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Redlining revisited: spatial dependence and neighborhood effects in mortgage lending
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Redlining revisited: spatial dependence and neighborhood effects in mortgage lending
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Content
REDLINING REVISITED: SPATIAL DEPENDENCE AND NEIGHBORHOOD
EFFECTS IN MORTGAGE LENDING
by
Duan Zhuang
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PLANNING)
August 2007
Copyright 2007 Duan Zhuang
ii
DEDICATION
To my family that support me all the way.
iii
ACKNOWLEDGEMENTS
This dissertation cannot be completed without the support of many people.
I would like to thank those who have helped me on the path towards this
dissertation during my studies at USC.
First of all, I am extremely grateful for the opportunity to have Prof. Stuart
Gabriel as my advisor. He patiently provided the vision, encouragement and
advice necessary for me to proceed through the doctoral program. His guidance,
understanding and insight during different stages of my graduate studies were
paramount in providing me a well-rounded experience to complete this
dissertation.
I also would like to thank Prof. Yongheng Deng for his assistance and
guidance in getting my graduate experience started on the right foot and providing
me with the foundation for the future research.
I am fortunate to have benefited greatly from the help of many other
faculty members at USC. I appreciate the generosity and support from Prof.
Genevieve Giuliano, Prof. Gary Painter, Prof. Dowell Myers, Prof. Tridib
Banerjee, Prof. Niraj Verma, Prof. David Dale-Johnson, Prof. Chris Redfearn,
Prof. Cheng Hsiao, Prof. Koichi Mera, and Prof. Judith Kildow at different stages
of my graduate studies. I also thank the outside member of my committee, Prof.
Delores Conway for her time and energy in supporting me.
iv
I would like to thank SPPD and the LUSK Center for Real Estate for
generous financial aids, the Department of Housing and Urban Development for
the EDSRG and DDRG supports, and Dr. Wei-Hui Chen for the fellowship at the
dissertation stage.
Finally, I would like to thank my family for their support and faith in my
abilities during the course of my studies. Without their encouragement, inspired by
the traditional belief of the Chinese culture that nothing is more valuable than
education, I may not have persevered in pursuing this goal for a doctorate degree
after my husband Sheng and my sister Ling.
v
TABLE OF CONTENTS
DEDICATION ........................................................................................................ ii
ACKNOWLEDGEMENTS ...................................................................................iii
LIST OF TABLES ................................................................................................ vii
LIST OF FIGURES .............................................................................................viii
ABSTRACT............................................................................................................ x
CHAPTER 1. INTRODUCTION ........................................................................... 1
Motivation of this Research............................................................................... 1
Widespread Intra-metropolitan Disparities in Mortgage Credit Allocation...... 5
Why Intra-metropolitan Disparity in Lending Outcome is a Problem............ 13
Roadmap of this Dissertation.......................................................................... 14
CHAPTER 2. LITERATURE REVIEW .............................................................. 16
Spatial Variation in the Demand and Supply of Mortgage Credit .................. 18
The Role of Spatial Dependence and Neighborhood Effects in
Lending Outcomes .......................................................................................... 34
A Two-Stage Spatial Analysis for Intra-metropolitan Lending
Outcomes ........................................................................................................ 41
Summary of the Existing Literature................................................................ 43
CHAPTER 3. DATA AND MAPPING RESOURCES, SAPTIAL MODELS,
INITIAL COMPUTATIONS, AND RESEARCH HYPOTHESES..................... 46
Data and Mapping Resources.......................................................................... 46
Major Spatial Models...................................................................................... 51
Initial Computations........................................................................................ 62
Research Hypotheses ...................................................................................... 76
vi
CHAPTER 4. THE GEOGRAPHICALLY WEIGHTED REGRESSION
APPROACH TO LENDING OUTCOMES ......................................................... 80
Research Approaches and Methodologies....................................................... 80
Empirical Framework...................................................................................... 82
Results and Analysis ....................................................................................... 84
CHAPTER 5. SUMMARY AND POLICY IMPLICATIONS .......................... 115
Spatial Methodology on Lending Outcomes: The GWR Application ......... 115
Enhance Mortgage Flow to Underserved Areas .......................................... 117
Summary ...................................................................................................... 118
BIBLIOGRAPHY............................................................................................... 119
APPENDIX: CONVENTIONAL CONFORMING PURCHASE LOANS ....... 128
vii
LIST OF TABLES
Table 1: 2002 Los Angeles Region Conventional Purchase Conforming
Loan Characteristics by Census Tract Income and Race........................ 9
Table 2: Descriptive Statistics for the 2000 Census Tract Level Variables......... 66
Table 3: Global OLS Results on 2002 Denial Rate ............................................. 86
Table 4: ANOVA Test of GWR against OLS...................................................... 87
Table 5: Explanation of GWR Results on Selected Variables............................ 92
viii
LIST OF FIGURES
Figure 1: US Homeownership Rates by Race, 2004............................................ 2
Figure 2: US Homeownership Rate and Gap by Location, 1984-2004 ............... 3
Figure 3: Relationship between Homeownership Rate, Denial Rate, and
Credit Flow .......................................................................................... 4
Figure 4: 2002 Composition of Conventional Purchase conforming Loan
Denial Rate by Median Census Tract Income.................................... 11
Figure 5: 2002 Composition of Conventional Purchase conforming Loan
Denial Rate by Median Census Tract Minority Population............. 11
Figure 6: 2002 Los Angeles Region Clusters on Census Characteristics .......... 72
Figure 7: 2002 Los Angeles Region Urbanized Area Denial Rate
Distribution ........................................................................................ 74
Figure 8: 2002 Significant Spatial Varying Coefficient of Black
Composition on Denial Rate .............................................................. 96
Figure 9: 2002 Significant Spatial Varying Coefficient of Tract Median
Income on Denial Rate....................................................................... 98
Figure 10: 2002 Significant Spatial Varying Coefficient of Tract Median
House Value on Denial Rate............................................................ 100
Figure 11: 2002 Significant Spatial Varying Coefficient of
Hispanic Composition on Denial Rate............................................. 102
Figure 12: 2002 Significant Spatial Varying Coefficient of Percentage
Blue-collar Workers on Denial Rate................................................ 105
Figure 13: 2002 Significant Spatial Varying Coefficient of Percentage
Same County on Denial Rate ........................................................... 106
Figure 14: 2002 Significant Spatial Varying Coefficient of Percentage
Same Household on Denial Rate...................................................... 107
ix
Figure 15: 2002 Significant Spatial Varying Coefficient of Percentage
College Degree on Denial Rate....................................................... 110
Figure 16: 2002 Significant Spatial Varying Coefficient of Percentage
below High School Degree on Denial Rate .................................... 111
Figure 17: Los Angeles Region Urbanized Area Estimated Denial Rate
below High School Degree on Denial Rate .................................... 113
Figure 18: Los Angeles Region Urbanized Area Estimated Denial Rate
Surface from the Geographic Weighted Regression, 2002............. 114
x
ABSTRACT
This study investigates spatial dependence and neighborhood effects in
mortgage lending disparities in the Southern California five-county region. In
doing so, it assesses indicators of primary mortgage market activity and their
determinants for the region as a whole. The study compiles data from the 2002
HMDA and the 2000 U.S. Census to undertake a variety of analyses, including
computation, assessment, and mapping of social-economic characteristics, as well
as home mortgage origination, denial rates, and secondary market purchase rates
by census tracts among sampled areas and population cohorts. Cluster analyses of
social-economic and mortgage parameters show distinctive patterns of spatial
clustering among tracts across the region. In observing these blueprints of spatial
dependence, the study further undertakes a geographically weighted regression
(GWR) to analyze spatial non-stationarity in the determinants of variability in
neighborhood primary market loan denial rates for the year 2002.
The modeling results reveal that significant spatial non-stationarity exists
between mortgage denial rates and neighborhood-level socioeconomic
determinants. Firstly, tracts exhibiting similar neighborhood-denial rate
relationship tend to cluster, and the effects and proximity of nearby tracts play
significant roles in the determination of the denial outcomes of the underlying
tracts. Secondly, the study finds that those locational attributes, including income,
xi
population, age, racial composition, housing stock, show significant and varying
impacts on mortgage denial rate pattern across space. Specifically, the established
relationship between tract denial rates and tract attributes is not necessarily
significant everywhere in the region. In particular, among traditionally
underserved areas and more affluent areas, there exist spatially varying
relationships between denial rate and tract racial composition, which shed lights on
the existence and varying causes of redlining across space. The study concludes
that mortgage lending patterns are better understood by the geographically-
weighted model than traditional Ordinary Least Square (OLS) regression
approaches on lending outcome, which ignore the spatial dependence among local
determinants.
1
CHAPTER 1
INTRODUCTION
I Motivations of this Research
Homeownership is a longstanding topic of both academic and policy
concerns because it is widely believed to encourage good communities and
citizenship (Green and White, 1997). For decades, the Federal Government has
made substantial efforts to promote fair housing so as to increase homeownership
rate among low-income and minority groups. On the whole homeownership rates
in the U.S. have been going up in recent years. However, huge disparities in
homeownership rates between high-income and low-income households, as well
as between whites and minorities (Figure 1) continue to be evident. According to
the Department of Housing and Urban Development’s (HUD) 2005 Annual
Performance Plan, while the overall homeownership rate in America reached 67.9
percent in 2003, the rate among households with income less than median family
income was only 51.9 percent during the same period. In 2002, only 49.1 percent
of African-American households and Hispanic households were homeowners,
compared to a rate of more than 70% for non-Hispanic white households.
2
Figure 1
Note: Unit of the X-axis is percent.
Most low-income and minority groups are concentrated in underserved
areas.
1
Census data show that, geographical concentration of poverty and
isolation of low-income households worsened in recent decades. As a result, the
homeownership gap between suburbs and central cities has widened between
1984 and 2004 (Figure 2). This has drawn considerable policy attention because
1
Underserved areas are metro/non-metro areas (as defined by the Office of Management and
Budget) with census tracts having a median income at or below 120 percent of the median income
of the metropolitan/state non-metro area and a minority population of 30 percent or greater; or a
median income at or below 90/95 percent of median income of the metropolitan/state non-metro
area.
US Homeownership Rates By Race 2004
(Source: U.S. Census)
0 10 203040 5060 70 80
Non-Hispanic White
African American
Hispanic
All Other Races
3
underserved areas’ relative low homeownership rates have hampered the national
homeownership goals initiated by the Federal Government.
2
Figure 2
Note: Data are from the U.S. Department of Housing and Urban Development.
Federal policy in recent decades has focused on increasing the
homeownership rate in areas with high concentration of low-income and minority
population, where homeownership had previously been low. In the late 1970s,
2
See http://www.whitehouse.gov/infocus/homeownership/ for details.
U.S. Homeownership Rate and Gap by Location
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
1984 1994 2004
Homeownership Rate %
19.5
20
20.5
21
21.5
22
22.5
23
Gap %
Central Cities Suburbs Gap
4
Congress passed the Home Mortgage Disclosure Act (HMDA) which has made
the mortgage lending outcomes more transparent. The HMDA data have been
used to identify credit demand in underserved areas that might otherwise have
been overlooked. To promote market efficiency, Congress has also enacted the
Community Reinvestment Act (CRA) in the 1970s, which requires federal
regulators to evaluate how depository institutions help meet the credit needs of
their communities.
3
Both acts have helped to promote homeownership rates in
underserved areas.
Figure 3
Relationship between Homeownership Rate, Denial Rate, and Credit Flow
Low level of
Credit Flow
Low
Homeownership
Rate
High Mortgage
Denial Rate
Low level of
Credit Flow
Low
Homeownership
Rate
High Mortgage
Denial Rate
3
In his 2005 speech, the former Federal Reserve Governor Mark W. Olson states the following:
“CRA was amended in 1989 to require that those evaluations be made public. The public
evaluations of CRA performance, together with the fact that the performance evaluations are
considered by regulators in connection with a bank or thrift's application to merge or acquire
another institution, have provided incentives for depository institutions to lend in all parts of the
neighborhoods they serve, including low- and moderate-income areas”. See
http://www.federalreserve.gov/BOARDDOCS/Speeches/2005/200505193/default.htm for details.
5
On the secondary market, Congress enacted the Federal Housing
Enterprises Financial Safety and Soundness Act (FHEFSSA) in 1992 to
encourage Fannie Mae and Freddie Mac, the two major government sponsored
enterprises (GSEs) to increase their purchases of mortgages on housing for low-
and moderate-income families and neighborhoods. The legislation authorized
HUD to set affordable housing goals (AHGs), one of which requires that a
percentage of units in properties mortgaged with loans purchased by the GSEs are
located in underserved areas.
II Problem: Widespread Intra-metro Disparities in Mortgage Credit
Allocation
The analyses in this dissertation are motivated by the trends in
homeownership rates. Evidently, geographical disparities in homeownership rates
importantly reflect the uneven flow of mortgage credit across locations, which is
often measured by the denial rates of mortgage applications in some specific
spatial units (e.g. census tracts) in the current mortgage lending literature.
Understanding the determinants of intra-metropolitan disparities in lending
outcome is the core of this research.
As a rapidly growing region with rich ethnic diversity, the Los Angeles
five-county area provides an interesting case study of mortgage lending outcome.
Following Gabriel and Rosenthal (2004), the initial computations summarized
6
measures from the HMDA
4
data that provide evidence of primary
5
and secondary
6
mortgage market activities for 2002. The computations focus on conventional
conforming purchase
7
(CCP) loan (see Appendix I) activities by census tracts
among sampled areas and population cohorts in the Los Angeles region. These
computations measure intra-metropolitan disparities in the mortgage lending by
calculating denial rate, origination rate, secondary market purchase rate, and share
of secondary market activity.
For each census tract, the first measure is the denial rate in the primary
market:
Primary Market Denial of Mortgage Applications
Primary Market Mortgage Applications
Denial Rate = (1)
4
See Chapter 3 for a detailed description of the HMDA data.
5
The mortgage market consists of two separate sections: the Primary Market and the Secondary
Market. The primary market is where loans are originated; mortgage lenders and banks loan
money to borrowers for the purpose of financing real estate transactions.
6
The secondary market manages mortgages that were originated in the primary market. It consists
of investors, both public and private, who buy the mortgage notes. This allows the mortgage
lenders to replenish the cash reserves, so that they can originate more mortgages to more
consumers. The investors profit from the interest that the mortgages charge.
7
This study is focused on conventional conforming purchase loans because they have terms and
conditions that follow the guidelines set forth by the two Government Sponsored Enterprises
7
(GSEs). “Conventional” financing, by definition, is not insured or guaranteed by the
federal government. These loans are granted according to strict loan qualification criteria such as
credit score, income-to-debt ratio and other requirements. Non-conforming loans have no set
guidelines and vary widely from lender to lender. In fact, lenders often change their own non-
conforming guidelines from month to month.
7
The second measure is the primary market origination rate, which is the
ratio of the number of primary market mortgage applications that are originated
relative to the number of primary mortgage applications received.
Primary Market Originations of Mortgage Applications
Primary Market Mortgage Applications
Origination Rate = (2)
Note that for each Census tract, the denial rate and origination rate do not
necessarily add up to 100 percent. This is because the data include withdrawals,
applications that are approved but not accepted, and files closed because of
incomplete information.
The third measure is the secondary market share of all mortgage loan
activity in the market, defined by:
Secondary Market Purchase of Loans
All Mortgage Market Activity
Secondary Market Share of Activity = (3)
This measure focuses on the secondary market activity of the government
sponsored enterprises (GSEs).
8
In addition, “all mortgage market activity”
includes the sum of primary market originations, denials, withdrawals, approved
but not accepted loans, and files closed because of incomplete information, while
loans purchased on the secondary market are not included. Note that because
8
In the HMDA data, the following types of secondary market purchasers are identified: FNMA
(Federal National Mortgage Association), GNMA (Government National Mortgage Association),
FHLMC (Federal Home Loan Mortgage Corporation), FAMC (Federal Agricultural Mortgage
Corporation in 2002; Farmers Home Administration and FAMC in 1992), Commercial Banks,
Savings Banks or Savings Associations, Life Insurance Company Affiliate Institutions (subsidiary,
or subsidiary of parent corporation), and “other” types of purchasers.
8
loans purchased could have been originated in prior years, this ratio can exceed
unity but is bounded below by zero.
The fourth measure is the primary indicator of the intensity of secondary
market activity. This measure is the ratio of the number of secondary market loan
purchases relative to the number of primary market loan originations, defined by:
Secondary Market Purchase of Loans
Primary Market Originations of Loans
Secondary Market Purchase Rate = (4)
The secondary market purchase rate provides an informative measure of
the intensity with which the secondary market is present in a given census tract,
while also being feasible to calculate from the HMDA data.
Table 1 is the cross-tabulation of each of these four measures by census
tract median income and racial composition for the five counties in the Los
Angeles region. The HMDA data are combined the on denial rate, origination
rate, secondary market share and purchase ratio with the census income and racial
information, and the data are stratified by county and income/racial groups.
