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10 08R
Endogenous Gentrification and
Housing-Price Dynamics
Veronica Guerrieri, Daniel Hartley, and
Erik Hurst
FEDERAL RESERVE BANK OF CLEVELAND
Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to
stimulate discussion and critical comment on research in progress. They may not have been subject to the
formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views stated
herein are those of the authors and are not necessarily those of the Federal Reserve Bank of Cleveland or of
the Board of Governors of the Federal Reserve System.
Working papers are available on the Cleveland Fed’s website at:
www.clevelandfed.org/research.
Working Paper 10-08R
June 2013*
Endogenous Gentrification and Housing-Price Dynamics
Veronica Guerrieri, Daniel Hartley, and Erik Hurst
In this paper, we begin by documenting substantial variation in house-price
growth across neighborhoods within a city during citywide housing price booms.
We then present a model which links house-price movements across neighborhoods within a city and the gentrification of those neighborhoods in response to
a citywide housing-demand shock. A key ingredient in our model is a positive
neighborhood externality: individuals like to live next to richer neighbors. This
generates an equilibrium where households segregate based upon their income.
In response to a citywide demand shock, higher-income residents will choose to
expand their housing by migrating into the poorer neighborhoods that directly
abut the initial richer neighborhoods. The in-migration of the richer residents
into these border neighborhoods will bid up prices in those neighborhoods,
causing the original poorer residents to migrate out. We refer to this process as
“endogenous gentrification.” Using a variety of data sets and using Bartik variation across cities to identify city-level housing demand shocks, we find strong
empirical support for the model’s predictions.
Keywords: gentrification, housing-price dynamics, housing-consumption
externalities.
JEL codes: R12, R21, I32.
*Original version July 2010. First revision February 2012. Second revision March 2012.
Note: The online robustness appendix that accompanies this paper is available at
http://www.clevelandfed.org/research/workpaper/2010/wp1008R2-appendix.pdf.
Veronica Guerrieri is at the University of Chicago Booth School of Business (Veronica.Guerrieri@Chicago-Booth.edu). Daniel Hartley is at the Federal Reserve Bank of Cleveland (Daniel.
Hartley@clev.frb.org). Erik Hurst is at the University of Chicago Booth School of Business (Erik.
Hurst@ChicagoBooth.edu). The authors would like to thank seminar participants at Chicago,
Cleveland State, Duke Conference on Housing Market Dynamics, Harvard, MIT, Oberlin, Ohio
State, Queen’s University Conference on Housing and Real Estate Dynamics, Rochester, Stanford,
Summer 2010 NBER PERE meeting, Tufts, UCLA, UIC, University of Akron, USC, Wharton,
Winter 2010 NBER EFG program meeting, Wisconsin, and the Federal Reserve Banks of Atlanta,
Boston, Chicago, Cleveland, Minneapolis, and St. Louis. They are particularly indebted to Daron
Acemoglu, Gary Becker, Hoyt Bleakley, V. V. Chari, Raj Chetty, Morris Davis, Fernando Ferreira,
Ed Glaeser, Matt Kahn, Larry Katz, Jed Kolko, Guido Lorenzoni, Erzo Luttmer, Enrico Moretti,
Kevin Murphy, Matt Notowidigdo, John Quigley, Esteban Rossi-Hansberg, Jesse Shapiro, and
Todd Sinai for their detailed comments on previous drafts of this paper. Guerrieri and Hurst would
like to acknowledge financial support from the University of Chicago’s Booth School of Business.
1
Introduction
It has been well documented that there are large differences in house price appreciation rates across
U.S. metropolitan areas.1 For example, according to the Case-Shiller Price Index, real property
prices increased by over 100 percent in Washington DC, Miami, and Los Angeles between 2000 and
2006, while property prices appreciated by roughly 10 percent in Atlanta and Denver during the
same time period. Across the 20 MSAs for which a Case-Shiller MSA index is publicly available,
the standard deviation in real house price growth between 2000 and 2006 was 42 percent. Such
variation is not a recent phenomenon. During the 1990s, the Case-Shiller cross-MSA standard
deviation in house price growth was 21 percent.
While most of the literature has focused on trying to explain cross-city differences in house
price appreciation, we document that there are also substantial within-city differences in house
price appreciation. For example, between 2000 and 2006 residential properties in the Harlem
neighborhood of New York City appreciated by over 130 percent, while residential properties less
than two miles away, in midtown Manhattan, only appreciated by 45 percent. The New York
City MSA, as a whole, appreciated by roughly 80 percent during this time period. Such patterns
are common in many cities. Using within-city price indices from a variety of sources, we show
that the average within-MSA standard deviation in house price growth during the 2000 - 2006
period was roughly 20 percent. Similar patterns are also found during the 1990s and 1980s. As is
commonly discussed in the popular press, these large relative movements in property prices within
a city during city-wide property price booms are often associated with changing neighborhood
composition. Returning to the Harlem example, a recent New York Times article discussed how
Harlem residents have gotten richer during the period when its house prices were substantially
appreciating.2
Our goals in this paper are threefold. First, we set out to document a new set of facts about the
extent and nature of within-city house price movements during city-wide housing price booms. The
house price appreciation for the city as a whole is just a composite of the house price movements
within all the neighborhoods of the city. Therefore, understanding the movements in house prices
across neighborhoods within a city is essential for understanding house price movements for the
entire city. Using a variety of different data sources, we show that there are substantial differences
across neighborhoods within a city with respect to their house price growth when the city as a
whole experiences a housing price boom.
Moreover, we show that there is a systematic pattern in this variation.
In particular, we
document three facts that are robust across time and data sources with respect to within-city
house price movements.
First, during city-wide housing price booms, neighborhoods with low
initial housing prices appreciate at much greater rates than neighborhoods with high initial prices.
Second, the variation in housing price appreciation rates among low housing price neighborhoods
1
See, for example, Davis et al. (2007), Glaeser et al. (2008), Van Nieuwerburgh and Weill (2010), and Saiz (2010).
See the article “No Longer Majority Black, Harlem Is In Transition” from the January 5th, 2010 New York
Times.
2
2
is much higher than the variation in housing price appreciation rates for higher housing price
neighborhoods. Finally, we show that the larger the city-wide housing price boom, the greater is
the difference in housing price appreciation rates between low house price and high house price
neighborhoods. Regardless of the interpretation we give to some of these facts in later sections, we
feel these facts alone are an interesting contribution to the literature on spatial variation in housing
price growth.
Our second goal is to develop a spatial model of a city that links within-city neighborhood
housing price dynamics with gentrification. We represent a city as the real line and each point on
the line is a location. Agents are fully mobile across locations and there is a representative firm that
can build houses in any location at a fixed marginal cost. The key ingredient of the model is that
agents are heterogeneous in their income and all agents prefer to live close to richer neighbors. The
relevance of such a neighborhood consumption externality in determining house prices is supported
by the recent empirical work of Bayer et al. (2007) and Rossi-Hansberg et al. (2010). We show
that there exists an equilibrium with full income segregation where the high income residents are
concentrated all together and the low income residents live at the periphery. The sorting, as in
Becker and Murphy (2003), is the result of the neighborhood externality where all agents are willing
to pay more to live closer to rich neighbors. Poorer residents are less willing to pay high rents to
live in the rich neighborhoods, so in equilibrium they live farther from the rich. Within the model,
house prices achieve their maximum in the rich neighborhoods and decline as one moves away from
them, to compensate for the lower level of the externality. For the neighborhoods that are far
enough from the rich, there is no externality, and house prices are equal to the marginal cost of
construction.
One of the main contributions of our model, and the basis for our subsequent empirical work,
is to explore the dynamics of house prices across neighborhoods in response to city-wide housing
demand shocks. Although there is no aggregate supply constraint and the city can freely expand,
average house prices increase in response to an increase in city-wide housing demand because of
gentrification. In particular, the neighborhoods that endogenously gentrify are the poor neighborhoods on the border of rich neighborhoods. For concreteness, we say that a neighborhood gentrifies
when some poor residents are replaced by richer ones, increasing the extent of the neighborhood
externality. For example, we consider a city hit by an increase in labor demand and a subsequent
wave of migration (Blanchard and Katz, 1992). The richer migrants prefer to locate next to the
existing richer households. As a result, they bid up the land prices in the poor neighborhoods that
are next to the rich neighborhoods causing the existing poor residents to move out and the city as
a whole to expand.
To sum up, our mechanism implies that unexpected permanent shocks to housing demand lead
to permanent increases in house prices at the city level although the size of the city is completely
elastic. This happens because gentrification bids up the value of the land in the gentrifying neighborhoods. Moreover, our model predicts that, in response to a positive city-wide housing demand
shock, land prices in poor neighborhoods that are in close proximity to the rich neighborhoods
3
appreciate at a faster rate than both richer neighborhoods and other poor neighborhoods. We also
find that average price growth within the city is affected both by the size of the housing demand
shock and by the particular shape of preferences, technology, and income distribution within the
city.
Our third goal is to provide explicit evidence showing that our endogenous gentrification mechanism is an important determinant of within-city variation in house price growth in response to
city-wide housing demand shocks. We do this in multiple ways. To begin, we provide an additional
fact about within-city neighborhood house price appreciation during city-wide housing booms. In
particular, we show that, as our theory predicts, among all the poor neighborhoods it is the poor
neighborhoods that are next to the rich neighborhoods that appreciate the most during city-wide
housing booms. This result holds in the 1980s, 1990s, and 2000s and holds using a variety of different measures of neighborhood housing price appreciation. Moreover, these results are robust to
including controls for distance to the city’s center business district, the average commuting time of
neighborhood residents, and proximity of the neighborhood to fixed natural amenities such lakes,
oceans, and rivers. Again, these results are consistent with the first order predictions of our model.
We then use a Bartik-style instrument to isolate exogenous city level housing demand shocks
(Bartik, 1991) and show that it is the housing prices in poor neighborhoods next to rich neighborhoods that appreciate the most in response to the exogenous city-wide housing demand shocks.
Our Bartik shock predicts expected income growth in a city between periods t and t + k based on
the initial industry mix in that city at time t and the change in industry earnings for the entire
U.S. between t and t + k. For example, in response to a one standard deviation Bartik shock, poor
neighborhoods within the city which directly border a rich neighborhood have housing prices that
appreciate roughly 7.0 percentage points (compared to a mean appreciation rate of 24.0 percent)
more than otherwise similar poor neighborhoods within the city that are more than 3 miles away
from rich neighborhoods. Again, these results hold controlling for distance to the center business
district and proximity to fixed natural amenities within the city.
Finally, we explicitly show that the neighborhoods that appreciate the most during the exogenous city-wide housing demand shock also gentrify. Gentrification - the out migration of poor
residents and the in migration of rich residents - is the key mechanism for the within-city house
price dynamics we highlight. For this analysis, we again explore the within-city response to a
Bartik-style shock. In particular, we show that in response to an exogenous city-wide demand
shock, poor neighborhoods close to rich neighborhoods experience larger increases in neighborhood
income, larger increases in the educational attainment of neighborhood residents, and larger declines in the neighborhood poverty rate than do otherwise similar poor neighborhoods that are
farther away from the rich neighborhoods. For example, average neighborhood income grows by
roughly 1.7 percentage points (compared to a mean growth rate of 14.9 percent) more in response
to a one standard deviation Bartik shock for poor neighborhoods that border the rich neighborhoods than it does for otherwise similar poor neighborhoods that are more than 3 miles away from
the rich neighborhoods. Lastly, we highlight that during both the 1980s and 1990s, most of the
4
poor neighborhoods that did in fact gentrify by some ex-post criteria were neighborhoods that were
directly bordering existing rich neighborhoods.
