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Essays on the economics of cities

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Content ESSAYS ON THE ECONOMICS OF CITIES
by
Thom Malone
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(URBAN PLANNING AND DEVELOPMENT)
August 2017
Copyright 2017 Thom Malone
Dedication
To my dear old Gran.
ii
Acknowledgments
First and foremost, I would like to thank my advisor and committee chair,
Chris Redfearn. Chris, his advice and support throughout my time at USC have
been invaluable. I appreciate the easy going co-working relationship we have with
one another and am proud of the papers we produced together. But, I also think
we have only scratched the surface of topics we have worked on together, and I
look forward to producing many important research papers together for some time
to come.
Myothercommitteemembers,MarlonBoarnetandRichardGreen,alsodeserve
thanks. Both have provided valuable feedback on my research. Moreover, they
have also given me great profession and career advice. I appreciate having both of
them behind me as I go forward.
Jenny Schuetz was a fantastic advisor for my first year. Urban economists
all understand the importance of path dependence, and I cannot imagine anyone
doing a better job a pointing me the right direction early on. Her continued advice
and support, when she really doesn’t have to do it, is definitely something I am
very grateful for.
Several other USC professors were valuable resources during my time as gradu-
ate student. Particular thanks are owed to Gary Painter and Mark Phillips. Both
iii
of whom were on my qualifying committee and both of whom gave me superb
feedback at many times over the last 4 years.
Jeff Zabel put me on my path to USC, I’m grateful to him for both suggesting
the Price School as possibility for me, and for his recommendation, without which
I doubt I would have been admitted.
HomeUnion gave me several internships during my time at USC. These experi-
ences gave me valuable exposure to the professional side of real estate investment
and startup environments that I thank them for. They also provided the data for
the third chapter in this dissertation.
The Lusk Center provided funding the second chapter of this dissertation, and
also funded conference travel for me several times. Thanks to everyone there for
the assistance.
Raven Molloy generously provided the loan frontier data in the first chapter. I
am thankful to her for that, as well as always being a friendly face at conferences.
The most important thanks go to Megan Miller, without whom I am fairly
certain I would not have made it past year 1 of this program.
There are many others who I am sure I have neglected here, but are equally
deserving. So, thanks to anyone who gave me any assistance of any kind over the
last 4 years. I am sorry I forgot you here.
Finally thanks to you, the person reading this. After all, writing isn’t really
writing until somebody reads it.
iv
Contents
Dedication ii
Acknowledgments iii
List of Tables vii
List of Figures ix
Abstract xiii
1 Introduction 1
2 Housing Market Spillovers in a System of Cities 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Motivating Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Estimating the GVAR . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.1 Individual VARX Models . . . . . . . . . . . . . . . . . . . . 23
2.5.2 Solving the Model across a System of Cities . . . . . . . . . 26
2.5.3 Specification of City Specific Models . . . . . . . . . . . . . 28
2.5.4 Testing for Weak Exogeneity . . . . . . . . . . . . . . . . . . 30
2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6.1 Responses inside Cities. . . . . . . . . . . . . . . . . . . . . 33
2.6.2 Spillovers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.3 Is the National relationship Driven by a Subset of Cities? . . 45
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.8 Appendix B: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3 The Durable Hierarchy of Neighborhoods in U.S. Metropolitan
Areas from 1970 - 2010 69
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Urban Stability & Change . . . . . . . . . . . . . . . . . . . . . . . 74
v
3.3 Measuring Hierarchy & Its Persistence . . . . . . . . . . . . . . . . 77
3.4 Metropolitan Area Stability . . . . . . . . . . . . . . . . . . . . . . 80
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.6 Appendix A: Levels vs. Ranks . . . . . . . . . . . . . . . . . . . . . 106
4 Index Consistency in the Presence of Asymmetric Information 109
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.2 Representativeness & Order of Aggregation . . . . . . . . . . . . . . 112
4.3 Data and Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.1 Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.2 Los Angeles . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.4 Empirics & Preliminary Results . . . . . . . . . . . . . . . . . . . . 143
4.4.1 Los Angeles . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5 Conclusions 159
Reference List 162
vi
List of Tables
2.1 Summary Statistics of the Response Employment to a 1 S.E shock
to Permits after 20 Quarters, All Cities. . . . . . . . . . . . . . . . 61
2.2 Summary Statistics of the Response Employment to a 1 S.E shock
to Permits after 20 Quarters by Census Region . . . . . . . . . . . . 61
2.3 Regressions of within City Response on City Characteristics . . . . 62
2.4 Summary Statistics of Spillovers from Permits to Employment . . . 63
2.5 Summary Statistics of Spillovers from Permits to Employment, con-
tinued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.6 Spillover Size by Origanating and Receiving City Population Quan-
tile (1 = Small City, 5 = Big City) . . . . . . . . . . . . . . . . . . 65
2.7 Regressions of Spillovers to Employment on ‘Distance’ Variables . . 66
2.8 Regressions of Spillovers on Originating and Receiving City Char-
acteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.9 Regressions of Spillovers on Originating and Receiving City Char-
acteristics, continued . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1 Rank Correlation for 1970 - 2010 in 8 Cities, Human Capital Variables 82
3.2 Rank Correlation for 1970 - 2010 in 8 Cities, Racial and Ethnic
Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
vii
3.3 DecadebyDecadeRankCorrelationsin8Cities,DensityandHuman
Capital Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4 Decade by Decade Rank Correlations in 8 Cities, Racial and Ethnic
Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5 Summary Statistics for Rank Correlations and Levels Correlations:
Human Capital Variables . . . . . . . . . . . . . . . . . . . . . . . . 107
3.6 Summary Statistics for Rank Correlations and Levels Correlations:
Race and Ethnicity Variables . . . . . . . . . . . . . . . . . . . . . 108
4.1 Municipalities and Mean Observations . . . . . . . . . . . . . . . . 123
4.2 Comparison of Indexes Locally-Pooled Relative to Globally-Pooled . 149
4.3 Comparison of Index Performance Relative to Locally-Pooled Hedonic151
viii
List of Figures
2.1 GDP, Residential Investment, and Non-Residential Investment at
the National Level, 1997-2012 . . . . . . . . . . . . . . . . . . . . . 50
2.2 Permits in Eleven Biggest Metros,1988-2015 . . . . . . . . . . . . . 51
2.3 Employment in Eleven Biggest Metros, 1990-2015 . . . . . . . . . . 51
2.4 Building Permits, and GDP in Los Angeles, 1990-2010 . . . . . . . 52
2.5 Building Permits, and GDP in New York, 1990-2010 . . . . . . . . . 52
2.6 Building Permits, and GDP in San Francisco, 1990-2010 . . . . . . 53
2.7 Building Permits, and GDP in Dallas, 1990-2010 . . . . . . . . . . . 54
2.8 Building Permits in Boston, New York City, and Philadelphia, 1994
- 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.9 Building Permits in Los Angeles, San Francisco, and San Diego,
1994 - 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.10 Building Permits in Los Angeles, Miami, Washington D.C, and Las
Vegas, 1994 - 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.11 Response of Employment to a 1 S.E shock to Permits, All Cities. . 57
2.12 Cities where the Lead-Lag Relationship Holds (Blue) and Cities
where it does not (Red). . . . . . . . . . . . . . . . . . . . . . . . . 58
2.13 Distribution of Spillovers from a 1 S.E shock to Permits after 10
Quarters in a selection of Cities. . . . . . . . . . . . . . . . . . . . . 58
ix
2.14 Spillovers from a 1 S.E Shock to Permits in Four Largest Cities. . . 59
2.15 Spillovers from a 1 S.E Shock to Permits in Four Largest Cities. . . 59
2.16 Response of Employment in All Cities to a 1 S.E Shock to Permits . 60
3.1 Illustrating What High and Low Rank Stability Looks Like . . . . . 84
3.2 Distribution of % Change in Rank of Census Tract for House Price 88
3.3 DistributionofEducationPercentileChangesineachDecade, Houston 89
3.4 Densities of Rank Correlation in Each Decade for all Cities, Human
Capital Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.5 Densities of Rank Correlation in Each Decade for all Cities, Racial
and Ethnic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.6 Map of Education Percentile Change from 1970 to 2010, Houston . 93
3.7 Map of Education Percentile Change in each Decade, Houston . . . 94
3.8 Map of Education Percentile Change in each Decade, Houston . . . 95
3.9 Map of House Price Percentile Change in each Decade, Las Vegas . 96
3.10 Map of House Price Percentile Change in each Decade, Las Vegas . 97
3.11 Map of Income Percentile Change in each Decade, Charlotte . . . . 98
3.12 Map of Income Percentile Change in each Decade, Charlotte . . . . 99
3.13 SpatialCorrelationinEducationPercentileChangesineachDecade,
Houston . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.14 SpatialCorrelationinHousePricePercentileChangesineachDecade,
Las Vegas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.15 Spatial Correlation in Income Percentile Changes in each Decade,
Charlotte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.16 Distributions of P-Values for Spatial Correlation Tests for 40 Year
Percentile Change, All Variables . . . . . . . . . . . . . . . . . . . . 102
x
3.17 DistributionsofP-ValuesforSpatialCorrelationTestsinEachDecade,
All Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.1 Relative Price Appreciation by Submarket - Stockholm . . . . . . . 124
4.2 Relative Composition of Observed Sample - Stockholm . . . . . . . 125
4.3 Price Appreciation Relative to 1981 - Stockholm, 1990 . . . . . . . 127
4.4 Sample Selection Relative to 1981 - Stockholm, 1990 . . . . . . . . 128
4.5 Price Appreciation Relative to 1981 - Stockholm, 1999 . . . . . . . 129
4.6 House Price Appreciation Across Los Angeles . . . . . . . . . . . . 131
4.7 House Price Appreciation Across Los Angeles . . . . . . . . . . . . 132
4.8 House Price Appreciation Across Los Angeles . . . . . . . . . . . . 133
4.9 House Price Appreciation Across Los Angeles . . . . . . . . . . . . 134
4.10 House Price Appreciation by Structure Type, 2000 - 2015 . . . . . . 135
4.11 House Price Appreciation by Lot Size, 2000 - 2015 . . . . . . . . . . 136
4.12 House Price Appreciation by 2000 Quartile, 2000 - 2015 . . . . . . . 136
4.13 House Price Appreciation by Distance from City Center, 2000 - 2015 137
4.14 Density of Housing Sales in Los Angeles, 2004, 2008, 2012, and 2015 139
4.15 Density of Housing Stock, 2000 and 2010 . . . . . . . . . . . . . . . 141
4.16 Density of Sales by Number of Times Sold, 2000 - 2015 . . . . . . . 142
4.17 Density of Housing Sales in L.A County by Property Type, 2000 -
2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.18 LocalPriceIndexesandGloballyPooledAggregatePricesforStock-
holm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.19 Local Share of Aggregate Stock vs. Local Share of Observed Sales . 146
4.20 Locally-Pooled Indexes Relative to Globally-Pooled Indexes - Malmö148
4.21 Aggregate Price Indexes Relative to Locally-Pooled Hedonic Index
- Malmö . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
xi
4.22 Locally Pooled Indexes and Globally Pooled for Los Angeles, 2000-
2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.23 Local Indexes vs Globally Pooled Index for L.A, 2000-2015 . . . . . 154
4.24 Globally Pooled Indexes relative to Locally Polled Indexes for Los
Angeles, 2000-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
xii
Abstract
This dissertation explores three separate issues related to the economics of
cities. Though they each have their own separate motivations behind them, there
is a common thread in the chapters in that they each help us further understand-
ing that aggregated geographic units such as cities can be better understood by
focusing on the variation within them rather than the variation between them.
The first chapter looks at how the relationship between housing and business cycle
is different from city to city and shows how cities interact with one another. The
second focuses on the internal structure of cities and looks at how which cities
have a very stable structure and which do not. The final chapter shows how city
level house price indexes can be misleading if they do not properly account for
asymmetries within the city’s submarkets.
xiii
Chapter 1
Introduction
Thisdissertationexplorestheeconomicsofcitiesin3essays. Thoughsomewhat
disparate, the papers do have a common tread between them in that focus on
what can learned by the exploration of subgroups, whether those subgroups are
the individual cities within the United States of Americas larger system of cities,
or the neighborhoods within a city like Los Angeles. Concentrating on subgroups
is incredibly important because in focusing on aggregate statistics great deals of
useful, often the most useful information for understanding the answer to question,
is lost. This is particularly prevalent in the context of cities. It has been well-
documented that over the past several decades, cities have been diverging from
one another in terms of their house prices, incomes, education, and wealth. As
cities become more and more different from one another, the idea that can be
adequately described by looking at a single trend, statistic, or index has a weaker
footing.
The first chapter follows this theme by exploring a reanalyzing a famous
national economic trend in the context of a system of codependent cities. It is
well-documentedthathousingleadsthebusinesscycleatthenationallevel. Dating
back as far as the great depression, nearly every recession or boom has been pre-
ceded by a respective drop or rise in residential investment (Green, 1997; Leamer,
2007). However, neither the business cycle nor the housing cycle is truly national
in their nature. Historically, the severity and timing of both vary greatly across
cities. This has been acknowledged in the literature (Ghent and Owyang, 2010),
1
but the possibility that different cities housing markets and economies could be
interacting and spilling over amongst one another has not yet been considered.
I use a Global Vector Autoregression to model building permits and employ-
ment at the metro level for 78 cities in the U.S from 1990-2015, then link these
models together in a system of cities. The model reveals several results of interest.
First, the status of residential investment as a leading indicator for the business
cycle is questionable at the metro level, and is found to be true in only 47 of 78
cities. Second, shocks to housing in cities do spill over into other cities. In fact, in
many cases the responses to shocks are larger in other cities than in those where
the shocks originated. Thus, the national relationship between housing and the
economy appears to be created by a collection of cities housing markets spilling
over into other cities. Third, the largest spillovers are often not found in adjacent
cities to those where the shock occurred. This indicates that factors other than
physical distance, such as trade, are the channels shocks are transmitted through.
In the second chapter, jointly authored with Chris Redfearn, studies patterns
of neighborhood stability within and across US metropolitan areas. Using Census
tract data covering over 200 U.S metropolitan areas from 1970 to 2010 we examine
several socioeconomic variables to define a neighborhood hierarchy and ask how
durable it is over time. Despite the substantial changes that have occurred in
metropolitan America over the sample period, we
find remarkable persistence in the rank of Census tracts by population density,
income, education, and house prices, with many cities having rank correlations of
over 0.75. And while racial and ethnic variables appear to be less persistent, all
seven variables exhibit a significant trend toward more stability over time. Even
in the presence of large shocks to the metropolitan economy, a majority of MSAs
retain the same basic spatial hierarchy they had decades ago. When hierarchies are
2
disturbed, it appears that shocks are highly spatially correlated. This pattern of
stabilityandchangehassignificantimplicationsforhowweanalyzeandunderstand
urban areas and their change.
Thefinalpaper, alsojointlyauthoredwithChrisRedfearn, highlightstheroleof
housingsubmarketsintheconstructionofaggregatehousingpriceindexes. Internal
metropolitan dynamics produce uneven appreciation and sales rates that can lead
to biased estimates of aggregate price because the sample on which they are based
is representative neither of the stock nor its appreciation. The proposed solution
is to estimate local indexes, aggregating these indexes by the housing stock they
represent rather than by their share in the observed sample of sales. During the
last housing crisis and recovery local indexes consistently find a lower peak, less
severe crash, and stronger recovery when compared with conventional “global”
indexes that oversampled lower priced homes relative to their share of the stock.
Overall, these results suggest that submarket price and volume dynamics should
not be ignored when making inferences about aggregate house prices.
3
Chapter 2
Housing Market Spillovers in a
System of Cities
2.1 Introduction
The lead-lag relationship between housing and the business cycle at a national
level has been well documented in the literature (e.g. Green (1997), Coulson &
Kim (2000), Leamer (2007)). However, it is easy to see that there has been great
variation by metropolitan area in house prices during recent upturns and down-
turns in the national housing market. While many works recognize this ( Head
et al. (2014), Malpezzi (1999)), few account for the possibility that the housing
cycles of different metros could potentially interact and lead to spillovers amongst
one another. Such studies assume that a metropolitan area constitutes a housing
market in and of itself, and choose to model different cities as being independent
of one another. In this paper I choose to model this relationship from a different
perspective; allowing shocks to cities housing and labor markets to transmit them-
selves to other cities. The paper is thus attempting to answer the questions: Why
does the housing lead the business cycle in some cities but not others? Do shocks
to local housing markets spill over into other local economies? And in turn, is the
lead-lag relationship between housing and the business cycle driven by the housing
markets of a particular set of cities? If spillovers from shocks to particular cities are
prevalent, it could be that stabilizing residential investment in these areas would
4
have some stabilizing effect on the business cycle as a whole. The work is, to my
knowledge, the first to account for spillovers among different areas when looking
at the relationship between the housing cycle and the business cycle.
The main empirical task of the paper is to model both the residential invest-
ment and the business cycle in a system of cities where one changes in one city
are allowed to spill over into another city. DeFusco et al. (2013) and Greenaway-
McGrevy & Phillips (2016) have used reduced form approaches to model spillovers
between an MSAâĂŹs housing market (exclusive of the rest of the macroeconomy)
and its neighboring housing markets. This approach works well, but I instead opt
to take an approach that allows all the cities in the sample to exist simultaneously
in a system. The preferable way of doing this would be to use a large-scale VAR,
that allows all the cities variables to enter into each other equations as endogenous
regressors, but this cannot be done is this context due to the curse of dimen-
sionality. To approximate such a large scale VAR, I use a Global Vector Auto
Regression (GVAR). The GVAR works similarly to a VAR, but instead of allowing
all the other cities variables to enter each other’s equations as endogenous, only
the variables of that city are allowed to be endogenous. Other cities variables enter
into each cities equation as weakly exogenous, and the individual models are then
linked together by some predetermined factor meant to proxy for the unobserved
connections that tie together cities’ housing and business cycles.
The GVAR has mostly been used in a cross-country setting, as in Hiebert
& Vansteenkiste (2009) or Cesa-Bianchi (2013), but can easily be used to model
housingmarketsatlowerlevels. Forinstance, Vansteenkiste(2007)foundevidence
of house price spillovers between the 31 largest US states using the method. This
study builds upon these earlier uses of the method by placing MSA level employ-
ment and building permits in the model. This allows me to measure spillovers
5
between not only housing markets but also the other elements of the business
cycle throughout a system of cities. These spillovers can then be identified using
generalized impulse response functions (GIRFs) to assess how shocks to building
permits manifest themselves in other cities employment over time.
Several interesting results are found in the GIRFS. The first is consistent with
the findings of Ghent & Owyang (2010); the lead-lag relationship between housing
and GDP is not consistently observed across the metropolitan area. The GIRFs for
the response of a city’s employment to an innovation in that same city’s building
permits are only positive in 47 of 78 cities. For the other 31 cities, an innovation
in permits actually elicits a negative response in employment.
Those cities where the response is positive are found to be different from those
where the response is negative in a number of ways. First, they tend to be geo-
graphically concentrated in the Midwest, and South rather than on the coastlines.
Second, cities were people have relatively little debt relative to their income are
also more likely to have a positive response. This is likely because of the variations
in marginal propensity to consume across regions. Shocks to housing lead to the
business cycle in areas where people spend less deleveraging debts, and instead
spend any shocks to income on purchasing durable goods.
The GIRFS also show that cities in the sample are not independent of one
another. There are significant spillovers to other cities employment when building
permits are shocked in a city. The spillovers do not seem to be particularly asso-
ciated with the distance between places. Spillovers are more often larger between
citiesthathaveheavymigrationflowsbetweenthemandthathassimilarindustrial
compositions. Moreover, the biggest recipients of spillovers from most cities are
New York, Los Angeles, and Chicago. This raises the possibility that these cities
are ‘hubs’ of sorts, and contrasts with some existing results in the literature. For
6
example, DeFusco et al. (2013) found that the greatest spillovers between housing
markets to be between neighboring cities. Similar results have been found in other
Saks (2008) and Zabel (2012) where cities are connected via labor markets and
migration flows.
Third, in those cities where housing leads the business cycle, spillovers mean
that it also leads the business cycle in other cities. Thus, it appears that the
national lead-lag relationship is created through movements in these cities’ housing
markets rippling through other cities’ economies. Responses from an innovation in
permits in these cities show substantial effects in employment in all the cities in the
sample. These spillovers are large enough that the response to a shock to permits
outside of a city is often as large as inside the city itself. Impulse responses from
a shock to permits in the cities where housing does not lead the business cycle fail
to elicit any statistically significant employment spillovers.
The paper proceeds as follows; section 2.2 provides the background and reviews
the current literature considering both spillovers between housing markets and the
relationship between housing and the other components of the business cycles, sec-
tion 4.3 explains the data used in the analysis, section 2.4 provides some motiving
facts about housing and business cycle, and differences between cities housing mar-
kets, section 2.5 outlines the estimation of the GVAR model, section 4.4 presents
the results. Finally, in section 2.7 the paper is summarized, shortcomings are
discussed, and potential future extensions to the work are provided.
2.2 Literature Review
The literature that this paper most directly follows is a purely empirical one
concerned the temporal lead-lag relationship between residential investment and
7
other components of the business cycle. The earliest contribution that I know of
in this literature is Green (1997), that examines whether residential and non-
residential investment granger cause GDP and vice versa using data from 1957
to 1992. The paper shows that residential investment granger cause GDP and
GDP in turns granger causes non-residential investment. The paper is entirely
empirical, but Green does provide some intuition by explaining that the differences
in the individual tax treatments of residential investment are a path that it could
’exogenously’ move through to affect GDP and create the observed relationship.
Coulson & Kim (2000) built upon these results by modeling residential investment,
GDP, and non-residential investment in a VAR. The impulse response functions
fromtheirmodelshowthatresidentialinvestmentisamoreimportantdeterminant
of GDP than non-residential investment.
The most prominent paper that documents the temporal relationship between
housing and other elements of the business cycle is Leamer (2007). This study
presents strong evidence that residential investment leads other elements of the
business cycle and recommends a modification to monetary policy that would
replace the output gap with changes in housing starts. The biggest contribution of
the paper is the presentation of a very interesting stylized fact; eight of the last ten
recessions were preceded by a downturn in residential investment. Furthermore, in
six of the last ten recessions, residential investment was the greatest contributor
to the changes in GDP the year before the recession and only twice did it not
contribute significantly.
Interestingly, both Green (1997) and Leamer (2007) find that only residential
investment, and not house prices, lead the business cycle. Leamer suggests the
reason behind residential investments importance it that housing has a persistent
volume cycle, but not a persistent price cycle. He reasons that if house prices are
8
sticky downwards, a decline in demand adjusts the volume of sales and not the
prices, causing a decline in construction. If prices could quickly adjust when the
housingcyclegoesdown, thennormalsalesvolumewouldquicklyreappear, butthe
sluggishness of prices makes the volume cycle very extreme and in turn, this makes
housing so important in recessions. Given the rather extreme volatility in house
prices shown since the paper was written, the idea that house prices are sticky
downwards seems doubtful, however. Overall, rigorous testing of the mechanism
that drives the lead-lag is still missing from the literature.
The most similar paper in the literature to this study is Ghent & Owyang
(2010). They investigate the relationship between housing and the business cycle
using cross-sectional variation across cities. Their key finding is that although
housing appears to be an important driver of cyclical fluctuations at a national
level, the local results cast doubt on the idea that there is a direct channel from
housing markets to local employment. Despite this, the paper still finds that
permits lead the cycle in over 80 percent of their sample. This paper builds upon
these results; by accounting for potential spillovers between metros I allow for the
possibility that the national trend could be driven by specific cities or regions.
The most recent paper that I know of in this literature is Strauss (2013) that
finds the relationship is consistent at the state level. His analysis also shows that
permits and consumer expectations are highly correlated, leading the author to
infer that permits are driven by expectations, and that permits lead employment
because there is a delay between the issue of permits and the time construction
begins.
This paper uses a Global Vector Autoregression (GVAR) to assess spillovers
from shocks to housing permits in one city on employment in other cities. The
method was originally developed in Pesaran et al. (2004), and di Mauro et al.
9
(2007), and has mostly been used to assess financial linkages and dependencies
between countries. However, there is a growing body of literature that applies this
method to assess the linkages between housing markets at different geographical
levels. At the cross-country level, Cesa-Bianchi (2013) used a GVAR to investi-
gate whether or not shocks to housing demand in particular countries affect real
economic activity in other countries. The author used orthogonalized impulse
response functions (OIRFs) to show that US housing demand shocks are quickly
transmitted to the domestic real economy, leading to short-term expansion of real
GDP. Though this result is unsurprising given the literature showing that housing
leads the business cycle, a more interesting result is that, these shocks have similar
effects on the real economic activity of other advanced economies. The spirit of
the paper is similar to this one, in that is primarily measuring the effect of changes
in the housing market in one location on other locations economies.