9
Table 1: 2002 Los Angeles Region Conventional Purchase Conforming Loan Characteristics by Census Tract Income and Race
# of
Tracts
# of
Loans
Denial
Rate
Origination
Rate
Secondary
Market Share
Secondary
Market
Purchase
Ratio
Los Angeles Less than 25K 354 23,072 18.2% 43.6% 18.5% 35.1%
25K to 50K 841 113,551 12.0% 50.1% 29.2% 46.4%
Income over 50K 470 64,169 8.0% 54.2% 36.0% 52.1%
Minority < 50% 787 107,589 9.0% 53.5% 34.4% 50.7%
Minority > 50% 878 93,203 14.2% 47.3% 25.1% 42.8%
Race Minority < 5% 37 54 9.3% 33.3% 41.2% 77.8%
Orange Less than 25K 46 1,436 16.2% 43.4% 23.8% 42.5%
25K to 50K 234 29,113 12.1% 49.2% 30.2% 47.8%
Income over 50K 230 44,433 6.9% 55.1% 35.9% 50.7%
Minority < 50% 416 63,827 8.0% 53.9% 34.8% 50.2%
Minority > 50% 94 11,155 15.4% 45.2% 25.7% 44.7%
Race Minority < 5% 39 689 6.8% 59.5% 43.5% 60.7%
Riverside Less than 25K 55 2,355 16.4% 46.0% 25.5% 44.1%
25K to 50K 93 72,028 9.7% 52.1% 32.7% 49.8%
Income over 50K 9 11,446 7.7% 53.7% 35.8% 52.0%
Minority < 50% 126 80,821 9.2% 52.6% 33.4% 50.2%
Minority > 50% 31 5,008 15.5% 45.0% 25.0% 44.1%
Race Minority < 5% 34 36 2.8% 66.7% 8.8% 12.5%
San Bernardino Less than 25K 48 5,355 18.0% 42.1% 19.6% 37.3%
25K to 50K 111 44,268 11.8% 49.1% 29.0% 45.9%
Income over 50K 24 14,616 8.2% 52.5% 36.6% 53.3%
Minority < 50% 136 51,786 10.4% 50.9% 32.4% 49.2%
Minority > 50% 47 12,453 16.0% 42.9% 19.8% 36.6%
Race Minority < 5% 10 15 13.3% 46.7% 16.7% 28.6%
Ventura Less than 25K 10 743 9.4% 54.9% 35.0% 52.0%
25K to 50K 64 10,921 10.3% 53.9% 28.5% 42.5%
Income over 50K 59 11,508 6.6% 58.4% 36.1% 49.6%
Minority < 50% 104 18,273 7.8% 57.2% 34.6% 48.5%
Minority > 50% 29 4,899 11.0% 52.0% 24.8% 38.2%
Race Minority < 5% 6 43 4.7% 55.8% 38.7% 50.0%
Note: Numbers are summarized from the 2002 HMDA data.
This table and the related graphs reveal numerous important patterns of
lending outcome of this region for 2002. Figure 4 shows that in four counties
(LA, Orange, riverside, and San Bernardino), conventional loan denial rates fall
with the rise of tract median income. Figure 5 shows that in all five counties,
denial rates are much higher in census tracts with higher minority composition. In
table 1, origination rate patterns are the opposite. The origination rate is higher in
10
high income and low minority share tracts. Besides a few outliers, secondary
market share of activity and loan purchase to origination ratios similarly rise with
tract income status, and decline with the rise of neighborhood black and Hispanic
population shares. While these trend patterns are clear, the absolute values of the
four measurements are also important.
It is observed that:
• The highest denial rates are observed in tracts with median income less
than 25K in both LA and San Bernardino counties. The lowest denial
rates are found in tracts with less than 5% minorities in Riverside and
Ventura counties.
• Origination rates do not vary much between 25-50K and over 50K
median income tracts. The highest origination rate is found in tracts
with less than 5% minorities in Riverside County.
• The highest secondary market shares are found in tracts with less than
5% minorities in LA and Orange counties.
• Similar to the results on secondary market shares, the highest
secondary market purchase ratios are found in tracts with less than 5%
minorities in LA and Orange counties.
11
Figure 4
Note: Data are from the 2002 HMDA.
Figure 5
Note: Data are from the 2002 HMDA.
2002 Comparison of Conventional Purchase Conforming Loan
DENIAL RATE
by Median Census Tract Minority Population Proportion
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
Los Angeles Orange Riverside San Bernardino Ventura
Minority < 50% Minority >=50%
2002 Comparison of Conventional Purchase Conforming Loan
DENIAL RATE
by Median Census Tract Income
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
20.0%
Los Angeles Orange Riverside San Bernardino Ventura
Less than 25K 25K to 50K over 50K
12
From Table 1 it is also evident that high denial rate tracts are concentrated
in underserved areas. Traditionally, central cities were often regarded as
underserved in the locational framework because of the substantial concentration
of poverty and minority groups in those areas. However, the definition of
underserved areas has changed overtime to employ the concentration of minorities
and the level of income within a census tract as the criteria for designation. This
is based on the research done by Shear (1995), who modeled the level of credit
needs in metropolitan areas and found that not all of areas within central cities
suffer from concentration of poverty and high housing costs and that some areas
outside of central cities do. Therefore, the categorization should be based on
income and concentration of minorities rather than its geographic location. The
approach to defining underserved areas was regulated in HUD’s final rule (HUD,
1995). Furthermore, one study (McClure, 2001) shows that the level of lending in
underserved areas is much lower than that in well-served areas. Despite the fact
that the definition of underserved areas only includes the income and minority
measures, these areas are expected to have lower levels of lending, thus
“underserved”.
Summarizing the above, there is suggestive evidence here that areas with
lowest secondary market purchase rates tend to also have very high denial rates.
Lending outcomes are the combination of primary market originations and
secondary market purchases. If one seeks to better understand what drives the
13
observed widespread geographical variation in denial rates and purchases in the
secondary market, understanding that relationship between them is as important.
III Why Intra-metropolitan Disparities in Lending Outcome is a Problem
Since it is costly to gather full information on individual borrowers,
lenders may sometimes use neighborhood income/racial composition as a proxy
for unknown information of borrowers when making lending decisions, which
further hinders the homeownership opportunities for low-income or minority
borrowers. As a result, low-income or minority borrowers are at a considerable
disadvantage to accumulate wealth through house price appreciation. There is
some evidence that inner-city minority neighborhoods, relative to suburban areas,
have experienced lower appreciation in house prices.
9
Secondly, such geographical disparities related to race and income may
cause other social and economic problems. Higher denial rates lead to lower
neighborhood house price growth, which is a major factor of higher level of
default within the neighborhood. Defaults result in abandoned structures that tend
to make the neighborhood less desirable, which in turn promulgates additional
defaults in the future. In addition, since housing is a major source for the
accumulation of wealth, high denial rates lead to neighborhood instability, which
9
For example, Kim (1995) finds that price appreciation in all-minority neighborhoods was 3.5
percent lower than all-white neighborhoods for the period 1971 to 1993 in Milwaukee.
14
hampers the growth of residential capital and the upward economic opportunities
for low-income and minority families.
10
IV Roadmap of this Dissertation
This dissertation seeks to understand the intra-metropolitan geographic
incidence of mortgage credit flow by investigating the spatial dependence and
neighborhood effects associated with mortgage lending outcomes. In doing so,
this study compiles data from the 2002 HMDA and the 2000 U.S. Census to
undertake a variety of analyses, including computation, assessment, and mapping
of social-economic characteristics as well as home mortgage denial rates by
neighborhoods (represented by census tracts). Cluster analysis on the social-
economic and mortgage parameters show distinctive patterns of spatial clustering
among tracts across the region. In examining these blueprints of spatial
dependence, the study further undertakes a geographically weighted regression
(GWR) to analyze the spatial non-stationarity of the determinants of variability in
primary market neighborhood loan denial rates for the year 2002.
This dissertation is organized as follows. Chapter 2 provides a summary of
the literature review. Chapter 3 summarizes the results of data mapping, analysis
and initial computations and brings in the research hypothesis. Chapter 4 presents
10
The March 2000 Current Population Survey shows that about 28 percent of families with
annual income less than $10,000 have moved in the previous year. However, only 11 percent for
families with annual income exceeding $90,000 have moved during the same period.
15
the modeling framework and results of the geographically weighted regression
approach to lending outcomes. Chapter 5 draws the conclusions from this
research and discusses about its policy implications.
16
CHAPTER 2
LITERATURE REVIEW
For the past few decades, substantial academic and policy debate has
emerged over intra-metropolitan lending disparities in the U.S. credit and housing
markets. The conceptual framework of this dissertation is built upon such
discussions and the root of the research in this dissertation stems from two sets of
literature. The first set lies in the examination of lending disparities in the
mortgage market. In the late 1980s, the Atlanta Journal - Constitution published
The Color of Money, a Pulitzer Prize-winning series of articles that described
mortgage redlining in metropolitan Atlanta during the early years of that decade.
The series examined observed disparities between mortgage flow to white and
minority neighborhoods, controlling for income levels. After more than a decade,
Stephen Ross and John Yinger brought about The Color of Credit: Mortgage
Discrimination, Research Methodology, and Fair-Lending Enforcement, which
moves the debate forward by providing a comprehensive analysis of lending
disparities. Despite decades of research, the debate over the existence and the
causes of lending disparities still carries on.
The second set of literature is comprised of the exploration of spatial
dependence and neighborhood effects in the lending literature. There is
increasing awareness of the important role location plays in social and economic
17
status for individuals and housing market outcomes.
11
According to Can (1998),
the role of geographic location can be examined in two interconnected ways. One
form of geographic influence involves localized externalities associated with the
absolute location of the house. These types of externalities are described in terms
of spatial dependence because they capture the spatial spillover effects of
neighboring units on a given spatial unit. For example, a deteriorating
neighborhood would be a source of negative externality to adjacent
neighborhoods. In addition to the spillover effects, overall neighborhood
characteristics such as socioeconomic factors will also enter into lending activities
and result in market outcomes. These kinds of influences are called neighborhood
effects.
Despite the recognized importance of geographic location for mortgage
practices, its incorporation into research has been limited. The existent research
has not resolved the central issues to this debate: what are the determinants of
such lending disparities, and what is the role of spatial factors play their roles in
the determination thereof. Although methods are available in spatial
econometrics to facilitate such kind of research, there have been limited
applications in the current mortgage lending literature.
12
An explicit spatial
11
Goodman (1989) identifies this as one of the major research areas for microeconomic analysis
of housing markets and reinforces the notion that neighborhood does ‘‘matter’’ in housing
research.
12
Only a few recent studies have applied spatial analytical tools to examine neighborhood effects
on housing prices (e.g., Can 1990, 1992b; Can and Megbolugbe 1997; Dubin 1992; Pace and
18
process is needed to measure and quantify accurately the roles of spatial
dependence and neighborhood effects in determining mortgage market behavior
and outcomes. In this dissertation, both types of influences associated with
geographic location are covered.
I Spatial Variation in the Demand and Supply of Mortgage Credit
The outcome of the locational differentials on housing demand and supply
is the systematic spatial variation in the distribution of mortgage credit as we
discussed in Chapter 1. For most households, home purchase is the single largest
lifetime economic and social investment. Mortgage demand is derived from the
demand for housing, which is a function of households’ income, wealth, family
status, amenity preferences and other socioeconomic factors. Since there exist
explicit relationships between households’ mortgage demand and residential
choices, the spatial structure of housing demand results in similar spatial patterns
of mortgage demand. The result is the intra-metropolitan spatial variation in the
demand of mortgage credit as we observed in the Los Angeles area.
On the other hand, the supply of mortgage credit is based on financial
institutions’ willingness to provide financing given market risks, which includes
the availability of mortgage credit, cost of capital, borrowers’ risk characteristics
and related pricing. Isolating market risk involved (such as borrowers’ income
Gilley 1997), in population density models (Griffith and Can 1995), or in mortgage market
outcomes (Anselin and Can 1995).
19
and credit), whether financial institutions are sensitive to locational differences in
their underwriting decisions to provide housing credit is the key question in the
redlining literature.
13
1.1 Demand
Neighborhood demand of mortgage credit is also an aggregate outcome of
borrower’s social and economical characteristics, such as income, endowment,
employment status, education, and race. Differences in household incomes and
other factors, along with systematic spatial variations across neighborhoods, lead
to spatial segmentation. Within a given metropolitan area, differing segmentation
can be found in household income, race and ethnicity, and related lifestyle
choices, which results in residential segregation in an urban area.
Understanding the forces that lead to segmentation in the urban area has been
a major topic of social science research. “Spatial Inequality" is defined in terms
of differences in income across places. Recent research has indicated a growing
gap between rich and poor places in metropolitan America. Orfield (1997) found
that in the mid-1990s the fiscal inequality of suburbs increased in 25 large metro
areas. Abramson and VanderGoot (1995) show that income segregation in
metropolitan areas was significantly greater in 1990s than in the 1980s. Rusk
(1993) hypothesized that once per capita income in a central city falls below 70
13
See the discussion on redlining later in this chapter.
20
percent of that of its suburbs, it cannot regain its economic strength. In their
recent paper, Swanstrom and Flack (2004) tested these theories by examining
trends in "spatial inequality" in the 50 largest metros between 1980 and 2000.
They found segregation and concentrated poverty help to explain differences in
the path of spatial inequality.
Accordingly, various factors, including race or income inequality, may lead to
residential segregation in an urban area. For example, households with high-
income or young children may prefer single-family in a suburban area with better
environmental and/or educational quality. Singles or households with modest
incomes may prefer rental units in inner-city neighborhoods with easy
accessibility. Differences in residential choices lead to differential aggregate
demand of mortgage credit on the neighborhood level. Furthermore, Can (1998)
argued that, for those with financial constraints and those that are subject to
discrimination or have limited information about housing and neighborhood
choices, it is expensive to move and settle in another location. As a result,
neighborhood effects can have long-lasting influences on the social and economic
outcomes for those households. Hence it is important to ensure that households
facing such constraints not become spatially isolated in undesirable
neighborhoods but instead have locational choices and opportunities similar to
those of households with better economic conditions. Having adequate flow of
21
credit among households facing such constraints is the key to mitigate the spatial
isolation and segregation for the upward mobility of such households.
1.2 Supply
On the supply side, the availability of mortgage credit has significant
influences on lending outcomes, especially for low-income and underserved
households. Research on mortgage redlining has sought to measure spatial bias in
the distribution of mortgage funds resulting from non-economic considerations
(see, for example, Canner and Gabriel 1992; Holmes and Horvitz 1994; Munnell
et al. 1996). This section covers the studies on systematic credit-rationing across
space, including lending outcomes analysis, the process-based discrimination
model, as well as the outcome-based redlining model, which set the theoretical
framework in this dissertation.
1.2.1 Lending Outcomes Analysis
a. Differences in Flow of Credit
Concerns about disadvantaged neighborhoods being "redlined” led to the
passage of the Community Reinvestment Act (CRA) in 1977. The CRA directly
addressed the policy concern that banks and thrifts may have been taking deposits
from inner city, minority, or lower-income neighborhoods, and lending those
funds elsewhere.
Specifically, the CRA's main target was to make sure that
22
borrowers in disadvantaged neighborhoods were not discriminated in terms of
access to mortgage credit. During the mid 1990s, the Fannie Mae Foundation
initialized a study of mortgage lending patterns in the Atlanta metropolitan area.
This study showed that compared to their white counterparts, Atlanta's middle-
income African-American neighborhoods still captured considerably less
conventional home loan purchase lending by depository institutions. Therefore,
the aggregate evidence that raised concerns about intra-metropolitan lending
discrepancies in the 1980s were still very evident in the 1990s.
14
b. Variations in Mortgage Rates
Lending disparities may be evidenced in more subtle forms. Historically
average interest rates across regions varied by as much as a percentage point,
reflecting geographic imbalances in mortgage lending practice.
15
The maturation
of the secondary market and the mortgage insurance industry has substantially
reduced differences in mortgage interest rates by geographic location or loan-to-
value ratio (LTV). However, rate differentials may remain for both economic
(e.g., differences in origination or servicing costs, credit risk, points, and
borrowers' search cost) and non-economic reasons.
14
See Holloway (1998) and Holloway and Wyly (1999 and 2001) for details about the related
studies.
15
Compared to the conforming segment of the market, there is much more geographical variation
in mortgage rates in the jumbo market. In 2003, Countrywide Home Loans listed spreads between
jumbo and conforming loans of 23 to 60 basis points, depending on the state and the rate/point
combination. See http://www.fanniemae.com/media/issues/2003 for details.
23
Whether rate differences represent legitimate pricing to compensate
lenders for variation in credit risk, economic returns by neighborhood, or subtle
forms of redlining is still in question. Avery et al. (1994) found higher mortgage
rates in low- and moderate-income areas, even after controlling for a variety of
borrower, loan, and neighborhood characteristics. One interpretation of their
finding suggests that loan applications in such areas may have carried higher rates
to compensate for the greater credit risk. Alternatively, those results could be
evidence that redlining may subtly occur in those areas.
c. Disparities in Denial Rates
Denial rates are an important factor in lending outcomes analysis since
they capture both the demand side and supply side forces. Mortgage denial rates
for minorities and low-income families are also major indicators of trends in
homeownership rates. HUD’s 2005 Annual Performance Plan shows that the
ratio of home purchase disapproval rate between minorities and other applicants
was 176.3 percent in 2002. According to the Plan, the primary cause of
differences in mortgage approval between ethnic groups is differences in average
disposable income and creditworthiness. However, in some cases, lenders have
been shown to discriminate against minority applicants and properties in
underserved areas by disapproving the mortgages.