As noted above, a key ingredient in our model is the existence of neighborhood consumption
externalities in that individuals get utility from having rich neighbors relative to poor neighbors.
Although, we do not explicitly model the direct mechanism for the externality, we have many potential channels in mind. For example, crime rates are lower in richer neighborhoods. If households
value low crime, individuals will prefer to live in wealthier neighborhoods. Likewise, the quality and
extent of public goods may be correlated with the income of neighborhood residents. For example,
school quality - via peer effects, parental monitoring, or direct expenditures - tends to increase with
neighborhood income. Finally, if there are increasing returns to scale in the production of desired
neighborhood amenities (number and variety of restaurants, easier access to service industries such
as dry cleaners, movie theaters, etc.), such amenities will be more common as the income of one’s
neighbors increases. Although we do not take a stand on which mechanism is driving the externality, our preference structure is general enough to allow for any story that results in higher amenities
being endogenously provided in higher income neighborhoods.
Our work adds to the large literature on neighborhood gentrification.3
Some of this litera-
ture highlights correlates with neighborhood gentrification. For example, both Kolko (2007) and
Brueckner and Rosenthal (2008) emphasize that the age and quality of the housing stock within a
poor neighborhood is an important predictor of whether or not that poor neighborhood ever gentrifies. Additionally, there is a separate strand of work that emphasizes the importance of spatial
dependence - either theoretically or empirically - in predicting neighborhood gentrification. For
example, Brueckner (1977) finds that urban neighborhoods in the 1960s that were in close proximity to rich neighborhoods got relatively poorer between 1960 and 1970 (as measured by income
growth). Kolko (2007) finds that poor neighborhoods bordering richer neighborhoods in 1990 had
larger income growth between 1990 and 2000 than otherwise similar poor neighborhoods that were
next to other poor neighborhoods. Our addition to this literature is that we propose a model
that explains both of these facts and then formally test the model’s predictions. During periods
of declining city-wide housing demand in urban areas (like the suburbanization movement during
the 1960s), the richer neighborhoods on the border of the rich areas will be the first to contract.
Conversely, during periods of positive increases in city-wide housing demand (like that associated
with the migration back to cities during the 1990s), the poor neighborhoods bordering the richer
neighborhoods will be the first to gentrify.4
Our work also complements recent papers which have highlighted the theoretical and empirical
importance of residential consumption externalities. For example, our theoretical model builds
upon the insights of Benabou (1993) which looks at neighborhood sorting within a city where
3
For a recent review of this literature, see Kolko (2007).
There is a separate literature looking at the effect of direct public policies on neighborhood gentrification. See,
for example, Busso and Kline (2007), Kahn et al. (2009), Rossi-Hansberg et al. (2010), and Zheng and Kahn (2011).
Our work complements this literature by highlighting gentrification that is not the result of government policy but
instead endogenously results from the actions of private agents responding to city-wide housing demand shocks.
4
5
there are human capital externalities and the work of Becker and Murphy (2003) which looks at
neighborhood sorting in a world with exogenous income groups where all agents have a preference
to live around richer neighbors. From a theoretical standpoint, our work adds to this literature by
examining the dynamics of sorting and house prices in response to city-wide housing demand shocks
thereby generating a gentrification process. Recent empirical work that has documented that cities
are not only centers of production agglomeration, but also centers of consumption agglomeration
include Glaeser et al. (2001), Autor et al. (2010), and Rossi-Hansberg et al. (2010).
Most relevant
for our work is the recent paper by Bayer et al. (2007) which empirically documents the importance
of neighborhood consumption externalities by showing that individuals are willing to pay more to
have more highly educated and wealthier neighbors, all else equal.
2
Data
Our primary measure of within-city house price growth comes from the Case-Shiller zip code level
price indices.5 The Case-Shiller indices are calculated from data on repeat sales of pre-existing
single-family homes. The benefit of the Case-Shiller index is that it provides consistent constantquality price indices for localized areas within a city or metropolitan area over long periods of time.
Most of the Case-Shiller zip code-level price indices go back in time through the late 1980s or the
early 1990s. The data was provided to us at the quarterly frequency and the most recent data we
have access to is for the fourth quarter of 2008. As a result, for each metro area, we have quarterly
price indices on selected zip codes within selected metropolitan areas going back roughly 20 years.
There are a few things that we would like to point out about the Case-Shiller indices. First, the
Case-Shiller zip code level indices are only available for certain zip codes in certain metropolitan
areas. For some of our analysis, we focus our attention only on the zip codes within the main city
in the MSA. For example, we look at the patterns within the city of Chicago instead of just the
broad Chicago MSA. When doing so, we only use the MSAs where the main city within the MSA
has at least 10 zip codes with a usable house price index.6 Second, we only use information for
the zip codes where the price indices were computed using actual transaction data for properties
within the zip code. Some of the Case-Shiller zip code price indices were calculated using imputed
data or data from some of the surrounding zip codes. We exclude all such zip codes from our
analysis.7 Third, the Case-Shiller index has the goal of measuring the change in land prices by
removing structure fixed effects using their repeat sales methodology. However, this methodology
5
The zip code indices are not publicly available. Fiserv, the company overseeing the Case-Shiller index, provided
them to us for the purpose of this research project. The data are the same as the data provided to other researchers
studying local movements in housing prices. See, for example, Mian and Sufi (2009). Unfortunately, we only have
the data through 2008 and, as a result, we cannot systematically explore within-city house price patterns during the
recent bust. We have been unsuccessful in our attempts to secure the post 2008 data from Fiserv.
6
We list the MSAs and cities used in our Case-Shiller analysis in Appendix Table A1.
7
As a result, the Case-Shiller zip codes that we use in our analysis do not cover the universe of zip codes within a
city. Only about 50 percent of the zip codes in the city of Chicago, for example, have housing price indices computed
using actual transaction data. The fraction in other cities is closer to 100 percent. A more complete discussion of the
zip codes with imputed house price data can be found in the NBER working paper version of the paper: Guerrieri et
al. (2010).
6
only uncovers changes in land prices if the attributes of the structure remain fixed over time. If
households change the attributes of the structure via remodeling or through renovations, the change
in the house prices uncovered by a repeat sales index will be a composite of changes in land prices
and of improvements to the housing structure. When the Case-Shiller index is constructed steps
are taken to minimize the effect of potential remodeling and renovations.8
We augment our results using information on the percent change in median house price at the
neighborhood level from the 1980, 1990, and 2000 U.S. Censuses.9 The primary benefit of the
Census data is that it is available at very fine levels of spatial aggregation. In particular, we can
examine within-city differences in housing price dynamics at both the level of zip codes and census
tracts. We compute within-zip code or within-census tract appreciation rates by computing the
growth in the median house price across similarly defined levels of disaggregation between 1980 and
1990 and between 1990 and 2000. The Census data, however, are not without limitations. Unlike
the repeat sales methodology of the Case-Shiller index, the Census data is simply the growth in
the median house price within a zip code or census tract. As a result, it may be confounding
movements in land prices with movements in structure quality for the median house. Moreover,
the median house value, in terms of quality, could be changing over time. For example, as low
quality housing gets demolished, the median price in a neighborhood may increase with no change
in either land prices or structure attributes for the remaining properties. We can partially address
this limitation by including controls for the changes in neighborhood housing stock characteristics
when using this measure. In the NBER working paper version of our paper, we show that the zip
code level price indices from Case-Shiller and the Census data track each other very closely. As a
result, we feel confident in using the Census data to explore house price dynamics at the sub-zip
code level.
Finally, throughout the paper, we compute MSA level house price appreciation rates using
Federal Housing Finance Agency (FHFA) metro level housing price indices if the Case-Shiller house
price series is not available for the MSA. For the MSAs where both data sets exist, the Case-Shiller
and FHFA data track each other nearly identically.
3
New Facts About Within City House Price Dynamics
In this section, we outline a series of new facts about the nature of housing price dynamics across
different neighborhoods within a city (MSA) during city (MSA) wide housing price booms. Unlike
8
For more information on the construction of the Case-Shiller indices see the Standard and Poor’s web-site which
documents their home price index construction methodology. See http://www.caseshiller.fiserv.com/about-fiservcase-shiller-indexes.aspx. In the NBER working paper version of the paper, we also document all the main empirical
patterns in the paper using the Zillow house price index. The Zillow index, at least partially, overcomes some of
the deficiencies of the Case-Shiller index in that it allows the broad attributes of the structure (e.g., square footage,
number of bed rooms, etc.) to change over time. The patterns we document using the Case-Shiller index are nearly
identical to the patterns we find using the Zillow index for the MSAs and time periods where both indices overlap.
9
Most of the tract-level Census data that we use comes from the Neighborhood Change Database which is distributed by GeoLytics. The Neighborhood Change Database provides variables from the 1970, 1980, and 1990
Censuses that have been re-weighted for the 2000 tract boundaries.
7
previous attempts to study within-city house price movements, we analyze these patterns simultaneously for a large number of cities and for multiple time periods.10 As we show, there are many
systematic patterns that emerge with respect to house price dynamics across neighborhoods within
a city during city-wide housing price booms.
3.1
Fact 1: Within City House Price Growth Variation is Large
Table 1 shows the degree of between- and within-MSA variation in house price appreciation separately during the 2000-2006 period (row 1) and the 1990-2000 period (row 2). Columns 1 and
2 focus on cross-MSA variation in house price appreciation for comparison to the within-MSA or
within-city variation. When focusing on the cross-MSA variation, we use FHFA data (Column 1)
and Case-Shiller data (Column 2).11 As seen from Table 1, there is large variation in price appreciation across MSAs during the 1990s and the 2000s. This is consistent with the well documented
facts discussed in Davis et al. (2007), Glaeser et al. (2008), Van Nieuwerburgh and Weill (2010),
and Saiz (2010). Specifically, the cross-MSA standard deviation in house price growth using the
FHFA data was 33 percentage points during the 2000-2006 period and 17 percentage points during
the 1990-2000 period.
The next three columns of Table 1 show within-city or within-MSA, cross-zip code variation in
house price appreciation for the same time periods. For columns 3 and 4, we use data from the
Case-Shiller indices and show the results for all available zip codes within the MSA (column 3) and
then for all available zip codes in the main city of the MSA (column 4). In column 5, we show
the results for the within-city cross-zip code standard deviation in house price appreciation using
the Census data for the 1990-2000 period. When using the Census data in column 5, we restrict
the sample to be the same as the Case-Shiller sample. The results in these columns show that
the within-MSA variation during the 2000-2006 period was about one half as large as the crossMSA variation but was still substantial at 18 percentage points. During the 1990-2000 period, the
within-city variation was of the same order of magnitude as the cross-city variation at about 15
percentage points.