The method was also used in Hiebert & Vansteenkiste (2009); where quarterly
data on 10 Euro countries was used to construct a GVAR for real house prices, real
per capita disposable income and the real interest rate. The generalized impulse
response functions (GIRFs) contrast Cesa-Bianchi (2013), finding limited evidence
long term spillovers between different countries in the Eurozone. A stronger shifter
ofhousepriceactivityisdomesticlong-terminterestrates, whichwasfoundtohave
long-term effects on house prices.
The US housing market was modeled in a GVAR framework at the state level
in Vansteenkiste (2007). This paper used data from the 31 largest US states over
the period 1986-2005 to investigate the extent that house prices spillover between
states. The GIRFs show some interesting results; cross state spillovers for house
prices are found, and the effect of a shock is state dependent, with shocks to states
10
thathavearelativelylowerlandsupplyelasticitieshavingamuchstrongerspillover
effect than other states.
This paper is not the first to investigate interactions between different MSAs
housing markets. DeFusco et al. (2013) investigates whether or not contagion was
an important factor in the last housing cycle. They find evidence of house price
contagion in the latest boom period. Particularly, price elasticities between one
MSA and its closest to the neighbor (defined by euclidean distance) range from 0.1
to 0.27. Local fundamentals and expectations of future fundamentals have very
limited ability to account for the estimated effect, indicating that the effect is a
pure contagion effect driven by irrational forces.
There is also a growing literature that explores the connection between housing
markets and labor markets at the metropolitan level that this paper adds to. In
particular, Saks (2008) investigates the differences in housing supply between
metro areas, and how it generates substantial variation in house prices across the
United States. Using a VAR she finds that locations with fewer construction
barriers experience more residential construction and smaller increases in house
prices in response to an increase in housing demand. Specifically, an increase
in labor demand is also associated with an increase in wages but no change in
house prices. Interaction terms show when housing supply has constrained the
increase in demand leads to higher house prices, along with a higher level of wages,
and a smaller increase in employment (because migration flows into the area are
constrained).
Zabel(2012) builds upon Saks (2008) by investigating how the housing market
affects the flow of workers across cities through both the relative mobility of home-
owners relative to renters and the relative cost of housing across metro areas. He
11
estimates a VAR of migration, employment, wages, house prices and housing sup-
plydatafrom277USMSA.Theimpulseresponsefunctionsshowthattheeffectsof
labor supply and housing demand shocks exhibit substantial variation when eval-
uated at different values of the homeownership rate, the price elasticity of housing
supply and relative house prices. This study did allow for spillover effects in the
VAR, but such spillovers are only accounted for in the nearest neighbor.
The relationship between housing and GDP has also received considerable
attention in the macroeconomics literature. This studies usually work by incorpo-
rating housing explicitly into aggregate equilibrium ”real business cycle” (RBC)
models in the spirit of Kydland & Prescott (1982).
Davis & Heathcote (2007) is the first paper to model shocks of production
affecting housing in the RBC framework. In this model, there are 2 types of
firms; those who produce intermediate goods and those that transform interme-
diate goods into a good for final consumption. Within these two types, there are
three types of intermediate good producers; construction, manufacturing, and ser-
vices. These "industries" produce from a stock of capital and labor rented from
households. There are also three types of final good producing firms within the
model; a firm that produces a good for either household consumption or business
investment, a firm that produces residential investment and a firm that produces
housing. The first two types of firms use all three intermediate goods in produc-
tion. The third firm uses residential investment and land to make housing. Only
when one assumes that the amount of new land available in the economy in each
new time period is fixed does the model have a closed form solution. This solu-
tion has great success at modeling the relative volatility of residential investment,
accurately predicting it to be about twice as volatile as non-residential investment.
12
However, the solution is less successful in matching the data along three dimen-
sions that are very relevant to this study; the volatility of house prices is greatly
underestimated, a negative correlation between residential investment and house
prices is predicted. Most importantly residential investment is usually not found
to lead GDP and non-residential investment is usually not found to lag GDP.
More recent works in the RBC literature have made some resolutions to the
most unrealistic findings in Davis & Heathcote (2007). Fisher (2007) that shows
when housing is instead modeled as a separate capital stock in and of itself in
the production function, the lead-lag relationship of residential investment, GDP,
and non-residential investment is restored. Van Nieuwerburgh et al. (2015) uses
a heterogeneous agent equilibrium model with collateral constraints to generate
considerably more volatility in house prices within the framework to Davis &
Heathcote (2007). By doing so they improve the lead-lag relationship even more so
than Fisher (2007). The reasons behind the lead-lag relationship are also explored
in Kydland et al. (2012) that shows that fixed-rate mortgages may be the key.
They find that the lead in residential investment is driven by those structures that
rely on mortgage finance and it is specifically fixed-rate mortgages that account for
growth in residential investment that leads the growth in real GDP. Furthermore,
the dynamics of the 30-year mortgage interest rate suggest that mortgages are
relatively cheap ahead of an economic upturn. The reasons behind this are not
clear, however.
The results in Kydland et al. (2012), are compelling and have a believable
and intuitive story behind them. However, it is doubtful that they explain the
relationship between housing and the business cycle entirely. Particularly, the
lead-lag relationship goes back as far as reliable data does. For instance, Leamer
(2007) showed that the Great Depression was preceded by a crash in residential
13
investment in the late 1920s. Fixed-rate mortgages, however, were not developed
until after the Federal Housing Administration (FHA) was created as part of the
National Housing Act in 1934. So this suggests that the relationship could be
driven by other factors. Furthermore, fixed-rate mortgage law does not vary across
the country, so it is unclear how they could cause the relationship to hold in some
cities but not in others. Overall, while great strides have been made, both the
empirical literature and the RBC literature still have a limited understanding of
why it exists in the first place.
2.3 Data
The ’cities’ in the analysis follow the 2009 Metropolitan Statistical Area (MSA)
definitions created by the US Census Bureau. For parsimonious reasons, the analy-
sis uses only a subset of cities in the United States. In an effort to keep the sample
as representative as possible, the cities used are the top 50 cities in terms of pop-
ulation (not including cities in the non-contiguous United States), plus a group of
28 smaller cities picked to ensure adequate geographic coverage. These are listed
in tables 2.4 and 2.5 and shown in figure 2.12, where we see the cities account
for quite a large amount of the United States in terms of geographic area. They
are similarly representative in terms of population, and GDP. Specifically, as of
the 2010 Decennial Census, the total population of the sample is 182,012,755 thus
accounting for around 3 quarters of the total 249,157,649 people living in urban-
ized areas in 2010. It is similarly representative in terms of GDP, accounting for
$9,503,012 million of total $13,459,787 million in 2010
1
. The time period covered
runs from the first quarter of 1990 to final quarter of 2015 for a total of 100 time
1
These numbers are according to the Bureau of Economic Analysis (BEA).
14
periods in each city. Subsets of the data can certainly be taken, but the period
would have to be at least 9 years to ensure that enough degrees of freedom are
available to estimate all the parameters in the model. Likewise, the data could also
be extended back before 1990, but this would mean fewer cities could be included
in the model.
I use the count of new building permits issued in each city to measure housing
market activity. This is preferred to house prices since there are mixed results in
the literature concerning the connection between house prices and GDP (Iacoviello
(2005)). Of course, it would be best to use residential investment itself, but the
only available data on this is at the national level. However, housing permit data
is made available at the metro level every month in the Census Bureaus’ building
permits survey. Each building permit represents a potential construction, so it
carries a close relationship with residential investment. Indeed, Ghent & Owyang
(2010)findsthatthecorrelationbetweentheband-passednationwidetimeseriesfor
building permits and residential investment is over 98 percent. Another alternative
would be to use the value of building permits issued instead of the count. I did
experiment with this and it did not notably alter any results, so I choose to only
present results from the count of building permits to save space, and because it
has an easier interpretation since there is no need to adjust for inflation.
To represent the broader economy I use metro level employment data from
the Bureau of Labor Statistics ’Smoothed Seasonally Adjusted Metropolitan Area
Estimates’ that counts all nonfarm employees in an MSA. Employment is preferred
over metro level GDP, since the latter is only available annually, and not quarterly.
Nationwideemploymentcarriesa90percentcorrelationwithGDP,soitreasonable
to use as an indicator of the business cycle.
15
In order to control the greater macroeconomic environment, several nationwide
variables that may affect both housing and employment are also included. For
national monetary policy, the federal funds rate is included. Also, the national
level core consumer price index (CPI), the 30-year conventional mortgage rate
and, to measure credit turmoil, the spread between 3-month commercial paper
and 90 day Treasury bills. I also include the West Texas Intermediate (WTI) price
of Oil per barrel. It is important to take account of these factors, as evidence has
been found to suggest that national level variables may be a better indicator of
metro level economic changes than the metro level changes themselves Ghent &
Owyang (2010).
The last metro level variable is the physical distance between two each city in
the sample. This is for creating weighting matrices in the GVARS that are used
to compute the weakly-exogenous outside city variables. I compute the physical
distance between each city based on the latitude and longitude coordinates pro-
vided in the Census Bureau’s ‘Gazetter’ files. I measure the distance between the
two cities as the orthodromic or ‘great circle’ distance between two cities. I then
take the inverse of this so that cities closer to one another have a stronger interde-
pendence. These are then normalized so that sum of the inverse distance between
any one city and all the others in the sample is equal to unity. This is the same as
when a distance matrix is used in spatial econometrics. A small caveat is that the
coordinates used for the cities are based on the center of ’urbanized areas’ rather
than the OMB CBSA definitions, so there will be a small amount of measurement
error since these locations do not perfectly overlap with one another.
16
For robustness, I along performed the analysis with two other weighting vari-
ables; industrial distance and migration flows. This did not return any notably
different results, so it is not presented here
2
.
In order to explain the variation in results from city to city a number of other
metro level variables are included in the analysis, but used outside of the main
GVAR. These include housing supply elasticity measures from Saiz (2010), public
loan to income ratios from Mian et al. (2013) that combines information from
the Federal Reserve Bank of New York Consumer Credit Panel with IRS data on
incomes, measures of metro level credit constraints from Anenberg et al. (2017),
various demographic and socioeconomic variables found in the Census and Amer-
ican Community Survey, house prices from the Federal Housing Finance Agencies
Metro Level House Price Indices, and information on the stringency of local hous-
ing regulation from the ‘Wharton Residential Land Use Regulation Index’.
2.4 Motivating Facts
As mentioned, the literature shows a strong connection between residential
investment and the other elements of the business cycle. This is shown in figure
2.1 where we see the lead-lag relationship from the last quarter of 1997 to last
quarter of 2012. To isolate the cyclical component of the data, all 3 series are
passed through a Baxter-King (BK) filter in the frequency domain. The low-pass
BK filter is preferred over the more common Hodrick-Prescott (HP) filter because
it is designed to remove the low-frequency variation in the data, rather than the
high-frequency variation that characterizes booms and busts. Looking at the 3
series we clearly see that, though they all appear to have the same cycle, there a
2
IfofinterestthefullresultsandrobustchecksfromthealternativeGVARmodelsareavailable
in an excel file from the author on request.
17
clear temporal displacement between residential investment, real GDP and non-
residential investment. Residential investment clearly leads real GDP which in
turn leads non-residential investment.
It is particularly interesting to see that the relationship appears to fit the data
best for the most recent recession. This could be considered surprising given the
great downturns in house prices during the last crash, as it had been suggested
that the reason that housing leads the business cycle being that downward stick-
iness in house prices lead to a very extreme volume cycle. However, even with
little downward friction in house prices, the latest recession was preceded by a
downturn in residential investment, as was the recovery. This limits the appeal of
this explanation of the phenomenon.
Furthermore, this finding is somewhat contrary to the existing consensus that
has found housing has been uncharacteristically weak during the recovery from the
great recession (Yellen (2013), Rognlie et al. (2014)). This figure does not dispute
that the housing recovery has been weak, rather it emphasizes that despite this
weakness it has still been a leading indicator for the rest of the recovery. This casts
doubt on whether the link between housing and the business cycle is causal, given
that residential GDP has been less of a contributer to GDP in the last recovery
than it has in the past. It could be that residential investment, GDP, and non-
residential investment are simply different aspects of the business cycle that occur
in different phases. That is, they could still have the same common driver behind
all three components, such as monetary policy or consumer expectations, and it is
just that the driver takes longer to have an effect on some components than others.
In addition to the casual observation in figure 2.1, more rigorous investigation
for this can be performed by testing for granger causality. To do this I estimate
a VAR(2) with all 3 series as endogenous variables, where the lag order 2 was
18
chosen as according to the Alkaline Information Criterion (AIC). As suggested
by Geweke et al. (1983), I use a simple F-Type test. The test statistic on the
procedure is 7.2263, so the null that resident investment does not granger cause
GDP is rejected. This updates the findings in Green (1997) that rigorously shows
the same granger causal relationships between the 3 series in a longer data series,
(from 1957 to 1992).
Itisimportantatthispointtonotethatboththehousingcycleandthebusiness
cycle have substantial regional variation. This is displayed in figures 2.2 and 2.3
that show time series for, respectively, building permits and employment in the
11 largest MSAs in the US in terms of population
3
as well as the US as a whole.
Again, all series have been filtered with a BK band pass in the frequency domain
so as to more easily detect the cycle rather than the trend. The great dispersion
between the extent and timing of the cycles is clear. Though some appear to move
in synchronous relationships (for example, Miami and Los Angeles in house prices)
, others appear to have very little in common (for example, New York and San
Francisco in permits).
While the evidence for the lead-lag relationship at the national level is clear,
the evidence is weaker at the metro level. Figures 2.4 to 2.7 display the series for
housing permits in place of residential investment
4
and metro level GDP for the
Los Angeles, Dallas, New York and San Francisco Metropolitan Statistical Areas
(MSA)
5
. In these figures, there appears to be great inconsistency both between
cities and within the same cities over time in how well the relationship holds. In
3
Population as of 2010 via the census bureau. See ?? for details.
4
It is reasonable to swap out residential investment for building permits. The correlation
between the two at a national level is over 98 percent.
5
I use the 1999 OMB definitions of Metropolitan Statistical Areas. Details on these can be
found at http://www.census.gov/population/metro/data/pastmetro.html
19
Dallas, permits appear to have been a strong indicator of the GDP throughout the
entire period displayed, mirroring the national trend perfectly. The same could be
said of San Francisco. However, in Los Angeles, the trend only seems to hold after
the year 2000. In the 1990s, however, permits went through several upturns and
downturns while employment moved smoothly upwards. New York shows no real
evidence of the trend, except for in the 2007 crash.
A more thorough investigation into this was conducted in Ghent & Owyang
(2010) which found that the lead-lag relationship held in 80 percent of their the
MSAs in their sample, but also found that national level permits were, in fact, a
better predictor of employment than a cities own permits. More rigorous inves-
tigation of this trend will be performed in this paper in the first section of the
results, by assessing the response a cities employment to a shock in its building
permits. However, the information in these figures can motivate looking at this
relationship at the metro level quite well. That it exists nationally, but not, but
not in all metros, and even in some metros in some time periods but not others, all
suggests that housing in particular set of cities could be driving this relationship.
Another important stylized fact to be noted is the connection between different
housingmarkets. Itiseasytoestablishthathousingistheleadingindicatorofboth
upturns and downturns in the business cycle and that there is substantial variation
in housing markets between different metropolitan areas. However, this variation
does not exclude the possibility of co-movement and spillovers between the housing
markets in different metros. While the most obvious places to look for these with
any particular MSA would be those metros in a close physical proximity, this is
not necessarily the where one should end their search. Figures 2.8 to 2.10 show
some suggestive evidence of this. In figure 8 we see the time series of building
permits in New York, Boston and Philadelphia (all series are passed through a
20
Baxter-King so as to more easily detect the cycle rather than the trend) show all
appear to follow an extremely similar pattern. Such a result would seem to suggest
an important role for physical proximity in housing markets.
However, not all nearby metro areas move in sync with one another. Often,
the movements in a city’s housing market can have more in common with a city
on the other side of the country than its neighbors. Figure 2.9 shows time series
for permits of Los Angeles, San Diego, and San Francisco, despite their physical
proximity being roughly similar to the cities in cities in figure 2.8 they do not
appear to share common features in their cycles to the extent that the northeastern
cities do. Figure 2.10 tells a different story, here we see that house prices in
Los Angeles, Miami, Washington D.C. and Las Vegas have all shown remarkably
similar patterns in spite of the vast physical distance between the cities. This
motivates a model that allows for codependency amongst all cities into a single
system, rather than just linking one city to its nearest geographic neighbors.
When we combine this idea that co-movement and spillovers could be quite
common with established facts about the lead-lag relationship between the housing
and GDP, it is reasonable to think that shocks to specific metros could have large
spillovers not only into other cities housing markets but their broader economies
as measured by metro level GDP or employment. Particularly, the reason why
housing leads the business cycle at the national level, but not necessarily at the
metro level could be because cities housing markets are not entirely independent
of one another. If this were true, then we would expect to find responses in
employment or GDP to shocks in residential investment, not only in that city but
in others too.
That a shock to one isolated area of the economy could spread a larger (and
not necessarily adjacent) area has important implications for the understanding
21
of the business cycle and whether location specific attempts to stabilize specific
housing markets could have stabilizing effects on the economy over a broader area.
It is this that motivates next section of the paper that lays out the framework for
a GVAR model that assesses these possibilities.
2.5 Estimating the GVAR
There are two common approaches when modeling housing and the rest of the
economy: the VAR model and the structural model. While the structural model
is typically taken from some applicable economic theory, the VAR is atheoretical
using the lags of dependent variables as regressors. The choice between the two
models has to do with the type of question being answered and the whether or not
there are appropriate instruments available. While the VAR has the advantage of
being more general, it has the disadvantage of its parameters often not having a
clear practical interpretation, so they are not useful for testing hypotheses directly.
However, since I am interested in the response of a cities housing permits and
employment to exogenous shocks, and not the direct interpretation of coefficients
a VAR would seem more appropriate in my case. Furthermore, it seems unlikely
that one would be able to find valid instruments for a structural model.
Though my preferred strategy would be to model permits and employment as
endogenous to one another in a large scale VAR, this would cause serious problems
when attempting to answer this question. If one were to estimate an unrestricted
VAR(p) model with, say, k endogenous variables covering N cities, the number
of unknown parameters will be unfeasibly large, of order p(kN-1)
6
. So using a
more traditional panel VAR approach is infeasible due to the often referred to
6
In my case N=78, k=2, and, though it is at the disclosure of the researcher, p=2 is probably
a good guess at what the AIC would choose, given previous results in the literature. So we
22
’curse of dimensionality’ creating insurmountable computational limitations. To
dealwiththisIutilizeaGVARframeworkwhichavoidssuchproblemsbyimposing
an assumption of weak exogeneity on the variables not contained within the metro
itself.
The following subsections present the general details of the GVAR used in the
analysis. The first deals with the estimation of each city’s own individual VARX
model one-by-one, while the second shows how the models are linked together
as a system of cities. The remaining subsections consist of particulars of model
specification, as well as testing the model’s assumptions, and checking the model
is robust and well-behaved to alternative specifications.
2.5.1 Individual VARX Models
I begin by modeling individual VARX models for each city in the sample. To
motivate this, suppose we have N + 1 cities indexed by i = 0, 1,...,N. In order
to approximate the large scale VAR that I would prefer to estimate, every cities
employment and building permits are included in every other city’s model in two
vectors.
Speaking formally, each city, i, is modeled in the VARX(2,2) structure:
x
it
=a
i0
+a
i1
t + Φ
i1
x
i,t−1
+ Φ
i2
x
i,t−2
+ Λ
i0
x
∗
it
+ Λ
i1
x
∗
i,t−1
+ Λ
i2
x
∗
i,t−2
+u
it
(2.1)
wherex
it
is a 2x1 vector containing cityi’s building permits and change in employ-
mentattimet. Thatis,x
it
= (Permits
it
, ΔEmployment
it
). Irefertotheseas‘inside
city’ variables. x
∗
it
is similarly a 2x1 vector of employment and permits in every
parameters of order 2(78x2− 1) = 144. The data only covers 100 quarters, so there are not
enough degrees of freedom to estimate this.
23
other city that I refer to as ‘outside city variables’, and u
it
is a serially uncorre-
lated and cross-sectionally weakly dependent process. If preferred, the number of
inside and outside city variables are allowed to vary across cities to control for
some city specific factors, though I choose not to do so here. The outside city
variables are computed as weighted averages of the corresponding inside city vari-
ables of all cities, with the weights being specific for each different city. That is,
x
∗
it
=
P
N
j=0
w
ij
x
jt
, where w
ij
, j = 0, 1,...,N are a set of weights such that w
ii
= 0
and
P
N
j=0
w
ij
= 1. The weights are analogous to a spatial weighting matrix in a
spatial auto regression or spatial error model in that they are determined by the
modelers choice meant to convey the importance or connectedness of a given city
i to some other city j. I use a physical distance for the presented results, but
also performed robustness checks that weight by industrial distance and migra-
tion. While physical distance is obviously time variant, the time varying nature of
a cities industrial composition and its migration flows mean that a different weight-
ing matrix which is additionally indexed by time, w
iit
, is used in those VARXs.
These results were not notably different and are available from the author upon
request.
Though the GVAR framework can be applied to either stationary or integrated
variables or both. Estimation is performed taking into account the integration
properties of each variables’ time series in order to account for short-run and long-
run relations
7
. To do this, I rewrite equation (1) in VECMX form:
Δx
it
=c
i0
−α
i
β
0
i
[z
i,t−1
−γ(t− 1)] + Λ
i0
Δx
∗
it
+ Γ
i
Δz
i,t−1
+u
it
(2.2)
7
In this case, it is reasonable to interpret long run relations as cointegrating, perhaps reflecting
the overall national trend.
24
wherez
it
= (x
0
it
,x
∗0
it
)
0
,α
i
is ak
i
xr
i
matrix of rankr
i
andβ
i
is a (k
i
+k
∗
i
)xr
i
matrix
of rankr
i
. If we partitionβ
i
as (β
0
ix
,β
∗0
ix
)
0
conformable toz
it
, ther
i
error-correction
terms defined by equation (2) can be written in the form:
β
0
i
(z
it
−γ
i
t) =β
0
ix
x
it
+β
∗0
it
x
∗
it
− (β
0
i
γ
i
)t (2.3)
this allows for the possibility of co-integration both withinx
it
and betweenx
it
and
x
∗
it
and hence I am also allowing for the possibility of co-integration across x
it
and
x
jt
for i6=j.
Each VECMX model is estimated separately for each city conditional on x
∗
it
treating the vector x
∗
it
as I(1) weakly exogenous with respect to the parameters of
the conditional model in equation (2). Specifically, the equation (2) is estimated
using a reduced rank regression, taking into account the possibility of cointegration
both within x
it
and between x
it
and x
∗
it
. Estimating the model this way allows
one to obtain the number of co-integrating relations, r
i
, the speed of adjustment
coefficients, α
i
, and the cointegrating vectors, β
i
, for each individual city model.
Finally, the system is extended to include not only just inside city variables,
x
it
, and outside city variables,x
∗
it
but also a vector of country-level factors,d
t
, that
are the same in every city’s economy. Here I have included the federal funds rate,
oil prices, TED spread, and the 30 year fixed mortgage rate in each time period.
Practically, this is done by including these variables as part of a city’s outside city
variables in every city, and not applying the weighting matrix to them. The weak
exogeneity assumption is also applied to d
t
.
25
2.5.2 Solving the Model across a System of Cities
Despite the estimation of each city’s VARX model in equation (2) individually,
the GVAR framework requires that the model is solved in terms of our entire
system of cities as a whole.
To do this with the same set of VARX(2,2) models described in equation (1):
x
it
=a
i0
+a
i1
t + Φ
i1
x
i,t−1
+ Φ
i2
x
i,t−2
+ Λ
i0
x
∗
it
+ Λ
i1
x
∗
i,t−1
+ Λ
i2
x
∗
i,t−2
+u
it
As before, define z
it
as the vector (x
0
it
,x
∗0
it
)
0
and rewrite (1) for each city as:
A
i0
z
it
=a
i0
+a
i1
t +A
i1
z
i,t−1
+A
i2
z
i,t−2
+u
it
(2.4)
where
A
i0
= (I
k
i
,−Λ
i0
)
A
i1
= (Φ
i1
, Λ
i1
)
A
i2
= (Φ
i2
, Λ
i2
)
Thenextistousethematriceslinkingthecities,W
i
, definedbytheaforementioned
weights w
ij
to obtain the identity:
z
it
=W
i
x
t
(2.5)
where x
t
= (x
0
0t
,x
0
1t
,...,x
0
Nt
)
0
is a kx1 vector that collects all the endogenous vari-
ables in the system and hence W
i
is a (k
i
+k
∗
i
)xk matrix.
26
From the identity in (5) it is straightforward to show:
A
i0
W
i
x
t
=a
i0
+a
i1
t +A
i1
W
i
x
t−1
+A
i2
W
i
x
t−2
+u
it
(2.6)
stacking each of these individual models yields the model for x
t
:
G
0
x
t
=a
0
+a
1
t +G
1
x
t−1
+G
2
x
t−2
+u
t
(2.7)
where
G
0
=