24
As part of the 1989 thrift legislation, for the first time lenders were
required to report data on race, gender, and income of home loan applicants and
the disposition of loan applications. With the new application-level Home
Mortgage Disclosure Act (HMDA) data, researchers initiated studies that tested
the relationship between applicants’ race and the likelihood of loan denial.
16
Those studies showed that minority applicants are more likely to be denied a loan
than white applicants, even after controlling for individual and property
characteristics included in the expanded HMDA data.
However, several studies showed that the correlation between area racial
composition and lending flows disappears when more variables accounting for
risk and economic fundamentals are included. Using the HMDA data, Schill and
Wachter (1993) examined whether the racial and ethnic composition of the
neighborhood where loan applicants wish to purchase, refinance, or improve their
homes is related to lenders’ decisions to accept or reject their applications. The
results indicated that neighborhood racial composition does appear related to loan
disposition. They also used 1990 HMDA data to study race effects in
Philadelphia and Boston. They found that although individual race is a significant
determinant of loan denial, when adding several other neighborhood "quality"
variables, racial composition becomes insignificant.
16
See Chapter 5 for the details about the HMDA data.
25
1.2.2 The Process-based Mortgage Discrimination Model
Several studies in the 1970s and 1980s utilized non-HMDA data about
individual mortgage applicants and sought to evaluate discrimination
hypotheses.
17
Since 1990, HMDA reporting has required lenders to collect data
on individual applicant’s characteristics. These data allow researchers to estimate
reduced-form discrimination equations in the following form to model the
process-based model, which incorporates a comprehensive set of variables on
both individual and neighborhood levels (Ross and Yinger, 2002):
Probability of loan denial for a given individual = f (area social economic
factors, applicant characteristics) (5)
The most influential work under this framework is the so-called Boston
Fed Study, undertaken by researchers at the Federal Reserve Bank of Boston,
which was initially released in 1992 and published in the American Economic
Review in 1996 (Munnell et al. 1996). Equipped with complete access to the case
files on 1990 home-mortgage applicants from Boston banks, the authors were able
to control for applicant’s creditworthiness. The study found that after controlling
for all objective indicators of applicant characteristics, lenders still rejected
minorities 56 percent more often than otherwise identical whites. Statistically,
this research provided some evidence of disparate treatment.
17
See Listokin and Casey (1980), Schafer (1978), and Ahlbrandt (1977).
26
However, some of the study’s conclusions are questionable. Some critics
have focused on methodological issues such as data errors, sensitivity to outliers,
and the exclusion of factors important in the lending process. Further, the home
mortgage lending system involves very complex processes. Applicants and
lenders are required to make several decisions in a sequence: the applicant selects
a lender; the applicant and lender select a certain mortgage loan product after
negotiation, the lender approves or denies the application, and then an approved
applicant decides whether to accept the loan. The Boston Fed’s study only
focuses on the early application stage and does not address those issues explicitly.
Rachlis and Yezer (1993) argue that equation (1) is not adequately identified if
the market processes might affect the ethnicity groups differently in different
stages. Nevertheless Carr and Megbolugbe (1993) replicated the study and found
that the presence of many miscoded or atypical observations did not materially
alter the study’s results.
The Cultural Affinity Hypothesis
Several authors have extended the problem further. Hunter and Walker
(1995) argue that if lenders have "cultural affinity" with white borrower
applicants, but not with minority borrower applicants, their information costs with
whites will be much less than that with minorities, and they will make many more
loans to whites than to equally creditworthy minorities.
27
This is the so called “cultural affinity” hypothesis. The tests of the
hypothesis interpret cultural affinity as a form of statistical discrimination;
however, there is no presumption that the white and minority groups differ in their
underlying creditworthiness. Instead, the issue is that the cost of collecting extra
information is higher for minority applicants, presumably because the white loan
officer has to make additional efforts to collect this information.
Why does the extra information collected for white applicants result in a
more favorable outcome for whites? The first answer assumes that the credit
characteristics lenders cannot observe have a larger variance for minority than for
white applications because of lack of cultural affinity with minority applicants. If
lenders are risk-averse, this assumption implies that lenders will be more likely to
turn down a minority than a white application even if the two applicants have the
same observed creditworthiness. The second possible answer is that white loan
officers are not trying to learn more about white applicants’ creditworthiness, but
are instead trying to build the best possible case for each white applicant, often by
collecting additional supporting information. This view is not different from the
more traditional explanation that white loan officers are simply prejudiced against
minority applicants. In summary, this latter version of the cultural affinity
hypothesis is little different from discrimination against minority groups.
No scholar has yet found a convincing way to differentiate the above
explanations. Hunter and Walker (1995) investigated their cultural affinity
28
hypothesis with the Boston Fed Study’s dataset to test “whether loan officers’
decisions on white applicants depend less on formal information, such as credit
history, financial obligations, and the like, than they do on minorities”. The main
form of their test is to determine if two key variables—the obligation ratio and
their credit history indicator—have a larger impact on loan denial for blacks and
Hispanics than for whites. They found support for the first effect but not the
second, thus interpreted this result as support for the cultural affinity hypothesis.
The larger impact of the obligation ratio for minorities than for whites could arise
because minorities and whites tend to go to different lenders with different
underwriting guidelines, not because individual lenders use different guidelines
for minorities and whites.
1.2.3 The Outcome-based Redlining Model
Redlining was originally considered a spatial process. Historically,
redlining is the practice whereby mortgage lenders figuratively draw a red line
around minority neighborhoods and refuse to make mortgage loans available
inside the red lined area.
18
In the 1960s, community activists in Chicago used the
word “redlining” to describe the redlines savings and loan associations had drawn
around the neighborhoods they were not willing to lend to (Pogge, 1992).
18
The origins of the term "redlining" in Dade County Florida can be traced to the Home Owners
Loan Corporation (HOLC), a federal New Deal agency of the 1930's. HOLC developed an
elaborate appraisal and rating system for different neighborhoods in cities across the country.
These neighborhood appraisals were plotted on "residential security maps". These maps were used
for years afterwards as a tool for deny loans to residents of Dade County's black communities.
29
Although several different ideas about redlining hold that redlining can be
process-based or outcome-based (Yinger, 1995), consensus in the academic and
policy fields generally agree that redlining involves ideas about creditworthiness
that have more to do with the location of the underlying property and less to do
with the mortgage applicant him/herself.
19
However the different ideas about
redlining do not conflict and the distinctions remain important for the conceptual
and methodological explorations and they complement each other (Hillier, 2003).
Broadly defined, racial redlining encompasses not only the direct refusal
to lend in minority neighborhoods, but also procedures that discourage the
submission of mortgage loan applications from minority areas, and marketing
policies that exclude such areas. As regards lending outcomes, redlining exists
when minority neighborhoods receive a smaller flow of mortgage funds than
comparable white neighborhoods, all else equal.
20
Redlining by this definition is
illegal according to the Community Reinvestment Act (CRA) of 1977.
Researchers used HMDA data to construct the outcome-based redlining models of
the form:
Mortgage flows in a given area = f (area economic variables, area social
variables) (6)
19
Redlining was originally a spatial concept, referring to specific areas not receiving appropriate
amounts of mortgage credit; only recently the process-based redlining employs individual-level
data with the availability of HMDA data.
20
See Ross and Yinger (2004).
30
The basic theory behind this line of research is as follows. Area economic
variables might legitimately affect housing value, and hence mortgage flows.
However if mortgage decisions are based solely on economic fundamentals, then
area social variables, including neighborhood racial composition, should be
insignificant. Redlining arises when area race affects loan flows, when controlling
for complete economic fundamentals with no omitted variable bias. In summary,
redlining occurs when a given market transaction costs more or is less likely to be
approved in a geographic area with a high minority population (or in an inner-city
location) than in a low minority (or suburban) area, when differences in these
areas’ economic characteristics are considered (Ross and Yinger, 2002).
Therefore redlining disadvantages agents in a location independent of their
individual characteristics.
Several researchers have used this form in tests for redlining. One
approach is to estimate equation (2) by census tract; in this case, redlining is
assumed to exist if higher-minority population is a negative determinant of loan
flows. Nevertheless, this model often suffers from omitted variable bias and
oversimplifies the demand-supply mechanism and its determinants, and one
should be cautious in interpreting results from this form of research. First of all,
these studies do not control for whether lower loan flows in minority areas are due
to lower loan demand there (Benston 1981). Secondly, due to greater lending risks
associated with redlined areas, it is difficult to determine whether the disparity in
31
lending flow is due to bank redlining behavior or by economic factors. Thirdly,
mortgage flows to a given area depend on the joint probability of applications to
the lender, for a specific type of mortgage, approval of the lender, and finally the
acceptance of the borrower. Without controlling the above information, the above
model provides no convincing evidence on redlining.
Therefore, great care must be taken in specifying a redlining equation.
Future research on outcome-based redlining should not only focus on the supply
side, but also try to incorporate demand side factors. For this purpose, the denial
rate model of the demand and supply of mortgages is an alternative approach. For
example, in a census tract, demand for loans can be measured by primary market
mortgage applications, and supply by mortgage market denials, and denial rate is
calculated from Equation (1). This approach makes it possible to construct a
redlining model capturing both the demand and supply side forces for a given
census tract.
Mortgage denial rates in a given area = f (area economic variables, area
social variables) (7)
According Becker, et al. (1971), discrimination occurs whenever agents
who individually share some common characteristic can complete a market
transaction only at a higher cost or more stringent terms than other agents; it also
occurs when agents sharing this characteristic are less likely to succeed in an
uncertain market transaction, or have less access to resources. By this definition,
32
denial-rate disparity can provide valuable insights into the existence of redlining.
In direct economic terms, racial redlining reduces housing finance options for
borrowers in minority neighborhoods and weakens competition in the mortgage
market. This often results in higher mortgage costs and less favorable mortgage
loan terms. More subtly, racial redlining discourages minorities from pursuing
home ownership opportunities and in the broadest sense further entrenches the
debilitating sociological effects of racial discrimination.
Modeling Redlining as a Spatial Outcome
To date, only limited research, including the Boston Fed’s study, has
considered the relationship between discrimination against individuals and
neighborhoods (see, for example, Schill and Wachter, 1993; Holloway, 1998;
Holloway and Wyly, 2001). These papers combine individual level data with
neighborhood characteristics such as minority composition and income level.
Accordingly, such approaches are still within the framework of process-based
examination (Equation 5). Simple calculations of rejection rates by census tract
do show higher rates in tracts with higher minority composition.
However, after
controlling for borrower characteristics, most of these studies have been
unconvincing or have not found evidence of geographic discrimination.
21
21
For example, Schill and Wachter (1993)’s results on Boston and Philadelphia do not support the
hypothesis that financial institutions redline neighborhoods when including proxies for
neighborhood risks.
33
The basic ideas underlying process-based models are as follows. After
fully controlling for individual and neighborhood-level factors, if neighborhoods
with higher proportion of minorities exhibit higher denial rates, there is evidence
of discrimination. However, similar to the “neighborhood effects” research we
see in economics and social sciences (Cotterman 2001; Kling, Ludwig, and Katz,
2004), these analyses integrate neighborhood effects without considering the
spatial proximity of geographic units with similar outcomes. While the
conclusions from the above research may tell us whether neighborhoods with high
proportion of minorities are underserved in general, they fail to tell us whether
spatially contiguous areas are underserved, and if so, location of those
underserved areas.
The research presented in this dissertation moves beyond the current
mortgage lending literature in two important ways. First of all, since most of the
current research examines redlining with applicant-level data in conjunction with
neighborhood characteristics, they are still considered process-based studies. In
this study, census-tract level aggregate data and spatial models are used to
identify the actual location of the underserved areas and the neighborhood
characteristics that affect the lending outcomes. In addition, the definition of
neighborhood is exogenous and a function of spatial unit. Compared to existing
studies, such an approach is outcome-based and spatial.
34
Secondly, the Los Angeles five-county region presents an ideal case for
the lending outcome tests. Often regarded as a racially stratified metropolitan
area, it provides a full spectrum of geo-racial profiles as well as a large number of
geo units (census tracts) for the spatial modeling. The goal of this research is to
contribute to the existing literature in redlining and mortgage lending in general,
and to shed light on some of the continuing debate over the existence and the
degree of racial disparities in lending by explicitly modeling the geography of the
race-based lending outcomes.
II The Role of Spatial Dependence and Neighborhood Effects in Lending
Outcomes
The goal of spatial analysis is to examine spatial relationships (e.g.,
adjacency, proximity, contagion, and interaction) among geographic units in the
determination of spatial outcomes in the modeled socioeconomic phenomena
(Can, 1998). In contrast to traditional statistical analysis where spatial structure is
generally ignored, spatial analysis builds upon locational information to model
spatial associations in order to enhance an understanding of the underlying causal
processes and mechanisms.
35
Spatial dependence exists when the value associated with one location is
dependent on those of other locations.
22
Spatial dependence results from spatial
interaction effects (e.g., externalities or spill-over effects).
2.1 Spatial Dependence
2.1.1 The Spatial Contingency Model
Under the Boston Fed’s theoretical framework, Holloway and Wyly
(2001) updated the original “The Color of Money” study with new data. They
expanded the analysis by using the applicant level HMDA data which were not
available for the original research and by empirically examining the hypothesis
about the geographically contingent influences of applicant’s race on denial
probabilities. They argued that drawing a simple distinction between the
discrimination against individuals and against neighborhoods is not sufficient and
may be mis-specified in evaluating discrimination. Alternatively, they
incorporated the interaction of applicants’ racial and ethnic identity with the racial
and ethnic composition of neighborhoods, and argued that the experiences of
minority and low- to moderate- income applicants vary considerably across
neighborhoods.
Under the hypothesis of geographical contingency where both spatial
variations in the impact of racial identity on denial probabilities and in the
outcome of loan approval coexist, this research argues that mortgage markets are
22
See https://www.geoda.uiuc.edu/support/help/glossary.html for details.
36
functionally and by nature geographically contingent. It is innovative in that on
top of the base model which is very similar to the Boston Fed’s specification, this
research introduces the interaction term “Black * %Black in a Census tract” in
their redlining model, as well as “Black*Median Household Income”,
“Black*%Black” and “ Black*med HH inc * % Black” in the contingent effects
model. The results show that black applicants exhibit the highest conditional
denial probabilities in predominantly white, high-income neighborhoods in
Atlanta, while white applicants show their highest conditional denial probabilities
in the predominantly black, low-income neighborhoods, which to some extent
shed light on the concerns about redlining.
2.1.2 The Spatial Contagion Process
In the spatial literature, neighbors are generally defined in two ways. The
first definition uses spatial contiguity as the basis for determining neighbors, i.e.
spatial entities are considered to be ‘‘neighbors’’ if they share a common
boundary. Giuliano et al. (2006) used this definition combined with employment
density measures to define urban employment centers. The second approach is to
take distance measures. This definition is consistent with Tobler’s (1970) first law
of geography, which states that “All things are related, but nearby things are more
related than distant things”. According to Can (1998), based on the spatial
interaction theories which imply that the strength of interaction is a function of
37
distance among spatial units, this definition states that the closer spatial units will
exert a larger influence on each other than more distant ones.
23
To test the spatial contagious process, Anselin and Can (1995) used an
exploratory spatial approach to the examination of the spatial structure of 1990
mortgage originations for Dade County, FL. Specifically, local spatial statistics
were used to identify areas that exhibit statistically significant clustering of high
and low levels of mortgage activity (i.e., ‘‘hot spots’’), which are the only areas
where there were statistically significant spatial clustering of mortgage activity.
The geographic distribution of mortgage activity for the rest of the study area
exhibited a more or less random distribution. They further discovered that spatial
clustering was stronger for block groups with low levels of activity than for those
with higher levels of activity. They concluded that this may point to the presence
of structurally different processes in high and low mortgage activity regions in the
mortgage origination process.
Anselin and Can’s (1995) study suggests an interesting opportunity to
investigate the spatial dependence of locational attributes in the determination of
lending outcome. First of all, investigating the distribution of attribute values
against their neighbors in geographic space can provide insights for hypothesis
generation as well as for spatial exploration of known data sets. The results can be
23
According to Can (1998), information on neighbors is formally stored in what is known as a
connectivity or weight matrix (W), which has dimensions of N by N (where N is the number of
spatial entities in the study area such as census tracts). Elements of W, wij, are the proximity
values either based on adjacency or distance.
38
very useful in investigations of ‘‘contagious’’ processes in neighborhood change.
Secondly, spatially varying attributes can be used in spatial econometric models
to estimate geographic segmentation of lending outcomes. In summary the spatial
process in this study can provide new insights in modeling housing market
dynamics.