The final two columns of the table show within-city cross-census tract variation for 1990-2000
period using the Census data. The sample in column 6 is restricted to census tracts that overlap
with the 496 zip codes used in the sample for column 5. Column 7, broadens the sample of census
tracts to include all tracts in all cities that contain at least 30 census tracts in 1990. As one would
expect, the within-city variation increases as the level of our definition of a neighborhood gets
smaller. For example, the cross-census tract variation in house price growth in the the 1990s was
roughly fifty percentage points. Collectively, the results in Table 1 show that within-MSA variation
10
Papers examining within city house price movements for a given city or small set of cities during the 1970s
and 1980s include Poterba (1991), Mayer (1993), Case and Shiller (1994), Case and Mayer (1996), and Case and
Marynchenko (2002). Ferreira and Gyourko (2011) build upon our work and provide additional facts about the
timing of booms and busts at the neighborhood level during the 2000s.
11
For reference, the house price appreciation rates using the FHFA MSA level index for the 1990-2000 and 2000-2006
periods for each MSA in our Case-Shiller sample are shown in Appendix Table A1.
8
in house price growth is around the same order of magnitude as the cross-MSA variation that has
received so much attention in the literature.
3.2
Fact 2: Initially Low Price Neighborhoods Within a City Appreciate More
than High Price Neighborhoods During City-Wide Housing Booms
The next fact we wish to highlight is shown in Figure 1 and Table 2. Figure 1 plots the house price
appreciation rate in each zip code within the New York MSA between 2000 and 2006 (using the
Case-Shiller data) against the median house price for the same zip codes in year 2000 (from the
Census). As seen from the figure, there is a sharp negative relationship between the initial level
of housing prices within the zip code and the subsequent appreciation rate in the zip code. On
average, zip codes with lower initial housing prices within the MSA appreciated at roughly twice
the rate as zip codes with higher initial housing prices within the MSA during this period.
Our choice of showing New York in Figure 1 is done for illustrative purposes. Table 2 shows
the relationship between the initial median housing price and the subsequent housing price growth
across neighborhoods within the city/MSA for a large selection of cities and metro areas during
different time periods. Specifically, Table 2 shows the mean growth rate in property prices over the
indicated time period for neighborhoods in different quartiles of the initial house price distribution
within the city or metro area. The last column shows the p-value of the difference in house price
appreciation rates between the properties that were initially in the top (column 1) and bottom
(column 4) quartiles of the housing price distribution within the city or metro area. This table is
the analog to the scatter plot shown in Figure 1. In all cases, the initial level of housing prices used
to define the quartiles in period t is defined using the median level of reported house price for the
neighborhood from the corresponding U.S. Census (i.e., 2000, 1990, or 1980 depending on the time
period studied). The house price appreciation is measured using the Case-Shiller index.
We can conclude a few things from the results in Table 2. First, the patterns found in Figure
1 for New York for the 2000-2006 period are also found in a wide variety of other cities and MSAs
during the same period. Second, as seen from Table 2, these within-city patterns are not limited to
the recent period. During the 1990s, Denver and Portland experienced large housing price booms,
and it was the low priced neighborhoods that appreciated at much higher rates than the high
priced neighborhoods. Likewise, during the 1980s, Boston experienced a large housing price boom
during which the low priced neighborhoods appreciated at much higher rates than the high priced
neighborhoods. Finally, there is also some evidence that poor neighborhoods fall the most during
city-wide housing price busts. For example, within San Francisco and Boston during the 1990s, the
poorer neighborhoods contracted slightly more relative to the richer neighborhoods.12
Are the results shown in Table 2 representative of the patterns in a broader sample of cities?
12
In Guerrieri et al. (2012) we present a case study of Detroit examining the protracted bust experienced there
from 1980 through the late 2000’s. In that paper, we find patterns that are consistent with those observed in San
Francisco and Boston in the 1990’s. Those patterns show the reverse of the gentrification patterns documented during
booms within this paper.
9
The answer is definitely yes. To illustrate this, we estimate:
i,j
∆Pt,t+k
Pti,j
= µj + ω1 ln(HPti,j ) + i,j
t,t+k
(1)
i,j
where ∆Pt,t+k
/Pti,j is the growth in housing prices between period t and t + k within neighborhood
i in city or MSA j using the various house price series and HPti,j is the median house price in
neighborhood i in city or MSA j in year t as measured by the U.S. Census. Given that we also
include city or MSA fixed effects, µj , all of our identification comes from variation across neighborhoods within a city/MSA. The variable of interest from this regression is ω1 which estimates the
relationship between initial median house prices in the neighborhood and subsequent neighborhood
housing price growth. We run this regression using different neighborhood house price series and
for different time periods. For all specifications, we weight the data using the number of owner
occupied housing units in the neighborhood during period t (from the Census).
To conserve space, we do not show the results of this regression in the main text. However, in the
online robustness appendix that accompanies this paper, we show the results of this specification
for different time periods, different measures of house price growth, and different samples. The
results across the different specifications are very consistent. For cities experiencing a city-wide
housing price boom, it is the neighborhoods with the initially low housing prices that appreciate
the most. For example, during the 2000-2006 period, restricting the sample to all zip codes with a
Case-Shiller house price index, and using the Case-Shiller index to measure zip code housing price
growth, our estimate of ω1 is -0.24 with a standard error of 0.05.
One concern one may have about the results in Figure 1, Table 2, and the regressions results
from equation (1) is that they are driven by transitory measurement error or temporary shocks.
For example, a neighborhood that got a temporary negative shock to house prices today would
have both lower house prices today and a higher growth rate between today and tomorrow as
the temporary negative shock abated. This story is not, however, responsible for the results we
document. To illustrate this fact, we can re-estimate equation (1) instrumenting HPti,j with house
prices in the neighborhood 10 years earlier. Specifically, our estimate of ω1 is -0.26 with a standard
error of 0.05 when we instrument for 2000 neighborhood house price levels using 1990 neighborhood
house price levels.
Notice, this estimate is nearly identical to the OLS estimate reported in the
prior paragraph.
In the robustness appendix, we also show that the difference between the house price appreciation of initially low price neighborhoods within the city and initially high price neighborhoods
within the city increases with the size of the city-wide housing price boom.
10
3.3
Fact 3: The Variance in Appreciation Rates is Also Higher for Initially Low
Price Neighborhoods During City-Wide Housing Booms
Returning to Figure 1, another feature of the data for the New York MSA is that the house price
appreciation rate among initially low priced neighborhoods exhibits substantially more variability
than the house price appreciation rates among initially high priced neighborhoods. In particular, the
standard deviation of housing price growth between 2000 and 2006 for neighborhoods in the lowest
initial house price quartile for the New York MSA was 29 percent while the standard deviation of
house price growth during the same time period for neighborhoods in the top initial house price
quartile for the New York MSA was only 6 percent. The difference is significant at less than 1
percent level.
This difference in variability of growth rates between initially low priced neighborhoods and
initially high priced neighborhoods within a city during a city-wide housing price boom is a robust
feature of the data across the many cities in our sample. Again, we formally document these facts
in the online robustness appendix that accompanies the paper. When cities experience housing
price booms, the variability in house price growth among initially low price neighborhoods is much
higher than the variability of house price growth among initially high price neighborhoods. Pooling
the MSAs in our sample, the standard deviation of housing price growth between 2000 and 2006
for neighborhoods in the lowest initial house price quartile within each MSA was 61 percent while
the standard deviation of house price growth in the top initial house price quartile was 46 percent.
This difference is also significant at the less than 1 percent level.
3.4
Fact 4: Poor Neighborhoods Closer to Rich Neighborhoods Appreciate
More than other Poor Neighborhoods During City-Wide Housing Booms
What explains the increased variation in house price appreciation across the poorer neighborhoods?
In this subsection, we highlight the role of proximity to richer neighborhoods as being an important
determinant of house price appreciation of poorer neighborhoods within a city during city-wide
housing price booms. Moreover, we show that the relationship between the proximity to richer
neighborhoods and house price appreciation of poorer neighborhoods remains strong even after we
control for proximity to jobs within the city and to fixed natural amenities within the city.13
13
There are many theories that can explain within city differences in house price appreciation. For example, if
cities are viewed as centers of production agglomeration, as in the classic work by Alonso (1964), Mills (1967), and
Muth (1969), neighborhoods that are close to jobs will have higher land prices than neighborhoods that are farther
away. Likewise, Rosen (1979) and Roback (1982) show that land prices within the city can differ based on their
proximity to a desirable fixed natural amenity. In this section, we show that proximity to rich neighborhoods is an
important determinant of within city house price movements above and beyond proximity to jobs and proximity to
fixed natural amenities within the city.
11
To begin, we describe the data by estimating the following regression:14
i,j
∆Pt,t+k
Pti,j
i,j
i,j
i,j
= µj + β1 ln(Disti,j
t ) + ΓXt + ΨZt + t,t+k
(2)
where ln(Disti,j
t ) measures the log of the distance (in miles) to the nearest zip code in the city
that resides in the top quartile of neighborhoods with respect to median housing prices in period
t.
15
The variable of interest in the above regression is β1 , the coefficient on ln(Disti,j
t ). All of our
regressions also include city fixed effects, µj . As a result, our identification comes from within-city
variation. We report heteroscedasticity robust standard errors that are clustered at the city level.
When estimating the above regression, our sample only includes low housing price neighborhoods within the city. We define low housing price neighborhoods as those neighborhoods whose
median housing price at time t is in the bottom half of neighborhoods with respect to median
housing prices across all neighborhoods in city j at time t.16 As above, we use the Census data
to define the level of period t median housing prices for each neighborhood when segmenting the
sample.
The vector Xti,j includes a series of variables designed to control for initial differences
across the neighborhoods. These controls include the log of median household income of residents
in neighborhood i in period t, the log of the median initial house price in neighborhood i in period
t, the fraction of the residents in neighborhood i in period t that are African American, and the
fraction of the residents in neighborhood i in period t that are Hispanic. When the Census data is
used to compute housing price appreciation, we also include a vector of variables to proxy for the
change in structure quality within the neighborhood between t and t + k.17
We also include a vector Zti,j which is designed to control for the other potential mechanisms
which can generate differential price movements across neighborhoods within a city. Specifically,
we control for the average distance to the closest center business district within the city as reported
by the 1982 Census of Retail Trade.18 The Census data provide another measure of proximity to
jobs in that they track how long it takes for individuals in the neighborhood to get to work. Given
this, we also include the mean commuting time of individuals within neighborhood i during period
t as an additional control. Finally, we control for the distance to fixed natural amenities like major
lakes, rivers, and oceans that are within 10 miles of the city.
14
Given that neighborhoods within a city have different amounts of homeowners or potential housing market
transactions, all regressions are weighted by the number of owner-occupied housing units in the neighborhood during
period t.
15
We measure distance from the centroid of each neighborhood.