A
00
W
0
A
10
W
1
.
.
.
A
N0
W
N











,G
1
=











A
01
W
0
A
11
W
1
.
.
.
A
N1
W
N











,G
2
=











A
02
W
0
A
12
W
1
.
.
.
A
N2
W
N











,
a
0
=











a
00
a
10
.
.
.
a
N0











,a
1
=











a
01
a
11
.
.
.
a
N1











,u
t
=











u
0t
u
1t
.
.
.
u
Nt











.
Since G
0
is known and is non-singular we can premultiply equation (7) by G
−1
1
to
yield the GVAR(2) model:
x
t
=b
0
+b
1
t +F
1
x
t−1
+F
2
x
t−2
+
t
(2.8)
27
where
F
1
=G
−1
0
G
1
F
2
=G
−1
0
G
2
b
0
=G
−1
0
a
0
b
1
=G
−1
0
a
1

t
=G
−1
0
u
t
finally equation (8) can be solved recursively for a number of purposely. I place no
restrictions on the covariance matrix Σ

= E(
t

0
t
), but this could be done if one
chose to do so.
When it is solved the GVAR model can model the interactions within the sys-
tem through three different channels; the first is the contemporaneous dependence
of inside city variables, x
i
t, on outside city variables, x
i
t
∗
, and its lagged values,
the second is the dependence of inside city variables, x
it
, on the national level
variablesd
t
and third (and of the most interest to this study) the dynamic depen-
dence of shocks in city i on the shocks in city j, as described by the between city
covariances.
2.5.3 Specification of City Specific Models
As a first test of the dynamic stability of the system; I test for stationarity
of variables in levels, first differences, second differences. This is done using an
Augmented Dickey-Fuller (ADF) test, based on univariate autoregressions of each
variable with the lag order set to 4. For log-levels, the tests use a regression that
includes a linear trend. When performed, I found that permits and employment
28
are I(1) in most cities. Those they do not appear to be I(1) appear to be I(2)
8
.
That most of the variables do not appear to be stationary in levels supports the
choice to include them in the model in levels.
The next step is the selection of lag orders and assessment of the cointegrating
relations in the individual VARX models. These models are, as stated before,
estimated in error correction form using a reduced rank regression. The rank of
the co-integrating space is computed using the Johansen trace statistic following
the procedure set out in Peseran, Shin and Smith (2000) for models that contain
weakly exogenous I(1) regressors
The selection of p
i
and q
i
corresponding to the lag orders of the inside city
and outside city variables in each individual cities respective models was made
according to Akaike Information Criterion (AIC) with the maximum lag lengths,
p
max
and q
max
, set to 2. The most common are lag structure selected is, (p
i
,q
i
) =
(1, 1), which is selected for 32 of the VARXs. The next most common structures
(p
i
,q
i
) = (2, 1), and (p
i
,q
i
) = (1, 2), which are the number of lags chosen in 28
and 9 cities each. The lag structure (p
i
,q
i
) = (2, 2), was chosen in the remaining
8 cities. The system is quite different between different cities with a handful
of the all the different possible lag structures being selected. This reflects the
strong heterogeneity among metro-level housing markets, that helps justify the
use of a GVAR to assess spillovers. Other approaches such as a vector spatial
autoregression, a panel VAR, or a reduced form approach are feasible alternatives
totheuseofaGVAR.However,suchmethodsdonotdiscriminatebetweendifferent
units, and rather report a single impulse response function, or a single coefficient
reporting the average effect. By doing so they miss the substantial differences
8
Full documentation of the specifications are not presented in the paper to save space. If of
interest, the complete results of all tests for stationarity, the lag orders of each model, and the
number of cointegrating relations are available on request.
29
in each individual housing market, and in turn, the large variance in the extent
of spillovers depending on both where shock that caused it originated from, and
where it is spreading to.
Lastly, I looked at the number of cointegrating relations in each individual
VARX. This is crucial since in order for there to be convergence in the impulse
response functions that assess the level of spillovers it must be that the system as a
wholeisstable. Thiswasdonebycomputingtherankofthecointegratingmatrixin
each separate VARX using the Johansen trace statistic following the procedure set
out in Peseran, Shin and Smith (2000) for models that contain weakly exogenous
I(1) regressors. Using this it was found that, in total, the GVAR model contains
103 cointegrating relations.
For the GVAR to be well behaved, it must be that the rank of the cointegrating
matrix does not exceed the number of cointegrating relations in all the individual
VARXcitymodels. Themodelcontains161endogenousvariableswithamaximum
lag order of 2 resulting in 322 eigenvalues. So at least 219 (that is, 322-103)
eigenvalues must fall within the unit circle on the complex plane. It happens that
exactly 265 of the eigenvalues fall within the unit circle and the remainders have
moduli less than unity. This indicates that the model is stable and that there do
exist some shocks will have permanent effects on the endogenous variables.
2.5.4 Testing for Weak Exogeneity
The GVAR model assumes that the outside city variables, x
∗
it
, as well as the
national level variables, d
t
, are weakly exogenous with respect to the long-run
parameters of the conditional model. Since this assumption is crucial for the
model to be well behaved, a brief tangent is taken here to familiarize readers with
the concept of weak exogeneity, and how it differs from other types of exogeneity.
30
The idea that the independent variables within a system must be regarded as
‘exogenous’ to the dependent variable for efficient estimation is at the heart of
most econometric work. Practitioners have long had an understanding that vari-
ables being exogenous depend on whether or not it can be taken as ‘given’, or
‘fixed’ without losing any information relevant to the task at hand. However, more
formal definitions of the concept did not exist until the seminal work of Engle et
al. (1983), which differentiated between 3 types of exogeneity; weak exogeneity,
strong exogeneity, and super exogeneity. Weak exogeneity is, predictably, the less
strict of the 3, but also gives the econometrician less flexibility than the other 2.
Speaking informally, a parameter can be regarded as weakly exogenous if knowl-
edge of its value provides no additional information about the potential range of
values the parameters of interest. So if weak exogeneity of a parameter holds,
then the marginal distribution of that parameter can be ignored, and estimation
will still be efficient. Strong exogeneity implies that a parameter is both weakly
exogenous and does not granger cause the parameters of interest. This allows not
only efficient estimation but also allows one to make valid n-step ahead forecasts.
Super exogeneity is the strictest of the 3 definitions and probably the closest to
the intuitive definition of exogeneity as something being ’outside’ of the system. A
parameter can be regarded as super exogenous to the parameters of interest if it is
both weakly exogenous, and the parameters of interest are invariant with respect
to the super exogenous parameter. This is much like weak exogeneity, only now
addition information about the super exogenous parameter gives us no additional
information about the parameter of interest itself, rather than just its range of
values
In the context of this study, weak exogeneity is synonymous with ‘long-run
forcing’, meaning that no long-run feedback from x
it
to x
∗
it
is allowed. Short-run
31
feedback, however, is allowed. Since my model is cointegrating, this means that
the error correcting terms, ECM
ij,t−1
, of the individual city VECMs do not enter
into the marginal models of the weighted outside city variables, x
∗
it
. This can be
formally tested. To do so, I carry out the procedure outlined in Johansen (1992)
and perform a joint test of the significance of the estimated error correction terms
inauxiliaryequationsfortheoutsidecityvariables. Specifically, forthelthelement
of x
∗
it
the following regression is run:
Δx
∗
it,l
=a
i,l
+
r
i
X
j=1
δ
ij,l
ECM
ij,t−1
+
s
i
X
k=1
φ
0
ik,l
Δx
i,t−k
+
n
i
X
m=1
ψ
0
im,l
Δ˜ x
0
i,t−m
+η
it,l
(2.9)
where ECM
ij,t−1
, j = 1, 2,...,r
i
are the estimated error correction terms corre-
sponding to the r
i
co-integrating relations found for the ith country model and
Δ˜ x
it
= (Δx
0∗
it
, Δ(e
∗
it
−p
∗
it
), Δp
0
t
)
0
. The weak exogeneity test is an F-test with the
(joint) null hypothesis; δ
ij,l
= 0,j = 1, 2,...,r
i
in equation (9).
I conducted the test at the 5% level, in general, the variables of interest (i.e.
permits, and employment), were to be well behaved, and only fail the test in 3 out
of 156 cases
9
. In particular, only employment in Pensacola, permits in Louisville,
and permits in Las Cruces cannot be said to be weakly exogenous to the weighted
outside city variables, x
∗
it
, for each of their individual models. Since they are so
few, and since each test was carried out independently of the others, I do not
regard these rejections as particularly concerning.
The national variables had more mixed results, while the federal funds rate and
the 30-year fixed mortgage rate appear to be well behaved, and only produce 1
rejection between the 2 variables (i.e. the 30-year fixed mortgage rate in Dallas).
ResultsfortheTEDspreadandthepriceofcrudeoil, however, aremoreconcerning
9
As with the model specification, I only summarize the weak exogeneity results in words to
save space. Full documentation of the test and results is available on request.
32
for the behavior of the model. The null is not rejected for the TED spread in 6
cities and is also not rejected for oil in 8 cities. This is an important caveat on the
model, but does not mean that the results are unreliable. At most,this may mean
that the some nationwide variables have not been completely ‘filtered out’ of the
results.
2.6 Results
The results show the generalized impulse response functions (GIRFs) for a
one standard error shock to permits in each city. GIRFS are used instead of the
traditional orthogonalized impulse response functions (OIRFs) in Sims (1980)
because they do not require any ordering of the variables. The responses are
cumulative and in levels for ease of interpretation.
2.6.1 Responses inside Cities.
Before assessing the evidence for spillovers, it is worth looking at the GIRFs
within the city that is shocked itself. This will help tell us the extent to which the
lead-lag relationship varies between cities, and use this regional variation to help
explain why it exists in the first place.
Themodelallowsmetopullout4differentinsidecityresponses; theresponseto
permits from a 1 S.E shock to permits, the response of permits from a 1 S.E shock
to employment, the response of employment from 1 S.E shock to employment, and,
the response that is of the most interest, that of employment from a 1 S.E shock
to permits. The dynamic profiles of this shock in all 78 cities are shown in four
figures 2.11.
33
The first thing to note from figure 2.11 is that the responses all seem to display
some sporadic behavior in the first few quarters, but generally appear to have
converged to a stable value by 10 quarters. This means that the responses can be
aptly summarized by looking a the point estimate of the response sometime after
the 10th quarter. Thus, I present summary statistics for the responses after 20
quarters in table 2.1. The point responses are in the top row, and in the second
row, I show a dummy variable that takes the value 1 if the response is positive.
The second row is equivalent to a dummy variable that takes the value 1 if housing
leads the business cycle in that city. The bottom row shows the response when the
shock is normalized to be a single permit in each city.
When looking at table 2.1 in conjunction with figure 2.11 we can see that,
consistent with previous results in the literature, the evidence that residential
investment leads the business cycle at the metro level appears to be mixed. Shocks
to permits only elicit a positive response in only 47 of 78 cities (i.e. 60 percent).
In the other 31 cities, the response to a permits shock is actually negative, the
opposite of what would be predicted by the national trend.
We can also look at the magnitude of responses. Table 2.1 shows that the
mean response from a 1 S.E shock to permits is just under 600 jobs. This should
be considered quite a high number, since the average standard error of city-wide
permits issued is 238, this translates to an average of 2.5 jobs for every new permit
issued.
However, concentrating on the mean alone masks the large variation between
cities. The standard deviation in table 2.1 is 4,272, more than 7 times the size
of the mean. This is because of a handful of cities (usually bigger ones), where
the shock is quite substantially larger than average. For example, the largest
response of 23,000 is found in New York where the standard error is 1277 permits,
34
this normalizes to a response of roughly 18 new jobs for each permit issued. In
Chicago, the corresponding numbers are 7,613 new jobs in response to a shock of
300 issued permits, or about 25 new jobs in response to each permit issued. By
far the largest negative response is in Los Angeles, where innovation of 1005 new
permits leads a response of about -13,231 job losses, or around 13 jobs lost for
every new permit issued.
Figure 2.11 and table 2.1 effectively show that the lead-lag relationship between
housing and the business cycle breaks down at lower geographic levels. However,
neither is able to explain why this relationship holds in some cities but not others.
Understanding this is important because in order to implement any kind of place
based housing policies to stabilize the business cycle, the transmission mechanism
between housing, and the business cycle must also be understood.
I first look at if the cities where housing leads the business cycle are concen-
trated in a particular region. Figure 2.12 shows the cities where permits lead
employment in blue, and those where it does not in red (i.e. the variable in row 2
of table 2.1). Table 2.2 shows the summary statistics of the spillovers by region.
From these we can see that Midwestern cities show are less likely to have housing
lead the business cycle. St. Louis, Kansas City, and Cleveland among others all
exhibit negative reactions in their employment. The cities that have large positive
responsesappeartomostlybelocatedintheNortheast, Texas, andNorthwestwith
New York, Boston, Dallas, Houston, and Seattle all exhibiting a positive response
after 20 quarters. The geographic trend is not conclusive, however, as it is clear
that even some adjacent cities (e.g. San Francisco and San Jose or Los Angeles
and Riverside) respond in different directions.
Since there is no overwhelming geographic trend, the next step is to look if
there are notable differences in the characteristics of the red and blue cities in
35
figure 2.12. This can be done by regressing both the variables in table 2.1 on
different city level variables.
The first set variables I use are the proportions of employees in a city who
work in a certain industry.
10
It could be that cities were employees are more
heavily concentrated in real estate related industries like construction, finance, or
renting and leasing services are more likely to have housing lead their business
cycles. Conversely, places that are heavily concentrated in other industries like oil,
could be more likely to have any shocks to housing are ‘washed out’ by movements
in those industries. This has some precedent at the national level, in 1951 and
1967 there were severe housing downturns that were, unusually, not followed by
recessions. Leamer (2007) attributes this to huge fiscal spending on to the Korean
and Vietnam War, respectively.
Leamer (2007) reckons that housing leads the business cycle because of the
stickiness of house prices. If people refuse to sell their houses when prices fall, this
means that shocks to housing will manifest themselves primarily through changes
sales volumes. This means that shocks to housing will lead to more jobs in con-
struction, brokerages, finance, etc. Strauss (2013) gives evidence for a similar
story for housing leading the business cycle during booms, showing that expec-
tations about the economy and the issuance of new building permits are highly
correlated. He infers that when people have expect a boom, they buy houses/start
renovations, which is shown in the many new permits being issued, however, it is
not until sometime later that the permits is actually constructed and real economy
10
My ’Industries’ are 2012 2-digit NAICS codes downloaded from the Census Bureau’s
’County Business Pattern’ series. I use information from 2001 in my regressions, but the
results are insensitive to year choice. More information on the series can be found at
http://www.census.gov/programs-surveys/cbp.html.
36
activity takes place. While these reasons are plausible they cannot explain why
the relationship is inconsistent from city to city.
Some of Leamer and Struass’s stories may be captured in the aforementioned
industrial compositions of cities. However, there may be another reason behind
why permits lead employment in so areas but not others- variation in the chances
that a permit will actually be built. A permit only represents potential construc-
tion, and it is common that it will never actually be followed through with, and
thus not result in any response in employment. I use five variables that may create
variation in this across; the ‘loan frontier’ of a city, the average debt to income
ratio in the city, the elasticity of its housing supply, how stringent its land use
regulations are, and the price of housing.
The idea behind using debt to income ratios is that they can cause the marginal
propensity to consume to differ from place to place. For instance, if a person
expects a rise in their income, they may request a permit for some anticipated
building that they intend to spend it on. However, they are a lot less likely to go
through with this building if they have a large amount of debt they need to pay off.
Alternatively, they may stretch out the construction over a longer period of time
(i.e. hire 1 workers for a 2 year project instead of 2 workers for a one year project)
or even use their own labor. This is similar to the mechanisms displayed in papers
such as Eggertsson & Krugman (2012), and Di Maggio et al. (2014), where the
debt is often attributing as being the reason for a slow recovery, because people
tend to deleverage before they spend more money on durable goods, dampening
the effects of expansionary monetary policy
11
.
11
Data on DTI ratios can be found at http://faculty.chicagobooth.edu/amir.sufi/data.html. I
use the 2001 ratio in my regressions, but the results can be replicated using any of the years.
37
Estimates of the ‘loan frontier’ are taken from Anenberg et al. (2017). They
developanestimateofthemaximumloanaborrowercouldobtaingiventheirFICO
score, income, and downpayment amount in each of the top 100 metropolitan areas
intheUSAbyyear
12
. Thisadequatelycapturesthedifferencesincreditavailability
across metro areas. The logic behind including this is similar to including the DTI
ratios in that places where credit can be more easily acquired have more means to
engage in building activity, leading to permits being fulfilled faster and at a higher
probability.
The loan frontiers also have an advantage in that they can be considered exoge-
nous. This isbecause they are disaggregated, so they can be projected using a ?
style instrument that uses shocks to national credit frontier. Identification rests on
the fact that local deviations from the nation trend are based on the distribution
of borrowers. I use the log of the loan frontier in the regressions because it has an
easier interpretation.
Mymeasuresforelasticityofhousingsupplyandstringencyofregulationarethe
estimates found in Saiz (2010) and the Wharton Residential Land Use Regulation
Index(Gyourko et al. (2008)), respectively. These are included because in places
where the housing supply is less elastic, and regulation is stricter, it is less likely
that a person will go through an approved permit because the costs of building
and construction are higher. House Prices are also included for the same reason.
Results for the regression are shown in table 2.3. I run each regression for 2
differentspecifications, thefirstisasimpleOLSregressionwherethepointestimate
of the response in the top row of table 2.1, and the second is a probit with the
dummy variable in the bottom row of the same table. The regression are run for
12
Again, I use the 2001 estimates of the loan frontiers since but the results can be replicated
using any years estimates.
38
each type of variable separately in the first ten columns, then all at the same time
in the final two columns.
The regressions produce ambiguous results for industries, house prices, regu-
lation, and the elasticity of housing supply. The coefficients are almost always
insignificant for these, and often change sign from specification to specification.
Debt to income ratios and loan frontiers (the top 2 rows of 2.3) appear to be the
most consistent predictor of a whether or not housing leads the business cycle in a
city. The OLS results indicate that an increase in the average DTI ratio of a city
by 1 will lower the response to a shock to permits by 4,328 jobs, or in other terms 5
less jobs per permit issued (see columns (1) and (2)). Similarly, the top row shows
a doubling the loan frontier increases a the response by 4886 jobs, or about 5 more
jobs per permit issued. These results actually get stronger when I control for all
the alternative variables of interest mentioned above (columns (7) and (8)) or if a
probit specification is used, but not OLS. The probit results indicate that raising
the ratio by 1 will make a city more than 38 percent less likely to have housing
lead the business cycle, and doubling loan frontier will make this 26 percent more
likely.
As mentioned, if a city has more debt relative to income, this does not do a
great deal to hinder the pursuit of building permit, since just having a permits
issued does not cost much. However, it does hinder people from actually going
through with having the permit built, since they are burdened with more debt, or
have fewer means to pay off their debt with. If a permit is issued but not built,
no actual economic activity will take place. Essentially, the argument is that a
higher DTI does not dampen the propensity of a person to pursue a permit, but
does inhibit their ability to build it, since they must also use their income to pay
off debt. Similarly, the loan frontier result indicate that housing leads the business
39
cycle in areas were the there are less constraints on credit. A lack of credit does
not prohibit getting building permitted, but it does make building the permit
considerably more difficult.
There are reasons to doubt this story though. Even the loan frontier estimates
can be considered plausibly exogenous, these regressions do not mean housing
is the cause of the business cycle. It is perfectly possible that access to credit
simply describes how other drivers of the business cycle manifest themselves in
across throughout the system of cities. For instance, the federal funds rate is set
nationally, and rates on mortgages eligible for GSE guarantee don’t vary across
the country. But the same rates can considerably different effects on different local
housing markets and economies because they interact with variables that do vary
locally. A lot of these variations may be captured in the loan frontier and DTI
variables. That is to say that resident investment and employment may simply be
different aspects of the business cycle that have a clear temporal ordering in some
cities where housing development is relatively easier to undertake because of looser
credit constraints in those cities. This limitation to the study is discussed further
in the concluding remarks.
2.6.2 Spillovers
I now move on to assessing the responses in employment to an innovation in
permits in all the cities besides the one where the shock originated. Tables 2.4 and
2.5 show the mean and standard deviation for each city’s spillovers to the other
77 cities in the sample. As with the within city responses, the results in this table
are calculated using the estimate of the point response in employment after 20
quarters. In most cities the average spillover is relatively small, but with a very
large standard deviation. Indicating that the responses at any given time period
40
follow negative binomial distribution with low means, where there a lot of relative
small and inconsequential spillovers, and a few very large ones to some particular
cities.
A few illustrative examples of the full distribution of spillovers are shown in
figure 2.13. We see that, consistent with what might be suspected from the means
and standard deviations, most spillovers are fairly small, indicated by the high
peaks of distributions close to zero. The mass of all three cities distributions are
very close to zero, but are skewed (right for New York and Houston, left for Los
Angeles), indicating there are a few cities that the spillovers to are very large.
The full dynamic response of employment to an innovation in building to per-
mits is shown for Chicago, Houston, Los Angeles, and New York in figure 2.14.
From this we can see that the responses of cities spillovers generally have the same
direction as the inside city spillovers. That is, if permits lead employment pos-
itively (negatively) within a city, they generally also lead positively (negatively)
outside of the city. This could be useful for reconciling the mismatch between
largely consistent status of the lead-lag relationship at the national level, and its
more murky status at the metro level. It could be that just a handful of cities are
responsible for this relationship. For example, New York has a within city response
of around 20,000 jobs to an innovation in employment. This is a large number,
but looking at it alone ignores that the response is all other cities sums to around
28,000 jobs. So the response to permits in the whole system of cities is actually
48,000 jobs. In Houston the corresponding numbers are 10,000 and 70,000, and
in Chicago they are 8,000, and 30,000. This will be looked at further in the next
subsection.
I next look at what determines the size of a spillover from one city to another.
To do this I first map the spillovers (after 20 quarters) for the same cities as in
41
figures ?? and 2.14. This can be seen in figure 2.15 where the color represents the
value the spillover (red for more positive, blue for more negative), and the size of
each point is the absolute value of the spillover.
The most striking finding in figure 2.15 is that the spillovers do not appear
to be to the closest neighbor of any of the cities. Take Houston for instance;
the spillovers are for New York, Chicago, Detroit, and Los Angeles are all larger
than Dallas, its closet large neighbor. Similar statements can be made about all
the other cities. That the same set of cities receives the strongest spillovers from
most cities indicates that they act as ‘hubs’ of sorts in economic activity, that are
strongly connected with all other parts of the country.
More evidence of this is found in 2.6 that shows the mean spillover and the
mean absolute value of spillovers by city size quintile. Looking at the rightmost
column we see that the regardless of the size of the origin city, the spillovers exhibit
a consistent pattern where the larger cities receive larger spillovers from cities.
To further characterize the connections that determine spillovers between I
regress the point estimates after 20 quarters (those summarized in tables 2.4 and
2.5) on three variables; the physical distance between the two cities, the migration
flow between the two cities in both directions, and the similarity of the cities
industrial compositions
13
. The results for this regression are shown in table 2.7.
The first column uses the spillover as the dependent variable, while the second uses
the absolute value of the spillover.
The results in table 2.7 show that the similarities between cities do not matter
much for determining the direction of the spillover. This is seen in column 1,
where all the coefficients are insignificant. However, different types of distance
13
Industrial similarities are measured by the taking the average squared differences between
each cities employment share in 2-digit NAICS sectors.
42
do matter when we look at the magnitude of a spillover, and ignore its direction.
Physical distance has a counter-intuitive negative effect, the coefficient in column
indicates that for every kilometer further apart two cities are, a shock to permits
in the original city will result in 0.2 more jobs, on average. So for two cities 1000
kilometers apart (roughly the distance between L.A and Salt Lake City), every
new 5 permits in each city will lead to 1 new job in the other. The migration
coefficient indicates that if the city the spillover originated in sends 1,000 to the
other city a year, then there we would expect to see 1 new job in the other city for
every 2 new permits issued in the originator. The industrial distance coefficient
is harder to interpret, but it roughly means that two cities with entirely different
industrial compositions would have a spillover 800 jobs smaller than they would if
their industries were identical.
Looking only at distance measures between two cities ignores the idea that
some cities might be ‘hubs’ that always experience a spillover no matter where
the originates. To look at this, I add the industrial composition, DTI ratio, loan
frontier, average income, average house price, WRLURI score, housing supply elas-
ticity, and population for both cities to the dependent variables in the regressions
found in table 2.7. The results of these regressions are shown in tables 2.8 and 2.9.
The first thing to note in the results is that though physical and industrial