2.2 Neighborhood Effects
Neighborhoods can be defined as discrete spatial entities that contain
households and housing structures with similar characteristics.
24
Typically,
households exhibit similar social, economic, and demographic characteristics
within neighborhoods. Since neighborhoods can vary significantly in terms of
scale, and the extent of similarity varies across neighborhoods, some
neighborhoods can be more homogeneous/heterogeneous than others.
In the housing market, neighborhood is essential since people are willing
to pay premium for the amenities it can provide. Four major differentiating
factors across neighborhoods may lead to positive or negative externalities for
residents: (1) accessibility; (2) physical environment; (3) social, economic, and
demographic context; and (4) public-service provision.
25
All those factors are
equally important for the residents. However in the mortgage lending context,
since neighborhoods are typically stratified on the basis of social, economic, and
24
See Chapter 3 for a more detailed discussion about neighborhood in the lending context.
25
See Can (1998).
39
demographic characteristics of residents, factor (3) is the most important in
determining the aggregated lending outcome.
According to Can (1998), household preferences, perceptions, and
knowledge about neighborhood differentials greatly influence resulting
neighborhood effects in market processes. This is because in the social,
economic, and demographic context, neighbors and neighboring structures are
major sources of spatial externalities that affect household residential satisfaction
and housing values in a neighborhood.
2.2.1 Neighborhood Information
Lin (2001) explores the role of information externalities and neighborhood
characteristics in mortgage lending. This study made the assumption that a
lender’s knowledge about a neighborhood depends on its physical distance to that
neighborhood. In addition, it proposes a measure of correlation in outcomes of
loans made for neighboring properties, to assess the effect of neighborhood
attributes. The empirical results reveal that loan rejection rates rise with increases
in the lender-property distance for applications received by small institutions.
Furthermore, the study concludes that the effect of neighborhood attributes is
modest, conditional on loan, applicant, and lender characteristics.
26
26
Further exploration in this paper indicates group disparities in these effects.
40
2.2.2 Neighborhood Effects and Default Risk
Similar to most of the process-based discrimination studies, Cotterman’s
(2001) analysis includes both neighborhood characteristics and attributes of the
individual loan and borrower to analyze default risk. In particular, the analysis
seeks to distinguish the effects of neighborhood race, ethnicity, and income from
the effects of the of the individual borrower's status. Research on the effects of
neighborhood characteristics on default has been somewhat limited in the past,
and this study's contribution to the literature is the inclusion of credit history data.
The analysis concludes that lower levels of tract income and higher levels of tract
black composition are associated with higher rates of default, whereas individual
borrower race and income are unrelated to default. This study further underscores
the importance of neighborhood attributes in determining mortgage market
outcomes.
In Cotterman’s (2001) earlier specifications, some experiments were
carried out to identify default effects flowing from neighborhood tracts. They
hypothesized that if the tract appropriately delimits the neighborhood,
characteristics of nearby neighborhoods may matter as well. In order to test the
assumption, they used the longitude and latitude of the centroid
27
of each census
tract in the Chicago MSA to calculate the distance between the centroids of each
pair of tracts. Using a few different functions to weight characteristics of other
tracts by distance from the own tract, they tried to examine whether default
27
Geometric center of each census tract.
41
probabilities at the loan level depend on the characteristics of not only one’s own
tract, but also the characteristics of other nearby tracts. In limited
experimentation, they were unable to find any impacts of neighboring tracts.
28
III Two-Stage Spatial Modeling Approaches
In the spatial literature, a two-stage approach is recommended for the
investigation of spatial structure in geographical data (Haining, 1990). According
to Can (1998) the first stage is called the exploratory spatial data analysis (ESDA)
and focuses on the measurement and quantification of spatial structure. This stage
is important for hypothesis formulation to feed into the next stage. The second
stage is called confirmatory data analysis (CDA) and involves modeling the
impact of spatial structure on behavior and outcomes. Can (1998) describes
those two stages as follows.
3.1 Investigation of Spatial Patterns and Hypothesis Formation
The first stage is to identify spatial patterns based on indicators of
locational factors in the data. A careful investigation of spatial structure in
geographic data sets is needed to test against their standard distributional
properties. In practice there exist three scenarios with similar distributional
properties but with distinctly different spatial arrangements. The first is positive
spatial autocorrelation, in which there exists clustering of similar values by
28
Unfortunately the details of those tests were not discussed in this report. It may be due to the
selection of proper weighting matrix and/or the bandwidth associated with the functions.
42
location. The second, on the contrary, shows clustering of dissimilar values,
which is called negative spatial autocorrelation. The third is a random spatial
arrangement, which is the underlying assumption of traditional statistical and
econometric methods. The hypothesis formulation for the second stage should be
based on the observations from this stage. Special attention needs to be paid on
the first scenario since it forms the basis of spatial modeling.
3.2 Spatial Modeling and Hypothesis Testing
The second stage is spatial process exploration and hypothesis testing,
which uses empirical model and spatial methods to explore systematically the
structural relationships among geographic distributions of selected attributes. This
stage is similar to the traditional econometric framework in terms of the emphasis
on hypothesis testing and estimation, but it focuses on the incorporation of spatial
pattern into functional relationships. The prerequisite of this stage is still the
empirical specification driven by economic theories because underlying structural
relationships have to be built on such foundation to explain any economic
process. The spatial econometric method simply enables the researcher to
combine economic theory with spatial information.
The focus of this stage is to test for spatial dependence in regression
residuals. Can (1998) states that the presence of spatial dependence indicates that
there is a systematic pattern in the spatial distribution of data values, which
implies nonrandomness in their distribution and violates the statistical assumption
43
of independence in regression analysis. Such dependence can result from the
presence of localized externalities in neighborhood processes such as in
segregation and clustering of socioeconomic attributes. Put it in a simple way,
where you are in space and who your neighbors are makes a difference in terms of
output.
IV Summary of the Literature Review and Dissertation Research Objectives
There exists a mismatch between theoretical models, which are mostly
focused on racial preferences, and empirical studies, which cannot capture the
complete information on borrowers’ risk factors and preferences. In particular, it
is difficult to unravel the effects of neighborhood race and other attributes in most
of the studies reviewed here. So far much of the research conducted with the
HMDA data ignores determinants of geographic variations in lending outcome, or
simply attribute them to local variations in risk to supplement the individual-level
characteristics.
The redlining analysis aims at assuring geographic equity in access to
capital and offers one measure of banks’ success in achieving these goals.
However, redlining has proven a difficult topic to study, because the underlying
behavioral models are difficult to specify.
• As a result, no strong consensus has emerged in the redlining literature. In
the case of process-based redlining, the lack of controls for borrowers’
44
credit history makes inferences difficult. In the case of outcome-based
redlining, which has received the most attention, most but not all of the
literature finds some sign of redlining, but there is no consensus on the
appropriate methodology. More research is clearly needed.
• There exists disconnect between spatial dependence and neighborhood
effects in the current literature. So far most studies conducted with the
HMDA data simply attribute determinants of lending outcomes to global
variations in risk without taking into account local risks and spatial
spillover effects.
This dissertation seeks to contribute to the existing literature in the following
aspects.
In this study, census-tract level aggregate data and spatial models are used to
identify the actual location of the underserved areas and the neighborhood
characteristics that affect the lending outcomes. Compared to existing studies, the
approach is outcome-based and takes into account spatial variation and
dependence.
Secondly, following the framework of the two-stage spatial process, this study
aims to investigate the determinants of intra-metro lending disparities by
analyzing spatial dependence and neighborhood effects jointly. Both spatial
dependence (with distance measures) and neighborhood social/economic
45
characteristics are taken into consideration by explicitly examining the
geographically contiguity of the social/economic lending associations.
Thirdly, the Los Angeles five-county region presents an ideal case for the
study of lending outcomes. Traditionally regarded as a racially segregated
metropolitan area, it provides a full spectrum of geo-racial profile as well as an
abundance of geo units (census tracts) for the spatial modeling. The goal of this
research is to contribute to the existing literature in redlining and mortgage
lending in general, and to shed light on some of the continuing debate over the
existence and the degree of disparities in lending.
46
CHAPTER 3
DATA AND MAPPING RESOURCES, SAPTIAL MODELS,
INITIAL COMPUTATIONS, AND RESEARCH HYPOTHESES
I Data and Mapping Resources
The spatial modeling of lending outcomes in empirical housing research is
centered on the following resources.
29
30
29
Conducted by the Bureau of the Census for the U.S. Department of Housing and Urban
Development (HUD), the American Housing Survey (AHS) Data is a very comprehensive data
source on family composition, income, housing and neighborhood quality, and housing costs.
National data are collected every other year, from a fixed sample of about 50,000 homes, plus new
construction each year. The survey started in 1973, and has had the same sample since 1985,
making it possible to observe the changes in homes and households over the years. The distinct
feature of the AHS data is that it follows housing units instead of occupants for a fixed sample,
which makes it possible to identify mortgage flow for each individual property. The AHS data
also contains extensive data covering the household, structure and neighborhood information.
Relevant to this research are micro-level data on income, age, marital status, tenure status, home
values, and loan characteristics, etc. The information on mortgages is very comprehensive, which
includes the amount of loans, mortgage rates, mortgage payments, date of origination, loan terms,
etc.
Since this study is focused on the spatial distribution of lending outcome, it is necessary
to have detailed locational variables in the dataset. However, for disclosure reasons, the public
AHS data only has a variable indicating the region where the property is located. This makes it
difficult for any detailed analysis on intra-metropolitan mortgage flow. The Census Bureau has an
internal version of the AHS data, which offers county-level information for each property in the
AHS sample. Besides, HUD has compiled an AHS-Census Tract Match File, which provides an
interface between the AHS and the decennial Census and shows the census tract level information
for each AHS control variable. Nevertheless the process of getting approval to access those
datasets is very complicated.
30
The Federal Housing Administration (FHA) Loan Data consists of a large sample of FHA-
insured home purchase loans, which allows for diversification of local lending markets for the
analysis.
The dataset contains four types of information. First, individual loan records contain
information on borrower-related characteristics, such as borrowers’ credit scores at time of loan
application. This is crucial for the analysis of borrowers’ behavior. For example, data on the race
of the borrower and census measures of neighborhood racial composition enable assessment of
race-related effects associated with the performance of FHA-insured loans. Second, the dataset
47
The primary information used in many of the mortgage lending studies is a
dataset compiled as a consequence of the 1975 Home Mortgage Disclosure Act
(HMDA). HMDA controls the annual reporting of information, by mortgage
lending institutions with at least $10 million in assets, on the number and dollar
amount of both home mortgage and home improvement loans, by census tract.
Sophisticated statistical analysis of mortgage lending disparities requires clear
information about the decision of whether to accept or reject a mortgage loan
application. Since the passage of the Financial Institutions Reform, Recovery,
and Enforcement Act of 1989, HMDA data have also included the race, gender,
and income of mortgage loan applicants. With these new requirements, lenders
also report the loan denial rates by racial/ethnic groups, and by location, which
make it possible to measure lending disparities in those dimensions.
31
HMDA data are routinely used to compare a lender's denial rates for
minority and white loan applicants, as a measure of their loan performances with
regard to minorities. But HMDA data alone cannot prove or disprove the
existence of lending discrimination, because they do not provide enough
has property-related measures of local housing market performance, including house price
appreciation and volatility. Third, each loan record file is matched to neighborhood and
metropolitan area socioeconomic indicators from the 1990 Census of Population and Housing,
such as unemployment rates. Fourth, loan-related information such as loan-to-value ratio is also
attached. For instance, appended with each loan record there is information indicating termination
date of each loan and reason for termination.
The FHA data is ideal for mortgage performance study. However, samples in this dataset
only include information of approved loans. For lending disparity study, the information of
denied loans and the characteristics of their applicants is as important. Besides, similar to the
internal AHS file, the access to the FHA data is also very difficult to get.
31
See Ross and Yinger (2004) for details.
48
information to control for all relevant differences between white and minority
borrowers. Even though HMDA data now include borrowers' race and income,
they do not include critical information on the wealth and debt levels of loan
applicants, their credit histories, the characteristics of properties serving as
collateral, the terms of loans for which applications were submitted, or the
underwriting criteria used to determine eligibility. Therefore, as discussed before,
researchers should be very cautious about what can and cannot be said about
discrimination in mortgage lending.
32
Since different geographic areas have different social-economic
compositions, matching applications and denials with those patterns of the
underlying location from the census data may indicate whether area social factors
are the significant determinants of loan flows at the local level. Consequently,
combined with census data and spatial information about the neighborhoods, the
HMDA evidence can be used to examine geographic patterns of residential loan
applications and denials by neighborhood.
32
The Boston Fed Study uses the HMDA data for the Boston area and collected 38
additional variables for each application in the sample, covering the whole set of information
needed to control for applicants’ creditworthiness. However, certain questions regarding the data
still remain, which could possibly undermine the credibility of the original findings. For instance,
if important variables on the borrowers are indeed omitted, the estimated impact of race on the
approval decision may be overstated, because it partly reflects the impact of other factors that vary
with race and ethnicity. Therefore even with the Boston Fed data, the reduced-form single-
equation model for mortgage denial cannot yield convincing results for the test of discrimination.
Nonetheless the HMDA data can be well applied in the examination of intra-metropolitan
variation in mortgage flow which does not require complete information for each individual
applicant.
49
Based on the overall examination of the modeling requirements and the
information availability for this research, three major data and mapping resources
are utilized. They are:
• The 2002 HMDA data. This dataset is used to examine the geographic
pattern of residential loan applications, denials and secondary market
purchases rate by census tract;
• The 1990-2000 Census Comparability File from the California
Department of Finance. This dataset contains a comprehensive list of the
tract-level social-economic variables;
• The Los Angeles Region 2000 Geographic Information System (GIS)
shape file. This file allows for the view of the mortgage and census
information in thematic maps and makes it possible to present spatial-
varying regression results in a visual form.
1.1 The 2002 HMDA Data
HMDA data contains information regarding local social-economic
indicators by census tract. However, the tract level data with 2002 HMDA is
based on 1990 census geography and significant changes could have happened
during a period of over a decade. Therefore, it is necessary to combine 2002
HMDA with the most recent 2000 census data with the 1990 census tract
boundary.
50
1.2 The Census 2000 Data on 1990 Tracts
The census tract level data used in this study are from the 1990-2000
Comparability File from the California Department of Finance. The file was
created to simplify tract-level comparisons of California census data over time
and view the historical census data in thematic maps. Census tract boundaries
have changed since 1970, making the process of comparing tracts difficult. In
order to make comparisons over time, standardized tracts were established. In
this case, 1990 census tracts were used as the baseline and the data from 2000
census were converted to their 1990 census tract equivalents.
The census dataset contains information on income, demographics and
housing. First, it has information on tract median family income. Second,
demographic information includes race/ethnicity composition, age distribution,
marital status count, education attainment, occupation division, residence of
previous census year. These are important factors for the analysis of tract loan
flow. For example, data on the measures of neighborhood racial composition
enable assessment of race-related effects associated with loan disposition. Third,
the dataset has property-related measures of local housing market, including
numbers of housing units by type, median housing value and median housing rent.
51
1.3 The GIS Shape File
The Los Angeles Region 1990 GIS shape file is from the Southern
California Association of Governments (SCAG). The employment data are
developed by SCAG to report to the State Economic Development Department
(EDD) of the California Labor and Workforce Development Agency. Because the
US census changes tract boundaries for every census cycle, the 1990 census tracts
was chosen as the unit of analysis to match to the 2002 HMDA census tract
indicator, and all the 2000 census data were converted to 1990 census tract
geography. There are 3,373 tracts covering a total area of about 20 million acres
for the whole Los Angeles five-county region. The interest of this research is the
Urbanized Areas (UA) of this region since the rural areas contain tracts with
extremely low housing density. Based on the US Census Bureau’s definition,
tracts outside of the UA were eliminated, which result in 2,479 tracts covering a
total area of about 5 million acres (just under 8,000 square miles).
33
II Review of Major Spatial Models
Recent research has explored a variety of approaches for analyzing spatial
data. These approaches can be broadly characterized as comparison of estimated
coefficients across geographic units; tests for spatial distribution; examination of
33
The US Census Bureau defines an urban area as: "Core census block groups or blocks that have
a population density of at least 1,000 people per square mile and surrounding census blocks that
have an overall density of at least 500 people per square mile."
52
spatial autocorrelation and variation; tests for geographic concentration, and
analysis of urban spatial structure. Each of these approaches has its
representation in the housing and urban form literature, and helps to improve our
understanding of spatial variation of lending and urban spatial patterns.
Below we provide a brief review of recent spatial econometric methods in
empirical work in housing and urban form.
a. Comparison of Estimation Coefficients across Intra-metropolitan Areas
A direct way of examining spatial variations across intra-metropolitan
areas is to compare estimation coefficients across geographic divisions. Using a
three-level nested logit model (NMNL) of household mobility, homeownership
tenure, and residential location choice, Gabriel and Painter (2003) assessed the
intra-metropolitan geography of minority homeownership as regards to variations
of household endowment and neighborhood amenity. They conclude that as those
characteristics change, the geography of housing tenure choice can change
substantially over a large metropolitan area. The authors also found that despite
substantial rising economic status and homeownership, the urban settlement
patterns of blacks remain significantly more concentrated than those of whites or
Latinos.