16
Sometimes in the text we will refer to these neighborhoods as “poor neighborhoods”. We do this for expositional
ease. We also used an income based measure to define poor neighborhoods. Given the very high correlation between
neighborhood average income and neighborhood housing prices, the results are broadly consistent if we segment
neighborhoods by initial income as opposed to initial house prices.
17
These controls include: the change in the fraction of homes in the tract that are single-family-detached, the
change in the fraction that have zero or one bedrooms, the change in the fraction that have two bedrooms, the
change in the fraction that have three bedrooms, the change in the fraction built in the past 5 years, the change in
the fraction built between 5 and 20 years ago, the change in the fraction built between 20 and 40 years ago, and the
change in the fraction built between 40 and 50 years ago.
18
The CBD data can be found at http://www.census.gov/geo/www/cbd.html.
12
Table 3 shows the results of the above regressions using different time periods, different housing
price appreciation measures, and different levels of aggregation. The first two columns show the
results for the 2000-2006 period where we use Case-Shiller house price indices. In column 1, we
exclude the Z vector of controls in order to gauge their impact when in column 2 we include both
the X and Z vectors of controls. The specific sample for the results in columns 1 and 2 is all zip
codes which were (1) in Case-Shiller cities where a Case-Shiller index exists and (2) in the bottom
half of zip codes within in the city in 2000 with respect to median house prices. There are 236 such
zip codes.
The results in columns 1 and 2 show that there is some systematic variation in house price
appreciation rates among the poor neighborhoods during the 2000-2006 period. In particular, it
is the initially low price neighborhoods in 2000 which were in close proximity to the high price
neighborhoods that appreciated more than otherwise similar initially low price neighborhoods.
These results hold even after controlling for proximity to the city’s Central Business District (CBD),
average commuting times, distance to fixed natural amenities and the X vector of neighborhood
controls (column 2).19
In terms of economic magnitudes, the estimates are non-trivial. For
example, the results in column 2 suggest that low priced neighborhoods that were roughly 4 miles
away from higher price neighborhoods appreciated at 12.4 percentage point lower rates than low
priced neighborhoods that were roughly 1 mile away from higher priced neighborhoods (0.062 *
2, p-value < 0.01). Given that the average neighborhood house price appreciation rate for the
neighborhoods in our sample during this period was roughly 90 percent, the estimated relationship
with distance to high price neighborhoods is non trivial.
In columns 3 - 6, we show similar results for the 1990 - 2000 period. All specifications in
these columns control for both the full vector of X and Z controls. In columns 3 and 4, we use
the Case-Shiller data on Case-Shiller zip codes. The difference between the two columns is that
j
j
in column 4 we also include an additional regressor: ln(Disti,j
t ) ∗ Bustt,t+k where Bustt,t+k is an
indicator variable taking the value of one if city j experienced non-positive housing price growth
between t and t + k. We do not include this variable in the 2000-2006 period because all cities
in our sample experienced a positive house price increase. However, as seen from Appendix Table
A1, some cities in our Case-Shiller sample experienced real housing price declines during the 1990s.
As seen from column 4, the relationship between house price growth among poor neighborhoods
close to and far from high price neighborhoods differs depending on whether the city experienced
a positive or non-positive housing demand shock during the period. In particular, the cities that
did not experience a housing price boom had very little difference in housing price growth between
poor neighborhoods that were close to high price neighborhoods and poor neighborhoods that were
farther away (-0.067 + 0.070). However, for cities that experienced a positive city-wide housing
19
In a recent paper, Glaeser et al. (2012) focus on house price appreciation of neighborhoods close to city centers.
They show neighborhoods close to city centers appreciate more than other neighborhoods during the 2000s - particularly if poverty is concentrated in the city center. Building on our methodology, they find that about one-third of
the effect of the house price growth of neighborhoods close to the center city can be attributed to the endogenous
gentrification story that we highlight.
13
price increase, the estimated relationship in the 1990s mirrored what we found in the 2000 - 2006
period. The estimated coefficient on log distance during the 1990s was -0.067
In columns 5 and 6, we show that the results are roughly consistent using the Census data
during the 1990-2000 period. We define neighborhoods as census tracts and use different samples.
In column 5, the sample is all census tracts within only the 28 Case-Shiller cities. In column 6,
the sample is census tracts in any U.S. city that has at least 30 census tracts contained within the
city. There were 173 U.S. cities in 1990 that met this condition.20 Column 6 shows that the main
results still hold when examining price movements at the level of census tracts and that the results
are not simply limited to Case-Shiller cities. In column 7, we show the results for the 1980-1990
period. The specification in column 7 is analogous to the one shown in column 6 aside from the
fact that it looks at the 1980-1990 period for the 110 U.S. cities in 1980 that had at least 30 census
tracts contained within the city. The patterns in the 1980s are similar to those found in the 1990s
and early 2000s. It is important that the results are similar between the Case-Shiller and Census
housing price measures. In Section 5, we explore the response of within-city house price dynamics
to exogenous city-wide housing demand shocks as a test of our endogenous gentrification theory.
To get enough power, we need to use the large samples shown in columns 6 and 7 for which only
the Census housing price measures are available.21
In summary, the results of this section show that (1) there is a tremendous amount of variation
across neighborhoods within a city with respect to house price appreciation during a city-wide
house price boom, (2) it is the poor neighborhoods that systematically appreciate more than the
rich neighborhoods during a city-wide house price boom, (3) the variance in house price growth is
also higher among the poor neighborhoods during a city-wide house price boom, and (4) among
the poor neighborhoods it is the poor neighborhoods that are in close proximity to the richer
neighborhoods that systematically appreciate at the highest rates during a city-wide house price
boom. Again, we think these facts are interesting in their own right. Additionally, these facts will
be consistent with the theory of endogenous gentrification that we develop in the next section.
4
Model
In this section, we develop a spatial model of housing prices across neighborhoods within a city
consistent with the facts documented in the previous section and based on a positive neighborhood
externality: people like to live next to richer neighbors. We do not micro-found the source of this
externality and leave the model flexible enough to encompass alternative possible stories behind
the preference for richer neighborhoods, such as lower crime rates, higher school quality, and more
positive neighborhood amenities. Whatever micro-foundation one prefers, the presence of such an
20
In the online robustness appendix, we specify in detail all our sample criteria when using the expanded set of
census tracts. In particular, we discuss how we select census tracts that are consistently defined over time.
21
We also performed a series of additional robustness specifications on our results. These results are shown in
our online robustness appendix. For example, Brueckner and Rosenthal (2008) show that the age and quality of the
housing stock could be an important determinant of which neighborhoods will subsequently gentrify. Our results are
robust to the inclusion of the initial age of the housing stock in our specifications.
14
externality generates a gentrification process in response to a city-wide increase in housing demand.
We are interested in exploring the relationship between gentrification and house price dynamics in
response to city-wide housing demand shocks.
4.1
Set up
Time is discrete and runs forever. We consider a city populated by Nt infinitely lived individuals
comprised of two types: a continuum of rich households of measure NtR and a continuum of poor
households of measure NtP . Each period households of type s, for s = R, P , receive an exogenous
endowment of consumption goods equal to y s , with y P < y R .22
The city is represented by the real line and each point on the line i ∈ (−∞, +∞) is a different
location. Agents are fully mobile and can choose to live in any location i. Denote by nst (i) the
measure of households of type s who live in location i at time t and by hst (i) the size of the house
they choose. In each location, there is a maximum space that can be occupied by houses which is
normalized to 1,23 that is,
R
P
P
nR
t (i) ht (i) + nt (i) ht (i) ≤ 1 for all i, t.
Moreover, market clearing requires
Z
+∞
−∞
nst (i) di = Nts for s = R, P.
(3)
The key ingredient of the model is that there is a positive location externality: households like
to live in areas where more rich households live. Each location i has an associated neighborhood,
given by the interval centered at i of fixed radius γ. Let Ht (i) denote the total space occupied by
houses of rich households in the neighborhood around location i,24 that is,
Z
i+γ
Ht (i) =
R
hR
t (j) nt (j) dj.
(4)
i−γ
22
The assumption that there are only two types of households (rich and poor) is for simplicity. One could extend
the model to allow for a continuum of income types. The models implications would then depend on the shape of
the income distribution and on the way in which the externality is modeled. In particular, the externality would be
equal to some weighted average of the income of the households who live in each neighborhood.
23
Our notion of space is uni-dimensional: if there is need for more space to construct houses we assume that the
neighborhoods have to expand horizontally. We could enrich the model with a bi-dimensional notion of space, by
allowing a more flexible space constraint in each location. For example, we could imagine some form of adjustment
cost to construct in each location, so that in reaction to a demand shock the city can expand both in the horizontal
and in the vertical dimension. Our model is the extreme case with infinite adjustment cost on the vertical dimension
and no adjustment costs on the horizontal dimension. Our mechanism would go through if we allow some convex
adjustment costs to the vertical margin.
24
An alternative is to define the neighborhood externality Ht (i) as the measure of rich households living in the
neighborhood around location i (or even as their average income). However, this would make the model less tractable
without affecting the substance of the mechanism. A more interesting extension would be to relax the assumption
that a neighborhood has a fixed size and make the concept of a neighborhood more continuous. Again the main
mechanism of the model would survive this change, but the price schedule would look smoother.
15
Households have non-separable utility in non-durable consumption c and housing services h.
The location externality is captured by the fact that households enjoy their consumption more if
they live in locations with higher Ht (i). The utility of a household of type s located in location i
at time t is given by us (c, h, Ht (i)), where u (.) is weakly concave in c and h. For tractability, we
s
assume that u takes the following functional form: us (c, h, H) = cα hβ (A + H)δ , where α, β, and
δ s are non negative scalars and A is a constant that prevents utility from being zero when H takes
the value of zero.25 Moreover, we assume that δ R ≥ δ P , so that rich households who generate the
externality benefit from it at least as much as poor households. We want to stress that all of the
implications of our model go through even if δ R = δ P .
On the supply side, there is a representative firm who can build housing in any location i ∈
(−∞, +∞). There are two types of houses: rich houses (type R) and poor houses (type P ). Each
type of household only demands houses of his own type. The marginal cost of building houses of
type s is equal to C s , with C R ≥ C P . If the firm wants to convert houses of type s̃ into houses
of type s, he has to pay C s − C s̃ . The (per square foot) price of a house for households of type
s in location i at time t is equal to pst (i). Hence there is going to be construction in any empty
location i as long as pst (i) ≥ C s . Moreover, if the firm wants to construct a house of type s in a
location occupied by a house of type s̃, he has to pay the converting cost and the additional cost
of convincing households of type s̃ to leave. Hence, there is going to be construction of houses of
type s in any location occupied by agents of type s̃ if pst (i) ≥ C s − C s̃ + ps̃t (i).
Finally, there is a continuum of risk-neutral competitive intermediaries who own the houses
and rent them to the households. The intermediaries are introduced for tractability. If we allowed
the households to own their houses, nothing would change in steady state, but the analysis of a
demand shock would be more complicated.26 The (per square foot) rent for a house of type s in
location i at time t is denoted by Rts (i). As long as the rent in location i at time t is positive, the
intermediaries find it optimal to rent all the houses in that location. Also, for simplicity, assume
that houses do not depreciate. Competition among intermediaries requires that for each location i
the following arbitrage equations hold:
pst (i)
4.2
=
Rts (i)
+
1
1+r
pst+1 (i) for all t, i, s.