distance more or less maintain their effects on spillovers, migration connections
are no longer significant. So the spillovers that occur are probably not due to
people moving to another city in response to the shock to permits, taking jobs
with them when they move.
Second, the characteristics of the recipient city seem to be the most impor-
tant features for determining the magnitude of the spillover, but not the direc-
tion. Places where a higher proportion of people are employed in construction,
43
manufacturing, and service based industries, tend to be larger recipients of larger
spillovers. Bigger cities, also, will receive bigger spillovers. House prices, housing
supply elasticity, and regulation are not significant. Higher DTI ratios predict a
smaller spillover.
At first glance the importance of a recipient city’s industries seems plausible.
When a house is built, this will not only lead to increases in employment where
the house is built, but also in the places that materials and services used when
building are produced. A house built in Columbia, MO will create some jobs
for local contractors, but it is also most likely financed with a loan from a bank
headquartered in a city like New York that was then securitized in Washington
D.C, perhaps used concrete developed in Houston, etc. This results indicate that
this, ‘all roads lead to Rome’ story, is more likely than the common stories of
diffusion found in studies that look at house price spillovers such as DeFusco et al.
(2013).
An important caveat on this interpretation, however, is that table 2.8 shows
negative coefficients for cities where more people are employed in finance or real
estate meaning that they actually receive smaller spillovers. Why such results
exist is not totally clear, and indicates the need of a more nuanced approach to
determining reasons behind spillovers
Third, the characteristics of the origin city do not do much to determine the
either size of the spillover, but do have a detectable effect on its direction. These
results are, for the most part, the same as those found in table 2.3, only now the
industrial variables are more likely to be significant. Suggest that the direction
of spillover is, like the within city response itself, largely a function of the local
conditions in the city like the loan frontier and debt to income ratios.
44
Overall, the most interesting result here is that some cities may act as ‘hubs’
of sorts in economic activity, that are strongly connected with all other parts
of the country. Furthermore, that the strongest spillovers are in both adjacent
cities and very distant ones indicates that things such as industrial similarities,
migration, and common tastes and preferences could are also potential conduits
that connect cities and transmit spillovers. This indicates that activities such as
monetary policy that stimulate both the economy and the housing market, could
have widely different effects across space. More testing is required to determine
what specifically determines whether is a hub or more isolated. The results at
the moment suggest that the most important characteristics are population and
industrial composition.
2.6.3 Is the National relationship Driven by a Subset of
Cities?
That housing leads the business cycle consistently at the national level, but
inconsistently at the metro level is somewhat puzzling. If different metro housing
markets were truly independent and the relationship was causal, this should not be
possible. This leads us with two possibilities; the first is that in the markets where
the relationship holds are large enough so that the trend shows up at a national
level too. This would imply that metros are independent, and instead that there
is some third initial condition present in those cities that interacts with residential
investment causing a response in employment. The second is that metros are not
independent, and instead that when residential investment rises in one place, the
response in employment is found in other metros. This does not imply that the
relationship is causal, but does not exclude it either.
45
Given previous results in the literature (Ghent & Owyang (2010)) have showed
that national residential investment leads employment even in those cities where
local residential investment does not, and the spillovers I have found, the second of
those scenarios seems more likely. To look more closely at this, I define the cities
where the relationship was found to hold in the above subsection as a particular
region, and those cities where the relationship does not hold as another region
and rerun the GVAR as detailed in section 5. I then look at the impulse response
functions for a shock to each region on all employment in the cities in the sample.
If it is true that the relationship is driven by a particular few cities, then the cities
where the relationship did hold should elicit a positive response, while the cities
that did not should elicit a negative response, or none at all. This is shown in figure
2.16, note that, as before, the response here are cumulative. As expected, the cities
where the relationship held have a impulse response function that is positive, and
large. It shows a marginally decreasing response, similar to the pattern seem in
the individual cities spillovers, that settles into a permanent effect at around 20
quarters. The point estimate of this is between 2 and 2.5 million jobs, however,
the 95 percent lower bound extends down to as low as 200,000. So the estimate is
not particularly precise.
Compare this to the response of the cities where the relationship did not hold.
This is shown by the red lines in figure 2.16. It is clear that at no point is the
response significantly different from zero. This indicates that national lead-lag
relationshipisprobablydrivenbythecitieswheretherelationshipdoesholdhaving
spillovers, where shocks to their permits lead employment in other cities.
46
2.7 Conclusions
Thehousingmarketandtherestofthebusinesscycleshareastrongconnection,
with housing being a leading indicator for other components. Given that there is
great dispersion between different MSAs housing markets, I have used a GVAR to
model this relationship at the metropolitan level and investigated the possibility
of spillovers from housing markets to labor markets.
The GVAR shows that, consistent with previous results in the literature, hous-
ing does not lead employment in every metro area, but only in a subset. For
my sample the relationship is found to hold in 47 of 78 cities. I find that this
mismatch can be somewhat reconciled by accounting for spillovers between metro
areas. That is, I find that in those metros where the relationship holds there is
also a substantial dynamic reaction in other areas employment. Thus, it appears
that the lead-lag relationship at the national level is in fact driven by a handful
of cities, where shocks to residential investment elicit large dynamic responses in
employment across the nation. These responses are even found in cities where
the relationship does not hold. For example, Los Angeles, a city where shocks to
building permits actually have a negative response in employment, is nearly always
the recipient of a positive spillover regardless of the origination city.
The reasons why some cities have housing lead their business cycles but others
appear to be loosely related to geography, and to credit constraints. The latter
indicates that the reason behind the inconsistency across cities is possibility due to
some places having a higher propensity of a building permits actually being built.
However, it could also be possible that lack of credit constraints allow the business
cycle to express itself through housing, that is necessarily invested in before real
economic activity occurs during construction some time later. The paper does not
investigate which of these possibilities is more likely.
47
Another interesting result is that the spillovers between cities are not always
biggest in adjacent cities. In particular, Los Angeles, New York, and Chicago are
among the biggest responders for nearly all cities. This implies both that cities
economies are connected by more than just distance, and raises the possibility
that things biggest cities have diverse industrial compositions that the rest of the
country depends on for such things as construction.
There are important policy implications of these results. Since only some cities
are responsible for driving the relationship between housing, and the rest of the
business cycle this implies that there will be substantial cross regional effects in
bothnationalmonetarypolicy, andmorelocalizedhousingpoliciesandregulations.
There work does have several shortcomings that must be acknowledged. Par-
ticularly, I am unable provide much insight as to whether or not the relationship
is causal. There are reasons to believe that the relationship could be due to the
income tax treatment of residential investment, or the regulatory environment of
housing finance. For example, when tax law gives residential investment special
treatment on things such as accelerated depreciation, or capital gains through
property tax limits, it attracts capital to it. Indeed, Kydland et al. (2012) has sug-
gested that the key connection lies in the 30 year fixed mortgage rate. The only
insight this work does provide on that front is that whatever this condition is must
vary across space. Meaning that the relationship cannot be explained entirely by
something that rests in national policy. In this sense, it may be promising to look
at cross country differences in the relationship between residential investment, and
the business cycle, since this may reveal something that the city level data does
not.
However, the reasons to believe that the relationship is only correlation are
also very reasonable. It could be that housing is simply on the margin because it
48
is durable, after all Leamer (2007) found that other types of durable investment,
such as cars, are also a leading indicator. This again limits the feasibility of policy
implications of work in this area, since without establishing a causal connection
between the two it is not clear whether policy aimed at will actually be effective or
not. At most, the findings of the paper should be viewed as an indication of how
the business cycle will manifest itself across different regions, and that no matter
where the housing market shocks occur, spillovers mean that effects will find their
way back to the large cities that drive the national cycle.
Furthermore, the paper has yet to confirm what characteristics of cities predict
that it will receive a large spillover. At this point, the best we can say is that
characteristics of the origin city appear to determine the direction of the spillover,
and the characteristics of the receiving city determine its magnitude. A more
nuanced approach that the simple regressions run in this paper is likely needed to
pin down exactly what these characteristics are. this will also be a focus in future
versions of the paper.
49
Appendix A: Figures
Figure 2.1: GDP, Residential Investment, and Non-Residential Investment at the
National Level, 1997-2012
−0.2
−0.1
0.0
0.1
0.2
1998 2000 2002 2004 2006 2008 2010 2012
Date
GDP
Res. Investment
Non−Res. Investment
50
Figure 2.2: Permits in Eleven Biggest Metros,1988-2015
−1000
0
1000
2000
3000
1990 1995 2000 2005 2010 2015
Date
City
nyc
la
chi
dal
hou
phi
was
mia
atl
bos
sf
Figure 2.3: Employment in Eleven Biggest Metros, 1990-2015
−50
−25
0
25
50
1990 1995 2000 2005 2010 2015
Date
City
nyc
la
chi
dal
hou
phi
was
mia
atl
bos
sf
51
Figure 2.4: Building Permits, and GDP in Los Angeles, 1990-2010
−0.3
−0.2
−0.1
0.0
0.1
1990 1995 2000 2005 2010
Y ear
Per
Emp
Figure 2.5: Building Permits, and GDP in New York, 1990-2010
−0.2
−0.1
0.0
0.1
1990 1995 2000 2005 2010
Y ear
Per
Emp
52
Figure 2.6: Building Permits, and GDP in San Francisco, 1990-2010
−0.3
−0.2
−0.1
0.0
0.1
1990 1995 2000 2005 2010
Y ear
Per
Emp
53
Figure 2.7: Building Permits, and GDP in Dallas, 1990-2010
−0.1
0.0
0.1
1990 1995 2000 2005 2010
Y ear
Per
Emp
Figure 2.8: Building Permits in Boston, New York City, and Philadelphia, 1994 -
2011
−25
0
25
1995 2000 2005 2010
Y ear
City
bos
nyc
phi
54
Figure 2.9: Building Permits in Los Angeles, San Francisco, and San Diego, 1994
- 2011
−500
0
500
1000
1995 2000 2005 2010
Y ear
City
la
sf
sd
55
Figure 2.10: Building Permits in Los Angeles, Miami, Washington D.C, and Las
Vegas, 1994 - 2011
−1000
−500
0
500
1000
1995 2000 2005 2010
Y ear
City
la
mia
was
lv
56
Figure 2.11: Response of Employment to a 1 S.E shock to Permits, All Cities.
−10000
0
10000
20000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Quarters
Response in Employment
57
Figure2.12: CitieswheretheLead-LagRelationshipHolds(Blue)andCitieswhere
it does not (Red).
20
30
40
50
−120 −110 −100 −90 −80 −70
lon
lat
Figure 2.13: Distribution of Spillovers from a 1 S.E shock to Permits after 10
Quarters in a selection of Cities.
0.0000
0.0003
0.0006
0.0009
0.0012
−5000 −2500 0 2500 5000
Response in Employment after 20 Quarters
Density
City
CHIC917
HOUS448
LOSA106
NEWY636
58
Figure 2.14: Spillovers from a 1 S.E Shock to Permits in Four Largest Cities.
CHIC917 HOUS448
LOSA106 NEWY636
0
10000
0
10000
1 2 3 4 5 6 7 8 9 1011121314151617181920 1 2 3 4 5 6 7 8 9 1011121314151617181920
Quarters
Response in Employment, Thousands
Figure 2.15: Spillovers from a 1 S.E Shock to Permits in Four Largest Cities.
59
Figure 2.16: Response of Employment in All Cities to a 1 S.E Shock to Permits
60
2.8 Appendix B: Tables
Table 2.1: Summary Statistics of the Response Employment to a 1 S.E shock to
Permits after 20 Quarters, All Cities.
N Mean St. Dev. Min Max
Point Response 78 595 4,272 −13,231 22,918
Dummy Response 78 0.603 0.493 0 1
Response to 1 Permit Shock 78 2.42 14.79 −25.13 112.10
Table 2.2: Summary Statistics of the Response Employment to a 1 S.E shock to
Permits after 20 Quarters by Census Region
Region Mean Median SD Min Max
Point Response
Northeast 4,449.175 296.930 7,845.960 -222.910 19,485.460
Midwest 275.501 -46.218 2,384.650 -3,155.236 7,613.285
South 1,009.319 78.293 4,650.572 -7,405.320 22,918.930
West -666.956 185.669 2,972.212 -13,231.590 2,222.843
Dummy Response
Northeast 0.833 1 0.408 0 1
Midwest 0.400 0 0.507 0 1
South 0.625 1 0.492 0 1
West 0.640 1 0.490 0 1
61
Table 2.3: Regressions of within City Response on City Characteristics
Dependent variable:
OLS Probit OLS Probit OLS Probit OLS Probit
(1) (2) (3) (4) (5) (6) (7) (8)
Loan Frontier 4,886.20
∗∗
0.36
∗∗∗
5,978.80
∗∗
0.26
∗∗
(2,195.50) (0.12) (2,992.08) (0.14)
DTI −4,328.80
∗∗∗
−0.03 −9,741.62
∗∗∗
−0.38
∗∗
(1,504.77) (0.17) (2,568.04) (0.19)
Prop Construction −19,332.32 1.80 81,073.75 6.20
(47,486.91) (4.95) (53,053.90) (5.95)
Prop Manufacturing −41,452.56 −2.44 8,522.99 0.29
(44,998.99) (4.69) (48,130.34) (5.39)
Prop Trade 42,558.46 −1.23 111,383.00
∗
2.65
(57,907.19) (6.04) (58,966.92) (6.61)
Prop Finance −30,476.55 −14.99
∗
5,708.88 −10.84
(72,626.79) (7.57) (73,484.96) (8.23)
Prop Real Estate 45,175.10 −10.88 201,445.20
∗∗
−3.54
(70,596.36) (7.36) (81,008.24) (9.08)
Prop Services 6,665.08 0.34 51,789.17 2.36
(41,522.42) (4.33) (42,339.95) (4.74)
Elasticity −231.37 0.004 −327.92 −0.02
(387.31) (0.04) (365.63) (0.04)
Wharton −125.94 0.14
∗∗
−149.42 0.07
(578.68) (0.06) (560.40) (0.06)
House Prices 245.26 0.06 585.09 0.05
(1,210.17) (0.13) (989.94) (0.11)
Constant −21,322.28 −1.38 −7,150.48 2.12 −1,595.26 −0.09 −88,771.86
∗∗
−2.25
(15,589.94) (1.76) (35,948.56) (3.75) (14,220.30) (1.49) (43,670.32) (4.89)
Observations 61 61 78 78 78 78 61 61
R
2
0.10 0.01 0.06 0.13 0.005 0.07 0.23 0.17
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
62
Table 2.4: Summary Statistics of Spillovers from Permits to Employment
City Mean Std. Dev
Albuquerque, NM -86.50458 847.7489
Atlanta-Sandy Springs-Roswell, GA 11.34522 809.2130
Atlantic City-Hammonton, NJ 124.73612 700.5778
Austin-Round Rock, TX 126.11491 756.4561
Baltimore-Columbia-Towson, MD 258.75992 943.5186
Bend-Redmond, OR -375.21036 1188.4450
Birmingham-Hoover, AL 656.93631 1340.1245
Boston-Cambridge-Nashua, MA-NH 948.20969 1330.1801
Charlotte-Concord-Gastonia, NC-SC 183.65085 744.0768
Charleston-North Charleston, SC 80.54406 851.7843
Chicago-Naperville-Elgin, IL-IN-WI 395.86183 776.3000
Cincinnati, OH-KY-IN -465.13223 1013.1053
Cleveland-Elyria, OH -501.55995 1146.3006
Columbia, MO -341.16792 1335.7104
Colorado Springs, CO -350.65355 1107.6324
Columbus, OH -93.94319 519.3398
Dallas-Fort Worth-Arlington, TX -301.17712 1048.2297
Denver-Aurora-Lakewood, CO 269.65613 1067.8010
Des Moines-West Des Moines, IA 308.99835 756.0310
Detroit-Warren-Dearborn, MI -69.82934 798.5872
Durham-Chapel Hill, NC -112.21609 1570.0034
Fairbanks, AK -57.92569 799.3063
Farmington, NM 280.30316 1165.7882
Grand Rapids-Wyoming, MI -682.58890 1034.6986
Greeley, CO -755.25658 1121.7647
Greensboro-High Point, NC -359.60571 954.2729
Houston-The Woodlands-Sugar Land, TX 1126.33627 2086.8781
Indianapolis-Carmel-Anderson, IN -125.64732 675.9441
Jacksonville, FL 140.60718 617.5841
Johnson City, TN 146.12105 734.4702
Kansas City, MO-KS -618.49383 1241.0591
Las Cruces, NM 83.38441 1478.2859
Las Vegas-Henderson-Paradise, NV -121.52502 778.5111
Los Angeles-Long Beach-Santa Ana, CA -473.46856 1132.3642
Louisville/Jefferson County, KY-IN -106.65875 1171.1868
McAllen-Edinburg-Mission, TX 26.13104 1023.0269
Medford, OR 69.06792 868.6539
Memphis, TN-MS-AR -441.41877 1154.0195
Miami-Fort Lauderdale-West Palm Beach, FL 219.82284 500.7187
Milwaukee-Waukesha-West Allis, WI 127.45112 788.6264
Minneapolis-St. Paul-Bloomington, MN-WI 176.69546 615.7743
Missoula, MT -515.73215 820.4533
Nashville-Davidson–Murfreesboro–Franklin, TN -368.28021 725.1262
New Orleans-Metairie, LA 322.42364 798.7447
New York-Newark-Jersey City, NY-NJ-PA 367.62222 767.9606
63
Table 2.5: Summary Statistics of Spillovers from Permits to Employment, contin-
ued
City Mean Std. Dev
Ocala, FL -590.82967 1182.5434
Ocean City, NJ 286.49756 1064.6272
Oklahoma City, OK -209.21387 1557.0437
Omaha-Council Bluffs, NE-IA 285.01835 1305.5851
Orlando-Kissimmee-Sanford, FL -129.42567 1050.6353
Palm Bay-Melbourne-Titusville, FL 508.11034 809.5200
Pensacola-Ferry Pass-Brent, FL 615.81578 1020.6491
Philadelphia-Camden-Wilmington, PA-NJ-DE-MD 201.46448 1163.9119
Phoenix-Mesa-Scottsdale, AZ -605.38813 916.1187
Pittsburgh, PA 36.12025 826.5619
Portland-Vancouver-Hillsboro, OR-WA 98.86769 629.5887
Pueblo, CO 75.08950 999.4793
Punta Gorda, FL 514.23968 1274.5071
Reno, NV -139.61577 602.4797
Richmond, VA 399.00740 973.7698
Riverside-San Bernardino-Ontario, CA 26.26579 1209.1445
Rome, GA 98.47348 812.4426
Sacramento–Roseville–Arden-Arcade, CA -183.05979 1197.3785
Salt Lake City, UT -544.32012 779.5085
San Antonio-New Braunfels, TX -206.32057 1357.3028
San Diego-Carlsbad, CA 122.60866 906.4371
San Francisco-Oakland-Hayward, CA -467.74584 1036.6033
San Jose-Sunnyvale-Santa Clara, CA 302.71018 684.2586
Santa Fe, NM -369.96662 2215.8776
North Port-Sarasota-Bradenton, FL -329.77784 1381.1906
Seattle-Tacoma-Bellevue, WA 522.26830 1305.4519
St. Louis, MO-IL 115.22052 883.3373
Stockton-Lodi, CA -802.84284 1326.3987
Tallahassee, FL -445.24090 1165.9499
Tampa-St. Petersburg-Clearwater, FL 35.66828 704.9328
Tulsa, OK 622.51203 1495.8502
Virginia Beach-Norfolk-Newport News, VA-NC -146.48945 662.1421
Washington-Arlington-Alexandria, DC-VA-MD-WV -443.16427 1274.8921
64
Table 2.6: Spillover Size by Origanating and Receiving City Population Quantile
(1 = Small City, 5 = Big City)
Orig. Pop Rec. Pop Spillover |Spillover|
1 1 15.6943619 64.37947
1 2 4.1483060 126.01432
1 3 -92.9620557 399.95696
1 4 32.8338495 436.98441
1 5 38.3912561 1438.42935
2 1 -17.4617132 69.58373
2 2 -23.4065429 148.75920
2 3 15.0607586 410.57405
2 4 -81.4472047 501.50903
2 5 -288.7613272 1418.75753
3 1 -0.2912726 77.77865
3 2 8.6736943 142.51487
3 3 -12.5771663 410.68195
3 4 4.4223515 489.45795
3 5 21.3659116 1320.39205
4 1 11.3031350 68.91275
4 2 -24.1833919 124.23520
4 3 -61.0267464 367.74027
4 4 -50.7097400 434.73339
4 5 -230.9317577 1214.39336
5 1 8.3725325 80.83920
5 2 16.3648686 151.93280
5 3 76.6845620 438.27147
5 4 80.9969526 574.31839
5 5 327.5039611 1694.75446
65
Table 2.7: Regressions of Spillovers to Employment on ‘Distance’ Variables
Dependent variable:
Spillover |Spillover|
(1) (2)
Physical Distance −0.002 0.037
∗∗∗
(0.012) (0.010)
Industrial Distance 541.454 −1,337.874
∗∗∗
(447.479) (392.356)
Migration Flow 0.116
∗
0.487
∗∗∗
(0.064) (0.056)
Constant −60.781 471.543
∗∗∗
(42.632) (37.381)
Observations 6,796 6,796
R
2
0.001 0.016
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
66
Table 2.8: Regressions of Spillovers on Originating and Receiving City Character-
istics.
Dependent variable:
Spillover |Spillover| Spillover |Spillover|
(1) (2) (3) (4)
Phy. Dist −0.01 0.03
∗∗∗
−0.01 0.03
∗∗∗
(0.01) (0.01) (0.01) (0.01)
Ind. Dist 1,410.09
∗∗∗
−1,178.24
∗∗∗
338.52 −1,597.60
∗∗∗
(467.74) (372.69) (517.52) (415.93)
Mig. Flow 0.13
∗∗
0.05 0.09 0.06
(0.06) (0.05) (0.07) (0.05)
Rec. Construction 84.53 3,824.36
∗∗
984.16 4,209.17
∗∗
(2,314.00) (1,843.75) (2,299.43) (1,848.02)
Rec. Prop Manufacturing −12.14 12,331.75
∗∗∗
112.98 12,495.11
∗∗∗
(1,455.49) (1,159.71) (1,438.66) (1,156.23)
Rec. Prop Trade −3,603.94
∗∗
11,396.60
∗∗∗
−2,857.52
∗
11,617.08
∗∗∗
(1,698.85) (1,353.61) (1,688.29) (1,356.86)
Rec. Prop Finance 1,576.67 −6,136.65
∗∗∗
1,315.62 −6,309.63
∗∗∗
(2,184.82) (1,740.83) (2,164.80) (1,739.82)
Rec. Prop Real Estate −11,168.31
∗∗∗
32,498.22
∗∗∗
−10,816.41
∗∗∗
32,596.40
∗∗∗
(2,543.25) (2,026.42) (2,519.17) (2,024.62)
Rec. Prop Services −1,265.37 7,620.90
∗∗∗
−761.91 7,810.97
∗∗∗
(1,264.04) (1,007.17) (1,255.08) (1,008.69)
Rec. DTI 371.44
∗∗∗
−680.05
∗∗∗
355.74
∗∗∗
−688.67
∗∗∗
(76.42) (60.89) (75.85) (60.96)
Rec. Loan Frontier −7.60 52.77
∗∗∗
12.12 55.36
∗∗∗
(9.25) (7.37) (5.95) (5.37)
Rec. Population −0.001 17.78
∗∗∗
0.23 17.80
∗∗∗
(4.45) (3.54) (4.40) (3.53)
Rec. Wharton −0.22 8.74 −3.57 7.78
(15.99) (12.74) (15.84) (12.73)
Rec. Elasticity 32.53
∗∗∗
−98.15
∗∗∗
30.77
∗∗∗
−97.87
∗∗∗
(11.68) (9.30) (11.58) (9.31)
67
Table 2.9: Regressions of Spillovers on Originating and Receiving City Character-
istics, continued
Dependent variable:
Spillover |Spillover| Spillover |Spillover|
(1) (2) (3) (4)
Orig. Prop Construction 5,228.16
∗∗
3,917.37
∗∗
(2,299.59) (1,848.14)
Orig. Prop Manufacturing −3,177.80
∗∗
2,172.46
∗
(1,438.45) (1,156.06)
Orig. Prop Trade 2,574.88 841.27
(1,688.17) (1,356.76)
Orig. Prop Finance −5,117.19
∗∗
−4,027.33
∗∗
(2,164.24) (1,739.37)
Orig. Prop Real Estate 2,077.48 1,480.04
(2,521.11) (2,026.18)
Orig. Pop Services 2,139.22
∗
175.05
(1,254.16) (1,007.95)
Orig. DTI −460.88
∗∗∗
12.71
(75.85) (60.96)
Orig. Loan Frontier −4.38 −1.41
(8.67) (6.97)
Orig. Population 6.55 1.49
(4.39) (3.53)
Orig. Wharton −64.06
∗∗∗
1.23
(15.84) (12.73)
Orig. Elasticity −52.75
∗∗∗
17.44
∗
(11.59) (9.32)
Constant 1,227.99 −5,802.70
∗∗∗
542.33 −6,141.71
∗∗∗
(1,072.21) (854.32) (1,533.20) (1,232.21)
Observations 6,958 6,958 6,958 6,958
R
2
0.01 0.19 0.03 0.19
Adjusted R
2
0.005 0.19 0.02 0.19
Note:
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
68
Chapter 3
The Durable Hierarchy of
Neighborhoods in U.S.
Metropolitan Areas from 1970 -
2010
3.1 Introduction
Neighborhood change is well-studied. Gentrification, suburbanization, filter-
ing, racial tipping, local economic development, and more broadly, the dynamics
offirmandhouseholdlocationchoiceallhaverichandlong-establishedliteratures.
1
However, there has been little study of what the cumulative, net effects of these
changes are on how households reorganize themselves in response. That is, we rou-
tinely find significant partial equilibrium results in these literatures but generally
do not ask about the larger context in which they occur. To this point there has
been little thorough documentation of just how stable neighborhoods are relative
to each other. Most studies focus on change in a particular variable on interest,
in a particular geographic area, or at a particular point in time, and often with a
1
See Card et al. (2008),Guerrieri et al. (2013),Brueckner & Rosenthal (2009),Rosenthal
(2008),Baum-Snow (2007),Bayer et al. (2007) for just a few examples.
69
specific policy in mind.
2
Indeed, we often go to great lengths to hold constant the
larger context so that we can isolate and identify these individual dynamics. This
is a gap in the literature that we believe this study addresses.
The intent of this research is to provide a broader context for this large and
growing literature on neighborhood change. In particular, we study the opposite
of change, looking at broad patterns in the stability of neighborhoods with regard
to their rank within a metropolitan area. While the long-term stability of the
hierarchy of cities well-established, little is known about how stable neighborhoods
arewithinthem.
3
Welookatmorelocally,atthehierarchyofneighborhoodswithin
metropolitan areas. We make several contributions that address this gap in the
literature.
We find that density begets more density. The Census tract ranks of population
density is consistently the most stable over time. Be it Los Angeles – with 9 million
new residents during our sample period – or Bridgeport, Connecticut – with its
consistent small declines over time – places that were the most dense in 1970
remain the most dense in 2010. But, while population density is broadly stable
over time, variables correlated with human capital (here education, income, and
house prices) are also highly correlated over time. The least persistent are race
and ethnicity, but these relationships appear to change significantly over time.
We document both the level of persistence in the hierarchies of neighborhoods
within metropolitan areas over the last 40 years and the fact that this persistence
is rising. This is true across a diverse set of metropolitan areas. Despite the widely
2
Exceptions to this include Rosenthal (2008) that documents long running cyclical behavior
in neighborhood income, and Lee & Lin (2013) that shows natural amenities (like beaches) can
‘anchor’ a neighborhood so that it remains high income.
3
Gabaix (1999) gives an excellent summary of this insights from this literature.
70
different starting points and shocks over time, the overt regularity that appears is
that stability is the norm.
Interestingly, we find a high degree of spatial correlation in movement among
the hierarchy. That is, when a tract moves up or down within the hierarchy,
those nearby tend to move in kind. This implies that most tract changes within
a metropolitan area are not drawn from a common distribution and instead are
a product of larger shocks that cause new development in large areas of the city.
However, as time goes forward and more cities edge toward stasis, spatial correla-
tion also seems to be subsiding. Collectively, the results that during our sample
period these hierarchies emerge despite extraordinary shocks to urban America.
Once established, these hierarchy exhibit a broad trend toward ossifying.
Consider the evolution of Los Angeles. Over the course of the last 45 years, the
Los Angeles metropolitan statistical area (MSA) grew from less than 10 million
residents to over 19 million residents. The employment base in the Los Angeles
MSA more than doubled from 4.5 million to more than 9 million jobs – adding
approximately the entire labor force of Chicago. New homes, new commercial
real estate, and new freeways were built. A whole new mass transit system was
added. At the same time the nature of the employment base changed significantly,
with wholesale changes in the types of work and workers associated with the long
evolution from traditional manufacturing to a service – and higher-human capital
– economy. But, perhaps the most notable changes were seen in the racial/ethnic
composition of the region. In 1970, Los Angeles county had 1.2 million Hispanic
residents. This grew to almost 5 million in 2010, becoming the largest ethnic group
in the regions.
Despite these extraordinary shocks to fundamentals, the correlation of neigh-
borhood housing price ranks from 1970 to 2010 is greater than 0.60, the rank
71
correlation of income is 0.75, for population density it is a high 0.85
4
. Los Angeles
could easily be described as the most dynamic metropolitan area in the country
over this this period, but much of how it is organized hierarchically and spatially
remains very similar to what it was 40 years ago.
In this paper, we find that this persistence is not unique to Los Angeles and,
in fact, is quite common in US metropolitan areas. For the full sample of 263
metropolitan areas in the US, we find many MSAs at or above these levels of per-
sistence. And, among those that don’t exhibit high rank persistence from 1970
to 2010, we find regular patterns of stability and change within the subsamples.
These include a broad secular trend toward increasing stability over time, partic-
ularly the ranks of race and ethnic concentration. Moreover, we find that when
reordering happens, the changes in Census tract ranks are significantly correlated
spatially. Indeed, in some MSAs we can see a low overall rank stability explained
not by individual shocks across the MSA, but rather by large contiguous neigh-
borhoods that move together up or down in ranking. Around these neighborhoods
of change, there is often a great deal of stability. It is rare to find a single tract
deviate significant from its surrounding tracts.
More generally, these findings should give pause to those considering many
common approaches to analyzing urban and housing markets. We find a great
deal of stability, but certainly not stasis. Change is a given in urban areas, but
we find that a common feature of change is by neighborhood or submarket –
geographies that encompass many Census tracts. It is common for urban phe-
nomena to be studied using these tracts as units of analysis. We find that this
approach may mislead when it may be the case that tracts are not drawn from
4
Our proxy for a neighborhood are 2010 Census tracts. Throughout the paper, tract and
neighborhood are used interchangeably. This is discussed below.
72
the same distributions. Moreover, it is common to use fixed effects or, in the case
of differences-in-differences methods, impose a parallel shift assumption. We find
that these assumptions may be inappropriate in precisely the areas of change we