53
b. Test for Spatial Distribution
Crews et al. (2002) addressed policy-relevant questions about multifamily
mortgage originations (MFOs). Using kernel density estimation, variation in the
distribution among central cities and suburbs, underserved areas, and lender type
is examined. Then the authors used regression models to estimate the variables
most highly correlated with multifamily lending: tract income relative to MSA
median income and minority concentrations.
Fixed effect models are widely used in the intra-metropolitan lending
literature. Gyourko and Hu (2002) analyzed the spatial distribution of affordable
home loan purchases in twenty major U.S. metropolitan areas, and found that the
loan purchases made by Fannie Mae and Freddie Mac in support of the Low and
Moderate- Income Housing Goal do not match the spatial distribution of low- and
moderate-income households that apply for a mortgage. Furthermore, the
regression results show that neighborhood traits and risk factors of applicants are
correlated with the degree of spatial mismatch. Their findings are consistent with
a policy of the two GSEs targeting the purchase of Low and Moderate Income
Housing Goal loans in relatively high income tracts. However, fixed effect
models are only good for the analysis of inter-regional distributions, but not for
intra-metropolitan comparison since too many dummies are required if the sample
area includes numerous individual spatial units.
54
c. Test for Spatial Autocorrelation
In his paper on neighborhood quality and house price variation, Dubin
(2002) omits all neighborhood and accessibility measures from the set of
explanatory variables and instead models the resulting autocorrelation in the error
term. It appears to provide better estimation than simple hedonic estimation
without consideration of spatial dimensions. Some methodological issues relevant
to the estimation may also be considered addressing spatial econometrics issues.
These include the selection of the appropriate estimation strategy; the application
of diagnostic tests for the detection of spatial dependence and heterogeneity; and
the use of robust methods in the presence of heteroskedasticity.
d. Test for Spatial Heterogeneity
The mortgage literature acknowledges the existence of unobservable
borrower specific characteristics, such as culture, education, or access to
information that affects mortgage termination decisions. Deng et al. (2005)
proposed a way to capture the effects of these variables. Assuming that borrowers
of similar background tend to cluster together in neighborhoods, the authors
established a method to take advantage of this information. They combined the
three-stage maximum likelihood estimation (3SMLE) approach for competing
risks hazard model with random effect with the space-varying coefficient method
(SVC) to modify the covariance structure according to the spatial distribution of
55
the observations. Compared to the standard maximum likelihood estimation, their
method not only improved the model performance, but also yielded a number of
insightful spatial implications for mortgage termination behavior.
e. Test for Geographic Concentration
The test of degree of geographic concentration is widely applied in
research on industrial agglomeration. Glaeser (2002) used data from the Census
Bureau's Longitudinal Research Database to examine how relatively stable levels
of geographic concentration emerge from the dynamic shift of employment across
plants, firms, and locations. He not only tested industries' agglomeration levels
across the past two decades, but also the variation in the locations of these
agglomerations. He then decomposed aggregate concentration changes into
portions attributable to plant births, expansions, contractions, and closures, and
found the different determinants that reduce levels of geographic concentration, or
to reinforce agglomeration. Finally, he investigated the key factor that drives co-
agglomeration patterns. Such tests can be introduced in the housing literature to
test the aggregation of housing demand and supply.
f. Analyze Urban Spatial Structure
To date most of the studies on urban spatial structure have emphasized the
emergence of employment and/or population sub-centers as one characteristic
outcome of polycentrism. Employing a variety of research methods and criteria,
56
the various authors recognize different numbers of centers. Giuliano and Small
(1991), for example, used spatial contiguity as the basis for determining
neighbors, i. e. census tracts are considered to be ‘‘neighbors’’ if they share a
common boundary. The methods used to define individual employment centers
also involve a variety of arbitrary cutoff point selections such as density and total
employment to identify centers.
Originally developed by Getis and Ord (1992), a more general method
utilizing the Gi* statistic in an ArcView 3.0 GIS environment, promotes a
statistical approach to the examination and analysis of urban spatial patterns.
34
In
the paper, the authors look at employment patterns in terms of a surging surface
of agglomeration and dispersion instead of discrete sub-centers. Similar to the
locally weighted regression (LWR) method, this approach provides a
straightforward measure of job dispersion and produces a statistical surface that
can be used to evaluate changes in urban growth patterns. In addition,
constructing employment opportunities as a statistical surface gives a continuous
representation of the dispersed urban form.
It is important to recognize that the processes giving rise to employment
agglomeration are not likely to operate at only one given geographic scale.
34
The Gi* statistic (see Getis and Ord 1992; Ord and Getis 1995) is designed to measure the
extent of spatial association in attribute values within a specified distance of a given location.
Using this statistic, one can tell if the observed attribute value for a given observation is
statistically significant in its similarity to its neighbors.
57
Another advantage of the Gi* statistic is that, in a GIS environment, it can be used
to create surfaces showing employment intensity at a variety of different spatial
scales. For example, for the employment of five-county Los Angeles Region,
with each grid cell representing 0.1 to 1 square mile, the method can generate a
series of grids representing the Gi* and Gi* significance levels at each iteration.
These new grid themes can be automatically stored for comparison analysis. This
method can be potentially applied in the housing research to test the spatial
patterns of housing demand, supply, and credit flow.
g. The Geographically Weighted Regression
In the current housing literature, non-spatial regressions or global spatial
(spatial lag or error regression) approaches are commonly employed.
Investigation of neighborhood aspects is primarily conducted through non-spatial
regression analysis with indicators of neighborhood characteristics (Holloway and
Wyly, 2001; Avery, et al. 1999; Shill and Wachter, 1993.). The non-spatial
approach is best suited for larger scale study, such as city or state level spatial
units, since the high-level of data aggregation intends to mask subtle spatial
effects among spatial units (Gyourko and Hu, 2002). Alternatively, the global
spatial models are able to handle spatial dependence by explicitly including
spatial lags or spatial errors in the model construction to capture spatial
heterogeneity (Deng, et al, 2005). However, the spatial weighing mechanism,
with which the characteristics of a certain spatial unit affect its surrounding areas
58
is not fully addressed in the global spatial approach. In addition, due to its global
nature, the spatial regression only gives a general picture of spatial dependence
(Partridge, et al., 2006).
To overcome the limitations of the commonly used models, this study
intends to employ the geographically weighted regression (GWR) to investigate
spatial dependence and neighborhood effects in mortgage lending. Unlike
conventional regressions, which use equations to summarize global relationships
among the independent and dependent variables, GWR generates spatial data that
exhibit the spatial variation in the relationships among variables. Specifically,
GWR uses local spatial statistical techniques to analyze spatial nonstationarity,
defined as when the measurement of associations among variables differs from
location to location (Fotheringham et al., 2002). To explore and interpret spatial
nonstationarity, gradient maps are used to demonstrate the parameter estimation
and statistical significance for each location.
For each individual observation (spatial unit), GWR captures spatial
heterogeneity in responses to variables by estimating individual regressions. For
each regression, the sample includes the location of interest and other nearby
spatially-weighted observations (Fotheringham et al. 2002). The spatial weights
are decided by the distances between the center of the spatial unit of interest and
the centers of nearby units that are included in the regression, which represent the
adjacency effects for the number of neighboring locations within (or bandwidth).
In general, following the assumption that more proximate locations are more
59
alike, the weights decay with distance following a Gaussian decay function for a
fixed kernel or a bi-square decay function for an adaptive kernel. As a result, this
approach allows estimation of one regression for each observation so that the
resulting parameter estimates vary across the sample space (Partrige, et al. 2006).
How does a GWR model differ from a linear model? In a classic linear
regression model with spatial data we assume a stationary process:
y
i
= β
0
+ β
1
x
1i
+ β
2
x
2i
+… β
n
x
ni
+ ε
i (8)
The parameter estimates obtained in the calibration of such a model are constant
over space:
β’ = (X
T
X)
-1
X
T
Y (9)
which means that any spatial variations in the examination can only be measured
by the error term.
In a global regression framework we can map the residuals from the
regression to determine whether there are any spatial patterns or compute
autocorrelation statistics. In addition, we can also try to ‘model’ the error
dependency with various types of spatial regression models (Ord and Getis,
1995).
In a GWR framework, the spatial nonstationarity issues can be addressed
directly and explicitly. The essence of GWR lies in that it allows the relationships
we are measuring to vary over space. Following the econometric concept of the
GWR model (Fotheringham AS, et al. 2002), the model has the following form:
60
y(l) = β
0
(l) + β
1
(l) x
1
+ β
2
(l) x
2
+… β
n
(l) x
n
+ ε (l) (10)
where (l) refers to a location (center of a spatial unit) at which estimates of the
parameters are obtained. Therefore, the parameter estimates vary over space:
β’ = (X
T
W(l) X)
-1
X
T
W(l) Y (11)
where W(l) is a weight matrix specific to location l such that observations closer
to l are given greater weight than observations further away from l.
W
l1
0 .……..…..0
0 W
l2
…..……..0
W(l) = 0 0 W
l3
……..0
. . . .
0 0 0 ………W
ln (12)
where W
ln
is the weight given to data point n for the estimate of the local
parameters at location l.
The weighting schemes can be either fixed or adaptive (Fotheringham AS,
et al. 2002). Two examples of a fixed weighting scheme are the Gaussian
function (8):
W
ij
= exp[-(d
ij
2
/ h
2
)/2] (13)
where h is known as the bandwidth and controls the degree of distance-decay and
the bisquare function (9):
Wij
= [1-(d
ij
2
/ h
2
)]
2
if d
ij
< h
= 0 otherwise (14)
61
A spatially adaptive weighting function is like equation (10):
Wij
= exp(-R
ij
/ h) (15)
where R is the ranked distance or an optimal value of N in the GWR routine is
estimated in equation (11).
w
ij
= [1-(d
ij
2
/ h
2
)]
2
if j is one of the Nth nearest neighbors of i
= 0 otherwise (16)
Empirically, the results of GWR appear to be relatively insensitive to the
choice of weighting function as long as it is a continuous distance-based function.
However, the results will be sensitive to the degree of distance-decay no matter
what weighting function is used. Therefore an optimal value of either h or N has
to be obtained. This can be attained by minimizing a cross-validation score (12) or
the Akaike Information Criterion (13).
35
CV = ∑
i
[y
i
- y
≠i
’ (h)]
2 (17)
where y
≠i
’ (h) is the fitted value of y
i
with data from point i omitted from the
calibration
AIC = 2n ln( σ’) + n ln(2 π) + n[n+ Tr(S)] / [n - 2 - Tr(S)] (18)
where n is the number of data points, σ’ is the estimated standard deviation of the
error term, and Tr(S) is the trace of the hat matrix.
y’ = Sy (19)
35
See Fotheringham AS, et al. 2002 for detailed explanation.
62
Recently GWR has been used extensively in social and natural sciences
that relate to locational factors. A variety of topics using analytical utility of
GWR have been covered in recent publications. For example, using GWR
models, Mennis and Jordan (2005) studied environmental justice, Ernesto (2003)
explored the ecological inference problem, and Brunsdon et al. (2001) analyzed
climatological problems. In the urban and housing economics area, Longley and
Tobon (2004), Benson et al. (2005) and Farrow et al. (2005) investigated
geographic heterogeneity in regional socioeconomic processes related to poverty,
Partridge et al. (2006) studied the geographic diversity of U.S. non-metropolitan
growth dynamics, Lloyd and Shuttleworth (2005) applied it to commuting
research, Huang and Leung (2002) examined regional industrialization, and Yu
(2004) modeled housing market dynamics in the City of Milwaukee.
III Initial Computations
In the mortgage literature, the importance of neighborhood effects has
been recognized (Avery, 1996; Lin, 2001; Schill and Wachter, 1993; Holloway
and Wyly, 2001; Deng et al, 2005). However, in most of the empirical research
the effects of neighborhood have been isolated from their spatial context, i.e. the
locations of neighborhoods and the distances and contiguity among them are not
taken into consideration. As a result, the contribution of neighborhood
characteristics to lending outcome has been limited to random effects (Deng et al,
63
2005) or contingent impact (Holloway and Wyly, 2001). Lin (2001) took distance
measures in evaluating the relationship between denial rate and information
externality (measured by the distance between property location and lender
location), yet the spatial dependence of other neighborhood characteristics was
not tested.
3.1 Discussion of Neighborhood
In order to fully understand the effects of neighborhood characteristics in
the spatial context, it is important to know how to define neighborhoods, and how
sensitive the varying definitions of neighborhood are in the spatial models.
As mentioned in Chapter 2, neighborhoods can be defined as discrete
spatial entities that contain households and housing structures with similar
characteristics. The choice of the spatial unit to define neighborhood is very
important since the results from spatial models will be sensitive to the scale of the
units. Metropolitan Statistical Areas (MSAs) are arguably too large for studying
residential neighborhood interactions.
36
Ideally, the smaller the unit, the more
similarity the neighborhood can represent. To date the smallest neighborhood
unit used in the recent housing and mortgage literature is from the AHS data on
36
Metropolitan statistical areas are geographic entities defined by the U.S. Office of Management
and Budget (OMB) for use by Federal statistical agencies in collecting, tabulating, and publishing
Federal statistics. A metro area contains a core urban area of 50,000 or more population. Each
metro area consists of one or more counties and includes the counties containing the core urban
area, as well as any adjacent counties that have a high degree of social and economic integration
(as measured by commuting to work) with the urban core. See
http://www.census.gov/population/www/estimates/metroarea.html for details.
64
individual dwelling units, on their occupants and on their immediate neighbors.
37
For roughly one out of a hundred of dwelling units sampled, up to ten of their
nearest neighboring units are also sampled, which allows for in depth analysis on
the neighborhood processes which are likely to be obscured out at higher levels of
aggregation. However observations of lending outcomes (denial rates) are not
included in the AHS data, and it is not plausible to link the HMDA data with the
AHS data on the dwelling units’ level.
Most research in the housing and mortgage literature has used census
tracts to define neighborhood, which are geographical units with 3,500 to 7,000
inhabitants. From the perspective of housing and mortgage markets, census
tracts represent similar geographic division. Tracts are defined to be relatively
homogeneous in connection with socioeconomic status, living conditions, and
demographic characteristics. According to Cotterman (2001), the alternative of
using 6-digit zip coded to define neighborhood was found inferior, given lack of
homogeneity of the population within zip codes. Most importantly, the U.S.
census data offer very rich information on the tract-level, which is essential for
the investigation of neighborhood effects. In addition, the HMDA data contains a
census tract variable indicating the location of the underlying property, which
links the mortgage information with the socioeconomic characteristics on the tract
level. So far most of the research on lending disparities used this link to combine
HMDA and census data.
37
Ioannides (2001) presents an empirical investigation of residential neighborhood effects.
65
Anselin (1988) pointed out that if the ‘‘true’’ spatial scale of the
phenomenon under study is different from the one for which data are collected,
then it is certain that measurement errors will spill over the boundaries of spatial
units and result in systematic spatial variation. This is called the spatial
aggregation problem which pertains to the use of an incorrect areal unit for
surface partitioning in collecting or analyzing socioeconomic data (Haining,
1990). This problem is very important in social science research because some
information available in aggregate form may not necessarily correspond to the
‘‘true’’ scale at which spatial variations exist. Fortunately in most cases census
tracts are defined to be relatively homogeneous concerning socioeconomic status
and can be used as the appropriate spatial unit to analyze socioeconomic
problems.
3.2 Covariates Definition
The variables at the census tract level in this research include 16 social
economic indicators for the year 2000. Table 2 lists the indicators and their basic
statistics. In the Los Angeles region, census tracts vary widely by size of the
population, ranging from zero to close to 50,000 people per tract, and the average
size is about 6000. Median family income ranged from $0 to $200,000, with an
average of 50,000, which shows a diversified income profile for this region.
Average median house value is at 245,000, with the highest median value of $1
66
million among all tracts. The highest median rent is $2,000 with an average of
$780.
Twelve variables are used to represent the population composition of this
region. The region contains a high percentage of minority population. The
highest census tract share of black population is over 90% and the average is
about 8%. The average census tract share of Hispanic population is 38%, and the
highest is over 98%. The indicators on age cohort, marital status, education,
occupation and residency are also included in this dataset.
Table 2: Descriptive Statistics for the 2000 Census Tract-level Variables
Variable Mean Std Dev Minimum Maximum
Population (000s) 6.334 4.139 - 48.842
Median Age 33.577 6.868 - 79.000
Percentage of Black 0.077 0.140 - 0.911
Percentage of Hispanic 0.382 0.276 - 0.984
Percentage Age 5-17 0.196 0.059 - 0.525
Percentage Age 64+ 0.107 0.066 - 1.000
Percentage Married 0.389 0.084 - 0.863
Percentage College Degree 0.170 0.140 - 0.748
Percentage Below Highschool 0.162 0.107 - 1.000
Percentage Blue Collar 0.155 0.054 - 0.375
Percentage Same Household* 0.480 0.105 - 1.000
Percentage Same County* 0.309 0.070 - 0.591
Percentage Single Family Units 0.137 0.087 - 0.840
Median Family Income (000s) 50.082 23.843 - 200.001
Median House Value (000s) 244.543 154.324 - 1,000.000
Median Rent (000s) 0.780 0.295 - 2.001
Number of Tracts: 2479
Note: *Residence of more than five years.