(5)
Equilibrium
P
An equilibrium is a sequence of rent and price schedules RtR (i) , RtP (i) , pR
t (i) , pt (i) i∈R and of
R
P
allocations nt (i) , nPt (i) , hR
t (i) , ht (i) i∈R such that households maximize utility, the representative firm maximizes profits, intermediaries maximize profits, and markets clear.
Because of full mobility, the household’s maximization problem reduces to a series of static
25
Davis and Ortalo-Magné (2010) show that a Cobb-Douglas relationship between housing consumption and nonhousing consumption fits the data well along a variety of dimensions.
26
When the economy is hit by a positive demand shock, we will show that house prices appreciate by different
amounts in different locations. If households own their houses this would introduce an additional source of heterogeneity in wealth which would complicate the analysis.
16
problems. The problem of households of type s at time t is simply
s
max s cα hβ [A + Ht (i)]δ ,
c,h,i∈It
s.t. c + hRts (i) ≤ y s ,
where households take as given the function Ht (i), the rent schedule Rts (i), and the set Its of
locations where houses for type-s households are available. Hence, conditional on choosing to live
in location i at time t, the optimal house size is
hst (i) =
β
ys
for all t, s, i ∈ Its .
α + β Rts (i)
(6)
Households choose to live in bigger houses in neighborhoods where the rental price is lower and,
conditional on a location, richer households choose bigger houses. Given that households are fully
mobile, it must be that at each point in time, the equilibrium rents in different locations make them
indifferent. In particular, agents of type s have to be indifferent among living in different locations
where houses of their type are available at time t, that is, in all i ∈ Its .27 Then it must be that
Uts (i)
α β
≡α β
ys
α+β
α+β
[A + Ht (i)]δ
Rts (i)β
s
= Ūts for all t, s, i ∈ Its .
(7)
This, in turn, requires that
δs
Rts (i) = K s [A + Ht (i)] β for all t, s, i ∈ Its ,
(8)
for some constant K s . This expression is intuitive, as rents must be higher in locations with a
stronger externality. Moreover, rich households are more willing to pay higher rents for a given
locational externality, all else equal.
Proposition 1 If δ R ≥ δ P , there exists an equilibrium with full segregation. If C R = C P , an
equilibrium with full segregation exists if and only if δ R ≥ δ P .
This proposition proves that if δ R ≥ δ P there exists an equilibrium with full separation. In
particular, the proof proceeds by constructing an equilibrium with full segregation, where the rich
households are concentrated in the city center, while the poor households live at the periphery of
the city. This is the equilibrium we will focus on in the rest of the analysis. However, there may be
other equilibria with full segregation with more centers of agglomeration of the rich households.28
Moreover, let us highlight that there may be other types of equilibria, e.g. we can construct an
equilibrium with partial segregation, where intervals with only poor people alternate with intervals
27
If there was a location with construction of type s and no type s households living there, the intermediaries would
be willing to decrease the rent to 0 inducing households of type s to move into that location.
28
It is interesting to notice that, as long as these centers are far enough from each other, the implications in terms
of house prices are isomorphic to the equilibrium we focus on.
17
where poor and rich people coexist.29
Let us now proceed to the construction of our equilibrium. As a normalization, we choose point
0 as the center of the city. Then, I R = [−It , It ] and I P = [−I¯t , −It , ) ∪ (It , I¯t ], for some I¯t > It > 0.
t
t
Both the size of rich neighborhoods, It , and the size of the city, I¯t , are equilibrium objects. Given
that such an equilibrium is symmetric in i, from now on, we can restrict attention to i ≥ 0.
R
Since rich households live in locations where there are no poor, it must be that hR
t (i) nt (i) is
either equal to 1 or to 0 and is equal to 1 for all i ∈ [0, It ]. Then, we can easily derive the externality
function Ht (.) as follows:
(
Ht (i) =
for i ∈ [0, It − γ]
.
max {γ + It − i, 0} for i ∈ (It − γ, I¯t ]
2γ
(9)
That is, neighborhoods close to the city center are richer and enjoy the maximum degree of externality, while the farther a location is from the center the smaller the strength of the externality.
Figure 2 shows the externality Ht (i) for a given t as a function of the location. If I¯t > It + γ, there
are going to be locations at the margin of the city where the externality has zero effect. From now
on, we assume that the measure of poor households, NtP , is sufficiently large so that I¯t > It + γ.
Combining (8) and (9), we obtain
K R = RtR (It ) (A + γ)
−
δR
β
− δP
and K P = RtP I¯ A β ,
(10)
so that we can rewrite the rent schedules as
δR
β
min
{γ,
I
−
i}
t
RtR (i) = RtR (It ) 1 +
for i ∈ [0, It ] ,
A+γ
δP
max {γ + It − i, 0} β
P
P ¯
for i ∈ (It , I¯t ].
Rt (i) = Rt It 1 +
A
(11)
(12)
From the optimizing behavior of the representative firm, it must be that the price of a poor house
at the boundary of the city is equal to the marginal cost C P .30 Moreover, the price of a rich house
at the boundary of the rich neighborhoods must be equal to the price of a poor house, which is the
compensation needed to vacate poor households living there, plus the additional cost of transforming
P
R
P
a poor house to a rich one. This implies that pPt I¯t = C P and pR
t (It ) = pt (It ) + C − C . In
equilibrium prices are constant over time and hence arbitrage conditions (5) require that for each
location i ∈ Its prices satisfy
pst (i) =
1+r s
Rt (i) for all t, i, s.
r
29
(13)
However, we can show that there is no equilibrium with full integration, that is, where poor and rich agents
simultaneously live in every occupied location.
30
We assume that the economy starts with no housing and a fixed measure of poor and rich agents N P and N R .
Then at date 0 there is positive construction which pins down the housing price at the boundary of the city. See
footnote 30 for the case of a negative shock to the measure of agents if the economy starts with a positive stock of
housing.
18
Combining these conditions we obtain
RtP I¯t =
r
r
C P and RtR (It ) = RtP (It ) +
CR − CP ,
1+r
1+r
(14)
where, from (8) and (10), we have
r
RtP (It ) =
CP
1+r
A+γ
A + max γ + It − I¯t , 0
! δP
β
.
(15)
Combining these last two expressions with (11), (12), and (13) allows us to determine the rent
and the price schedules as a function of It and I¯t only. Figure 2 also shows the shape of the price
schedule as a function of the location.
In our full segregation equilibrium, the rich households are concentrated in the city center, while
the poor are located at the periphery. Equilibrium prices reflect the fact that locations that are
further away from the center of the rich enclave and closer to the space occupied by poor households
are less appealing. In particular, prices are the highest in the center of the rich neighborhoods.
As we move away from the center, prices start declining because the space in the neighborhood
occupied by rich households goes down. This segregation equilibrium is sustained by the fact that
the poor are unwilling to lower their non housing consumption by paying higher rent to get the
larger neighborhood externality.
To complete the characterization of the equilibrium, we need to determine the size of the city,
¯
It , and the size of the rich neighborhoods, It . Using market clearing (3) together with the optimal
housing size (6) and the fact that ItR = [−It , It ] and ItP = [−I¯t , −It , ) ∪ (It , I¯t ], we obtain the
following expressions for It and I¯t :
It
I¯t
β+δR
β+δR
β yR N R
β
−1
β
β
= γ + (A + 2γ)
−
(A + γ)
(A + γ)
− (A + 2γ)
(16)
α + β 2K R
δR + β
β+δ
δ
δP
P
β
β yP N P
− P
+1
−1
β
β
= It + γ + A β
−
A
A
−
(A
+
γ)
.
(17)
α + β 2K P
δP + β
−
δR
β
As intuition suggests, the rich neighborhoods cover a larger portion of the city when NtR (the
number of rich people) or y R (the income of rich people) are higher, and when the marginal cost of
construction C R or the interest rate r are lower. Moreover, the city overall is bigger when the there
are more rich households when the rich households are richer, when there are more poor households
or when the poor are richer. Likewise, the city is larger when the marginal cost of construction C P
or the interest rate are lower.
Finally, we have to check that the households choose their location optimally, that is, we have
to check that the rich would not prefer to move to a poor neighborhood and vice versa. More
precisely, we need to prove that UtR (i) ≤ ŪtR for all i ∈ It , I¯t and UtP (i) ≤ ŪtP for all i ∈ [0, It ]
where Uts (i) is defined in expression (7). In the Appendix, we show that both these conditions are
satisfied if δ R ≥ δ P , completing the proof of the Proposition.
19
4.3
Demand shock
We are now interested in analyzing how house prices, both at an aggregate and at a disaggregate
level, react to an unexpected increase in the demand for housing.31 We will do so by focusing on
the equilibrium with full segregation where all rich agents live in a connected interval, which we
constructed in the previous section.
In equilibrium, the aggregate price level is given by
Pt =
2
It
It
Z
0
2
pR
t (i) di + ¯
It − It
Z
I¯t
pPt (i) di,
It
where, from the analysis in the previous section,
"
pR
t (i)
pPt
=
C
P
γ
1+
A
δP
β
R
+C −C
P
#
min {γ, It − i}
1+
A+γ
δR
β
for i ∈ [0, It ] ,
δP
max {γ + It − i, 0} β
for i ∈ (It , I¯t ],
(i) = C
1+
A
P
(18)
(19)
with It and I¯t given by (16) and (17).
For concreteness, we analyze the economy’s reaction to a migration shock, but the price dynamics are equivalent if we consider any shock that increases housing demand, such as a positive
income shock or a reduction in the interest rate. Imagine that at time t+1 the economy is hit by an
unexpected and permanent increase in the population N . Let us assume that the measure of both
s
rich and poor households increase proportionally, that is, Nt+1
= φNts with φ > 1 for s = P, R. We
now show that the aggregate level of house prices permanently increases and prices in locations with
a higher initial price level typically react less than prices in locations where houses are cheaper to
start with and which are closer to the expensive neighborhoods. The new rich households moving
into the city want to live close to other rich households, so that the poor neighborhoods close to the
rich ones get gentrified and the poor households who used to live there move towards the periphery.
This is what we refer to as endogenous gentrification. The house prices in gentrified neighborhoods
are driven up due to our externality.
Let us define the function gt (.) : C P , p̄ 7→ [1, ∞), where gt (p) denotes the average gross
growth rate between time t and t + 1 in locations where the initial price is equal to p, that is,
gt (p) = Et+1
and p̄ ≡ [C P (1 + γ/A)
δP
β
pt+1 (i)
|pt (i) = p ,
pt (i)
+ C R − C P ] (1 + γ/ (A + γ))δR /β . The next proposition shows that after
31
The long run reaction of house prices would be symmetric in the case of a negative shock if we introduce some
degree of depreciation that is big enough relative to the shock. However, after a negative shock the economy would
not jump to the new steady state immediately, but there would be some transitional dynamics. Contact the authors
if you are interested in the full analysis of a negative demand shock in the presence of depreciation. Given our data,
we only focus on housing booms resulting from positive housing demand shocks.