want to study. Here, neighborhoods are not fixed nor are their positions relative
to other neighborhoods.
There are several likely explanations for why persistence is common and that
it may be increasing over time. In the case of declining MSAs, it could be fixed-
investment. Expanding on the ideas of Glaeser & Gyourko (2005), not only houses,
but commercial real estate and infrastructure are long-lived, influencing metropoli-
tan spatial organization for decades. In growing MSAs, it could be that regulation
pushes new development into places that are already comfortable with higher den-
sity, perpetuating populations density ranks. It could be most shocks are at the
household level which result the households moving up or down the housing hier-
archy, thereby preserving the ranks of house prices, income, or education. Or, it
could be that as MSAs grow the supply of available land for major development
are in increasing lower-quality locations, making it impossible for a new develop-
ment at the far periphery to enter this hierarchy near the top. This discussion of
the causes of stability are left for future research. We discuss these briefly while
summarizing results, but our task here is to document and organize the regularities
we find.
The rest of the paper proceeds as follows: we begin by placing this research
among the several literatures that touch it in Section 3.2. We discuss how we
chose “hierarchy” as an organizing framework and introduce how we measure it
in Section 3.3. In Section 3.4, we document a broad set of tendencies within
and across U.S. metropolitan areas. We conclude with some suggestions for paths
forward in Section 3.5.
73
3.2 Urban Stability & Change
Our pivot from focusing on neighborhood change to the stability of neigh-
borhood hierarchy falls into several literatures. An obvious starting point echoes
the literature on path dependence and the system of cities. It addresses natural
advantages from the distant past as important determinants of the characteristics
of cities, even after they become obsolete Arthur (1989); Bleakley & Lin (2012);
Cronon (2009); Ellison & Glaeser (1999). Beyond these, studies on path depen-
dence show a connection between economic growth and such things as early legal
systems (La Porta et al. (1998)), constitutions (North & Weingast (1989)), and
colonial origins (Acemoglu et al. (2001)). Similar studies have been applied in an
urban context, such as Davis & Weinstein (2002), and Brakman et al. (2004) that
show urban form can persist in cities even after they experience large-scale destruc-
tion that would allow decision makers to re-optimize land uses. The division of
Germany resulted in a permanent diversion of air traffic from Berlin to Frankfurt
(Ahlfeldt et al. (2015)), temporary reductions in the market for cotton during the
U.S Civil War had persistent effects on British towns that were heavy producers
(Hanlon (2014)). And, both Jedwab et al. (2015) and Brooks & Lutz (2013) finds
that rail facilities create changes in urban form and density that remain even after
those facilities are long gone.
Within metropolitan areas we certainly turn to Tiebout (1956) and the enor-
mousliteraturethatgrewfromit. Whileweappealtoalargerbundleoflocalgoods
and amenities, public goods are among them. Equally relevant is the quality-of-life
literature Roback (1982) address wages and house prices to understand location
specific amenities such as beaches or good weather. These bundles have emerged as
a result of extensive sorting. It is this sorting that may act as the most important
underlying cause of stability over time.
74
Another area in which the these literatures are related is Glaeser & Gyourko
(2005), who show that urban growth is rapid process, but decline is slow because
housing is durable. And indeed, we find that population growth, but not decline
is associated with lower rank correlations for all variables. For our purposes, these
paperssuggestacommonstructureintermsofthequestionsbeingasked. However,
we ask them of Census tracts within metropolitan areas.
Others look at contributing factors that lead to neighborhood change or sta-
bility. Redfearn (2009) documents the lasting explanatory power of significant
locations within Los Angeles. He shows that these maps almost 100 years old
can better explain the current organization of employment than do highway inter-
sections. He finds very high levels of persistence in the density of employment
spanning decades. Aaronson (2001) uses a VAR to look at race and income per-
sistence, finding racial composition is highly persistent and that income and racial
sorting are independent of each other.
Other types of papers discuss stability and change but along more narrow
dimensions. Bayer et al. (2007) finds that schools have a direct and indirect impact
on housing prices. Good schools attract households that offer other socioeconomic
benefits to the neighborhoods, suggesting correlation among human capital vari-
ables. Ellen & O’Regan (2008) looks at the stability and change of poorer neigh-
borhoods in urban areas. Though from different perspectives, both Boustan &
Margo (2013) andBaum-Snow (2007) look at a broad pattern of suburbanization.
And there is now a growing literature on gentrification as households seem to
be rediscovering urban living Kolko (2007); Guerrieri et al. (2013); Vigdor et al.
(2002). Indeed, the literatures around these and others are quite large. Collec-
tively, these represent precisely why we pursued stability more generally – each
of these papers are successful research efforts aimed at finding robust results on a
75
particular question, issue, or geography. All require careful control of the larger
context, but none address that context in any depth.
Onelastadditionalliteraturethatwerefertosomewhatisincomemobility. Our
motivationforlookingatneighborhoodstabilityisthussimilartothosestudiesthat
look at income mobility. Income mobility is generally regarded as an important
issue because a person’s income significantly impacts their well-being. Likewise,
given the existence of neighborhood effects, we should also care about the mobility
(or stability) of neighborhoods too. Thus, our measures for neighborhood stability
mirror measures of income mobility found in studies such as Chetty et al. (2014),
andDahletal.(2008), wheretherankofachild’sincomeisregressedontherankof
their parents income to identify the correlation between a child and parent relative
positions in the income distribution. We measure persistence, simply the converse
of mobility, by finding the correlation between a neighborhoods within-city rank
in one time period with its within-city rank in another time period. Since ranks
are relative they avoid issues of interpreting the change in levels between Censuses
that allows for much easier comparisons across time.
5
We are hopeful that our focus on aggregate stability may be useful for learning
more about specific dynamics. For example, filtering/cycling and tipping make
strong predictions about rank stability. In the case of filtering works such as
Brueckner & Rosenthal (2009) and Rosenthal (2008), describe neighborhoods as
undergoing long cycles where new housing starts off having a high value, and as it
depreciates the neighborhood filters down into a lower class neighborhood. This
process of filtering continues until a minimum value is reached at which redevel-
opment begins anew. This would be manifest in the ranks over time, wherein low
5
We have experimented with levels rather than ranks and found essentially the same qualita-
tive results. See Appendix A for some examples.
76
ranked tracts jumped to much higher rankings while the rest of the tracts slowly
declined with depreciation until it was their turn to be redeveloped. We find no
evidence of this process at work in describing macro-level changes in the arrange-
ment of neighborhood hierarchy. This does not mean that this process of cycling
is not happening, but that it is happening parcel by parcel, and in likely situations
in which the new housing isn’t built to significantly surpass the local market for
housing given its location.
Tipping may be more famous example of a particular urban dynamic
(e.g.Schelling (1969). Card et al. (2008) and others invoke various measures of
neighborhood ’tolerance’ to different types of racial compositions, while others
add human capital Redfearn & Ethingtion (2014), and income Malone (2016) as
additional factors that influence rapidly changing neighborhoods. All three of the
cited papers find significant tipping, but the two latter papers look at tipping’s
relevance with regard to the larger evolution of their MSAs in question. Neither
find that tipping was a regular factor in explaining the vast majority of urban
change along other dimensions.
The results do not deny the significance of the myriad micro-structures at work
in individual firm and household location choice. Quite the opposite, our goal is
to understand how all of these individual dynamics aggregate to the metropolitan
arrangement of economic activity. Despite the many good papers on changes,
stability is a dominant theme that warrants closer inspection.
3.3 Measuring Hierarchy & Its Persistence
Since a chief goal of this work will be to provide a broader and more holistic
view of neighborhood persistence and change than has generally been provided in
77
the literature up to this point, we use a wide range of variables to examine neigh-
borhood change and persistence. The list includes household income, house prices,
population density, share of people over age 25 with a bachelors degree, percent
white, percent black, and percent non-white Hispanics. For all these variables, we
use two measures to document their persistence. For long-term stability we use
the correlation between a neighborhoods within metropolitan rank in 1970 and
within metropolitan rank in 2010 (or, equivalently, the correlation between per-
centiles). For short-term stability, we use rank correlations over 10-year periods
(for example, the correlation between a tracts’ rank in 1970 and 1980).
A key challenge in this investigation is how to measure neighborhood persis-
tenceandchangeinawaythatisgeneralizableacrossdifferentvariablesobservedin
different times and places. Any empirical investigation into neighborhood change
will inherently be looking at the same neighborhoods across multiple time periods,
so we use the Neighborhood Change Database to hold geography constant over the
five Census years from 1970 to 2010
6
.
Several variables in our data have consistent support over time (from 0 to 1,
for the race/ethnicity, and unemployment variables), but others do not. The other
variables have distributions that can shift over time, making comparisons difficult.
Consider the meaning of a college degree over the last 40 years. In 1970, the
proportion of college graduates of people aged over 25 in the United States was
0.11, by 2010 this number had increased to 0.31. As such, looking at the change
in people with a bachelor degree outright in a particular neighborhood may not
give the most useful view of how the place is changing, since it does not take
6
The Neighborhood Change Database is a Propriety database from Geolytics Inc. It covers all
censuses from 1970 to 2010, giving tract level data that has been normalized so that the unit of
observation is the 2010 census tract, regardless of what year we are looking at. More information
on the data can be found on Geolytics website:www.geolytics.com
78
into account how other neighborhoods are changing. The same could be said for
looking at a characteristic like mean tract income or house price, both of which
are in nominal terms, and rise both with inflation and local supply and demand
fundamentals.
In order to take into account the broader context of change, we consider the
position of a neighborhood relative to other neighborhoods. As is common in the
literature, we assume that a metropolitan area constitutes a housing market, and
only consider neighborhoods relative to those in the same city. For example, in the
case of income, the neighborhood with the highest average income would receive
the rank 1, the neighborhood with the second highest income would receive the
rank 2, and so on. We denote this as R
ic,t
; where the i, c, and t subscripts denote
theneighborhood, thecityitisbeingrankedwithin, andforwhatyearrespectively.
Using the ranks, we can then create a measures of how a neighborhood moves
within a metropolitan area over time. The one we use the most is the correlation
between a neighborhoods income rank in 1970,and its income rank in 2010. The
correlations can be interpreted as measure of persistence (and conversely mobility
or change), that takes into account the broader context of how the other neigh-
borhoods within a metropolitan area are changing as a whole.
Using ranks certainly provides a strong measure of metropolitan-level persis-
tence and change, but it does have disadvantages too. It is not directly comparable
across metropolitan areas, since the rank cannot exceed the amount of tracts in
the metro area. Being ranked as the 100th richest neighborhood in Los Angeles, a
city with 2929 Census tracts is actually a higher position in the city distribution
than, say, being ranked 10th in Santa Cruz, CA; a city with only 53 Census tracts.
79
To get around this issue the percentile of the tract within the city distribution can
be used. This can be computed as:
P
ic,t
= 1−
R
ic,t
N
c,t
(3.1)
whereP indicatesthepercentileofneighborhoodi, withincitycintheyeartandN
the total number of Census tracts in cityc in yeart. A neighborhood’s percentile is
directly comparable across cities, so we can more fully use the panel capabilities of
data on neighborhoods that has normalized boundaries. Such a capability is being
able to compute the variance, V (P
ic,t
), or change of an individual neighborhoods
percentile, ΔP
ic,t
=P
ic,t
−P
ic,t−1
, across time.
There is one caveat to the use of percentiles; changes in the denominator, N
c,t
of equation 3.1 can produce non-meaningful shifts in the percentile. This is a
prevalent issue from 1970 to 1980; between these two Censuses, 5945 of the 2010
geography tracts went from being uninhabited to having non-zero populations.
This can substantially move a neighborhood’s percentile even when its rank has
not changed, especially in smaller cities. As an example of the problem, suppose
we have a city with 10 tracts in 1970, and that this doubled in 1980 to 20; if a city
was ranked 1st in both decades its percentile would shift from 0.9 to 0.95. This
does not exclude the use of percentiles to analyze neighborhood persistence and
change, but it is an important fact to keep in mind.
3.4 Metropolitan Area Stability
We begin with simple summary correlations for eight case study metropolitan
areas. There are Bridgeport (CT), Charlotte (NC), Detroit (MI), Houston (TX),
Indianapolis (IN), Las Vegas (NV), Los Angeles (CA), and Philadelphia (PA).
80
We chose these eight MSAs for their diversity, spanning small and large, growing
and shrinking, constrained and unconstrained, etc. The goal of this section is to
give some understanding of what the correlations mean. In particular, we want to
demonstrate the many ways a high and low rank persistence can be achieved.
Table 3.1 reports on the level of stability for our eight case MSAs with regard
to “Human Capital” variables – population density, education, house prices, and
income.
7
While population density is not inherently about human capital, we
have begun to see downtowns where population density is highest as places that
are attracting high human capital households.
The rank of population density is clearly the most stable of all the variables and
across all the eight MSAs. Bridgeport is small and has been losing population for
40 years. There is little new development in downtown, and what new housing has
been built is done on larger lots at the periphery. Los Angeles on the other hand
has added millions of residents and dwellings, but the rank stability with regard to
density is not too dissimilar from Bridgeport’s. Detroit’s populations has halved
during this sample and yet it’s rank stability with regard to population density is
the same as Los Angeles’. Houston and Charlotte are the exceptions. It may be
that these reflect their particular types of growth – with ample land in the case
of Charlotte and little regulation in the case of Houston. This will be discussed
below.
The other three variables reflect somewhat different patterns. Here, Los Ange-
les, Philadelphia, and Bridgeport share high long-run rank stability. But, the
others change more, with Charlotte and Las Vegas showing whole sale reordering
7
Population density is defined as the tract population divided by the land area of the tract,
education is measured by share of adults in the tract who have a college degree, house prices
are the tract mean house price according to self-reported census data, and income in the average
family income for the tract.
81
Table 3.1: Rank Correlation for 1970 - 2010 in 8 Cities, Human Capital Variables
MSA Density Education House Price Income
Bridgeport 0.956 0.912 0.870 0.920
Charlotte 0.601 0.232 0.046 0.193
Detroit 0.820 0.673 0.537 0.623
Houston 0.593 0.446 0.325 0.270
Indianapolis 0.798 0.578 0.380 0.455
Las Vegas 0.519 -0.035 0.077 0.143
Los Angeles 0.848 0.790 0.644 0.756
Philadelphia 0.953 0.771 0.689 0.705
of the ranks in house prices. In these MSAs, education and income also show little
persistence. The remaining MSAs show somewhat high persistence over a period
of marked change for all of them.
Table 3.2 reports on the level of stability for three racial and ethnic variables.
The rank of black share within an MSA’s Census tracts is the most stable of the
three, with whites showing some rank stability and Hispanic show little except in
Los Angeles.
Table3.2: RankCorrelationfor1970-2010in8Cities, RacialandEthnicVariables
MSA Black White Hispanic
Bridgeport 0.633 0.709 0.529
Charlotte 0.150 0.088 0.114
Detroit 0.400 0.462 0.141
Houston 0.301 0.260 0.206
Indianapolis 0.578 0.607 0.288
Las Vegas 0.242 0.296 0.382
Los Angeles 0.453 0.527 0.600
Philadelphia 0.546 0.531 0.227
To give some understanding of what these rank correlations look like, look at
Figure 3.1. These figures show Bridgeport’s rank of population density in 1970
82
on the x-axis and the same for 2010 on the y-axis. The dotted 45 degree line
is echoed in the data and the smoothing spline in solid black. That is what a
96 percent rank correlation looks like. The upper right panel plots Houston’s 37
percent correlation of ranks for black shares of Census tracts in 1970 and 2010.
There is some concentration in the upper right where suggesting that the highest
concentration of blacks in 1970 remained the most highly concentrated 40-years
later. But, moreinterestinginthispanelistheverticallinetotheright. Thisshows
what new growth looks like. Here, the dots along the vertical line were places that
had no blacks in 1970. 40 years later these place have added a wide variety of
households, some have high shares of blacks, others don’t. But, these tracts begin
to hint at where the low overall stability may be found. The lower left panel shows
education persistence in Los Angeles. The smoothing spline closely follows the 45
degree line, but the data points suggest something far from highly stable as each
dot off the 45 degree line reflects changes in rank. Finally, Charlotte’s house price
ranks in the bottom right panel suggest no correlation.
Collectively, these exhibits would not surprise many, except perhaps Los Ange-
les and Detroit. Las Vegas, Houston, and Charlotte are places of growth and
change. Indianapolis, Bridgeport, and Philadelphia are different places in many
ways, but both have been relatively stable in terms of population – and without
large shocks, maybe there is little incentive to remake these hierarchies. Los Ange-
les and Detroit are more surprising because they have both had large shocks – one
negative, one positive – but the two share some common stability.
We next push deeper into the analysis that will help push past common wisdom
about these broad stories above. We start with Table 3.3. This repeats the same
table above but reports the correlation decade by decade. Cases where the cor-
relation dropped by 0.05 or more from the previous decade are underlined. Once
83
Figure 3.1: Illustrating What High and Low Rank Stability Looks Like
again Bridgeport matches expectations – little changes in any period for any of
the human capital variables, just as it did for the 40-year correlation. Among
the other more long-term stable MSAs, Detroit, Los Angeles, and Philadelphia all
report consistently high correlations for all the human capital variables. But, note
the decade-by-decade correlations among the other. Here Charlotte, Houston, and
Indianapolis all have many periods of marked stability. Indeed, Houston appears
to be sorting itself out after an economic/housing boom in the 1970s, but from
1980 on, the rank stabilities are all quite high. Indianapolis appears to be same but
for it being somewhat rearranged by the housing boom and bust in the 2000s. Las
Vegas and Charlotte, which both experienced significant growth and development
exhibit a general trend toward more stability decade by decade for all variables
but density.
It is here we see one of the surprising trends from this diverse set of MSAs.
There appears to be a broad trend toward rank preservation over time. Of 96
84
Table 3.3: Decade by Decade Rank Correlations in 8 Cities, Density and Human
Capital Variables
MSA Variable 1970-80 1980-90 1990-00 2000-10
Bridgeport Education 0.963 0.970 0.973 0.972
Bridgeport Density 0.986 0.996 0.995 0.985
Bridgeport Income 0.945 0.963 0.968 0.971
Bridgeport House Price 0.930 0.974 0.987 0.941
Charlotte Education 0.701 0.814 0.844 0.878
Charlotte Density 0.973 0.974 0.910 0.871
Charlotte Income 0.666 0.807 0.831 0.852
Charlotte House Price 0.586 0.769 0.874 0.709
Detroit Education 0.815 0.923 0.913 0.926
Detroit Density 0.960 0.983 0.982 0.959
Detroit Income 0.816 0.912 0.907 0.919
Detroit House Price 0.813 0.941 0.917 0.899
Houston Education 0.664 0.900 0.913 0.900
Houston Density 0.909 0.933 0.963 0.913
Houston Income 0.588 0.863 0.890 0.880
Houston House Price 0.557 0.871 0.900 0.826
Indianapolis Education 0.844 0.921 0.951 0.923
Indianapolis Density 0.978 0.983 0.972 0.958
Indianapolis Income 0.780 0.911 0.934 0.886
Indianapolis House Price 0.802 0.914 0.906 0.848
Las Vegas Education 0.672 0.685 0.729 0.736
Las Vegas Density 0.905 0.955 0.889 0.741
Las Vegas Income 0.637 0.700 0.649 0.785
Las Vegas House Price 0.638 0.771 0.740 0.754
Los Angeles Education 0.903 0.933 0.952 0.949
Los Angeles Density 0.949 0.967 0.984 0.952
Los Angeles Income 0.901 0.944 0.928 0.912
Los Angeles House Price 0.851 0.891 0.893 0.785
Philadelphia Education 0.889 0.944 0.951 0.939
Philadelphia Density 0.988 0.991 0.993 0.992
Philadelphia Income 0.883 0.932 0.938 0.917
Philadelphia House Price 0.891 0.956 0.954 0.898
possibilities in table 3.1, only 10 show a decline of 0.05 or more from decade to
decade. Such drops only exist for House Prices and Density, so are probably due
85
the massive amounts of development and house price fluctuations during the boom
and bust in the 2000s.
It is interesting to contrast the human capital variables with the racial and
ethnic variables using the same decade-by-decade format. There is broadly more
variation in rank correlations here than in the previous table, but the movement
toward more stability is more clear. With the exception of Las Vegas, every one of
the variables and MSAs show monotonically increasing rank stability over time.
Table 3.4: Decade by Decade Rank Correlations in 8 Cities, Racial and Ethnic
Variables
MSA Variable 1970-80 1980-90 1990-00 2000-10
Bridgeport Black 0.762 0.838 0.887 0.933
Bridgeport Hispanic 0.605 0.791 0.841 0.923
Bridgeport White 0.809 0.863 0.916 0.957
Charlotte Black 0.700 0.748 0.879 0.895
Charlotte Hispanic 0.156 0.118 0.270 0.701
Charlotte White 0.698 0.720 0.873 0.889
Detroit Black 0.582 0.782 0.817 0.903
Detroit Hispanic 0.241 0.380 0.458 0.628
Detroit White 0.625 0.846 0.853 0.934
Houston Black 0.515 0.836 0.923 0.912
Houston Hispanic 0.578 0.816 0.894 0.923
Houston White 0.516 0.862 0.926 0.898
Indianapolis Black 0.662 0.852 0.894 0.916
Indianapolis Hispanic 0.259 0.330 0.345 0.704
Indianapolis White 0.697 0.886 0.899 0.933
Las Vegas Black 0.524 0.714 0.640 0.606
Las Vegas Hispanic 0.631 0.620 0.729 0.787
Las Vegas White 0.545 0.720 0.588 0.713
Los Angeles Black 0.633 0.823 0.827 0.893
Los Angeles Hispanic 0.838 0.931 0.959 0.963
Los Angeles White 0.720 0.915 0.926 0.930
Philadelphia Black 0.825 0.903 0.865 0.932
Philadelphia Hispanic 0.338 0.486 0.562 0.757
Philadelphia White 0.810 0.898 0.886 0.940
86
While these broad trends are revealing, they mask how change occurs. That
is, ranks could be shocked randomly. But, we could not use rank correlation to
differentiatetheserandomshocksfrom, say, aprocesslikefiltering/cyclingifitwere
driving the reordering of Census tracts. In Figure 3.2 we plot the distribution of
rank changes in percent. If shocks were just noise, we’d see a familiar bell curve.
If, on the other had filtering/cycling were at work alone á la the sawtooth pattern
in Brueckner & Rosenthal (2009) and Rosenthal (2008), we’d see asymmetry in the
distribution of changes in rank: many small changes in rank moving down and then
a big move up in rank as redevelopment occurs. This is not apparent in any MSA
we examine. But, note that this does not deny that the long-cycle of depreciation
and redevelopment is at work. Rather, this points out that the micro-dynamics at
work in the larger literature on neighborhood change focuses on margins, not the
cumulation of them.
Figure 3.2 shows just how different are the patterns of change are among the
different MSAs. This figure is for changes in house price rank with the frequency of
change along the y-axis; the magnitude and direction of changes are on the x-axis.
Clearly, there are differences among the distributions of change. None of the distri-
butions are normal. Some are close to symmetric, many are far clearly asymmetric.
The patterns that are consistent are the three sharper peaked distributions are the
“stable” MSAs – Los Angeles, Bridgeport, and Philadelphia. Charlotte, Houston,
and Las Vegas are asymmetric blobs. Las Vegas shows a pronounced skew to the
left.
But it would again be premature to see the “unstable” MSAs as being evidence
that there is little stability even among the MSAs with high-variance distributions.
Figure 3.3 shows the decade-by-decade distributions of change look. The “blob”
that was the distribution in the previous figure has these four as the steps along
87
Figure 3.2: Distribution of % Change in Rank of Census Tract for House Price
Bridgeport−Stamford−Norwalk, CT Charlotte−Concord−Gastonia, NC−SC
Detroit−Warren−Dearborn, MI Houston−The Woodlands−Sugar Land, TX
Indianapolis−Carmel−Anderson, IN Las Vegas−Henderson−Paradise, NV
Los Angeles−Long Beach−Anaheim, CA Philadelphia−Camden−Wilmington, PA−NJ−DE−MD
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
−1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0
Change in Percentile, 1970 − 2010
Density
88
the way. They show three highly stable and clearly peaked distributions and only
one that is not. It seems that Houston’s hierarchy was forming in 1970s, but after
that first wave of change (via new development) the hierarchies began to ossify.
Figure 3.3: Distribution of Education Percentile Changes in each Decade, Houston
1970−1980 1980−1990
1990−2000 2000−2010
0
2
4
0
2
4
−1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0
Change in Percentile, 2000 − 2010
Density
These figures and tables are all drawn from the eight case study MSAs. We
examine the same trends among the full 263 MSAs in our sample. The first of
these is shown in Figure 3.4. The scale compresses the results, but make a larger
point about stability. The rank stability of population density among the full set
of MSAs is very high. Rank stability for education and income show a broad
trend toward higher stability over the full sample of MSAs. Only house prices
are an exception. And, here, the exception only in the final period from 2000 to
2010, during which America experienced it’s largest housing bubble and bust in
generations.
89
Figure 3.4: Densities of Rank Correlation in Each Decade for all Cities, Human
Capital Variables
Density Education
House Price Income
0.0
2.5
5.0
7.5
10.0
0.0
2.5
5.0
7.5
10.0
0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0
Rank Correlation
Density
Period
1970 − 1980
1980 − 1990
1990 − 2000
2000 − 2010
90
Figure 3.5 makes clear the trend toward more rank stability. All three variables
start with a smaller modal rank correlation than the other variables, and all three
of them show marked movement in the distribution of rank correlations to the
right - toward more stability.
These results document stability as a regular feature of urban areas. At some
level, these regularities are obvious. We know that the street grid in downtown
Boston looks similar as it did hundreds of years ago. But, while some features
of urban areas are clearly persistent, we have not looked at how persistent other
features and how pervasive persistence is. Among the older cities of the East
Coast, the stability is not a surprise. New York’s extensive investment in its
subways work to offer a durable locational advantage over others. But, what we
found surprising is the high and rising stability in places that are famous for their
change. Houston is well-known for the absence of zoning. Why would stability rise
to levels that match Los Angeles who is equally infamous for its ability to choke
development? There are number of possibilities. Natural amenities (beaches, hills,
etc), durable fixed investments (houses, roads, etc), regulation, and neighbors (i.e.
endogenousfactorsthatdependonothers)surelyallplayrolesinthis. Findinghow
to weight such factors contributions to stability would be a strong contribution to
the literature and will be be pursued in future companion papers. But it is beyond
the scope of this paper, which is intended to be largely descriptive.