67
3.3. Stage One Test: Examination of Spatial Clustering and Denial Rate
Concentration
Tobler’s (1970) first law of geography states that “All things are related,
but nearby things are more related than distant things”. In the urban economics
literature, core urban centers are typically associated with agglomeration
economies or production externalities that decay with distance, resulting in a
distance growth penalty (Hanson, 1997). In the racial segregation literature, it is
known that historical segregation has created geographically underserved areas
for minorities. The elevated level of segregation in the U.S. during the past
century has created urban clusters with high proportions of minorities. In the
redlining literature, by the original definition, when lenders discriminate a certain
area, they will try to avoid the whole spatially contiguous areas, not single
geographical units scattered throughout a region. All these lead to the basis for
the first-stage analysis, i.e. there exist concentration effects among areas with high
mortgage denial rates, and such concentration is correlated with the clustering of
area economic and social characteristics.
So the first step of this analysis is to conduct a spatial clustering analysis
of the census-tract level socioeconomic variables. If such clustering exists, there
is a need to control for such spatial non-stationarity among explanatory variables
and the clustering effects of geographical units.
68
Based on the assumption that census tracts of similar characteristics tend
to be close to each other, cluster analysis can demonstrates the efficiency of a
methodology for improving mortgage flow estimates for census tracts. For a
certain geographic district, such as a county, iterative cluster analysis can be
performed on its census tracts, based on the tract's values for a selection of
variables from the census data. This will result in a typology of different
clusters—neighborhood “types” based on demographic and economic variables
on racial composition, median income, and housing, etc.
3.3.1 The Multivariate Geographic Clustering Technique
A geographic clustering technique is used (Hargrove and Luxmoore,
1997) which links GIS with a statistical analysis package, SAS, in order to
achieve best fit estimation and to present the visual clustering outcome. Each of
the spatial clusters is relatively homogeneous with regard to the combination of
variables used to generate them. The number of final clusters is the best fit from
the K-means iterative cluster analysis.
The clustering technique involves taking each of the census tracts in the
region, retaining the x,y position information for later re-assembly. Each tract,
along with its 16 variable values, now becomes an observation in the multivariate
statistical analysis. A principal component analysis is performed on the raw data
associated with each Census tract, which removes correlations among the input
69
variables, standardizes the mean and variance, and reduces the dimensionality of
the data set. The k-means clustering algorithm (MacQueen 1967) iteratively
changes cluster assignments until a convergence criterion is met, and then the
map is rebuilt. The clustered map is then populated with clustering results. The
following is a summary of the theoretical discussion of the cluster analysis
conducted in this research.
Our data is a collection of locational characteristics of n spatial units
(Census tracts). Data consisting of measurements obtained for each unit can be
represented by a data matrix as the following X matrix, which is a rectangular
array with numbers arranged in p columns and n rows. In our sample, n equals
2479 Census tracts, and p equals 16 tract-level social-economic variables.
(20)
In this study we seek the clustering of spatial units, not the clustering of variables.
Data consisting of measures of dissimilarity between all pairs of two units can be
represented using a dissimilarity matrix D of the form.
70
(21)
Since our data in matrix X are all quantitative, the dissimilarity matrix D
can be constructed by means of a distance measure. We take the most commonly
used distance measure - the Euclidean distance which is the sum of the squared
differences between pairs of measurements. For units i and j with rows X i = (X i1,
…, X ip) and X j = (X j1, …, X jp) in X, respectively, the Euclidean distance is
(22)
Construction of a dissimilarity matrix from a distance measure yields a
symmetric matrix Dij. In order for the above distance measure to work, the key is
that the variables need to be of the same scale, as otherwise one or more variables
with the largest numerical values will dominate in the calculation of the distance.
In this study, 11 out of the 16 included variables are percentages and are of the
same scale. The other five (median age, population, median house value, median
family income, and median rent) are not of the same scale. We chose the
standardized Euclidean distance for the cluster analysis since its distance
measures are scale invariant, meaning multiplication of all values of a variable
does not change the distances. The distance function is defined as:
71
(23)
where S
2
are the empirical variances of the p variables. Tests of the cluster
analysis based on the above assumptions on the Los Angeles Region urbanized
tracts yield five distinct clusters (Figure 6), which reveal strong spatial
correlations among neighboring tracts. The largest cluster includes South-central
Los Angeles County, central city of Orange County, San Bernardino County,
Riverside County, Ventura County, and the central part of San Fernando Valley,
where most traditionally underserved tracts are located. The smallest cluster
includes coastal and mountain tracts of west Los Angeles County (Malibu and
Santa Monica Mountains) and costal area of Orange County. Median clusters
contain inner suburban tracts. The segment spatial pattern raises doubts of an
independent and uniform pattern, which is the presumption of the OLS regression
on tract level variables. The results reinforce the necessity to account for spatial
dependence in analyzing the data.
72
Scag-county.shp
Ca02_ua.shp
1
2
3
4
5
Scag-frw.shp
N
E W
S
2002 Los Angeles Region Clusters on Census Characteristics
Note:
1. Each color represents a cluster output from the cluster analysis based on the census-tract level
socioeconomic characteristics .
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 6
73
3.3.2 Test for Denial Rate Concentration
In comparison, a denial rate map shows similar patterns of clustering for
census tracts with higher denial rates (Figure 7). The largest clusters with highest
denial rates include most of South-central Los Angeles County, the central part of
Orange County, San Bernardino County, Riverside County, and the central part of
San Fernando Valley, where the most traditionally underserved tracts are located.
In addition, similar to Shear’s (1995) conclusion, the geographical results show
that not all of areas within central cities suffer from concentration of higher denial
rate and that some areas outside of central cities do.
74
Ventura
Los Angeles
San Bernardino
Orange
Riverside
Gwr.sh p
0 - 0.1
0.1 - 0.2
0.2 - 0.4
0.4 - 1
Scag-frw.shp
Scag-county.shp
N
E W
S
Los Angeles Region Urbanized Area Mortgage Denial Rate Distribution, 2002
Note:
1. The color legends show the denial rate gradient. Darker colors represent higher denial rates.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 7
75
3.3.3 Conclusions from the Cluster Analysis and Concentration Test
The conclusions from the above analysis are two folded. First of all,
current literature in social sciences shows that historical segregation has created
geographically underserved areas for minorities. As discussed earlier, by the
original definition, when lenders engage in redlining in a certain area, they will
stay away from the entire spatially contiguous areas, rather than single
geographical units scattered throughout a region (Hillier, 2003). Furthermore,
with the elevated level of segregation in the U.S. during the past century, areas
with high proportion of minorities tend to cluster (Seitles, 1996). The visual
results on the denial rates showed the existence of concentration effects among
areas with high mortgage denial rate, and such concentration is correlated with the
clustering of area economic and social characteristics, as exhibited by the results
of the cluster analysis.
Secondly, the results from the cluster analysis reveal strong spatial non-
stationarity of the tract-level social economic variables. The segment spatial
pattern raises doubts on an independent and uniform distribution of the error term,
which is the presumption of the OLS regression on tract level variables. As it’s
well appreciated that physical processes tend to be stationary while social
processes appear to be non-stationary, meaning the measurement of a relationship
depends part on where the measurement is taken. As a result, any relationship
that is not stationary over space will not be presented well by any traditional
76
statistical tests (Fotheringham, et al. 2002). Such dependence can result from the
presence of localized externalities in neighborhood processes such as in
segregation and clustering of socioeconomic attributes (Can, 1998). These results
reinforce the necessity of accounting for spatial dependence in analyzing the data
locally, since the global model may be misleading locally.
IV Research Hypothesis
Based on the overall scope of examining the existing literature on lending
disparities and locational effects, as well as the spatial clustering results from the
first stage estimation, the research tests the following hypotheses.
4.1 Spatial Dependence: proximity and interaction
The effects of elevated levels of segregation during the past century and
policy and programs designed to increase minority and low-income
homeownership have created geographically underserved areas of minorities
(Schill and Wachter, 1994).
38
Furthermore, those underserved areas tend to
cluster. While many current studies on mortgage lending incorporated
neighborhood characteristics as risk factors in analyzing disparities, most of them
38
This study examines possible spatial impacts of the CRA and finds that geographic disparities
may derive from discrimination, neighborhood and borrower attributes, as well as regulation itself.
The article also argues that for Boston, evidence is found for concentration effects that may result
from institutional factors, information economies, or regulation.
77
integrate neighborhood effects without considering the clustering effect and the
spatial proximity of geographic units with similar outcomes.
In theory, the strength of interaction is a function of distance among
spatial units.
39
This study hypothesizes that characteristics of nearby
neighborhoods matter in determining lending outcomes, i. e. whom and where
your neighbors are make a difference. Using census tracts to delimit
neighborhoods, this study will examine the effects of clustering and proximity,
i.e. to what extent denial probabilities at the neighborhood level depend on the
characteristics of not only one’s own tract, but also the characteristics and
distances of other nearby tracts.
4.2 Neighborhood Effects: the Relationship Between Neighborhood Effects
and Denial Rates Vary Across Neighborhoods
While to some degree the traditional models on lending outcomes attest
the relationship between denial rates and neighborhood effects (Schill and
Wachter, 1993; Munnel et al., 1996; Holloway, 1998; Holloway and Wyly, 2001),
the existence of spatial dependence in regression residuals casts doubts on the
conclusions from those studies regarding neighborhood effects. Theoretically, the
presence of spatial dependence indicates that there is a systematic pattern in the
spatial distribution of data values, which implies nonrandomness in their
39
The spatial interaction theories imply that the closer spatial units will exert a larger influence on
each other than distant ones. See Fischer and Getis (1997).
78
distribution and violates the statistical assumption of independence in the global
regression analysis (Can, 1998). This observation can also be manifested in
practice. For instance, on one hand, most research in lending outcomes show that
denial rates are positively related to the percentage of minority population and are
negatively related to income. Therefore geographically underserved areas, which
typically exhibit high concentration of minorities and low-income households,
will have higher denial probabilities if all else being equal. On the other hand,
policies and programs designed to increase minority and low-income
homeownership may have contributed to the creation of spatially-targeted areas.
Moreover, lenders’ locational perception and cultural preferences may also have
channeled low-income and minority borrowers to those areas. If spatially-
targeted housing policies have been effective, we would expect denial
probabilities to be lower in those areas. As a result, the relationship between
denial rates and neighborhood effects will vary across neighborhood contexts.
Put it in a simple way, where you are in the space matters in determining the
neighborhood - denial association.
Accordingly, the focus of this test is to evaluate whether such varying
relationships between denial rates and neighborhood characteristics exist across
space. In essence, redlining is place-based and must be identified through spatial
analysis. An emphasis on the spatial aspects of lending is critical for
investigations of redlining and it will reveal whether redlining exists, and if it
79
does, where the underserved spatially contiguous areas are and what
neighborhood factors contribute to it.
80
CHAPTER 4
THE GEOGRAPHICALLY WEIGHTED REGRESSION
APPROACH ON LENDING OUTCOME
I Research Approaches and Methodologies
1.1 Traditional Mortgage Flow Model by the OLS Regression
Empirical studies on lending outcome and redlining have been a common
practice of the housing economics literature. Many applications have been
witnessed to use area social-economic factors to analyze determinants of
mortgage flow in a reduced form structure. However, although the theoretical
basis of such models was logical, specifications for the model and methodology
often received criticism. The traditional mortgage flow model is usually in a
linear form calibrated by OLS regression in which the regression coefficients
represent locational attributes. Misspecification resulting from missing important
area determinants, collinearities among the determinants, and spatial dependence
often cast doubt on the traditional model.
Moreover, the traditional OLS model is a typical global model. It assumes
that there exists a stationary relationship between locational attributes within a
metropolitan area. Such presumption has been long challenged and debated
among housing economists (Yu, 2004; Watkins, 2001). As clusters of
neighborhood are relatively uniform sub-groups of the metropolitan housing
81
market, relationships may vary in different clusters but remain similar within each
cluster.
1.2 The Geographically Weighted Regression
Heterogeneity in locational characteristics could produce an outcome
whereby factors are found to increase it in some areas while reducing it in others,
yielding an average of about zero (Partridge, et al. 2006). A global regression
(e.g., OLS) could then lead to the erroneous inference that the factor does not
affect the outcome anywhere. However, successful local housing policy requires
knowledge of local socioeconomic processes and growth dynamics (Blank, 2005;
Nizalov and Loveridge, 2005).
This research intends to promote an alternative methodology, the
geographically weighted regression in investigating and modeling mortgage
lending dynamics. Recently the GWR approach has gained popularity in
accounting for potential geographic heterogeneity in socioeconomic processes. In
contrast to the global regression approach, GWR estimates separate coefficients
for each area. In each area’s individual regression, other areas in the sample are
weighted by their spatial proximity. Spatial weighting smoothes the spatial
variation in parameters, revealing broad locational differences in the parameters.
Specifically, the GWR approach does not assume a priori particular patterns of
the market non-stationarity. Instead it employs statistical methods to test whether
such non-stationarity exists. It hence would be an ideal tool in both exploring the
non-stationarity of the housing market dynamics and identifying the existence of
82
urban housing clusters. In the past few years, it has received intensive attention
among scholars in geography (Fotheringham et al. 1997, 1999, 2002) and urban
planning (Fotheringham et al. 1998; Leung et al. 2000a, 2000b; Paez et al. 2002a,
2002b). Most recently, it has been introduced into the urban housing studies (Yu,
2004) incorporated with the hedonic pricing model.
II Empirical Framework
The GWR Model to Control for Spatial Dependence and Neighborhood Effects
The observed spatial non-stationarity calls for a model to control for such
spatial dependence. To this end, this study utilizes the GWR technique to unravel
the issue of spatial dependence of the data, as discussed in the previous section.
GWR is developed specifically in dealing with spatial non-stationarity within
traditional regressions. In particular, GWR allows regression coefficients to vary
across space. Within the framework of GWR, the model of denial rate can be
expressed as:
Di (H) = β i0 + βin N + εi (24)
Where Di is the denial rate of a census tract, βi0 is the intercept term, and βin is
spatially varying coefficients of neighborhood attributes (Table 2).
(25)
0
(, ) ( , )
iii kiiiki
k
yuv uvx β βξ =+ +
∑
83
(26)
Adjustment of the GWR model follows a local weighted least squares
approach. Different from OLS, in GWR, a weighting scheme is imposed to
specific locations (census tracts) to assign weights. Hence the coefficients on
location i are calibrated. This weighting scheme is based on each individual
location’s spatial proximity to a location i, i.e. near locations have more influence
on the calibration than locations farther away.
To obtain the weights, a spatial kernel function must be imposed. Fixed
and adaptive kernels are the two typical spatial kernels. In the fixed kernel, an
optimum spatial kernel (bandwidth) will be obtained and applied over the study
area, which involves less computationally intensity (Yu, 2004). However,
according to recent empirical investigation (Paez et al., 2002a, 2002b;
Fotheringham et al., 2002), fixed kernel approach can produce large local
estimation variance in areas where data are sparse, and may mask subtle local
variations in areas where data are dense. In our tests, an adaptive kernel function
is used to seek a certain number of nearest neighbors to ensure a constant size of
local samples. This kernel might present more reasonable means in representing
the degree of spatial non-stationarity in the study area. In this study, the sizes of
0( , ) 0( , ) 0( , ) 0( , )
0( , ) 0( , ) 0( , ) 0( , )
0( , ) 0( , ) 0( , ) 0( , )
..
..
.. .. .. .. ..
..
ii ii ii ii
ii ii ii ii
ii ii ii ii
u v uv uv u v
u v uv uv u v
u v uv uv u v
βββ β
βββ β
βββ β
β
⎡⎤
⎢⎥
⎢⎥
=
⎢⎥
⎢⎥
⎢⎥
⎣⎦
84
census tracts vary significantly across space. To account for the impact of
neighboring tracts, contiguity plays more important roles than distance.
Therefore, the adaptive kernel function is more appropriate and is employed in the
GWR model.
III Results and Analysis
In this research framework, the denial rate of a census tract is specified as
a reduced form outcome of the aggregate socioeconomic characteristics of the
residents in that tract. Yet the influence of factors underlying characteristics can
vary geographically, producing heterogeneous mortgage lending outcomes. In this
section, the results from both a traditional OLS model and a GWR model are
presented and compared. Furthermore, the key determinants of the lending
outcomes analysis and how these may produce heterogeneous dynamics are
discussed in detail.
3.1 A Traditional OLS Model
In the first attempt, an OLS regression on denial rate is estimated and
results are reported in Table 3. The model performs well, and most independent
variables show significance on the 95% level. The results indicate that it is
plausible to model denial rates with tract social-economic variables, as manifested
in the previous literature.
