation and its association with related social and economic ills. The Graphic Detail article in the next issue of Cityscape (volume 13, number 3) will take this analysis further and examine the variation in segregation in the context of economic activity areas.

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Appendix Diversity Index (Theil’s Entropy Index)

Theil’s entropy index is formally defined as:

(1) where j is a jurisdiction and is p proportion of each racial group in jurisdiction j.8 The result is Dj, which is a continuous value that ranges between 0 and. Values closer to 0 indicate higher levels of segregation by one group or the other. Higher values indicate greater levels of diversity between the two groups.

In the context of place, the result is a nonlinear curve in which each unit increment or decrement along the scale has a different rate and magnitude of change. Values on either end of the curve have different qualitative meanings. Geographies are not simply the additive sum of their assets.9 The addition of each new asset transfers benefit in such a way as to compound that benefit to a greater degree as assets are accumulated through the increased combinations among other assets.

The converse is also true. As assets are removed from a place, the decline compounds the negative effects. Social, economic, and political behavior reacts to place changes and further induces other positive or negative effects, depending on whether assets are added or removed. A linear function does not capture this dynamic, because a constant is applied that produces no change in the rate or magnitude of the curve and only shifts the curve up or down uniformly. Lack of any change in the shape of the curve would represent a static impact on a place from assets being added or subtracted with no compounding effect, which is theoretically and empirically not supported.

This reexpression is due to the log function standardizing values by confining them to consistent range with each other. Logarithms applied to skewed data compress values in the lower tails while systematically enlarging values in the middle and in the upper tail. In particular, the natural log (as used in the entropy index) preserves the dispersion of the distribution in the transformed data, making it comparable to the original distribution given they are approximate each other.

This preservation permits the multiplication of pj with the log of pj to produce a meaningful result, because values close together in the original distribution remain close in the transformed distribution. The spreads between the two distributions have been stabilized so they can be added together to create the index from appropriately scaled components to produce a meaningful result.

Using a transformation that does not preserve the dispersion would result in the multiplication of mismatched original and transformed values of the same unit and distort the resulting curve.

In addition, outliers are made more prominent through the multiplication operation and are scaled relative to the other values in the lowest and highest classes. Large outliers are amplified so that the For a review of the mechanics of this index, see Wong (2003).

An asset is defined as (1) developmental, (2) commercial, (3) recreational, (4) physical, and (5) social, where a greater combination of each asset leads to an improved quality of life.

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group at the upper end and small outliers at the lower end do not significantly increase beyond their original value.

Localized Entropy Index

The localized index adjusts for lower level geographic variation and is formally defined as:

(2) where is now the average level of diversity of all tracts in jurisdiction j accounting for the variation, Ω is the number of tracts in jurisdiction j, Ni is the total population of the two racial groups in tract i, and Di is the same index in equation 1 but applied to each tract i. The two population groups for each tract i are multiplied by the local diversity index individually and summed up to jurisdiction j, forming a local interaction effect that weights the diversity commensurate with the size of the population of the two groups. The interactions capture the variation at the local level before the result is summed to the jurisdiction, thus adjusting for local levels of segregation. After the interactions are summed up for each jurisdiction, the result is rescaled back to the relative size of the total population of the two groups to create an average level of diversity. Now and preserves all the mathematical properties and interpretations from the original diversity index but is now adjusted for underlying geographical variation of segregation.





Frequency Distributions Each appendix exhibit number corresponds with the respective map exhibit number in the main body of the article (for example, exhibit 1 corresponds with exhibit A-1).

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Exhibit A-3 Diversity Levels of Cities and Counties—Equal Interval Classification 0.

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Exhibit A-4 Localized Diversity Levels of Cities and Counties—Equal Interval Classification 0.

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Acknowledgments The author thanks Michael O’Leary from Towson University for providing valuable comments toward clearly describing the mathematical operations behind the statistical equations used in this analysis. The author also thanks Jay Lee from Kent State University for providing comments on the geographical analysis.

The views expressed in this article are those of the author and do not represent the official positions or policies of the U.S. Department of Housing and Urban Development.

Author Ronald E. Wilson is a social science analyst in the Office of Policy Development and Research at the U.S. Department of Housing and Urban Development.

References Openshaw, Stan. 1994. The Modifiable Areal Unit Problem. London, United Kingdom: Geo Books.

http://qmrg.org.uk/files/2008/11/38-maup-openshaw.pdf (accessed March 23, 2011).

Reardon, Sean F., and Glenn Firebaugh. 2002. “Measures of Multigroup Segregation,” Sociological Methodology 32: 33–67.