20
an unexpected permanent positive demand shock, the aggregate price level permanently increases
and the price growth rate is higher in locations that had lower price levels initially, whenever prices
are higher than the minimum level, consistent with Fact 2.32
Proposition 2 Suppose the city exhibits an equilibrium with full segregation where all rich agents
live in a connected interval. Imagine that at time t + 1 the economy is hit by an unexpected and
s
permanent increase in population, that is, Nt+1
= φNts with φ > 1 for s = P, R. Then there is a
permanent increase in the aggregate price level Pt , and
Et+1
pt+1 (i)
pt+1 (i)
|pt (i) = p̄ < Et+1
|pt (i) < p̄ .
pt (i)
pt (i)
Moreover, if the shock is large enough, gt (p) is non-increasing in p for all p > C P .
Figure 3 illustrates the response of house prices in different locations to a positive demand shock
(a proportional increase in population). Given that the city is symmetric, the figure represents
only the positive portion of the real line. One can notice that both the size of the city I¯t and
the size of the rich neighborhoods It expand, and prices remain constant at the two extremes: in
the richest locations in the center of the city and far enough away from the rich neighborhoods.
Most importantly, prices strictly increase in the rich neighborhoods on the border of the poor
neighborhoods where the externality is below its maximum level and, even more, in the poor
neighborhoods that are physically close to the rich neighborhoods. Clearly, this makes the aggregate
level of prices in the city increase permanently.
The next proposition shows the main implication of our model: among the locations with initial
level of price equal to C P , the ones that appreciate the most are closer to the richer neighborhoods.
Proposition 3 Suppose the city exhibits an equilibrium with full segregation where all rich agents
live in a connected interval. Imagine that at time t + 1 the economy is hit by an unexpected and
s
permanent increase in population, that is, Nt+1
= φNts with φ > 1 for s = P, R. Then
d (pt+1 (i) /pt (i))
≤ 0 for pt (i) = C P .
di
Among the poor neighborhoods, it is the poor neighborhoods in close proximity to the richer
neighborhoods that should appreciate the most during a city-wide housing demand shock. This
proposition underlies the variation in appreciation rates among the poorer neighborhoods. The
poor neighborhoods next to the rich neighborhoods experience large price increases because they
gentrify. Rich households expand into the neighborhood thereby increasing the desirability of being
in those neighborhoods. This proposition is consistent with Facts 3 and 4 and lies at the heart
of our following empirical work. An increase in city-wide housing demand - perhaps do to an in
32
See the online appendix for all the proofs that are not in the text.
21
migration of rich residents - will cause poor neighborhoods on the border of richer neighborhoods
to gentrify. The empirical work that follows does, in fact, show strong support for this prediction.
Proposition 4 Suppose the city exhibits an equilibrium with full segregation where all rich agents
live in a connected interval. Imagine that at time t + 1 the economy is hit by an unexpected and
s
permanent increase in population, that is, Nt+1
= φNts with φ > 1 for s = P, R. Then the growth
rate in the aggregate price level is larger the larger is the increase in φ and, if the shock is large
enough, d2 gt (p) /dpdφ ≤ 0 for all p > C P where the derivative is well-defined.
This proposition shows that if two identical cities are hit by demand shocks of different sizes, the
one hit by the larger shock is going to feature both a higher aggregate price growth rate and more
price appreciation among the poor neighborhoods due to a higher degree of gentrification, consistent
with the facts. It is also easy to show that two cities with different initial income composition react
differently to the same demand shock. In particular, if the shock is large enough, the initially richer
city is the one that features both a higher aggregate price growth rate and higher within-city house
price convergence.
5
Housing Price Dynamics and Proximity to Rich Neighborhoods:
Exogenous Housing Demand Shock
In Section 3, we established empirical relationships that are consistent with our theory of endogenous gentrification. In particular, we documented that during a city-wide housing boom it is the
poor neighborhoods bordering the rich neighborhoods that appreciate the most. However, the prior
descriptive results do not make any claims about causation. In this section, we directly explore
whether an exogenous shock to housing demand in a city affects property prices differentially across
neighborhoods within that city in a way that is consistent with our theory.
5.1
Exogenous Housing Demand Shock: Bartik Instrument
To measure exogenous shocks to local housing demand for each city j between t and t + k, we use
the variation in national earnings by industry between t and t + k. This approach of imputing
exogenous income shocks for local economies was developed by Bartik (1991) and has been used
extensively by others in the literature as a measure of local labor demand shocks.33 In doing
so, we are explicitly equating local income shocks with local housing demand shocks. As shown
by Blanchard and Katz (1992), such positive Bartik-type local income shocks cause an influx of
population from other cities which puts upward pressure on city-wide housing prices.
To compute exogenous changes in city-level income, we use the initial industry composition of
residents within the city’s MSA in period t. Note, that even though we are examining house price
dynamics within a given city, our estimate of the local demand shock is based on the industry
33
See, for example, Blanchard and Katz (1992), Notowidigdo (2010), and Charles et al. (n.d.).
22
mix of the MSA as a whole. Given the amount of commuting into and out of the city from the
suburbs (in both directions), we feel that the MSA income shock is a broader proxy for city-wide
changes in housing demand. Then, for each MSAj , we compute the predicted income growth for the
MSA using the initial industry shares and the growth in income for individuals in those industries
between t and t + k for the entire U.S. (excluding residents from MSAj ).
For our results examining the neighborhood response to local housing demand shocks, we focus
on the 1980-1990 period. We analyze this period because there is significant variation across MSAs
in predicted MSA-wide average income growth based on industry composition during this time.
Specifically, we use the five percent samples from the 1980 and 1990 IPUMS data to compute
MSA-level predicted income growth. For this procedure, we use two-digit industry classifications.
Our measure of income is individual earnings. The only restrictions we place on the data are
that the individual had to be employed full-time (worked 48 weeks or more in the prior year and
usually worked more than 30 hours per week) and had to be between the ages of 25 and 55. Again,
when computing the predicted income growth for a given MSA, we exclude the residents of that
MSA in calculating the national income growth between 1980 and 1990 for each of the industries.
To compute the MSA predicted income growth, we simply multiply the industry growth rate in
earnings by the fraction of people between 25 and 55 in each MSA working full time in those
industries in 1980.
There is a large amount of variation in actual income growth by industry between 1980 and
1990. For example, the Security, Commodity Brokerage, and Investment Companies industry had a
real appreciation of annual earnings of roughly 59% during the 1980s. Likewise, the Legal Services
industry had a real appreciation of annual earnings of 55%. On the other hand, the Trucking
Services and Warehousing and Storage industry only had a real appreciation of annual earnings
of 3%. As a result of differences in industry mixes across MSAs, there is a nontrivial amount of
j
\ t,t+k to be the
predicted income variation across the MSAs. To set notation, we define IncShock
predicted income growth for the MSA corresponding to city j between t (1980) and t + k (1990)
based on the industry mix of residents in the MSA in 1980.
For our results in this section, our sample includes all MSAs that contain a city which has at
least 30 census tracts within the city. This will be the same sample that we used in column 7 of
j
\ t,t+k across these MSAs was 19.5 percent with a standard deviation
Table 3. The mean of IncShock
of 1.5 percent. As shown by others in the literature, the predicted Bartik income growth for the
MSA does in fact predict actual MSA income growth. A simple regression of actual MSA income
j
j
\ t,t+k yields a coefficient on IncShock
\ t,t+k of 2.26 (with a
growth during the 1980s on IncShock
standard error of 0.60) and a F-stat of 14.01.
To examine the effect of exogenous housing demand shocks on within-city house price dynamics,
we estimate a specification similar to (2):
i,j
∆Pt,t+k
Pti,j
j
i,j
i,j
i,j
i,j
\
= µj + β1 ln(Disti,j
t ) + β2 ln(Distt ) ∗ IncShock t,t+k + ΓXt + ΨZt + t,t+k
23
(20)
j
i,j
i,j
i,j
\
where ∆Pt,t+k
/Pti,j , ln(Disti,j
t ), IncShock t,t+k , Xt , Zt , and µj are defined as above. We are
interested in β2 , the coefficient on the interaction term. With this regression, we are asking whether,
for a given sized city income shock, poor neighborhoods within the city in close proximity to rich
neighborhoods within the city appreciate more than otherwise similar poor neighborhoods that are
farther away. For our measure of housing price growth, we use the Census data and for the measure
of neighborhood we use census tracts. As with the results above that use census house price data,
we include controls for changes in the neighborhood housing stock characteristics as part of our X
vector. Otherwise, the X vector is the same. Because our instrument is an estimated regressor, we
bootstrap our standard errors.34
5.2
Results
The results of estimating the above equation are shown in Table 4. In column 1, we estimate (20) as
it is specified. The variable of interest is in the second row and provides an estimate of β2 . As with
the simple descriptive results shown in Table 3, an exogenous shock to city income results in house
prices increasing more in poor neighborhoods that are in close proximity to rich neighborhoods
(coefficient = -2.33 with a standard error of 0.49). To help interpret the economic magnitude,
we consider the differential housing price response to otherwise similar poor neighborhoods which
are 1 and 4 miles away from a rich neighborhood in response to the MSA receiving a one-standard
deviation MSA-level predicted income shock of 1.5 percent. Given the estimated coefficient, a census
tract that starts in the bottom half of the city-wide house price distribution in 1980 appreciates
by 7.0 percentage points more when they are 1 mile from a high price census tract relative to an
otherwise similar census tract that is 4 miles away (-2.33 * 2 * 0.015). This result is non-trivial
and is in line with the general descriptive patterns shown in Table 3.
In column 2, we re-run the same specification replacing the log distance variable with two
dummy variables measuring the proximity to high housing price census tracts. We do this to
explore in greater depth whether the relationship between housing price growth and proximity to
richer neighborhoods declines monotonically as the poor neighborhoods become farther away from
the rich neighborhoods. Specifically, we replace the log distance measure with dummies indicating
whether the census tract was between 0 and 1 miles and between 1 and 3 miles, respectively, to
the nearest census tract in the top quartile of the city-wide house price distribution in 1980. We
are interested in the coefficient on the interaction between these dummies and the instrumented
change in neighborhood income. The house price response to an exogenous city-wide income shock
is positive and statistically different from zero for both distance ranges. Reassuringly, the house
price response is four times as large for census tracts that are between 0 and 1 miles from the high
housing price neighborhoods relative to census tracks between 1 and 3 miles from the high housing
price neighborhoods (p-value of difference of the two coefficients = 0.02). Given the average size of
34
For each iteration in the bootstrap procedure, we sample with replacement from the 1980 and 1990 IPUMS data
to calculate the first stage. Next, we sample with replacement from the census tracts in each of the cities in our
sample to calculate the second stage. We report standard errors calculated by repeating this process 2,500 times. We
also estimated the standard errors using only 500 repetitions. The results were very similar.