85
In addition, some of the intuitive relationships between denial rate and
social economic variables are supported by the data. For instance, the percentage
of black population and percentage of residents with lower than high school
degree are positively related to denial rate. Tract population, percentage of
residents over 64 year old, percentage of college graduates, percentage of
workers, percentage of residents staying in the same household or same county,
and percentage of single family units all show negative relationship with denial
rate. Surprising results are shown on median income and median house value,
which show positive coefficients on denial rate.
40
40
Discussion about individual covariates and related hypotheses are along with the GWR results
in the next section of this chapter.
86
Table 3: Global OLS Results on 2002 Tract Denial Rate
Variable Estimate
Standard
Error t Value Pr > |t|
Intercept* 0.467 0.111 4.200 <.0001
Population (000s)** (0.001) 0.000 (3.800) 0.000
Median Age (0.000) 0.001 (0.570) 0.571
Percentage of Black** 0.122 0.013 9.280 <.0001
Percentage of Hispanic 0.011 0.015 0.730 0.468
Percentage Age 5-17 (0.150) 0.144 (1.040) 0.298
Percentage Age 64+ ** (0.252) 0.129 (1.960) 0.050
Percentage Married 0.009 0.032 0.270 0.786
Percentage College Degree** (0.067) 0.029 (2.280) 0.023
Percentage Below Highschool** 0.287 0.036 7.990 <.0001
Percentage Blue Collar** (0.126) 0.048 (2.640) 0.008
Percentage Same Household** (0.134) 0.025 (5.450) <.0001
Percentage Same County** (0.127) 0.026 (4.930) <.0001
Percentage Single Family Units** (0.048) 0.010 (4.900) <.0001
Median Family Income (000s)* 0.00030 0.00016 1.950 0.052
Median House Value (000s)** 0.00005 0.00002 2.660 0.008
Median Rent (000s) 0.012 0.008 1.420 0.156
Number of Tracts: 2479 Adj R-Sq 0.339
Source DF
Sum of
Squares F Value Pr > F
Model 17 5.298 75.3 <.000
Error 2443 10.111
Corrected Total 2460 15.410
Note: Variables with * are significant on the 90% level; with ** are on the 95% level.
3.2 The GWR Process and the Comparison with OLS
The results from the OLS model reveal numerous important relationships
between mortgage denial rates and tract socioeconomic variables. However, the
relationship is built upon the theory of a stationary housing market, which is
unlikely to exist. The non-stationarity of the data has been manifested in the
cluster analysis. Similar test of the data is used in the following GWR model. The
87
optimal bandwidth distance or the optimal number of neighboring units used in
each observation’s regression is determined by cross-validation. In this case, the
model uses an adaptive kernel which is more suitable for irregular shaped units.
The optimal bandwidth in this analysis is presented in terms of the number of
nearest neighbors (as opposed to the distance in fixed kernel case). Based on
cross-validation, the optimal number of nearest neighbors was found to be 40 for
the sample of 2479 Census tracts in the region.
A tri-cube weighting method with 40 nearest neighbors is used to create
the surfaces with the each tract’s nearest neighbors receiving a much greater
weight.
The ANOVA test for GWR against the OLS model is presented in Table
4. Since GWR involves a regression for each of the observations in the sample
(2479 Census tracts), it is not appropriate to report the results in a table form.
Instead, the varying coefficients on selected variables are produced using Arcview
GIS 3.1, which provide a visual interface to understand the determinants of denial
rate.
Table 4: ANOVA test of GWR against OLS Model
Source SS DF MS
OLS Residuals 5.30 17 90.07
GWR Improvements 2.31 256 592.49
GWR Residuals 2.98 2206 6,582.41
Note: SS = sum of squares; DF = degree of freedom; MS = residual mean square.
88
The ANOVA test (Table 4) indicates that the GWR model offers
significant improvement in fit over the global OLS model. This indicates that
even taking into account the added complexity of the GWR model, it still
performs better than the OLS model. Results from Table 4 support the results
from the first-stage test that significant non-stationary relationships between
denial rate and neighborhood attributes exist in the Los Angeles Region.
Furthermore, it indicates that taking into account the spatial proximity in the
regression greatly improves the efficiency of the estimation.
The GWR approach has some major advantages over standard approaches.
First of all, since each census tract has its own constant term, the model is able to
account for tract fixed effects. In addition, because multiple explanatory variables
need to be controlled in this study, one possible shortcoming in standard
approaches is multicollinearity.
41
However, since the GWR approach produces
one regression for each underlying tract, examining the median and the entire
range of estimates should account for outlier effects (Partridge et al. 2006).
Since standard approaches estimate one fixed set of regression
coefficients, spatially clustered groups of tracts (as discovered in the spatial
cluster analysis) could have residuals that are either over or underestimated.
41
In econometrics, multicollinearity refers to linear inter-correlation among variables. It may
result in large changes in the estimated regression coefficients when a predictor variable is added
or deleted, or non significant results of simple linear regressions, or estimated regression
coefficients having an opposite sign from predicted.
89
Therefore, the second advantage the GWR approach has over OLS model is that it
can greatly reduce spatial error correlation when there is tract heterogeneity in the
GWR coefficients (Fotheringham et al., 2002). Compared to standard approaches,
in GWR, the resulting spatial correlation caused by the underlying heterogeneity
in the regression coefficients would be identifiable from standard spatial error
correlations that are generated by shocks from one tract to others.
On the other hand, since GWR uses a smaller sample size in each of the
regression, the resulting coefficients may be less efficiently estimated than those
from standard global approaches.
3.3 Results on Individual Covariates from GWR
3.3.1 GIS and Mapping
GWR is a relatively recent technique. Due to the complications in
displaying the results, a standard approach for mapping the results of GWR has
not yet been developed. Note that each GWR analysis can produce large amounts
of spatial data. In addition, ratio, nominal and numeric data can all be included in
the model. The estimation results may range over positive and negative values
(Mennis, 2006)
Although GIS is closely integrated in spatial information retrieving and
manipulation, most of the current applications are focused on its mapping and
monitoring functionalities. As a spatial data management system, its spatial
analytical aspects have remained largely unexploited. The implementation of the
90
geographically weighted regression in this research is through the Matlab spatial
econometrics functions (LeSage, 2004). Yet, results of the model are returned to
GIS for visualization.
There are a few challenges of mapping the GWR estimation results. First
of all, the spatial distribution of the parameter estimates must be presented along
with the distribution of significance (t-value), so that meaningful interpretation of
the results can be achieved. Some researchers have chosen to map only the
parameter estimates and not associated t-values (Huang and Leung, 2002), which
can be misleading as it may visually accentuate the areas of highest/lowest
parameter estimation, regardless of the significance of the estimate (Mennis,
2006). The second issue is data categorization and color scheme. The most
common method is the equal step approach, where the data range is divided into
classes of equal extent (Dent, 1999). Regarding the choice of color scheme, many
GWR researchers have employed a sequential no-hue color scheme. However,
this scheme is problematic in cases where the parameter estimate can be both
positive and negative for different locations.
To overcome the above issues, the mapping in this research follows the
following rules. First, to avoid the misleading emphasis of non-significant tracts,
only tracts with over 90% significance are colored. Second, we use a gradient
color scheme with hue colors. From the hue color one can tell whether the
estimation is positive or negative. Furthermore, the color gradient will specify the
ranges of the estimates, i.e. the darker the color, the higher the absolute value.
91
3.3.2 Statistical Significance
Figure 8 through Figure 16 show the significant surface of selected
individual attributes coefficients based on the mapping scheme.
42
From the
maps, the following observations emerge and the related spatial pattern of non-
stationarity merits further attention. First, the spatial clustering pattern of tracts
conforms to the first hypothesis, i.e. tracts exhibiting similar neighborhood-denial
rate relationships tend to cluster, and the effects and proximity of neighboring
tracts play significant roles in determining the denial outcome of the underlying
tracts.
Second, the established relationship between tract denial rates and tract
attributes is not necessarily significant everywhere in the region, which
corresponds to the second hypothesis of spatially varying neighborhood-denial
rate relationships. Unlike the global OLS model, within a local modeling
environment, some of the neighborhood attributes do not have a significant
influence on denial rate in specific areas. For instance, only 700 to 800 tracts out
of 2479 have significance on percentage of black, percentage of Hispanic,
percentage of below high school degree, percentage of college degree, percentage
blue-collar workers and median income; 800 to 950 out of 2479 are significant on
percentage resident of same county/household, and median house value (Table 5).
42
In all the maps, tracts with colors show significance on 90% level. Tracts without color show
no significance.
92
Table 5: Explanation of GWR Results on Selected Variables.
Variable
Number of
Tracts with
Significance Percentage Note
Percentage of Black 747 30.1% Figure 8: Majority show positive relationship.
Median Family Income (000s) 768 31.0% Figure 9: Majority show negative relationship.
Median House Value (000s) 823 33.2% Figure 10: Majority show negative relationship.
Percentage of Hispanic 731 29.5% No clear pattern.
Percentage Blue Collar 707 28.5% Scattered pattern.
Percentage Same County 958 38.6% Figure 13: Majority show negative relationship.
Percentage Same Household 946 38.2% Figure 14: Majority show negative relationship.
Percentage College Degree 791 31.9% Figure 15: Majority show negative relationship.
Percentage Below Highschool D 788 31.8% Figure 16: Majority show positive relationship.
Number of Tracts: 2479
Third, the varying magnitude of the coefficients reveals interesting
patterns. Most tracts of significance show both negative and positive relationships
between covariates and denial rate, where one relationship often dominates the
other, which reinstate the second hypothesis of spatially varying relationship.
Overview of the relationships on selected variables is also exhibited in table 5.
Fourth, statistically significant geographic variation in denial rates is
found for all social-economic variables with remoteness as measured by distances
from underlying census tracts in the GWR estimates. Interestingly, there is no
case in which the influence of any variable on denial rates does not vary spatially
across the Los Angeles region.
Fifth, in the OLS model, some social economic variables are found to have
insignificant effects, suggesting little marginal impact. However, the GWR
93
approach reveals a much richer pattern, showing that these variables may have
locally statistically significant effects that (regionally) offset one another. For
instance, in the OLS model, percentage of Hispanic population has no statistical
significance. Superficially, this would be interpreted as indicating that denial rate
is independent of the tract’s Hispanic composition. Yet, it might well be that
there are opposite relationships in different parts of the study area which tend to
cancel each other out in the calculation of the parameter estimates. While in the
GWR, the results show that it stimulates denial in some areas, while reducing it in
others.
To mitigate endogeneity problems, the explanatory variables are from
2000 census and are mapped to 1990 census tracts to match the to the 2002
HMDA geography. As described before, the GWR approach has significant
advantages in terms of reducing estimation biases while avoiding
multicollinearity. Although the expected effects of many of these variables seem
to be intuitive in the OLS model, most of the predicted effects of key variables are
spatially heterogeneous. Different local economic and urban development history
causes the influence of many of these variables to vary across this region. The
following section will explain such variation in more detail.
94
3.3.3 Analysis of Individual Covariates
• Percentage Share of Black Population
The pattern is very distinct on percentage of black population (Figure 8),
where most of the tracts with statistical significance show positive relationship
between the black composition and denial rates, which is consistent with the
result from the OLS model. The interesting observation is that most of the
statistically significant tracts are located in relatively affluent areas. For example,
west/costal LA, east LA, Long Beach, downtown Anaheim/Santa Ana, and San
Fernando Valley show high positive coefficients. Therefore, compared to the rest
of the region, the same magnitude of increase/decrease in percentage of black will
bring larger increases/decreases in denial rates for those areas. In comparison,
most of the traditional underserved areas like south-central LA do not show much
significance.
The results as regards the traditional underserved areas need special
attention. As discussed in hypothesis one, the common sense in lending outcome
is that denial rate is positively related to the percentage of minority population.
As a result, geographically underserved areas, where high concentration of
minority households is observed will have higher denial probabilities all else
being equal. However, on the other hand, housing policies and programs
designed to increase minority and low-income homeownership may have
contributed to the creation of spatially-targeted areas and helped to enhance credit
95
flow to those areas. If spatially-targeted housing policies have been effective, we
would expect denial probabilities to be lower in those areas. Consequently, the
relationship between denial rates and neighborhood effects will vary across
neighborhood contexts. Similar to Schill and Wachter (1993)’s results on Boston
and Philadelphia, results here do not show a statistically positive relationship
between denial rates and black composition in the spatially targeted areas.
Accordingly the assumption that financial institutions redline underserved
neighborhoods is not supported by this analysis.
However, results do shed light on the concerns about lending outcomes in
affluent areas with statistical significance, where race is still an important factor
in determining mortgage denial rates. One possible explanation is that lenders’
locational perception and cultural preferences may have channeled low-income
and minority borrowers out of the relatively well-off areas (Holloway and Wyly,
2001). In such case, redlining may exist in a subtle way.
96
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
Blk_sig.shp
- 8.411 - -4
-4 - 0
0 - 2
2 - 4
4 - 10.304
N
E W
S
2002 Significant Spatial Varying Coefficient of Black Composition on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on proportional of black population.
Tracts with colors represent regressions with statistical significance. Color legends show the values of
the coefficient estimation. The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 8
97
• Median Family Income
OLS results indicate positively significant coefficient for tract median family
income on denial rates (Figure 9), which seems to be counter-intuitive. The
estimation on this variable is two-folded. On one hand, lower income means less
affordability, which will inevitably result in higher denial probability. On the
other hand, higher income is associated with higher cost of housing and higher
mortgage qualification standards. According to Holloway and Wyly (2001),
lenders are constantly matching the socioeconomic status of the borrowers and the
locational characteristics the properties. In some cases they may have the
incentive to channel the minority borrowers away from traditional white
neighborhoods based on their perception about the match. Moreover, since
income level is one important dimension in the determination of underserved
areas, spatially targeted housing policies may help to increase credit flow to those
areas. If those two arguments are correct, we may expect a positive relationship
between median family income and denial rates. In the OLS model, it appears
that the second scenario dominates the estimation outcome.
The GWRs provide different results. Nearly one-third of the tracts are
statistically significant. Among those 768 tracts, about half of them are
negatively correlated with denial rates, which supports the traditional perception
about the income-denial relationship. Conversely, some scattered tract clusters in
98
south-central Los Angeles, San Fernando Valley, south Orange County and
southwest San Bernardino show positive results on median family income, which
supports the assumptions underlying the second scenario.
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
Sig_me dinc.s hp
- 0.0 25 - -0 .01
-0.01 - 0
0 - 0.025
0.025 - 0.05
0.05 - 0.075
N
E W
S
2002 Significant Spatial Varying Coefficient of Tract Median Income on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on tract median income. Tracts with colors
represent regressions with statistical significance. Color legends show the values of the coefficient estimation.
The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 9
99
• Median House Value
About one-third of the tracts in the region have significant coefficients on
median house value. The results on this variable (Figure 10) have a slightly
different pattern from the results on median family income. In general, the higher
the median house value, the more desirable the neighborhood is. Consequently,
most of the tracts show negatively relationship with denial rates. Only very few
tracts scattered in southeast Los Angeles and central Orange County have positive
coefficients. This result supports the traditional view about neighborhood-denial
relationships.
100
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
Sig_med_value.shp
-0.005 - -0.001
-0.001 - 0
0 - 0.001
0.001 - 0.002
0.002 - 0.007
N
E W
S
2002 Significant Spatial Varying Coefficient of Tract Median House Value on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on tract median house value. Tracts
with colors represent regressions with statistical significance. Color legends show the values of the
coefficient estimation. The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 10
101
• Hispanic Composition
While OLS results show no significance for some variables, the estimated
coefficients of GWR exhibit a different pattern in some cases. The outcome on
tract Hispanic composition is a good case to examine. The percentage of
Hispanic population variable receives no significance in the OLS model. In
comparison, in the GWR (Figure 11) outcome, nearly one-third of the tracts are
significant on the 90% level, however the overall pattern is more scattered than
the results for percentage of black. The visual results in Figure 11 demonstrate
how the tracts with high positive coefficient stand out among their neighbors (the
tracts with darker color). Surely GWR provides a better understanding of the
spatial and local pattern than OLS.
The scattered result on the Hispanic composition variable was anticipated
for the Los Angeles region. As of 2005, over 45% of the population in the Los
Angeles County are people with Hispanic or Latino origin, which surpassed the
population of non-Hispanic whites. In this sense, Hispanic cannot be considered a
minority population in the LA area. In addition, compared to the blacks, their
residential location choices exhibit more diverse patterns. Because of such high
concentration and diversity, the socioeconomic profile of the Hispanic population
is very dissimilar as well. It is not surprising to see the less distinct pattern of the
race-denial relationships for Hispanics.