Tufte, Edward R. 1983. The Visual Display of Quantitative Information. Cheshire, CT: Graphics Press.

Wong, David W.S. 2003. “Spatial Decomposition of Segregation Indices: A Framework Toward Measuring Segregation at Multiple Levels,” Geographical Analysis 35 (3): 179–194.

174 Graphic Detail Data Shop Data Shop, a department of Cityscape, presents short articles or notes on the uses of data in housing and urban research. Through this department, PD&R introduces readers to new and overlooked data sources and to improved techniques in using well-known data. The emphasis is on sources and methods that analysts can use in their own work. Researchers often run into knotty data problems involving data interpretation or manipulation that must be solved before a project can proceed, but they seldom get to focus in detail on the solutions to such problems. If you have an idea for an applied, data-centric note of no more than 3,000 words, please send a one-paragraph

Abstract

to david.a.vandenbroucke@hud.gov for consideration.

Separating the Good From

the Bad From the Ugly:

Indicators for Housing Market Analysis Brian A. Mikelbank Charlie Post Cleveland State University Introduction In the years before the current housing crisis, the Urban Center at Cleveland State University regularly produced housing indicators for the city of Cleveland, Ohio, and other geographic subareas within the Cleveland metropolitan area. As the housing market deteriorated into crisis, traditional market price and volume indicators became less useful, and analysts at the Center faced the fundamental challenge of determining what was occurring in these local housing markets.

Many local jurisdictions are undoubtedly exploring this same, uncharted territory. Those who analyze local housing markets need to gauge the (sometimes volatile) health of that market. Although national and regional indicators (for example, the S&P/Case-Shiller® Home Price Indices) are available for analysis, they provide no information on local market performance, and information at the municipal or neighborhood level is often crucial to making strategic planning decisions.

This article presents four lessons the Center learned about Cleveland’s local housing market and the data and tools used to identify the lessons. Although these approaches may not be as useful in every market, they may serve as a starting point for similar analyses and discussion.

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Lesson #1: Geography Matters Actually, geographic submarkets matter. Within Cuyahoga County, Cleveland and its suburbs are the broadest submarkets analyzed. Exhibit 1 shows the unadjusted median price for these submarkets since 1976, which is an indicator we update regularly. The exhibit illustrates three important trends. First, the median price in the city of Cleveland is typically about one-half of that in the suburbs. Second, despite the simplicity of this split (city versus suburbs), the comparison reveals distinct market features, as do subsequent divisions of the market, whether they are individual suburbs or city/suburban neighborhoods. Third, the recent price changes that motivated concern among city and suburban residents are obvious.

The analysts’ data task for exhibit 1, which was straightforward, involved receiving the transaction data directly from the Cuyahoga County auditor. Attributes included in the data were sales price, parcel number, and address, including municipality. The only necessary recoding was identifying all non-Cleveland sales as suburban.

Tracking foreclosure filings became a near-obsession among analysts in our region. Exhibit 2, which includes an additional geographic submarket of interest in Cuyahoga County—east versus west, shows the number of foreclosure filings on single-family properties among the four resulting submarkets—east, west, city, and suburb. It reveals a substantial east/west/city/suburb divide in the pattern of foreclosure filings—the problem is not simply between the city and the suburb.

Further, although attention was largely focused on the city of Cleveland, particularly its east side, single-family foreclosure filings in the suburbs generally outnumbered those in the city, on both the east and west side.

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80,000 60,000 40,000 20,000 Foreclosure filing data are available online through the Cuyahoga County Clerk of Courts. They include the filing date and parcel number. This analysis used parcel number ranges to assign parcels to neighborhoods and municipalities, which themselves are designated as east or west side.1 Lesson #2: The Market Is Fundamentally Different Now What many people failed to realize about the trends illustrated in exhibit 1 was that, although the price of the median sale had dropped, in some cases dramatically, the median sale itself had changed. Before the crisis, the median single-family house sale was an arms-length transaction between owner-occupiers. During the crisis, the median sale is much more likely to be a distressed sale, one affected directly by foreclosure. Thus, analysts at the Center identified, and examined separately, these two markets. They defined a sale as “directly affected” by the crisis if one of the following conditions was met:2 (1) the sale was a sheriff’s sale, (2) the house had sold at a sheriff’s sale in the past 2 years, or (3) the house had a foreclosure filing against it in the past 2 years.

These geographic assignments can also be made through geocoding in a Geographic Information System.

In this article, we do not address the question of indirectly affected houses, which occur when foreclosed houses affect the sales price of surrounding houses.

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If the sale met none of these conditions, the analysts considered it to be not affected by the crisis.



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