We offer one final set of exhibits on the patterns of stability and change: maps.
The four decade-by-decade distributions of Houston’s change in the ranks of edu-
cation did not display where these changes were occurring. Figure 3.6 shows the
spatial distribution of the changes in rank form 1970 to 2010. Figures 3.2 and 3.3
suggested a “blob” – lots of noise in rank change over the 40-year sample period.
This figure makes immediately clear that “noise” is not the right way to describe
91
Figure 3.5: Densities of Rank Correlation in Each Decade for all Cities, Racial and
Ethnic Variables
Black Hispanic
White
0
2
4
6
0
2
4
6
0.00 0.25 0.50 0.75 1.00
Rank Correlation
Density
Period
1970 − 1980
1980 − 1990
1990 − 2000
2000 − 2010
92
Figure 3.6: Map of Education Percentile Change from 1970 to 2010, Houston
the pattern of change. The right panel shows positive changes in ranks, while the
left panel shows declining ranks. The size of the dot represents the absolute value
of percentile change. The map is best described by ‘neighborhood’ change – not
random shocks to individual tracts. The marked cluster around the city-center in
the reflect a systematic decline in the rank of college graduates there relative to
the ranks elsewhere. Where did the most educated go? Largely to the outer ring
suburbs - to the immediate west and southwest, and to downtown.
Figures 3.7 and 3.8 show that it wasn’t a simple linear process. The 1970s
were a period of much dislocation – many dark blue and brown dots – as Houston
reorganized itself during its oil boom and bust. But in time, the number of signifi-
cant changes in rank declined as the hierarchy ossified. As this has happened, the
percentile changes do appear to become more clustered over time. This is clear
despite a 40-year period in which so much changed and where regulation, lakes,
93
oceans, or hillsides didn’t constrain development. It is here that the notion of a
durable hierarchy seems strongest. Once Houston when through its boom in the
1970s, it established a neighborhood hierarchy that still is apparent today.
Figure 3.7: Map of Education Percentile Change in each Decade, Houston
Even the other two highly “unstable” MSAs – Las Vegas and Charlotte exhibit
distinct patterns of change. Over the full sample, much of the ranks for the seven
variables have changed. But along the way change was highly clustered.
94
Figure 3.8: Map of Education Percentile Change in each Decade, Houston
Recall that by the end of the sample the correlations are systematically higher
and frequently as high as the other MSAs. It is then the that maps show more
randomness in the rank changes. Before that, whole regions within the MSA
appear to experience shared changes to fundamentals – both rises and falls in their
collective ranks. The rise of more randomness is expected if neighborhoods mature
95
Figure 3.9: Map of House Price Percentile Change in each Decade, Las Vegas
and stabilize, then it will be local shocks to tracts around the ossified hierarchy
that we see Las Vegas and Charlotte.
The strength of this spatial correlation can also be measured by modeling the
correlation between any two neighborhoods within a metros percentile change and
their distance from one another. Figures 3.13-3.15 mimic the maps in Figures
96
Figure 3.10: Map of House Price Percentile Change in each Decade, Las Vegas
3.6-??. All 3 cities confirm the basic facts we saw in the maps. Immediately adja-
cent tracts change together with correlations usually around 0.5. The correlation
declines as tracts become further apart and is close to zero by around 10 kilometers
in most cases.
The extent of spatial correlation also appear to declining as time goes forward.
This coincides with our observed increase in stability over the sample period. As
97
Figure 3.11: Map of Income Percentile Change in each Decade, Charlotte
a hierarchy solidifies, cities are becoming less subject to significant reorganization
when met with systematic shocks, and changes in the hierarchy are becoming
smaller. Furthermore, they are more and more looking like random draws from a
shared distribution.
98
Figure 3.12: Map of Income Percentile Change in each Decade, Charlotte
We extend this to our entire sample of 263 metros by running the Moran’s I test
forspatialautocorrelationineachcity
8
. Thisteststhenullhypothesisofnospatial
correlation by comparing the actual value of I against an expected value of I that
8
The specific formula for Moran’s I is I =
n
S0
n
X
i=1
n
X
j=1
w
ij
(x
i
− ¯ x)(x
j
− ¯ x)
n
X
i=1
(x
i
− ¯ x)
2
, where w
ij
is the
weight between observation i and j, and S
0
is the sum of all w
ij
’s: S
0
=
P
n
i=1
P
n
j=1
w
ij
.
99
Figure 3.13: Spatial Correlation in Education Percentile Changes in each Decade,
Houston
−1.0
−0.5
0.0
0.5
1.0
0 5 10 15 20 25
Distance (km)
Correlation
Period
1970 − 2010
1970 − 1980
1980 − 1990
1990 − 2000
2000 − 2010
Figure 3.14: Spatial Correlation in House Price Percentile Changes in each Decade,
Las Vegas
−1.0
−0.5
0.0
0.5
1.0
0 5 10 15 20 25
Distance (km)
Correlation
Period
1970 − 2010
1970 − 1980
1980 − 1990
1990 − 2000
2000 − 2010
is computed by randomly distributing the observed percentile changes of the city’s
tracts that decade 1000 time then taking the average I from these randomizations.
100
Figure 3.15: Spatial Correlation in Income Percentile Changes in each Decade,
Charlotte
−1.0
−0.5
0.0
0.5
1.0
0 5 10 15 20 25
Distance (km)
Correlation
Period
1970 − 2010
1970 − 1980
1980 − 1990
1990 − 2000
2000 − 2010
If the observed value of I is significantly greater than the expected value, then then
movement throughout the hierarchy is spatially correlated.
Figure 3.17 shows the distribution of p-values for this test for all 7 variables
in each decade. Figure 3.16 does the same for entire 40-year period. The trends
we found in our case studies appear to carry over to the entire sample. In each
decade, the overwhelming majority of cities reject the null hypothesis of no spatial
autocorrelation at the 5 percent level (shaded in gray). This is true whether we
look at change over the entire 40 year period or decade-by-decade.
These eight case study MSAs were selected because of the diversity, but all
eight show some convergence toward high rank stability and a high degree spa-
tial correlation. Obviously, there are different fundamentals at works across our
263 MSAs over 40 years, but these patterns are common throughout all of the
metropolitan United States.
101
Figure 3.16: Distributions of P-Values for Spatial Correlation Tests for 40 Year
Percentile Change, All Variables
Black Density
Education Hispanic
House Price Income
White
0
50
100
150
0
50
100
150
0
50
100
150
0
50
100
150
0.00 0.25 0.50 0.75 1.00
p−Value
Count
102
Figure 3.17: Distributions of P-Values for Spatial Correlation Tests in Each
Decade, All Variables
1970−80
Black
1970−80
Density
1970−80
Education
1970−80
Hispanic
1970−80
House Price
1970−80
Income
1970−80
White
1980−90
Black
1980−90
Density
1980−90
Education
1980−90
Hispanic
1980−90
House Price
1980−90
Income
1980−90
White
1990−00
Black
1990−00
Density
1990−00
Education
1990−00
Hispanic
1990−00
House Price
1990−00
Income
1990−00
White
2000−10
Black
2000−10
Density
2000−10
Education
2000−10
Hispanic
2000−10
House Price
2000−10
Income
2000−10
White
0
50
100
150
0
50
100
150
0
50
100
150
0
50
100
150
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
p−Value
Count
3.5 Conclusion
Inthispaperweaddresstheconverseofmostpapersinurbaneconomics. Unlike
these which ask why things change, we ask about the opposite of change. We aim
to understand metropolitan areas and their internal stability over time. While
there is some work on the system of cities, its hierarchy, and its stability, much less
has been undertaken on the persistence of hierarchies within metropolitan areas.
We find that not only are metropolitan hierarchies firmly established, but also
that these hierarchies are becoming more stable over time. Persistence is a strong,
even dominant, feature of U.S. metropolitan areas even as much of the research on
urban topics overlooks this larger context.
103
We find high levels of persistence – and exceptions to it – that are consis-
tent with what we know about change. Metropolitan areas that are lagging with
regard to population growth exhibit more stability than do places that grow faster.
Indeed, the least stable places are those that have the fastest population growth
and had large amounts of redevelopment, such as Las Vegas and Houston. But,
there are many places in which population growth is robust and yet rank stabil-
ity is quite high (e.g. Los Angeles). Where there is change sufficient to cause
reordering of the census tracts within their hierarchies, the change is often highly
spatial correlated. Importantly, those MSAs that do undergo reordering don’t all
experience shocks, rather beyond these spatially correlated shocks, relative ranks
remain stable. This suggests that shocks are not drawn from a single metropolitan-
level distribution. This has important implications for understanding metropolitan
areas.
To the extent that these hierarchies exist, they act to resist change from other
fundamentals. The introduction of a new passenger line that cuts through different
neighborhoods is likely to experience differential responses. But, importantly, a
fixed effect model that would control for omitted variables at the neighborhood
level could be highly problematic when the distributions for the surrounding areas
maybedrawnfromdifferentdistributions. Thisismoretrueof“diff-in-diff”models
that require a parallel shift among the treatment and control areas to recover an
unbiased estimate.
In this paper, we have focused on documenting these regularities and less on
explaining them. In a follow-up paper, we have begun with several simple models
that support the notion of a durable hierarchy. These include an a household-level
set of shocks that induce households to move up or down the hierarchy but oth-
erwise preserve the hierarchy. We also are including the distribution of location
104
qualitiesandthelimitedabilityofdeveloperstocreatehigh-qualitylocations. How-
ever these explorations evolve, this work suggests that there are durable hierarchies
within metropolitan areas that should condition our view of urban phenomena and
give us pause when we pool urban data within a metropolitan area. While they
may share a common labor market and common set of fundamentals, it appears
that housing markets within metropolitan areas have acted to sort locations and
that these there are other fundamentals are at work across them. This should color
the way we view data aggregated to the MSA-level and caution against pooling
simply because of shared membership in a metropolitan area.
There is growing evidence that urbanization is on the rise and that gentrifica-
tion is a more common topic in downtown areas. This would suggest that the rise
of urban hierarchies may be weakening now. But, this would be premature. The
ossification we find pervasive during the period from 1970 to 2010 captured a broad
stability in the spatial organization of types of economic variables. Certainly, it
was not stasis. Where we found changes that led to significant reorganization, it
typically occurred in clusters of tracts – something that appears consistent with
the narratives of gentrification: examples which include the Arts District in Los
Angeles, the Meat Packing District in New York, and Dogpatch in San Francisco.
It will take some time to see whether or not urbanization will lead to wholesale
reorganization of metropolitan areas. If the past is any indication, we might antic-
ipate a consistent stream of shocks to which firms and household respond, but that
most MSAs to retain their same basic spatial structure.
105
3.6 Appendix A: Levels vs. Ranks
Since we are concerned with the hierarchy of tracts in metropolitans areas
the body of the paper uses within MSAs ranks to measure change and stability.
However, the results presented remain regardless of the measure chosen. Tables
3.5 and ?? shows the mean and standard deviations of the correlations for both
ranks and levels. Comparing the means in the table make it obvious that the
rank correlations used in the body of the paper are actually slightly lower on
average than the corresponding correlations using levels. This should assuage any
concerns that the high levels of stability that we find are a artifact of choosing
ranks. Furthermore, the general trend towards stability shown in the paper also
remains as it is clear from the table that when the mean rank correlation rose (or
fell) between decades so did the levels correlation.
106
Table 3.5: Summary Statistics for Rank Correlations and Levels Correlations:
Human Capital Variables
Variable Period Rank Correlation Levels Correlation
Density 1970 - 1980 0.967 0.953
(0.036) (0.069)
Density 1980 - 1990 0.981 0.975
(0.023) (0.027)
Density 1990 - 2000 0.981 0.975
(0.043) (0.06)
Density 2000 - 2010 0.946 0.937
(0.062) (0.08)
Density 1970 - 2010 0.846 0.798
(0.124) (0.154)
Education 1970 - 1980 0.795 0.821
(0.116) (0.142)
Education 1980 - 1990 0.87 0.9
(0.079) (0.065)
Education 1990 - 2000 0.874 0.903
(0.085) (0.072)
Education 2000 - 2010 0.844 0.873
(0.094) (0.095)
Education 1970 - 2010 0.575 0.611
(0.182) (0.172)
House Price 1970 - 1980 0.77 0.8
(0.16) (0.15)
House Price 1980 - 1990 0.856 0.864
(0.139) (0.143)
House Price 1990 - 2000 0.872 0.881
(0.081) (0.113)
House Price 2000 - 2010 0.702 0.733
(0.162) (0.16)
House Price 1970 - 2010 0.318 0.383
(0.239) (0.221)
Income 1970 - 1980 0.753 0.77
(0.152) (0.178)
Income 1980 - 1990 0.849 0.863
(0.088) (0.095)
Income 1990 - 2000 0.838 0.856
(0.095) (0.103)
Income 2000 - 2010 0.821 0.831
(0.101) (0.11)
Income 1970 - 2010 0.499 0.53
(0.204) (0.209)
107
Table3.6: SummaryStatisticsforRankCorrelationsandLevelsCorrelations: Race
and Ethnicity Variables
Variable Period Rank Correlation Levels Correlation
Black 1970 - 1980 0.592 0.815
(0.222) (0.247)
Black 1980 - 1990 0.701 0.855
(0.225) (0.215)
Black 1990 - 2000 0.736 0.829
(0.231) (0.235)
Black 2000 - 2010 0.812 0.862
(0.16) (0.178)
Black 1970 - 2010 0.368 0.562
(0.21) (0.239)
Hispanic 1970 - 1980 0.336 0.439
(0.282) (0.352)
Hispanic 1980 - 1990 0.437 0.547
(0.322) (0.358)
Hispanic 1990 - 2000 0.508 0.583
(0.295) (0.321)
Hispanic 2000 - 2010 0.687 0.761
(0.226) (0.219)
Hispanic 1970 - 2010 0.277 0.295
(0.233) (0.269)
White 1970 - 1980 0.602 0.787
(0.227) (0.242)
White 1980 - 1990 0.762 0.869
(0.18) (0.173)
White 1990 - 2000 0.807 0.874
(0.17) (0.167)
White 2000 - 2010 0.868 0.901
(0.111) (0.119)
White 1970 - 2010 0.4 0.535
(0.207) (0.217)
108
Chapter 4
Index Consistency in the Presence
of Asymmetric Information
4.1 Introduction
Aggregate price measures are derived from a very small amount of information.
In the U.S. single family housing market, for example, only about seven percent
of the existing stock sells in any given year. Challenged by a heterogeneous and
infrequentlytradedgood,researchersturntothecommonly-usedaggregatehousing
price indexes. These begin by pooling sales observations, assuming that each is
drawn from a common distribution and thus that the underlying population mean
can be recovered. This assumption, however, is rarely considered critically in the
common construction of aggregate indexes despite substantial evidence of distinct
housing submarket and significant idiosyncratic price movements across time. Of
course, within a metropolitan area there are a strong shared set of fundamentals
and a common labor market that suggest that pooling data in conjunction with
commonly-used index approaches are appropriate. But, typically-pooled data can
weightsubmarketsthatmaynotberepresentativeofthestockaswholetooheavily.
The correction lies in adjusting the order of aggregation in the construction of
aggregate price indexes.
We refer to indexes that first pool observations and then apply statistical tech-
niques as “global-pooling” indexes. The FHFA and Case-Shiller indexes are the
109
most well-known of this type. To arrive at the price index for Detroit, say, all of
the observed sales within the metropolitan area for a particular quarter are gath-
ered and, after attempting to control for the housing ‘quality’, the average of all
prices forms the index. This is global in the sense that all observations are given
equal weight. The problem with the approach is that it assumes that the sample
of sold dwellings is representative of the housing stock as a whole. If it is not, the
price calculated from the observations - while reflective of the sample - may not be
reflectiveofthe stock. Moreover, additionalobservations fromtheover-represented
submarkets may lead to greater bias, not less.
The solution explored in this paper contrasts “global-pooling” with “local-
pooling.” That is, observations are first pooled within submarkets, indexes are
constructed locally, and then aggregate indexes are constructed by weighting the
local indexes by the share of the stock they represent rather than by their share
of observed sales. An obvious cost to this approach is the noise associated with
the necessarily smaller samples at the local level. Offsetting this is the fact that in
urban areas it is changes in the location premium that drive much of the movement
in house prices.
1
Our approach to local pooling puts a premium on measuring
changes in land and location. This is because housing and amenities are more
homogeneous at smaller geographic levels like census tracts or zip codes. Moreover,
local pooling allows for greater flexibility in estimating hedonic characteristics.
The underlying economic framework for this approach is straightforward.
Tiebout long ago formalized an explanation for diverse public goods within a labor
market. It’s easy to extend the same intuition for local private goods – restau-
rants, retail, etc. These two sets of characteristics define the neighborhoods that
1
Indeed, we learned from the last housing cycle that we didn’t experience a housing bubble,
we experienced a land bubble (see Bostic et al. (2007))
110
are priced into a house. Shocks to different types of households that occupy these
varying neighborhoods allow for clustered housing market behavior: both prices
andtransactionscandeviatesystematicallyfromtherestofothersubmarkets. The
other neighborhoods are substitutes, but imperfectly so. For instance, the increase
in the availability of subprime loans in the early 2000s resulted in lower-end house-
holds having greater access to credit, and in turn bidding up the price of low-end
houses. At the same time sales volumes will reflect that way these households are
adjusting to increased ability to pay. But this shock will not meaningfully prop-
agate to higher income households and their neighborhoods, since their access to
credit is unchanged. Similarly, shocks to particular parts of the income distribu-
tion, immigration, and others will be felt in some areas earlier than others. The
result is that the members in the pool of house sales may not reflect the stock as
whole, yielding aggregate indexes that are biased.
We use two disparate data sets to explore these issues. The first is 3.2 million
sales from DataQuick for the greater Los Angeles metropolitan area, covering all
sales 2000 to 2015. The second is nineteen years of Swedish housing transactions,
numbering over one million raw sales. The two data sets provide an excellent
opportunity to examine the impact that order of aggregation has on estimated
prices as measured by the most commonly used indexes: median, repeat-sale, and
hedonic. Both data sets cover periods of pronounced housing price changes, but
with different contexts behind them. The Swedish data afford us a chance to
examine variation nationally across markedly different metropolitan areas, while
the Los Angeles data allow us to look very locally because each sale is geocoded.
We provide evidence of pervasive idiosyncratic price movements and asym-
metric selection within housing markets. In some cases relative prices rise, as
sale propensities rise yielding over-representation of “winners” and an upward bias
111
in measured aggregate prices; in other cases, the opposite holds. This means
that local dynamics are at odds with the assumptions required for global-pooling
indexes to recover aggregate price levels for the stock as opposed to the sample of
sold dwellings. In the case of Los Angeles locally-pooled indexes show the peak of
the boom is overestimated, and the bust was not nearly as large as in the global
indexes suggest. We also see a stronger recovery in local indexes. These differ-
ences can be traced to fast-appreciating low end homes being over-sampled in the
2004-2008 period when a heavier proportion of loans in the market were subprime
and the housing in the central city being consistently under-sampled. These differ-
ences have large implications for studies of foreclosure, quality of life, and housing
wealth, which rely on aggregate house prices.
The paper proceeds first by addressing formally the order of aggregation in
the presence of idiosyncratic price movement. The data and stylized facts show-
ing asymmetric price appreciation and nonrandom sampling are then discussed
in detail in Section 4.3. Both the Swedish and Los Angeles results are presented
in Section 4.4. In Section 4.5, we outline our interpretation of these results and
discuss extensions.
4.2 Representativeness & Order of Aggregation
This section outlines the essential differences between aggregate price indexes
thatemploylocal-andglobal-poolingintheirconstruction. Global-poolingindexes
are those whose first step in construction is to pool all available observations within
geographic area of interest into a single data set. Typical applications of hedonic,
repeat-sale, and median indexes fall into this category. For this class of index
construction methods, controlling for factors that may be confounded with price
112
appreciation is left to the econometrician. For example, a hedonic index controls
for quality variation explicitly by pricing it and removing it from the estimate of
aggregate prices; repeat-sales indexes difference observations on identical dwellings
to remove quality variation from prices. Regardless of the index type, the data
are first pooled before the application of statistical methods. The argument for
aggregate pooling of observations is simple: each transaction contains information
about the level of prices, and by their accumulation a better understanding (and
more accurate estimation) of aggregate prices will be possible than with any subset
of the available data.
This intuition for “global pooling” is based on the premise that the stochastic
process that guides prices is the same for all dwellings in the geographic area
of interest - measured appreciation for any one dwelling is some mixture of true
aggregate appreciation and noise. In this case, the appeal to the Law of Large
Numbers is appropriate: the sample mean will tend to the true mean as the sample
size increases. Another way of describing this premise is as an assumption of
representativeness with regard to appreciation. So long as this is true any sample
of homes could yield consistent estimates of aggregate prices.
2
There are many plausible reasons why the house price appreciation could be
different across different housing units for reasons other than differences in the
physical structures of houses. Landvoigt et al. (2015) shows that house price
appreciation in San Diego in the first half of the naughts was greater for houses
with initially lower prices, presumably because of the expansion in ‘sub-prime’
2
In this case, “could” refers the usual caveats associated with index construction. Hedonic
indexes, forexample, typicallydependonassumptionsregardingfunctionalformandthestability
of attribute prices across time and space; repeat-sale indexes rely on strong assumptions about
time-invariant attribute bundles and prices. There is an extensive literature on these indexes and
their maintained assumptions. See especially JREFE 14(1-2), 1997 and AREUEA Journal 19(3)
1991.
113
mortgages during the time period. Works such as Genesove & Mayer (2001) and
Anenberg (2011) find evidence that sales prices can differ according to the loan-
to-value ratios on the property due to ‘loss aversion’ (the tendency for people to
strongly prefer avoiding losses to realizing gains). Similarly, Bracke & Tenreyro
(2016) use data on house sales in England and Wales to show that sale prices are
’anchored’ by the price the current owner paid.
Other studies find different rates of appreciation due to demand side factors
such as buyer income (Mayer (1993)) and age (Ortalo-Magné & Rady (1999)).
The Alonso-Muth-Mills model of a monocentric city also indicates gives reason
believe that appreciation could be different depending on how far a dwelling is
from the city center (see Bogin et al. (2016) for empirical evidence of this.). The
elasticity of housing supply could also vary within a metropolitan area, meaning
that even if demand side shifters were homogeneous across all buyers, they would
have different effects depending on where the house is located. This is what this
study will focus on in its empirical applications, where we choose to designate zip
codes as our submarkets.
Perhaps the strongest evidence of distinct local price paths is provided in two
papers on index construction techniques by Meese & Wallace (1991) and Goet-
zmann & Spiegel (1997). The former paper attempts to develop an alternative
methodformeasuringaggregatepricesthatisfreefrommanyofthestrongassump-
tions associated with the hedonic and repeat-sale approaches (assumptions they
find violated). The latter paper presents local index construction methods. Both
find significant idiosyncratic price movement at the local level (municipalities and
zip codes, respectively).
One solution for the global-pooling indexes is to control for non-random selec-
tion. The process, analogous to labor market research by Hausman & Wise (1977),
114
involves modeling the selection process and constructing an additional regressor
that captures the likelihood of inclusion in the observed sample. In principle, this
technique (or non-parametric variant thereof, e.g. Newey et al. (1990)) will pro-
duce price index estimates free of sample selection problems. Only a handful of
applications of this type of approach have been undertaken in the housing litera-
ture, most notably Gatzlaff & Haurin (1997), Englund et al. (1999a), and Hwang &
Quigley (2004). More recently Mason & Pryce (2011) has used a fractional probit
regression to adapt this approach when only aggregated data housing submarkets
is available This difficult approach requires both prices and the selection process
to be modeled accurately.
One solution for the global-pooling indexes is to control for non-random selec-
tion. The process, analogous to labor market research by Hausman & Wise (1977),
involves modeling the selection process and constructing an additional regressor
that captures the likelihood of inclusion in the observed sample. In principle, this
technique (or non-parametric variant thereof, e.g. Newey et al. (1990)) will pro-
duce price index estimates free of sample selection problems. Only a handful of
applications of this type of approach have been undertaken in the housing liter-
ature, most notably Gatzlaff & Haurin (1997) and Englund et al. (1999a). This
difficult approach requires both prices and the selection process to be modeled
accurately.
Hedonic and repeat-sales indexes are employed because the case has been well
made that housing is a heterogeneous good and that quality variation across time
and space can mislead users of less-sophisticated indexes. However, the accuracy of
these more sophisticated indexes depends crucially on the representativeness of the
sample. Typically, representativeness is assumed without verification. Without
more careful consideration of the sample, it is not clear whether the parameter
115
estimates from these techniques are generalizable. If, in fact, selection is non-
random and price appreciation is asymmetric, these indexes will recover only the
quality-controlled price indexes for the observed sample of sold homes but not for
the entire stock.
Once asymmetric price levels are introduced, the appeal to the Law of Large
Numbers does not hold unconditionally. To see this consider the following stylized
model of a unified housing market. In it there are two submarkets, A andB, with
populationsN
A
andN
B
. The stock of dwellings isN =N
A
+N
B
. For the simplic-
ity assume that these populations are constant over time. Furthermore, assume
that dwelling quality is uniform and time-invariant. The issue to be highlighted
in this paper is representativeness with regard to both selection and appreciation;
attribute heterogeneity, while more realistic, serves only to complicate the model
without adding any insight. As such, the usual conception of house prices as
quotient of house prices and dwelling quality,
V
it
=P
t
Q
it
+ε
it
, (4.1)
is simplified. Here, V
it
is the observed sale price, P
t
is the aggregate price level,
and ε
it
is variation in price due to buyer and seller heterogeneity. i and t index
dwelling and time, respectively. Q
it
is the dwelling quality and, for the purposes
of this paper, is assumed to be equal to one. In this homogeneous world, pricing
for individual dwellings in the two submarkets is given by
V
it
=ψ
A
it
+ε
it
∀i∈A (4.2)
V
it
=ψ
B
it
+ε
it
∀i∈B (4.3)
116
where ψ
A
it
∼ (P
A
t
,σ
2
A,t
) and ψ
B
it
∼ (P
B
t
,σ
2
A,t
). This allows prices within each sub-
market to move around a common (within-submarket) trend. Aggregate prices
then are a function of price movements within each submarket. True aggregate
prices are defined as
P
t
=
N
A
P
A
t
+N
B
P
B
t
N
A
+N
B
(4.4)
Selection into the sample of observed dwelling sales may also asymmetric across
submarkets. In this case,π
A
t
andπ
B
t
are the sale probability is submarkets,A and
B, respectively. The observed sample is then
n
t
=n
A
t
+n
B
t
(4.5)
wheren
A
t
=π
A
t
N
A
andn
B
t
=π
B
t
N
B
, the subsamples from each of the submarkets.
Recall that quality-control issues have been taken off the table by assuming a
homogeneous housing stock. Estimated aggregate prices are given by
b
P
t
=
1
n
t
X
i∈nt
V
it
=
1
n
A
t
+n
B
t