24
census tracts, almost all the initially poor census tracts within 1 mile of a rich census tract actually
abut the rich neighborhood. In other words, the biggest responses in prices within a city to a citywide housing demand shock are for those poor census tracts that border richer census tracts. The
estimated magnitudes are also nontrivial. In response to a one standard deviation instrumented
income shock, poor census tracts within 0 and 1 miles and within 1 and 3 miles appreciated by 6.1
and 1.5 percentage points more, respectively, than poor census tracts more than 3 miles away.
We wish to make four additional comments about the results in Table 4. First, given that we
are including city fixed effects, all our results are identified off of within-city variation. Second, as
with the results in Table 3, we are controlling for proximity to CBD, average commuting times, and
proximity to fixed natural amenities. Given this, our results are being driven by proximity to rich
neighborhoods above and beyond proximity to the center business district or fixed natural amenities
within the city. Third, although not shown, the results hold broadly for the 1990s as well but power
is more of an issue during that time period. Finally, we explored whether the responsiveness of
house prices in poor neighborhoods that were close to rich neighborhoods to Bartik shock was
greater in cities where housing supply was more inelastic. To do this, we further interacted our
distance to rich neighborhoods and our distance measure multiplied by the Bartik shock with Saiz’s
measure of MSA housing supply elasticity (Saiz, 2010). The point estimates of the triple interaction
indicated that the price response of poor neighborhoods bordering rich neighborhoods was stronger
in more inelastic cities. However, the standard error was much too large to be conclusive.
6
Housing Price Dynamics, Proximity to Rich Neighborhoods,
and Evidence of Neighborhood Gentrification
In this section, we examine more deeply the main mechanism of our model: after a city-wide housing
demand shock the poor neighborhoods next to the rich neighborhoods are the ones that appreciate
the most because they are the ones where rich households migrate to. This implies that neighborhoods that experience higher house price appreciation should also show signs of gentrification.
We show three sets of results documenting that the neighborhoods we focus on which experienced
higher house price appreciation also showed signs of gentrification.
6.1
A Descriptive Analysis
To analyze whether neighborhoods that experienced a rapid growth in prices also experienced signs
of gentrification, we estimate the following descriptive relationship:
i,j
∆Yt,t+k
Yti,j
= µj + β
i,j
∆Pt,t+k
Pti,j
+ ΓXti,j + ΨZti,j + i,j
t,t+k
i,j
i,j
where ∆Pt,t+k
/Pti,j , Xti,j , Zti,j , and µj are defined as above, and ∆Yt,t+k
/Yti,j , is the growth rate of
median household income from t to t + k in neighborhood i in city j. The regression asks whether
25
or not a neighborhood that experiences higher house price growth than other neighborhoods within
the city also experiences higher income growth than other neighborhoods within the city. In
this specification, we are equating neighborhood income growth with neighborhood gentrification.
In the work below, we try to explore different and perhaps broader measures of neighborhood
gentrification. However, given that the force in our model that drives the house price appreciation
of poor neighborhoods that abut rich neighborhoods is the exodus of poor residents which are
replaced by richer residents, we think neighborhood income growth is a good summary statistic for
the mechanism we are trying to highlight.
The results of this regression, using different samples, different measures of housing price growth
and different levels of aggregation for a neighborhood, are shown in Table 5. In columns 1 - 4, we
look at the relationship between income growth and house price growth across neighborhoods
during the 1990s. In column 5, we explore the relationship during the 1980s. In columns 1 and 2,
we restrict our analysis to Case-Shiller zip codes using Case-Shiller house price data (column 1) and
Census house price data (column 2), respectively, to compute housing price growth. In columns 3
- 5, we use Census house price data to compute housing price growth and define neighborhoods at
the level of a census tract. In column 3, we explore census tracts in Case-Shiller cities. In columns
4 and 5, we explore all census tracts in cities that have at least 30 consistently measured census
tracts over the decade. As with our analysis in Tables 3 and 4, we also restrict all samples to
include only neighborhoods within the city that are in the bottom half of the city’s house price
distribution in period t. As a result, the samples used for columns 1-5 of Table 5 are analogous to
samples used in columns 3-7 of Table 3, respectively.
The main take away from Table 5 is that there is a strong relationship between neighborhood
income growth and neighborhood house price growth regardless of the house price measure, regardless of the level of aggregation and regardless of the time period. Although not shown, these results
still hold even if we drop the X and Z vectors of neighborhood controls from the regressions.
6.2
An Ex-Post Analysis
In this subsection, we perform a different analysis to highlight the spatial nature of gentrification.
In particular, we identify all neighborhoods within cities that ex-post can be classified as having
gentrified according to some broad definition and we examine their spatial proximity to high income
neighborhoods. Our goal is to illustrate that when gentrification occurs, it almost always occurs in
poorer neighborhoods that border higher income neighborhoods.
For our analysis, we define a gentrifying neighborhood as a neighborhood within a city that starts
with median neighborhood house prices in the bottom half of the city’s house price distribution in
period t and where the median real income of neighborhood residents grows by either 50 percent or
25 percent between t and t + k. We use our broadest sample of cities with at least 30 consistently
measured census tracts for the 1980s and 1990s. Specifically, the samples we use are the same as
those used in columns 6 and 7 of Table 3.
For this analysis, we simply regress a dummy variable for whether the initially poor neighbor26
hood gentrified by some income growth metric on distance dummies to the nearest rich neigbhorhood and city fixed effects. As above, we define rich neighborhoods as those neighborhoods that
were in the top quartile of the city’s median house price distribution in period t. We define four
dummy variables to measure the poor neighborhood’s proximity to the nearest rich neighborhood:
between 0 and 0.5 miles, between 0.5 and 1 mile, between 1 and 2 miles, and between 2 and 3 miles.
Finally, we run such regressions separately for two measures of gentrification: neighborhood real
income growth greater than 50 percent during the decade and neighborhood real income growth
greater than 25 percent during the decade.
The results of these regressions are shown in Table 6. The results are quite striking. Take,
for example, the results where gentrification is defined as a poor neighborhood having average
neighborhood income growth increasing by at least 50 percent during the decade. Between 1980
and 1990, 11% of all poor neighborhoods gentrified by this metric. The comparable number between
1990 and 2000 was 5.9%. During the 1980s, the probability of gentrification was 7.0 percentage
points higher if the census tract was between 0 and 0.5 miles from a high house price neighborhood
than for a poor census tract that was more than 3 miles away from a rich neighborhood (column 1 of
Table 3, p-value < 0.01). The coefficient is large in economic magnitude. Given the base gentrifying
rate was 11 percentage points, a poor census tract being within 0 and 0.5 miles was associated with
a 64 percent increase in the probability of gentrification. During the 1990s, poor census tracts that
were within 0.5 mile of a rich census tract were 97 percent more likely to gentrify than poor census
tracts that were more than 3 miles away from the rich census tracts. Similar patterns are found in
both decades if we define gentrification as neighborhood income growth increasing by 25%.
Poor census tracts that were within 0.5 miles of a rich census tract almost always abutted the
rich census tract. Among the poor census tracts, as one moves farther away from the nearest rich
census tract, the probability of gentrification declines monotonically. These results are also seen in
Table 6.
The results are consistent with the housing price dynamics in our model: poor neighborhoods
tend to gentrify only when they are in close proximity to existing rich neigbhorhoods. The results
show that there is definitely a spatial nature to the gentrification process.
6.3
Exogenous Housing Demand Shock
In the final subsection, we complete our analysis by assessing whether exogenous city-wide demand
shocks cause poor neighborhoods in close proximity to richer neighborhoods to endogenously gentrify. As we saw in Table 4, poor neighborhoods in close proximity to rich neighborhoods had
house price growth that was larger than other poor neighborhoods in response to positive city-wide
Bartik shocks. In this subsection, we show that these close neighborhoods were also more likely to
experience signs of gentrification.
To look for signs of endogenous gentrification, we estimate the following:
j
i,j
i,j
i,j
i,j
\
Gi,j
t,t+k = µj + β1 ln(Distt ) + β2 ln(Distt ) ∗ IncShock t,t+k + ΓXt + t,t+k
27
(21)
where Gi,j
t,t+k is a measure of gentrification in neighborhood i of city j between t and t + k. Specifically, we use three measures of Gi,j
t,t+k : the percentage increase in neighborhood income between t
and t+k, the percentage point change in the poverty rate between t and t+k, and the percentage
point change in the fraction of residents in the neighborhood who had a college degree or more.
Aside from the change in the dependent variable, (21) is analogous to (20) estimated above for
j
\ t,t+k are
neighborhood housing price growth. Moreover, the sample and definition of IncShock
exactly the same as the specifications used to estimate (20) in Table 4.35
The results from estimating (21) are shown in Table 7. In response to a city-wide housing
demand shock, it is the poor census tracts that are in close proximity to the rich census tracts
that are much more likely to experience rising incomes, declines in the poverty rate, and rising
educational attainment of residents relative to poor census tracts that are farther from the rich
census tracts. Specifically, in response to a one-standard deviation instrumented income shock,
poor census tracts that were 1 mile from rich neighborhoods experienced income growth that was
1.7 percentage points higher than poor neighborhoods that were 4 miles away. Given that the
average census tract in our sample experienced income growth of 14.9 percent during the decade,
this represents an increase in income of 11 percent for poor neighborhoods that are close to rich
neighborhoods in response to a one standard deviation instrumented income shock. Likewise, poor
neighborhoods that are 1 mile from the rich neighborhoods experienced 23 percent lower increases in
the poverty rate and 25 percent higher increases in the fraction of residents with a college degree or
more relative to otherwise similar poor neighborhoods that are 4 miles from the rich neighborhoods.
7
Conclusion
In this paper, we explore the response of housing price dynamics across neighborhoods to a citywide housing demand shock. The main empirical fact that we document is that poor neighborhoods
on the border of richer neighborhoods experience the largest increase in house price appreciation in
response to a city-wide housing demand shock. In particular, we find that during the 1980s poor
neighborhoods that bordered richer neighborhoods had house prices that appreciated by 7.0% more
than otherwise similar poor neighborhoods which were farther away from rich neighborhoods in
response to a one standard deviation Bartik shock. Moreover, these neighborhoods simultaneously
experienced a more dramatic rise in resident income and education and a more dramatic decline in
the resident poverty rate.
We propose a model where positive city-wide housing demand shocks endogenously result in
neighborhood gentrification that is consistent with the facts. The key assumption is that all individuals prefer neighborhoods populated by richer households as opposed to neighborhoods populated
by poorer households. While we do not take a stand on the exact source of the externality, we
have in mind that richer neighborhoods have lower levels of crime, higher provisions of local public
35
Additionally, (21) does not include the Z vector of controls which were designed to capture other reasons why
house prices differed across neighborhoods.
28
goods, better peer effects, and a more extensive provision of service industries (like restaurants and
entertainment options).
Our work adds to that of of Brueckner (1977) and Kolko (2007) by showing that there is a large
spatial component to neighborhood gentrification. Aside from our results showing that it is the poor
neighborhoods next to the rich neighborhoods that respond the most to city-wide housing demand
shocks, we also show that proximity to rich neighborhoods is a defining feature of neighborhood
gentrification. Choosing neighborhoods that have ex-post gentrified, we find that the probability
of gentrification is 64 percent higher for neighborhoods that were within 0.5 miles of an existing
rich neighborhood than otherwise similar neighborhoods that were farther away.