102
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
S cag-county .shp
Scag-frw.shp
His_sig.shp
- 5.703 - -2
-2 - 0
0 - 2
2 - 4
4 - 6.31
N
E W
S
2002 Significant Spatial Varying Coefficient of Hispanic Composition on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on tract-level proportion of Hispanic
population. Tracts with colors represent regressions with statistical significance. Color legends show the
values of the coefficient estimation. The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 11
103
• Occupation Composition and Housing Tenure
Some other observations also appear to be interesting. Percentage of blue-
collar workers (Figure 12) shows significance on nearly one-third of the tracts,
where the pattern is dispersed. OLS has negative significant coefficients to the
same variable. Two variables on residency, the percentage of residents in the
same county in 1995 (Figure 13), and the percentage of residents in the same
household in 1995 (Figure 14) have similar stories. While OLS has negatively
significant coefficient on both of them, the GWR results show a more scattered
pattern on tracts with significance. In Figure 14, while most tracts show negative
relationship, some tract clusters in west, east, and south coast of Los Angeles,
coastal Orange County, northern Riverside, and southern Ventura do show
positive coefficient. In Figure 14, also a few tracts in west, east and south coast
of Los Angeles have positive impact on denial rate.
In urban theories, households are assumed to migrate in response to
differences in locational amenities. Household locational amenities are
positively affected with the wage rate and the amenity attractiveness of the area,
and negatively affected by land costs. According to Patridge, et al. (2006), the
amenity attractiveness of an area depends on both natural amenity stocks and an
endogenously determined factor associated with population density. Since there
are no other explicit variables representing the area amenities and employment
104
growth in the model, those two variables on housing tenure serve to address those
factors.
Graves and Mueser (1993) argue that even though most natural amenities
are relatively stable over time, their valuation can change because of rising
national income and household life-cycle considerations, inducing internal
migration. Moreover, Johnston et al. (2003) state that preferences for amenities
may be heterogeneous. The two variables regarding residency are the opposite of
migration, and to some extent they manifest the stableness of corresponding
neighborhood and sustained employment opportunities in the region. The GWR
results confirmed these assumptions by showing negative significance on most of
the tracts. Most of the costal neighborhoods, where amenity attractiveness plays
important roles, show constant negative relationship between the same county and
same household variables. In comparison, scattered inland areas, where
employment growth plays more important roles on household movement, show
positive or negative relationships. This is supported by the theory that if distance
matters in household migration, then geographically heterogeneous preferences
and differences in income may affect the valuation and growth of area amenities
(Partridge, 2006). Therefore, the results on areas dominated by dynamic
employment growth have more mixed results.
105
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
S ig_samehou.shp
-4.177 - -2
-2 - 0
0 - 1
1 - 2
2 - 3.41
N
E W
S
2002 Significant Spatial Varying Coefficient of Percentage Same Household on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on tract-level proportion of blue-collar
workers. Tracts with colors represent regressions with statistical significance. Color legends show the
values of the coefficient estimation. The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 12
106
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
S cag-county .shp
Scag-frw.shp
Sig_samecou.shp
- 3.7 81 - -2
-2 - 0
0 - 1
1 - 2
2 - 3.191
N
E W
S
2002 Significant Spatial Varying Coefficient of Percentage Same County on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on percentage of residents who have
lived in the same county for more than 5 years. Tracts with colors represent regressions with statistical
significance. Color legends show the values of the coefficient estimation. The darker the color, the more
positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 13
107
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
S ig_samehou.shp
-4.177 - -2
-2 - 0
0 - 1
1 - 2
2 - 3.41
N
E W
S
2002 Significant Spatial Varying Coefficient of Percentage Same Household on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on percentage of residents who have lived in
the same household for more than 5 years. Tracts with colors represent regressions with statistical significance.
Color legends show the values of the coefficient estimation. The darker the color, the more positive the
coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Figure 14
108
• Education Level
The two variables on education level, percentage of college graduates
(Figure 15) and percentage of below high school degree (Figure 16) showed
expected signs on the coefficients in the OLS model. The GWR results conform
to the conclusion and show a more detailed visual outcome in terms of where
these differences occur. Some small tract clusters in Los Angeles yield positive
coefficients for college degree variable, along with the majority showing negative
results. Most of the tracts in the region show positive coefficients for below high
school variable on denial rate, which reinstates the result on the OLS model.
Adamson et al. (2004) argue that acting as an agglomeration force, area
amenities may be particularly attractive to higher educated and skilled workers.
On the other hand, higher crime, taxes, land prices, traffic congestion, and
environmental pollution may cause households to move out of the cities,
particularly from the inner core (Glaeser, 1997). As a result, the distribution of
higher educated people is diverse. The GWR model here is not designed to test
such dispersed distribution. However, the results on the percentage of college
graduates variable confirmed that the effect of this variable on the marginal
change of denial rates vary geographically. This may be due to broad geographic
differences in amenities and industry structure, such that college educated
109
households and skill-based firms may prefer amenity-rich areas, drawing college
educated households away from amenity-poor regions (Partridge et al., 2006).
110
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
Sig_college.shp
-12.772 - -4
-4 - 0
0 - 2
2 - 4
4 - 11.435
N
E W
S
2002 Significant Spatial Varying Coefficient of Percentage College Degree on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on percentage of residents who have at least
college degree. Tracts with colors represent regressions with statistical significance. Color legends show the
values of the coefficient estimation. The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 15
111
Ventura
Los Angeles
San Bernardino
Riverside
Orange
GWR_result3.shp
Scag-county.shp
Scag-frw.shp
Sig_below.shp
-6.42 - -2
-2 - 0
0 - 2
2 - 4
4 - 4.534
N
E W
S
2002 Significant Spatial Varying Coefficient of Percentage Below High School on Denial Rate
Note:
1. This figure shows the coefficient estimations from the GWR model on percentage of residents who have less than high
school degree. Tracts with colors represent regressions with statistical significance. Color legends show the values of
the coefficient estimation. The darker the color, the more positive the coefficients are.
2. Blue lines are the major freeways in the Los Angeles area.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 16
112
3.3.4 Simulation Results
A simulation is conducted with all the variables set at their median values.
The estimated denial rate from the GWR model reveals a clear pattern of
concentrations of high denial rates in the central areas of each county (Figure 17).
The most pronounced tract cluster of high denial rate is the traditionally
underserved neighborhood in south-central Los Angeles, and others are Orange
County central cities, central, San Fernando Valley, east Los Angeles,
neighboring tracts of San Bernardino and Riverside Counties, and Los Angeles
port area. The smoothed surface on the estimated denial rate (Figure 18) is also
presented here, in which the high ridge represents the south-central Los Angels.
43
43
One of the major obstacles in the HMDA-related studies is the omitted variables
problem. The Boston Fed’s study collected additional information on borrowers’ characteristics
(particularly credit scores), which is by far one the most comprehensive studies in terms of data
coverage. Nevertheless the call for more Boston-type data is challenging since lenders are
unlikely to cooperate as they did in Boston. Even if researchers can have access to more data from
mortgage banks than general public, their data may not be sufficiently powerful to replicate the
Boston study.
To overcome this problem, researchers have designed special treatment in their models to
capture the missing information. For instance, Holloway and Wyly (2001) used an instrument
variable representing the probability that a lender will reject an application on the basis of credit
history problem to substitute the credit score variable. Gyourko and Hu (2002) adopted a ‘mean
household’ approach which used the mean values of lower-income applicants’ traits in each tract
to represent the tract value for each variable. Based on the assumption that certain types of
individuals tend to live near one another, their study employed applicants’ average income and an
estimated loan-to-value ratio (LTV) as proxies, which are observable in the HMDA data. It argues
that since both the payment-to-income ratio (PTI) are credit score are directly related to
applicants’ income and wealth, using these proxies should help control for differences in
applicant risk across tracts.
This study agrees that the missing tract-level variables such as PTI and credit scores are
correlated with income, which is included in the census-tract level aggregate data to control for
neighborhood risks across space. On the other hand, the definition of neighborhood in this study
is a function of spatial unit and completely exogenous to lending outcomes. Therefore the
113
approach of including applicants’ income and LTV as proxies for the missing tract values
suggested in Gyourko and Hu (2002) is not preferable in this context.
Residual_ols.shp
0.032 - 0.09
0.09 - 0.12
0.12 - 0.15
0.15 - 0.18
0.18 - 0.523
N
E W
S
Los Angeles Region Urbanized Area Estimated Denial Rate from Geographically Weighted Regression, 2002
Note:
This figure shows the coefficient estimations from the simulated GWR model (all tract-level socioeconomic variables are set
to their median values). Color legends show the values of the coefficient estimation. The darker the color, the higher the
estimated denial rates are.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 17
114
Note:
This figure shows the coefficient estimations from the simulated GWR model in a 3-D format (all tract-level
socioeconomic variables are set to their median values). The high ridge in the graph represents south-central Los Angeles.
Source: Calculations are based on the SCAG GIS shape file, 2000 census data, and the 2002 HMDA data.
Figure 18 Simulation Result
South-central Los Angeles
115
CHAPTER 5
SUMMARY AND POLICY IMPLICATIONS
I Spatial Methodology on Lending Outcome: The GWR Application
Recent decades have witnessed significant controversy as regards intra-
metropolitan geographical variability in lending outcomes. As most of the studies
assume a spatially stationary mortgage market that is unlikely to obtain, this study
takes a geographical approach, which does not presume such stationary across
space. Cluster analysis of tract-level socioeconomic characteristics discovers
strong spatial non-stationary among those covariates. This paper then develops a
GWR lending outcome model with the 2002 HMDA data for the Los Angeles
region to investigate such non-stationarity. The statistical results support the
hypothesis that there exist significant spatially varying relationships between
mortgage denial rates and neighborhood attributes. Such spatially varying
relationships are further mapped through GIS and reveal interesting patterns.
Specifically, the following important conclusions can be drawn based on this
study.
On the methodology side, this study tests for geographic heterogeneity on
the census tract level parameters and compares them to estimates obtained from
the OLS. The results suggest that there is significant spatial dependence in the
regression coefficients across broad geographic units of the Los Angeles region.
Similar to what is shown in the current lending literature; the incorporation of
locational effects improves the precision of coefficient estimates and increases the
116
predictive power of models.
44
Thus, a one-size fits all OLS approach to describe
denial rates appears simplistic.
Firstly, the established relationship between tract denial rates and tract
attributes is not necessarily significant everywhere in the region, and only GWR
can reveal this divergence spatially. Secondly, most spatial units with statistical
significance show both negative and positive relationships between covariates and
denial rates, where one relationship often dominates the other if the same variable
is significant in the corresponding OLS model. Thirdly, in some cases, standard
approaches would have concluded that there was no marginal effect of a variable.
However the GWR approach reveals the variables had substantial and statistically
significant effects in certain areas. This is especially important for policy
formulation because it enables researchers and policy analysts to evaluate the
effectiveness of alternative policy tools for controlling varying spatial outcomes.
On the policy side, both the GWR model and OLS model indicate the
significance on most socioeconomic variables. While economic variables, such as
income and median house values proxy economic fundamentals of neighborhoods
and are intuitively associated with lending outcomes, the significance of variables
on race shed lights on the concerns about redlining. In particular, redlining arises
when area racial composition affects loan flows, even when controlling for
economic fundamentals. The results from GWR provide a picture on where and
to what extent these concerns merit attention. In this study, the results do not
44
For example, see Can and Megbolugbe (1997).
117
show a statistically positive relationship between denial rate and black
composition in the spatially targeted areas. Accordingly the assumption that
financial institutions redline underserved neighborhoods is not supported by this
analysis. However the results shed lights on the concerns about lending outcome
in those affluent areas with statistical significance, where race is still an important
factor in determining mortgage denial rate. Redlining may exist in a subtle way.
II Enhance Mortgage Flow to Underserved Areas
Academic research aimed at underserved areas, typically neighborhoods
with high concentration of minority and low-income households will fulfill the
dual mission of lessening disparities and providing education to potential lenders
and others involved in the home buying process. Consequently, it will ultimately
benefit poor families and minorities in extending mortgage credit and achieving
homeownership.
Inevitably, households located in underserved areas most likely suffer
from redlining. HUD has made tremendous efforts to minimize the
homeownership gap between non-underserved areas and underserved areas to
better serve underserved population. However, the ratio of minority/non-minority
homeownership rates decreased from 75.2% in 1997 and 1999, to 72.4% in 2001.
Therefore, according to the HUD 2005 Annual Performance Plan, “the goal for
the FY 2004-2005 period is to reduce homeownership disparities, thus increasing
the ratio by 0.4 percent points from Calendar year 2003 levels by calendar year
118
2005”. In this research, the documentation and mapping of census tracts with
high minority concentration and high denial rates and the analysis of their spatial
pattern provides a clear picture of whether concentrations of high-minority tracts
and high denial-rate tracts follow the same trend of clustering, and how they
respond to the observed widening gap of homeownership rates between non-
underserved and underserved neighborhoods.
III Summary
Overall, the study is unique in terms of both its methodology and policy
implications. GIS and related spatial techniques provide the essential locational
information and tools for spatial statistical and econometric data analysis and
modeling. This information is a critical input for the application of spatial
exploratory methods as well as for detecting spatial structure in regression
analysis, estimating spatial models, and predicting spatial outcomes.
45
The results of the study can provide policy makers more powerful insights
of mortgage flow to different areas. Upon observing such disparities, policy
makers should promote policies in both the primary and secondary mortgage
markets to enhance equal opportunity for minorities to access housing finance in
areas with higher concentration of white population and to help residents living in
underserved areas become homeowners.
45
See Can (1998).
119
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Appendix: Conventional Conforming Purchase Loans
Any mortgage loan other than an FHA
46
, VA
47
or an RHS
48
loan is a
conventional one. Conventional loans may be conforming and non-conforming.
Conforming loans have terms and conditions that follow the guidelines set forth
by Fannie Mae
49
and Freddie Mac
50
. These two stockholder-owned corporations
purchase mortgage loans complying with the guidelines from mortgage lending
institutions, packages the mortgages into securities and sell the securities to
investors. By doing so, Fannie Mae and Freddie Mac, like Ginnie Mae, provide a
continuous flow of affordable funds for home financing that results in the
availability of mortgage credit for mortgage borrowers.
46
The Federal Housing Administration (FHA), which is part of the U.S. Dept. of Housing and
Urban Development (HUD), administers various mortgage loan programs. FHA loans have lower
down payment requirements and are easier to qualify than conventional loans. FHA loans cannot
exceed the statutory limit.
47
VA loans are guaranteed by U.S. Dept. of Veterans Affairs. The guaranty allows veterans and
service persons to obtain home loans with favorable loan terms, usually without a down payment.
In addition, it is easier to qualify for a VA loan than a conventional loan.
48
The Rural Housing Service (RHS) of the U.S. Dept. of Agriculture guarantees loans for rural
residents with minimal closing costs and no downpayment.
49
Originally established in 1938 by the Federal government, Fannie Mae is a private, shareholder-
owned company works to expand the flow of mortgage money by creating a secondary market.
Fannie Mae was authorized to buy Federal Housing Administration (FHA)-insured mortgages,
thereby replenishing the supply of lendable money. In 1968, Fannie Mae became a private
company operating with private capital on a self-sustaining basis. Its role was expanded to buy
mortgages beyond traditional government loan limits, reaching out to a broader cross-section of
mortgage borrowers.
50
Freddie Mac is a stockholder-owned corporation chartered by Congress in 1970 to keep money
flowing to mortgage lenders in support of homeownership and rental housing. Freddie Mac
purchases single-family and multifamily residential mortgages and mortgage-related securities,
which it finances primarily by issuing mortgage pass through securities and debt instruments in
the capital markets.
129
Fannie Mae and Freddie Mac guidelines establish the maximum loan
amount, borrower credit and income requirements, down payment, and suitable
properties. Fannie Mae and Freddie Mac announce new loan limits every year.
The following table exhibits the limits for one-family first mortgages for year
2001 to 2006.
Table: Conforming Loan Limits for One-Family First Mortgages
Year Amount
2006 $417,000
2005 $359,650
2004 $333,700
2003 $322,700
2002 $300,700
2001 $275,000
Note that refinance and home improvement loans are not included in the
data sample for this research.
Abstract (if available)
Abstract
This study investigates spatial dependence and neighborhood effects in mortgage lending disparities in the Southern California five-county region. In doing so, it assesses indicators of primary mortgage market activity and their determinants for the region as a whole. The study compiles data from the 2002 HMDA and the 2000 U.S. Census to undertake a variety of analyses, including computation, assessment, and mapping of social-economic characteristics, as well as home mortgage origination, denial rates, and secondary market purchase rates by census tracts among sampled areas and population cohorts. Cluster analyses of social-economic and mortgage parameters show distinctive patterns of spatial clustering among tracts across the region. In observing these blueprints of spatial dependence, the study further undertakes a geographically weighted regression (GWR) to analyze spatial non-stationarity in the determinants of variability in neighborhood primary market loan denial rates for the year 2002.
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Creator
Zhuang, Duan
(author)
Core Title
Redlining revisited: spatial dependence and neighborhood effects in mortgage lending
School
School of Policy, Planning, and Development
Degree
Doctor of Philosophy
Degree Program
Planning
Publication Date
06/06/2009
Defense Date
04/25/2007
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
neighborhood effects,OAI-PMH Harvest,redlining,spatial dependence
Language
English
Advisor
Gabriel, Stuart (
committee chair
), Conway, Delores (
committee member
), Deng, Yongheng (
committee member
)
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dzhuang@usc.edu
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Tags
neighborhood effects
redlining
spatial dependence