X
i∈n
A
t
ψ
A
it
+
X
i∈n
B
t
ψ
B
it
+
X
i∈nt
ε
it


 (4.6)
The error term ε has expectation zero, so
E[
b
P
t
] =
n
A
t
P
A
t
+n
B
t
P
B
t
n
A
t
+n
B
t
(4.7)
If the estimate
b
P
t
is to be unbiased, E[
b
P
t
] must equal P
t
, or
N
A
P
A
t
+N
B
P
B
t
N
A
+N
B
=
n
A
t
P
A
t
+n
B
t
P
B
t
n
A
t
+n
B
t
(4.8)
Let S
A
t
and S
B
t
be the share of the stock represented by the number of dwellings
in submarkets A and B, respectively. Let s
A
t
and s
B
t
be the respective shares of
117
each within the observed sample of sold homes. This yields a slightly different
expression of the same equality in Equation (4.8):
S
A
t
P
A
t
+S
B
t
P
B
t
=s
A
t
P
A
t
+s
B
t
P
B
t
(4.9)
This equality holds under one of two conditions. First, recognize thatS
A
t
= 1−S
B
t
and s
A
t
= 1−s
B
t
. Substituting and rearranging obtains
P
A
t
(S
A
t
−s
A
t
) =P
B
t
((1−s
A
t
)− (1−S
A
t
)) (4.10)
or
P
A
t
=P
B
t
(4.11)
So, any sample - regardless of sample selection - generates a consistent estimate
of aggregate prices when price levels among the submarkets have the same first
moment. This is important but not surprising. Of greater interest is under what
conditions the estimated aggregate price is consistent when price levels are asym-
metric across submarkets. Consider a rearrangement of Equation (4.9):
P
A
t
(S
A
t
−s
A
t
) =P
B
t
(s
B
t
−S
B
t
) (4.12)
IfP
A
t
6=P
B
t
, the equality can hold only if both quantities inside parentheses equal
zero - that is, if the submarket shares of stock and sales are identical. In other
words, if appreciation is not symmetric across submarkets, the sample must be
representative of the stock for global-pooling indexes to be consistent.
This stylized example of housing submarkets highlights a feature of housing
markets often overlooked in empirical research: the extent to which the sample
is representative with regard to appreciation. In other words, by globally pooling
118
observations, bias may increase with the addition of more observations. So long
as there are asymmetric price levels across submarkets, more observations from
an overrepresented submarket will simply bias aggregate prices to those of the
submarket.
A potential solution to the selection problem that doesn’t require as strong
an assumption of representative appreciation is a “locally-pooled” index. The
intuition for local pooling is straightforward and based loosely on the notion of
submarkets. Whileconceptuallyeasy, submarketsarenotoriouslydifficulttodefine
precisely in practice. Rothemberg et al. (1991) dedicate an entire book to the
effort, while Goodman & Thibodeau (1998) may be more representative of ongoing
research in the area. In it, the authors define roughly a submarket to include
dwellings with identical per unit price of housing services and bundles that are
approximate substitutes.
Theroleofsubmarketsinsampleselectionisclear. Inaunitaryhousingmarket,
where all dwellings are perfect substitutes, no two dwellings could have different
prices. Where there is relative scarcity, either in location or attribute bundles,
differencesinpricecanarise. SeeOrtalo-Magné&Rady(1999)forawell-developed
theoretical model of such internal dynamics. Briefly, examples could include a
shock to immigration and changes in the dynamics of “starter” homes, shocks to
equitiescausingasymmetricchangesinhigh-endhomeprices,orwhite-collarlayoffs
resulting in a decrease in price for middle-class housing. At some level, dwellings
within a metropolitan area share common fundamentals due to the competition
for land. This competition for land may place bounds on the divergence between
any two submarkets, but the bounds may be wide with significant idiosyncratic
dynamics across all submarkets.
119
These local dynamics pose problems for the “globally” pooled indexes because
the techniques used to construct them are not well equipped to handle asymmetric
appreciation or non-representative samples. The solution taken in this paper is to
pool observations locally, and then aggregate - not by the share of observations
but by the share of the housing stock in the particular area.
Local pooling can be illustrated by extending the same stylized submarket
example from above. Under this approach, estimated aggregate price levels are
b
P
t
=S
A
b
P
A
t
+S
B
b
P
B
t
=
S
A
t
n
A
t
X
i∈n
A
t
(ψ
A
it
+ε
it
) +
S
B
t
n
B
t
X
i∈n
B
t
(ψ
B
it
+ε
it
) (4.13)
with expectation
E[
b
P
t
] =S
A
t
P
A
t
+S
B
t
P
B
t
(4.14)
This right hand side of this expression is, in fact, the definition of true aggregate
price: local pooling of observations yields an unbiased estimate of aggregate prices
in the presence of asymmetric prices across submarkets.
Ofcourse,thetradeoffmadetoobtainanunbiasedestimateisthenoiseincurred
by smaller samples within each submarket. As ever with submarkets, definition
is part art, part science. For this work, the question is not what constitutes a
submarket, rather it is whether or not moving toward local pooling is appropriate.
Dividing the sample into submarkets unambiguously results in fewer degrees of
freedom at the local level. However, one mitigating factor is the extent to which
local heterogeneity is less than global heterogeneity, which if true reduces the need
for quality-controlled indexes. Moreover, if the number of indexes is large, even
noisy local indexes will produce a consistent estimate of aggregate prices.
120
The estimator for aggregate price level given in Equation (4.13) can be gener-
alized for M submarkets:
b
P
t
=
S
A
t
n
A
t
X
i∈n
A
t
(ψ
A
it
+ε
it
) +
S
B
t
n
B
t
X
i∈n
B
t
(ψ
B
it
+ε
it
) +··· +
S
M
t
n
M
t
X
i∈n
M
t
(ψ
M
it
+ε
it
) (4.15)
The empirical measures of local prices will be measured with error,
b
P
t
=S
A
t
(P
A
t
+δ
A
t
) +S
B
t
(P
B
t
+δ
B
t
) +··· +S
M
t
(P
M
t
+δ
M
t
) (4.16)
whereδ
X
t
ismeasurementerrorinsubmarketX. However, aslongaslocalmeasure-
ment error is noise (i.e., δ
X
t
∼ (0,σ
2
δ
)), the aggregate estimator remains unbiased:
E[
b
P
t
] =S
A
t
P
A
t
+S
B
t
P
B
t
··· +S
M
t
P
M
t
+
X
X∈A..M
δ
X
t
(4.17)
The summation of the errors will approach zero as the number of submarkets
increases.
3
And, therefore, the right-hand side of this expression is once more the
definition of the true aggregate price.
4.3 Data and Stylized Facts
In this section we provide information on the data we used and provide evi-
dence that the two assumptions required for global pooling (that is, symmetric
price appreciation across submarkets and submarket sales shares are the same
as submarket stock shares). The first subsection shows asymmetric appreciation
3
Isn’t the logical conclusion then to treat every dwelling as its own submarket? No, because
omitted dwellings (those that do not sell) represent omitted submarkets. Local pooling, in
principle, requires all submarkets be represented in the sample.
121
amongst submarkets in Sweden from 1981 - 1999. The second subsection shows
that neither assumption holds for Los Angeles over the period from 2000 - 2015.
4.3.1 Sweden
The data used in this subsection consists of 1,000,0000 housing sales in Sweden
from 1981 to 1999. These observations have been compiled by Statistics Sweden
from two sources: tax assessment records–which contain detailed physical charac-
teristics of the dwelling–and sales records, which contain the date of sale, location,
and transaction price. Dwellings are uniquely identified so that multiple sales of a
single unit can be distinguished from those dwellings that sell only once during the
sample period. The tax assessment records include detailed characteristics of the
property which will be used in constructing hedonic indexes, as well as enforcing
the constant quality assumption implied in the repeat sales index. The data also
contain crude information about the buyer and seller so that obvious non-market
transactions can be removed
4
.
Of particular use for this research are the geographic variables. Each observa-
tion is identified by region, county, municipality, and parish. For the purposes of
this paper, submarkets are defined as municipalities - the rough equivalent of U.S.
Census tracts. Some municipalities are quite small. In order to ensure price level
estimates in each municipality for each quarter, only municipalities with at least
three observations in each quarter over the 19 year period are included. Both the
locally- and globally-pooled indexes are based on these data. Table 4.1 reports the
total number of municipalities, the
4
The data are described more completely in Englund et al. (1998) and Englund et al.
(1999b).Since these have been published, the data have been expanded so that they now span
nineteen years, from 1981 to 1999, and approach 1,000,000 observations throughout Sweden.
122
Table 4.1: Municipalities and Mean Observations
Total Total
Total Mean Sales Municip’s Mean Sales Municip’s Mean Sales
Region Municip’s per Qtr. obs≥3 per Qtr. obs<3 per Qtr.
1 26 69.57 21 81.34 5 20.16
2 52 43.45 43 50.80 9 8.35
3 35 37.59 31 41.64 4 6.15
4 51 42.88 25 62.95 26 23.59
5 91 28.64 20 68.61 71 17.38
6 41 33.48 34 37.87 7 12.13
7 15 38.49 10 51.81 5 11.83
8 29 26.17 16 42.12 13 6.53
number of municipalities above and below the 700 threshold, and the mean
number of sales per quarter. The table makes clear that many municipalities have
too few observations for the construction of local price indexes. Future work will
include these observations by pooling adjacent municipalities.
Recallthediscussionaboveregardingtheconditionsunderwhichglobal-pooling
indexes were able to recover population parameters from the sample of sold
dwellings. There were two: either the submarkets share uniform price processes or
the relative proportions of submarket sales in the observed sample reflect those of
the housing stock. The paper uses two crude means to identify submarkets; again
the focus is on representativeness. The first is illustrative of submarkets based on
attribute bundles, the second is based on location. Both approaches result in the
123
same interpretation and both should serve to demonstrate the difference between
global- and local-pooling.
Consider the following ad hoc taxonomy of housing markets. Dwellings are
divided into five submarkets based on the results of a hedonic regression. The
regression includes characteristics related to size (lot size, living area, number of
garages) and to quality (kitchen quality, the presence of a recroom, sauna, tiled
bath, etc). The regression results allow the dwellings to be ranked by their overall
size and quality (by interacting the respective regression coefficients and attribute
values). From these indexes, the sample can be divided into submarkets. For the
purposes of illustration, the following discussion uses five submarkets: small/low-
quality, small/high-quality, large/low-quality, large/high-quality, and medium size
and medium quality (referred to as “mid/mid”).
For Region 1, the greater Stockholm area, Figure 4.1
Figure 4.1: Relative Price Appreciation by Submarket - Stockholm
Relative Price
1985 1990 1995 2000
0.85 0.90 0.95 1.00 1.05 1.10
Small, Low Qual
Small, High Qual
Large, Low Qual
Large, High Qual
Mid Size, Mid Qual
124
demonstrates the violation of the first condition under which the global-pooling
indexes may be consistent. It shows the relative price levels of the first four sub-
markets relative to the medium-size/medium-quality submarket based on hedonic
price indexes constructed using only the sales from each submarket. It is clear
from this figure that the submarkets do not share identical price processes. Stan-
dard errors are not shown, but the null hypothesis that they do share the same
processes can be rejected at the one-percent level.
Given asymmetric price processes, global-pooling indexes can still be consistent
if submarket shares in the observed sample match their shares in the housing stock.
Figure 4.2 demonstrates
Figure 4.2: Relative Composition of Observed Sample - Stockholm
Year
Relative Observations
1985 1990 1995 2000
0.6 0.8 1.0 1.2 1.4
Small, Low Qual
Small, High Qual
Large, Low Qual
Large, High Qual
Mid Size, Mid Qual
that for the case of Stockholm, this condition does not hold. For example,
large/high-quality dwellings appreciated 15 percent more over the sample period
at the same time their share of the observed sales grew by forty percent. On
125
the other hand, large/low-quality dwellings lagged in appreciation as their share
of observed sales fell. Granted, these are ad hoc submarkets, but the figures do
point to inferential problems for any global-pooling index: over time, the observed
sample is not representative of the stock. So, while the global-pooling indexes may
be consistent estimates of the sample parameters, they may be biased estimators
of the population parameters.
This partition, by bundles of dwelling attributes, ignores the most important
single attribute of housing: location. The five submarkets are aspatial within a
region of Sweden that contains qualitatively distinct submarkets across its core,
suburbs, and periphery. Figures 4.3 through ?? address both prices and sample
selection in a spatial context. The first two of these show relative median prices
and sample shares across the Stockholm region, comparing the surface of median
prices in 1990 to a baseline of 1981. Figure 4.3 shows a relative higher appreciation
in median price in the city center and to northern part of the region. Figure 4.4
relates the analog for observations. It shows that relatively more observations
from West of the center are found in the sample of sold dwellings in 1990 than in
1981. Figures 4.5 and 4.4 repeat the exercise for the same region nine years later,
comparing prices and sample selection in 1999 to 1981.
126
Figure 4.3: Price Appreciation Relative to 1981 - Stockholm, 1990
10 20 30 40 50
X
10 20 30 40 50
Y
1
1.5
2
2.5
3
3.5
Rel HPI
127
Figure 4.4: Sample Selection Relative to 1981 - Stockholm, 1990
10 20 30 40 50
X
10 20 30 40 50
Y
-6
-4
-2
0
2
4
Rel Obs
128
Figure 4.5: Price Appreciation Relative to 1981 - Stockholm, 1999
10 20 30 40 50
X
10 20 30 40 50
Y
1
2
3
4
5
6
Rel HPI
Again, the center shows relatively higher appreciation, but by 1999 areas to
the east and west of the center gained more than the rest as well. The sample
selection picture for 1999 shows non-uniformity in the sample.
These simple metrics of asymmetry with regard to price levels and sample
selection cast doubt on the ability of global-pooling indexes to recover population
parameters. This finding is robust to submarket definition: essentially any mean-
ingful partition of the data yields idiosyncratic price and selection paths. Many
definitions of submarkets were explored with little difference in interpretation.
4.3.2 Los Angeles
For the Los Angeles metropolitan area, we use data consisting of individ-
ual house sales complied from public records by the real estate services firm
129
Dataquick(DQ). It has since been purchased by private data vending company
CoreLogic and is available in products from that company called RealQuest and
ListSource. Dataquick themselves compiled the data from tax assessors records,
and as such their national data covers over 97 percent of all real estate transactions
in the United States in the sample period. Our sample covers Los Angeles County,
Orange County, Ventura County, Riverside County, and San Bernardino County,
from the first quarter of 2000 to the fourth quarter of 2015.
We filter the DQ data in several ways to remove data that either irrelevant or
clearly an error. Notably, we record house price as missing if it is more than $10
million. This effectively removes several observations that have sale prices that are
implausibly high. Similarly, we also code observations as missing if there bedroom
to bathroom ratio (or vice versa) of over 5. We also code the square-footage
statistic as missing if the house has a positive number of bedrooms or bathrooms
and 0 for square-footage, since this is logically impossible.
To compare sales data to the universe of housing stock we use data from the
2000 and 2010 Census taken from two sources, the Neighborhood Change Database
(NCDB), and public use microsamples (IPUMS). The NCDB is aggregated to the
tract level, and gives us information on the distribution of housing in each tract. In
particular, we take the number of housing units of all types in the tract, the num-
ber of bedrooms, bathrooms, total rooms of all types, date the house was moved
in to, decade the house was built in, self-reported house price, and whether the
house is owner-occupied or rented. We also use the NCDB for sociodemographic
information on the neighborhood, namely the racial composition, average family
income, and proportion of adults with a college degree in the neighborhood. The
microdata gives us more detailed information on the characteristics of housing
130
structures, since it is not aggregated, but does not give us the same level of geo-
graphic specificity as each observation is only identified at the public use microarea
(PUMA) level.
The L.A data has a specific advantage in that each observation is geocoded
with specific coordinates. Figures 4.6 to 4.9 map the price appreciation across Los
Angeles during throughout the boom, bust, and recovery. The underlying data for
the figure are median house prices calculated by zip code. The same figure can
be produced using quality controlled indexes, but this is left out for the sake of
brevity. Brighter red areas represent higher price growth over the period.
Figure 4.6: House Price Appreciation Across Los Angeles
The maps makes it clear that price appreciation was no even across space over
the time price, thus violating the first assumption of global pooling. Figure 4.6
shows that during the boom price appreciation was strongest south of downtown
L.A extending through to downtown Long Beach, and in the San Fernando Valley
area at the top corner of the map. However, even if it not to the same extreme
131
degree, price appreciation was strong throughout all of the L.A. Even the areas
that experienced the slowest appreciation (upper income areas like Santa Monica,
Beverly Hills, and Manhattan beach area) still had the median sale price nearly
double.
Figure 4.7: House Price Appreciation Across Los Angeles
Figure 4.7 shows nearly the exact inverse of the previous figure. Those areas
that experienced the greatest gains during the boom saw similarly extreme declines
intheirsaleprices. SouthCentralLosAngelesappearstohavebeenhitthehardest
withpricesdecliningby50percentormore. Interestinglywealsoseethattheupper
income areas that saw the smallest amounts of appreciation in the boom managed
to maintain their sale prices (Santa Monica, Beverly Hills, and Manhattan beach
are all shaded orange).
132
Figure 4.8: House Price Appreciation Across Los Angeles
Figure 4.8 shows that during the stagnant period after the bust the same upper
income areas as before managed to maintain values, but so did the downtown and
San Fernando Valley areas that experienced the biggest crash. Some areas also
continued to decline, most notably those around downtown.
133
Figure 4.9: House Price Appreciation Across Los Angeles
Figure 4.9 shows that the recovery has been driven by housing in the downtown
LosAngelesareainthecenterofthemap, slightlynorthoftheareawheretheboom
and bust were focused. That said, most of the map is shaded yellow, indicating
thtat moderate price increases have occured throughout the city.
Taken together, figures 4.6 - 4.9 tell a very interesting story about how the
housing boom and bust played out in Los Angeles. Appreciation is clearly asym-
metric with the boom and bust been driven driven by the rise and fall of house
prices in the area South of downtown and the San Fernando Valley, while the
recovery is driven by housing in Downtown area. House prices in upper income
areas like Beverly Hills or Manhattan Beach on the other hand, experienced a less
extreme cycle. The housing in these structures varies in several important ways.
The areas where the boom and bust were concentrated are typically smaller lots,
with smaller houses, lower prices, and less amenities.
134
The trends seen in the maps can be further verified by looking at some local
indexes over the time 2000 - 2015 period. Figures 4.10, 4.11, and 4.13, show house
price appreciation by structure type, lot size, and price in a base year respectively.
Combinedtheyseemtoshowthatappreciationwasgreatestamongstsmallersingle
family units, in denser downtown areas that were closer to the bottom of the house
price hierarchy. However, the degree of asymmetry has also varied greatly across
time.
Figure 4.10: House Price Appreciation by Structure Type, 2000 - 2015
135
Figure 4.11: House Price Appreciation by Lot Size, 2000 - 2015
Figure 4.12: House Price Appreciation by 2000 Quartile, 2000 - 2015
136
Figure 4.13: House Price Appreciation by Distance from City Center, 2000 - 2015
In figure 4.10 we divide sales into 4 types; large/small single family units and
large/small condominiums. Where a unit is counted as large if it has 3 or more
bedrooms. Each line represents the median price for these units. The plot shows
similar patterns of appreciation up until 2005, declines post 2007, and recovery
post 2012 regardless of the structure. However, it is notable that the peak of small
single family homes in 2006 and 2007 is substantially higher than any other type of
structure with a maximum value more than 3 times that of in the year 2000. None
of the other types went above 2.7 in that period. This likely reflects the nature of
the housing boom that was driven by the expansion of subprime mortgages that
were be disproportionately used to purchase smaller units.
The other notable difference in that condos behave very differently than single
family units during the stagnant period of 2009-2012 after the crash. Condo’s
137
appear to have not fallen as sharply as single family homes. Potentially reasons
for this will be discussed in the next section.
Figure 4.11 shows median house prices of units divided into quartiles based on
their lot size where 1 is used to denote the smallest lots and 4 the largest. It is clear
from this that the smallest 50 percent of lots experienced the most aggressive price
increases during the housing boom. Interestingly, the indexes do not converge as
in figure 4.10, but instead seem to main their order throughout the recovery.
The same story is found in figure 4.12 that shows house price appreciation by
their 2000 quartile
5
. This is done by taking the median sale price each zip code in
2000 then allocating every sale in the data a quartile based on this price. In this we
see a similar pattern to the other figures expect that the price of the lowest quartile
(denotedasquartile1inthefigure)showingthestrongestpriceappreciationduring
the boom and bust and the 4 quartile realigning during the recovery. It is also
greatlyexaggeratedcomparedwithotherfigures, consistentwiththenarrativethat
the boom was driven by smaller, cheaper units that received a demand shock due
to improved access to credit amongst lower income borrowers.
Finally, we look at appreciation when houses are divided by their distance
from downtown Los Angeles. This is seen is figure 4.13 that shows house price
appreciation has consistently been stronger the closer to the CBD but the extent
to which this is true varies across time. It is clear that appreciation during the
boom was fairly symmetric across submarkets, diverged greatly at the peak of
the boom, was symmetric during the crash and stagnant period, and has again
begun to diverge in the recovery. Clearly the recovery has been much stronger in
areas closer to the CBD than other areas. This possibly reflects the trend of urban
5
The same figure can be reproduced using quartiles from any year during the sample period
138
revival and gentrification in downtown areas that has been widely documented and
that housing is more inelastic in areas closer to CBDs seen in Glaeser et al. (2006).
While the exhibits thus far show that there is asymmetric price appreciation
amongstsubmarketsweknowfromsection4.2thatthisdoesnotmeanthatglobally
pooledindexeswillbebiased. Forthistobethecaseitmustalsobethatsubmarket
shares are different from their shares of the underlying stock. The last set of figures
in this section provide evidence that the distribution of housing sales across space
shifted frequently through the boom, bust, and recovery. These shifts mean that
different areas and types of housing are over represented relative to their share of
the stock in global indexes.
Figure 4.14: Density of Housing Sales in Los Angeles, 2004, 2008, 2012, and 2015
First, we show heat maps of the quantity of house sales in 2004, 2008, 2012,
and 2015 in figure 4.14. Brighter, and more densely red spots show where house
sales were most frequent in that year.
139
The 2004 panel shows the bulk of housing sales to be concentrated in downtown
areas. The San Fernando Valley had the most sales, followed by areas such as
downtown Los Angeles, and Downtown Long Beach. This is not too surprising,
given that these are all very densely populated areas.
Comparing the 2004 panel with the 2008 panel, it is clear that just after the
peak of the boom all house sales in L.A were concentrated in a San Fernando
Valley(the top left corner of the map), and to a lesser extent South Central Los
Angeles. The panel also shows less sales overall. The 2012 panel shows that sales
were stronger during this period, and were mostly concentrated in South Central
area, and the San Fernando Valley, similar to in 2004. The 2015 panel, however,
shows that most sales occurred slightly north of this area, closer to downtown Los
Angeles.
Figure 4.14 shows similar patterns to those seen in figure 4.6 to 4.9. Indicating
a positive correlation between price appreciation and sales quantities. This is
important for globally pooled indexes because, generally speaking, this means that
fast appreciating neighborhoods may take up a greater share of observations than
slow appreciating units.
That the distribution of housing sales shifts over time means that its represen-
tativeness of the underlying stock changes over time too. This can be assessed by
looking at the distribution of the housing stock. This is shown in figure 4.15. Since
we are using data from the Census to get our housing stock numbers, the panels
show only 2000 and 2010, though the spatial distribution of the housing stock is
virtually unchanged between the two years.
The differences between it the maps of sales and the maps of the stock are
stark. The South Central L.A hot spot has completely disappeared, and the San
Fernando Valley and Downtown Long Beach have dulled. Furthermore, a new
140
Figure 4.15: Density of Housing Stock, 2000 and 2010
hot spot has emerged in Downtown L.A, showing the density of housing stock is
very monocentric. So, despite representing the bulk of the housing stock of L.A
county, housing in Downtown is not traded very frequently, and is consistently
underrepresented in global indexes. This means that our locally pooled index in
the next section will downweight many of areas where sales and appreciation were
the strongest in the period, and instead more heavily weight the housing close to
downtown. Since we have already seen that appreciation is greatest close to the
CBD this means most globally pooled indexes should be underestimates.
There are other differences between the housing stock and housing sales, and
ways that housing sales vary across time that are important to point out. The
first is the To investigate this we again look at heat maps of the sale locations,
but make a different map for houses by that sold more than once in the decade.
This is shown in 4.16. From this it is clear that the single sales are much more
141
evenly spread out than repeat sales, the large hot spot in South L.A only appears
in the map of homes that sold more than once. The other, smaller, hot spots at
Downtown Long Beach, Manhattan Beach, and in the San Fernando are also duller
in the left hand panel of the figure.
Figure 4.16: Density of Sales by Number of Times Sold, 2000 - 2015
Sale type also varies greatly across space. Figure 4.17, replicates figure ??
twice, once using only Condo’s, another time using only SFR.
This shows that all of the ‘hot spots’, with the exception of downtown L.A,
consist almost entirely of condo sales. Property types are clearly not randomly
dispersed across space, especially for Condo’s. So, the ‘typical’ house sale depends
on the location. This is important because many popular indexes consist of only
single family units, but doing so means that submarkets where other housing types
make up most of the stock are underrepresented.
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Figure 4.17: Density of Housing Sales in L.A County by Property Type, 2000 -
2015
4.4 Empirics & Preliminary Results
The empirical work centers on the most commonly cited housing price indexes,
these are the median, repeat-sale, and hedonic price indexes. There are numerous
variations on each, but the goal of this section is to test for differences between the
local- and global-pooling approaches and therefore only the typical formulation
of each index is employed. Mean and median price indexes are common in the
business press, but have fallen from favor in academic work as they do not control
for quality differences. The National Association of Realtors (NAR) median price
index is an example of a simple index in wide use. A variant of the repeat sales
approach is employed by the FHFA in the construction of their metropolitan house
price indexes. Hedonic indexes are popular where data are rich enough to support
their estimation, but this is not often the case.
143
The theoretical model discussed earlier derived two conditions under which
globally-pooled sample observations could be used to recover the population
parameters. The first condition required that all of the observations could be
drawn from the same stochastic price process, in which case any sample would be
representative with regard to appreciation. The second condition required that
submarket shares of observations were equal to submarket shares of the dwelling
stock. The previous section suggests that there is good reason to doubt that either
section is true.
In this section we apply the local pooling solution suggested earlier. This
method creates individual indexes for each submarket, then taking the weighted
mean of these indexes where the weights are that submarket share of the housing
stock. Defining a submarket is, of course, more art than science, and providing
a comprehensive answer to the question ’what is a submarket?’ is beyond the
scope of this paper. In light of this, we use geographic areas as our submarkets
(specifically, we use zip codes), as there is a general consensus that locations within
a city define a submarket of some kind in that everyone who lives there has access
to a common set of local amenities.
Figure 4.18 suggests that the first condition does not hold; Figure 4.19 suggests
that the second does not.
The first of these two figures shows both the set of municipal housing price
indexes as well as the globally-pooled hedonic price index for the Stockholm region.
These local indexes are significantly different from one another - they do not share
thesamepriceprocess. (Thisistypicalofalleightregions.) Thefigureissuggestive
of a non-representative sample as most of the local indexes fall below the aggregate
index. It is not possible to determine from the figure, since stock weighting may
yield the same aggregate price index. But it is easy to see from this figure how
144
Figure 4.18: Local Price Indexes and Globally Pooled Aggregate Prices for Stock-
holm
Year
Index Number (1981:I=1.00)
1985 1990 1995 2000
1 2 3 4
Local Hedonic Indexes
Globally-Pooled Hedonic Index
non-random selection could lead to bias in measured aggregate prices: consider a
sample of sold dwellings from only the top half of the index distribution. Of course,
such a sample is not found in practice, but as the second figure shows, municipal
shares of observations can differ substantially from the municipality’s share of the
region’s housing stock. In it, the time-varying lines are the municipal share of
observed sales from period to period, while the horizontal lines are the municipal
145
Figure 4.19: Local Share of Aggregate Stock vs. Local Share of Observed Sales
Year
Share of Stock/Sample
1985 1990 1995 2000
0.05 0.10 0.15 0.20 0.25 0.30
shares of the housing stock.
6
When the stock-share line is above the sample-share
line, the municipality is under-represented in that period.
7
In order to examine differences between indexes based on locally- and globally-
pooled samples, a simple set of comparisons were constructed. First, four globally-
pooled indexes were constructed for each of eight regions in Sweden. These indexes
are constructed as typically implemented in practice. In particular, the repeat sale
6
To be clear, the dwelling stock is calculated by totaling any dwelling that sells at least once
during the 19-year sample period. As such, the stock is understated by the amount of dwellings
that do not sell at all. While imperfect, this definition is sufficient for the purposes of examining
the difference between the time-varying weights implied by fluctuating sales and the fixed weights
implied by the share of dwellings sold over the sample period.
7
What is also clear from the figure is that a few of the municipalities dominate the stock and
sale shares. This may explain the lack of decisive findings as to the relative levels of aggregate
prices as measured using locally- and globally-pooled indexes. This is discussed in more detail
below.
146
indexes are built using the weighting approach developed in ?.
8
The hedonic
regressions include eighteen measures of housing quality (including lot size, living
area, age, and dummies for one- or two-car garage, sauna, fireplace, tiled bath,
roof type, quality of insulation, and quality of kitchen, as well as dummies for each
municipality).
Local indexes are constructed analogously. For each municipality, mean,
median, repeat sale, and hedonic indexes are estimated. The hedonic specification
at the municipal level obviously does not include the municipal dummies found in
the global hedonic specification. Aggregate price indexes are built by weighting
the local indexes by the respective municipality’s share of the dwelling stock.
The first question is whether or not the order of aggregation matters. Figure
4.20 shows the relative difference between local and global pooling in the Malmö
region for the four indexes: mean, median, repeat sale, and hedonic. It indicates
that meaningful differences exist only for mean and median indexes. This pattern
is consistent across all eight regions as indicated in Table 4.2. It reports the mean
standard deviation of the index relatives. As in the figure, the table supports the
notion that the order of aggregation is relevant only for the simple indexes. This
is somewhat surprising given the wide dispersion of local prices and sample shares
displayed in Figures 4.18 and 4.19. The modest difference between the locally-
and globally-pooled repeat sale and hedonic indexes is likely due to the dominance
of a handful of municipalities in the sample. In all the regions, there are one
to three central municipalities from which a significant minority of observations
are drawn. In fact, an example of this can be seen in Figure 4.2, where two
8
Two forms of the auxiliary regression were explored, one with and the other without squared
time between sales. The results presented here are based on just the linear term; that is, squared
residuals are regressed on a constant and time between sales only. Differences in the subsequent
weighted regressions were negligible.
147
Figure 4.20: Locally-Pooled Indexes Relative to Globally-Pooled Indexes - Malmö
Year
Local-Pooling Index/Global-Pooling Index
1985 1990 1995 2000
0.98 1.00 1.02 1.04 1.06 1.08
Mean
Median
Hed-Dt
RS-Naive
municipalities contain 45 percent of the stock. Future work will decompose these
large municipalities into their component parishes to maintain a more balanced
sample of submarkets.
9
The second question is whether the set of indexes measure the same phe-
nomenon. That is, are the indexes interchangeable? Much has been made of the
differences in underlying samples and maintained hypotheses among the different
indexes. Meese & Wallace (1991) find problems with both repeat sale and hedo-
nic indexes sufficient to suggest use of a median index in their stead. Advocated
9
To date, two levels of geographical aggregation have been examined: parish and municipality.
The first of these created many problems with parishes too small to support repeat sale indexes;
the second, presented here, appears to be too broad a geographical area. Initial results from the
parish-level analysis showed greater difference between the locally- and globally-pooled repeat
sale and hedonic indexes.
148
Table 4.2: Comparison of Indexes Locally-Pooled Relative to Globally-Pooled
Average Percent Difference, Standard Deviation in Parentheses
Index Region
I II III IV V VI VII VIII
Mean -0.70 -0.94 4.17 0.38 2.06 2.79 -2.35 2.71
(1.8) (2.0) (1.7) (2.2) (2.0) (1.7) (2.8) (3.2)
Median 0.75 0.77 8.77 2.94 3.56 7.59 7.74 6.28
(1.4) (2.6) (3.0) (3.3) (2.5) (3.0) (4.3) (3.4)
Repeat Sale -0.92 0.19 1.99 0.95 1.77 0.69 0.05 -0.34
(0.4) (0.4) (0.6) (0.4) (0.6) (0.7) (0.8) (0.9)
Hedonic -1.01 0.01 -0.86 0.19 0.08 -2.76 -1.20 -0.38
(0.4) (0.6) (0.4) (0.5) (0.6) (0.6) (0.8) (0.8)
as well in their paper is the use of a non-parametric estimator that is free of the
assumptions required of the quality-controlled indexes. Their paper, however, does
not consider the representativeness of the observed sample. In this paper, as in all
housing price index research, there is no “truth” against which to measure index
construction methods. In the spirit of the Meese and Wallace paper, the aggregate
index based on locally-pooled hedonic regressions is used as the benchmark. It is
the most flexible and employs the most information from market transactions of
the indexes examined.
Figure 4.21 shows several aggregate housing price indexes relative the locally-
pooled hedonic index, again for the Malmö region. Apparent in the figure is the
wide variability of the global mean and median indexes. As is well known, these
indexes are subject to quality variation. The repeat sales indexes, both locally-
and globally-pooled, drift higher relative to the benchmark. This phenomenon has
been documented before in Englund et al. (1999b) in which these differences with
149
Figure 4.21: Aggregate Price Indexes Relative to Locally-Pooled Hedonic Index -
Malmö
Year
Index Relative to Locally-Pooled Hedonic
1985 1990 1995 2000
0.95 1.00 1.05 1.10 1.15
Local Mean
Global Mean
Local Median
Global Median
Local Hed-Dt
Global Hed-Dt
Local RS-Naive
Global RS-Naive
the hedonic indexes are attributed to unmeasured quality change in the sample
dwellings.
The locally-pooled median index shows remarkably similar behavior vis-á-vis
the benchmark locally-pooled hedonic price index and is a significant improve-
ment relative to its globally-pooled counterpart. The locally-pooled median is
particularly close to the benchmark despite the absence of control for the quality
differences apparently manifest in the globally-pooled median index. The basis for
this is two-fold. First, local quality variation is less extensive than global varia-
tion and therefore quality-control is less of an issue locally. In particular, locally
pooled indexes successfully capture local land values which are a dominant com-
ponent of observed dwelling prices. Second, as shown in Equations 4.15, 4.16, and
150
Table 4.3: Comparison of Index Performance Relative to Locally-Pooled Hedonic
Average Percent Difference, Standard Deviation in Parentheses
Index Region
I II III IV V VI VII VIII
Global Mean 4.92 0.66 -5.01 3.72 3.08 -4.61 4.81 -3.88
(5.0) (3.4) (2.8) (4.0) (4.3) (3.0) (6.4) (4.4)
Global Median 0.34 -2.80 -10.55 -0.81 -0.12 -9.28 -1.85 -9.70
(1.8) (2.8) (3.3) (3.0) (2.5) (3.1) (6.0) (3.5)
Global RS -3.55 0.95 1.08 3.53 -7.32 3.51 5.13 2.83
(2.1) (2.5) (3.6) (4.2) (2.6) (3.8) (5.5) (3.3)
Global Hedonic 1.02 -0.01 0.87 -0.19 -0.07 2.84 1.22 0.39
(0.4) (0.6) (0.4) (0.5) (0.6) (0.7) (0.8) (0.8)
Local Mean 4.11 -0.34 -1.08 4.06 5.14 -1.98 2.20 -1.40
(3.4) (2.0) (2.0) (2.7) (3.6) (2.3) (4.0) (2.1)
Local Median 1.08 -2.11 -2.78 2.02 3.40 -2.46 5.57 -4.12
(1.6) (1.5) (2.3) (1.8) (2.0) (2.2) (4.5) (2.5)
Local RS -4.43 1.15 3.09 4.52 -5.67 4.22 5.17 2.48
(2.1) (2.5) (3.5) (4.3) (2.7) (3.9) (5.2) (3.4)
4.17, locally-pooled indexes are consistent estimators of aggregate prices so long
as measurement error at the local level is not correlated across municipalities.
These results are consistent across the eight regions, as reported in Table 4.3.
Thetablereportsmeanandstandarddeviationsfortheindexrelatives-thepercent
difference between the indexes and the benchmark locally-pooled hedonic index.
In general, the locally-pooled median exhibits smaller differences than the others
and is more stable. The broad similarity of the locally-pooled median and hedo-
nic indexes points to a potential solution to a central problem in index choice.
Researchers interested in aggregate prices are often forced to choose between
median and repeat sale indexes as data are typically unavailable to estimate hedo-
nic indexes, hence the popularity and extensive usage of the OFHEO and NAR
151
indexes. The results presented in Table 4.3 suggest that the benchmark index is
recoverable with a simple set of sales data: sale price, date of sale, and dwelling
location (even crudely identified).
These results are preliminary, but they are promising. The availability of mini-
mal sets of sales data implies that unbiased aggregate housing price indexes may be
constructed without having to make the assumptions required of the repeat sales
index or be subject to the quality variation that haunts the mean and median as
useful measures of aggregate prices.
4.4.1 Los Angeles
Figure 4.22 shows the local indexes for all zip codes within the 5 counties in
the greater L.A area in color, and the globally pooled index for the entire of L.A
in black. The left panel shows indexes based on a hedonic regression, the center
panel shows the median, and the right most panel shows a weighted repeat sales
index constructed using the Case-Shiller method. The extreme dispersion of the
individual zip code indexes around the globally pooled index make it clear that the
extent and timing of price appreciation and depreciation vary greatly within the
metroarea. Combinedwiththeinformationweknowfromtheprevioussectionthat
looking solely at sales can mean that certain submarkets will be overrepresented
in a globally pooled index this justifies the use of a locally pooled index for the
metro area.
Another interesting note about the submarket indexes is the great degree of
similarity across methods. The average absolute difference between the two is only
4 points, and the average correlation between the two is over 0.96. This most likely
indicates that housing structure is more homogeneous in quality at local levels, so
there is less need to control for differences in quality at these levels.
152
Figure 4.22: Locally Pooled Indexes and Globally Pooled for Los Angeles, 2000-
2015
153
Figure 4.23: Local Indexes vs Globally Pooled Index for L.A, 2000-2015
154
Figure 4.24: Globally Pooled Indexes relative to Locally Polled Indexes for Los
Angeles, 2000-2015
Figure 4.23 shows the globally pooled index against the median and hedonic
indexes shown in the black lines in figure 4.22, and a weighted repeat sales index.
Figure 4.24 shows the ratio of the globally pooled indexes to the relative indexes.
The locally pooled indexes are each the weighted mean of the colored lines in figure
4.23, where the weights are that submarkets share of the overall housing stock in
2000
10
. The figures show several features that we might expect given the evidence
in the previous section.
10
We also used the 2010 housing stock as weights and found the same results.
155
First, all the indexes show a great degree of symmetry in the during both the
boom, indicative of the great symmetry of price appreciation across submarkets
seen in the previous section.
Second, the locally pooled indexes have a lower peak for the boom than all
the others, particularly the repeat sales index. This is not surprising, the evidence
in section 4.3 showed indicated that fast appreciating areas were overrepresented
relative to the housing stock during the 2000 - 2008 period. The repeat sales index
shows the highest peak for the boom, indicative of its own selection problems
found seen in figure 4.16 where we saw that repeat sales were heavily concentrated
in South Central L.A during the sample period.
The overstatement of the boom by globally pooled indexes relative to locally
pooled ones is most likely due to the demand shock caused by the expansion of
credit to lower income individuals through subprime loans. This demand shock
was concentrated in the lower priced markets, because access to credit for buyers
in higher priced submarkets remained relatively unchanged over the period. The
result is that lower priced, smaller homes became overrepresented relative to both
earlier years and to its share of the overall housing stock.
Third, the locally pooled index also find a less severe crash and a stronger
recovery than globally pooled indexes. This is probably because the global indexes
underrepresent downtown L.A, where figure 4.9 shows that price appreciation has
been the strongest. Future versions of this paper will explore the implications of
these findings for such things mortgage default and calculating the value of the
housing stock.
156
4.5 Conclusions
The goal of this paper was to examine the relative performance of indexes using
an alternate order of aggregation. Typical construction of aggregate indexes begins
by pooling all relevant observations - a process we call “global pooling.” Global
pooling implicitly assumes that observation are representative with regard to price
level and the dwelling stock. These assumptions are typically made without verifi-
cation. The first issue the paper addresses is representativeness and the potential
bias that arises from non-representative samples.
In a stylized example, two conditions were derived under which global pool-
ing indexes could recover the population parameters from a sample of observed
dwellings. First, appreciation could be symmetric across submarkets; second,
selection into the sample could be random. In other words, in the presence of
asymmetric appreciation, the sample needed to be representative of the dwelling
stock. In practice, both conditions were shown to be violated in the case of both
the Swedish and Los Angeles housing markets covered in our data.
An alternative approach to aggregating all observations is to pool observations
within smaller levels of geography, construct local indexes at this level, and then
build aggregate price indexes by weighting the local indexes by their share of the
stock rather than by their share of observed sales. This has the effect of reducing
thebiasinducedbynon-representativesamples. Whereasanadditionalobservation
from an over-represented submarket biases global pooling indexes toward prices in
that submarket, the additional observation improves local price estimates and, in
turn, aggregate price estimates in the locally-pooled indexes.
Empirically, the difference between local- and global-pooling indexes was great-
est for the mean and median indexes, but only very modest for the repeat sale and
157
hedonic indexes. The results are preliminary but surprising given the wide vari-
ation in price appreciation at the local level and in their share of the observed
sample over time. In particular, the Los Angeles results are compelling in that
the locally pooled index outperforms the popular FHFA and Case-Shiller indexes
by detecting the start of both the bust and the recovery first. Furthermore, it
suggests that these indexes overstated the severity of the housing crash and the
understated the strength of the recovery.
One potentially important result in comparing the estimates of aggregate prices
produced by the various indexes is that the locally-pooled mean and median
indexes track the estimates of the “best” index. In particular, the locally-pooled
median index tracks closely the locally-pooled hedonic index (which was chosen
as the benchmark due to its flexibility across submarkets and its use of the most
information of all the indexes). This similarity offers the potential for an unbiased
aggregate price index free of the assumptions implicit in the repeat sales using a
minimum of transaction data. More work is required to buttress these results, but
these initial results are promising.
158
Chapter 5
Conclusions
The 3 essays in this dissertation have provided new insights into some familiar
economic issues by viewing them through the lens of cities. The first chapter
showed that the lead-lag relationship between housing and the business cycle that
is prevalent at the national level is less robust when looked at city by city. A
deeper understanding of the relationship can be gained by appreciating the role
of spillovers amongst the different cities’ economy’s when there are movements
in their housing markets. The second has found that despite the great attention
paid to neighborhood change (particularly the issue of gentrification) the internal
structure of cities is actually quite stable over the long term. Furthermore, they
are getting more stable, not less, as time goes forward. The final essay deals with
construction of house price indexes for cities, and finds that traditional indexes
that weight every house sale can substantially miss the mark (that is, be biased)
because they incorrectly weight the appreciation trends of different submarkets
within cities.
None of the chapters are the final word on their subject matter. The intention
of this dissertation is start conversations, rather than finishing them, and there
are many interesting questions raised in this dissertation that deserve attention in
future papers. The first chapter would be well complemented with a study that
explains why investigates if shocks to housing truly cause the business cycle, or if
they are simply expressions of the same cycle. The methods could also be extended
to look at spillovers for other variables between cities, or could even be looked at
159
within cities. The second chapter leaves aside explaining the noted increase in
stability in US cities over time. Future work could focus on cities expanding, and
as they do, solidifying their internal structure since new neighborhoods on the
periphery are too far from the city center to be considered viable substitutes to
the currently existing ones. The final chapter could be extended to many applica-
tions that rely on aggregate house price measures, such as mortgage default, and
calculations of aggregate housing values. Furthermore, it could be extended to
other times and places as well. This provide more evidence of whether or not there
are aggregate house price indexes have a consistent, time invariant bias to them.
Each chapter of this dissertation stands on its own as a self contained piece
of research. However, I believe more general lessons can be learned that run all
3 of them. The focus on cities is important because it teaches what we can learn
when build up from the local to the aggregate, rather than taking the aggregate
at face value. This is seen in the first essay, where a remarkable consistent trend
at the national level breaks down at the metro level. Of course, I reconcile this
through allowing for spillovers between cities, but it shows that there is important
information in the variation amongst that is ignored when looking only at the
national relationship. Although, this may not even be taking things far enough,
the second and third essays find consideration differences within a city that largely
go missing when looking at say, a metro level house price index.
Thus, if the reader is take only one thing from this, I hope it is that they view
aggregate statistics with some skepticism. Not because they are wrong necessarily,
but simply because they are often too coarse to provide a useful answer to a ques-
tion. For instance, the goal of an index is usually to take a large, multidimensional
set of characteristics, and sum them up in one number. A better appreciation of
160
what is really going can be gained by looking at the set of individual statistics that
went into the index.
161
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Abstract (if available)

Abstract This dissertation explores three separate issues related to the economics of cities. Though they each have their own separate motivations behind them, there is a common thread in the chapters in that they each help us further understanding that aggregated geographic units such as cities can be better understood by focusing on the variation within them rather than the variation between them. The first chapter looks at how the relationship between housing and business cycle is different from city to city and shows how cities interact with one another. The second focuses on the internal structure of cities and looks at how which cities have a very stable structure and which do not. The final chapter shows how city level house price indexes can be misleading if they do not properly account for asymmetries within the city's submarkets.

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Creator Malone, Thomas Denis (author)

Core Title Essays on the economics of cities

School School of Policy, Planning and Development

Degree Doctor of Philosophy

Degree Program Urban Planning and Development

Publication Date 07/17/2017

Defense Date 06/13/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag business cycle,Economics,house prices,Neighborhoods,OAI-PMH Harvest,Real estate,Urban Planning

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Redfearn, Christian (committee chair), Boarnet, Marlon (committee member), Green, Richard (committee member)

Creator Email tdmalone@usc.edu,thomas.malone@outlook.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-400128

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