We also present a series of new facts about within city house price movements during city-wide
housing booms. As far as we know, we are the first paper to systematically analyze the differential
housing price dynamics across neighborhoods within cities during city-wide housing price booms.
We show that the within-city variation in house prices is almost as large as the well documented
cross-city variation in house prices during the last three decades. Also, we document that poor
neighborhoods experience larger housing price increases and a greater variation in housing price
increases relative to richer neighborhoods during city-wide housing price booms. The larger the citywide housing price boom, the more poor neighborhoods appreciate relative to rich neighborhoods.
Although our gentrification results only exploit the variation in house price appreciation among
poor neighborhoods during city-wide housing price booms, the facts we document suggest there
are many other interesting patterns in the data worth exploring in future work.
29
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Rosen, Sherwin, “Wage-based Indexes of Urban Quality of Life,” Current Issues in Urban Economics,
1979, 3.
Rossi-Hansberg, Esteban, Pierre-Daniel Sartre, and Raymond Owens III, “Housing Externalities,”
Journal of Political Economy, 2010, 118 (3), 485–535.
Saiz, A., “The Geographic Determinants of Housing Supply,” Quarterly Journal of Economics, 2010.
Zheng, S. and M.E. Kahn, “Does Government Investment in Local Public Goods Spur Gentrification?
Evidence from Beijing,” NBER Working Paper 2011.
31
Housing Price Growth versus Initial Housing Price 2000-2006: New York MSA
.5
1
1.5
New York MSA Zip Codes
11.5
12
12.5
Log Median Price 2000
13
13.5
Case−Shiller Growth Rate 2000−2006
R2 = 0.47, a = 6.14, ß = −0.43 (0.05) N = 105
Figure 1: Figure shows the initial house price in a zip code in 2000 versus the subsequent house
price growth in that zip code between 2000 and 2006. The sample includes all zip codes within
the New York metro area for which a Case-Shiller house price index exists. We measure the initial
house price using median home value from the 2000 Census. We use the Case-Shiller index to
compute the growth rate in house price between 2000 and 2006.
32
Model Generated Externality and House Prices across Neighborhoods
1
ht(i)nt(i)
It-γ
It
It+γ
It-γ
It
It+γ
Itbar i
Ht(i)
2γ
γ
C2
β/α
Itbar
i
pt(i)
C
It-γ
It
It+γ
Itbar
i
Figure 2: Figure shows the model predicted relationship between the size of the rich neighborhood
(top panel), the value of the neighborhood externality (middle panel), and the house price in the
neighborhood (bottom panel). For this figure, we assume C P = C R . This is done for illustrative
purposes.
33
House Price Response across Space to a Migration Shock
p(i) 25.7
25.6
25.5
after the shock
25.4
25.3
before the shock
25.2
25.1
25
24.9
0
0.2
0.4
0.6
0.8
1
1.2
i
Figure 3: We set α = .8, β = .8, δ R = .2, δ P = 0, A = 1, γ = .1, r = .03, y R = 1, y P = .5, C R =
C P = 25, N R = N P = .5. The shock is an unexpected and permanent increase in φ from φ = 1 to
φ = 5.
34
Table 1: House Price Growth Variation Across MSAs and Across Neighborhoods Within an MSA
or City
Time Period
(1)
(2)
(3)
(4)
(5)
(6)
(7)
2000 - 2006
(observations)
0.33
(384)
0.42
(20)
0.18
(1,693)
0.18
(497)
-
-
-
1990 - 2000
(observations)
0.17
(348)
0.21
(17)
0.16
(1,498)
0.17
(496)
0.15
(496)
0.40
(4,021)
0.54
(16,161)
Between
MSA
Between
MSA
Within
MSA
Within
City
Within
City
Within
City
Within
City
-
-
Zip
Code
Zip
Code
Zip
Code
Census
Tract
Census
Tract
FHFA
Case
Shiller
Case
Shiller
Case
Shiller
Census
Census
Census
Variation
Neighborhood Definition
House Price Data
Notes: Table shows the between MSA standard deviation of house price growth (columns 1 and 2) and the withincity/MSA standard deviation across neighborhoods (remaining columns) for different house price measures, different
time periods, and different definitions of neighborhoods. The Case-Shiller data is available for the 1990s and the
2000s. The Census house price growth measure is available only during the 1990s. For column 1, we use all 384
MSAs available in the FHFA data. For column 2, we use the 20 MSAs for which Case-Shiller reports an index. For
columns 3 - 5, we use all available zip codes for which a reliable Case-Shiller index exists. See the text for details. In
column 6, we use all census tracts that overlap the zip codes used in column 5. In column 7, we use all census tracts
in all cities where there at least 30 census tracts within the city. See text for additional details. For the Census data,
the top and bottom 1 percent of neighborhoods with respect to median home price growth are dropped.
35
Table 2: Housing Price Growth by Initial Price Quartile, Case-Shiller Data
(1)
Quartile 4
(2)
Quartile 3
(3)
Quartile 2
(4)
Quartile 1
(5)
p-val of
Quartile 4 = Quartile 1
2000 - 2006: Housing Booms
Chicago, City Level
Chicago, MSA Level
New York City, MSA Level
Boston, MSA Level
Los Angeles, MSA Level
San Francisco, MSA Level
Washington D.C., MSA Level
0.53
0.47
0.64
0.40
1.21
0.35
1.29
0.66
0.50
0.76
0.47
1.41
0.41
1.37
0.72
0.49
0.86
0.54
1.58
0.49
1.49
0.88
0.69
1.11
0.61
1.76
0.61
1.61
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1990 - 1997: Housing Booms
Denver, MSA Level
Portland, MSA Level
0.51
0.41
0.50
0.52
0.52
0.49
0.89
0.69
0.00
0.00
1984 - 1989: Housing Booms
Boston, MSA Level
0.65
0.70
0.75
0.84
0.00
1990 - 1997: Housing Busts
San Francisco, MSA Level
Boston, MSA Level
-0.08
-0.05
-0.07
-0.08
-0.11
-0.13
-0.14
-0.11
0.00
0.00
Notes: This table shows the mean Case-Shiller house price appreciation rates for neighborhoods grouped by quartile
of initial housing prices, during different time periods. Quartile 4 has the highest initial price zip codes within the
city while quartile 1 has the lowest initial price zip codes within the city. Each row labels a city or metro area for a
given time period.
36
Table 3: Regression of Neighborhood House Price Appreciation on Distance to Nearest High-Price
Neighborhood and Other Controls, Across Different Samples With Different House Price Measures
Time Period
(1)
(2)
(3)
(4)
(5)
(6)
(7)
-0.061
(0.021)
-0.062
(0.019)
-0.044
(0.029)
-0.067
(0.037)
-0.231
(0.042)
-0.136
(0.032)
-0.140
(0.029)
-
-
-
0.070
(0.044)
0.068
(0.051)
0.077
(0.029)
0.083
(0.032)
House Price Measure/
Neighborhood Aggregation
C-S
Zip
Code
C-S
Zip
Code
C-S
Zip
Code
C-S
Zip
Code
Census
Census
Tract
Census
Census
Tract
Census
Census
Tract
Time Period
00-06
00-06
90-00
90-00
90-00
90-00
80-90
Vector of Z Controls Included
No
Yes
Yes
Yes
Yes
Yes
Yes
Number of Observations
236
236
223
223
3,099
7,955
4,253
Mean Log Distance to Nearest
High-Price Neighborhood
1.23
1.23
1.22
1.22
0.401
0.499
0.322
Std. Dev. Log Distance to Nearest
High-Price Neighborhood
0.524
0.524
0.488
0.488
0.778
0.719
0.716
Log Distance to Nearest High-Price
Neighborhood
Log Distance to Nearest High-Price
Neighborhood * City Wide Bust Indicator
Note: Table shows regression of neighborhood house price appreciation between period t and t+k on log distance
to nearest high price neighborhood within the neighborhood’s city, city fixed effects, and a vector of neighborhood
controls. High price neighborhoods are those neighborhoods that are within the top quartile of average neighborhood
house prices in year t. We restrict our analysis in this table to those neighborhoods within the city which were in
the bottom half of the house price distribution in period t. See text for additional sample descriptions and discussion
of the controls included. Robust standard errors, clustered by city, are shown in parentheses. All regressions are
weighted by the number of owner occupied housing units in the neighborhood in the initial year.
37
Table 4: Regression of House Price Appreciation on Proximity to Nearest High-Price Neighborhood,
Census Data 1980 - 1990
(1)
(2)
Log Dist. to Nearest High-Price Neighborhood
0.35
(0.09)
-
Log Dist. to Nearest High-Price Neighborhood *
Bartik Predicted City-Wide Income Shock
-2.33
(0.49)
-
Dummy: High-Price Neighborhood Within 0 - 1 Miles
-
-0.64
(0.22)
Dummy: High-Price Neighborhood Within 1 - 3 Miles
-
-0.15
(0.10)
Dummy: High-Price Neighborhood Within 0 - 1 Miles *
Bartik Predicted City-Wide Income Shock
-
4.09
(1.17)
Dummy: High-Price Neighborhood Within 1 - 3 Miles *
Bartik Predicted City-Wide Income Shock
-
0.99
(0.51)
Note: Table reports the results from the regression specified by Equation (20) from the text. The sample is the same
as that used in Table 3, column 7. Standard errors bootstrapped. First stage is re-sampled from IPUMS, second
stage from census tract tabulations, and stratified by city (2,500 repetitions). P-value on test of whether last two
coefficients in column 2 are equal is 0.020.
Table 5: Regression of Neighborhood Income Growth on Neighborhood House Price Appreciation,
Across Different Samples With Different House Price Measures
(1)
(2)
(3)
(4)
(5)
0.145
(0.053)
0.406
(0.069)
0.076
(0.022)
0.088
(0.021)
0.076
(0.024)
C-S
Census
Census
Census
Census
Neighborhood Aggregation
Zip
Code
Zip
Code
Census
Tract
Census
Tract
Census
Tract
Time Period
90-00
90-00
90-00
90-00
80-90
223
223
3,099
7,955
4,253
Mean Neighborhood House Price Growth
0.331
0.146
0.586
0.512
0.240
Std. Dev. Neighborhood House Price Growth
0.479
0.348
0.967
0.747
0.788
Neighborhood House Price Growth
House Price Measure
Number of Observations
Note: Table shows regression of neighborhood income growth between period t and t+k on house price appreciation,
city fixed effects, and a vector of neighborhood controls. The vector of neighborhood controls is the same as in Table
3. Also, as in Table 3 and 4, we restrict our analysis to those neighborhoods in the bottom half of the neighborhood
house price distribution in period t. The specifications in columns 1 and 2 use low price zip codes from Case-Shiller
cities where a Case-Shiller price index exists in 1990 and 2000. The specification in column 3 uses all census tracts
in Case-Shiller cities. The specifications in column 4 uses all census tracts from all cities in the U.S. which have
at least 30 consistently defined census tracts between 1990 and 2000. The specification in column 5 uses all census
tracts from all cities in the U.S. which have at least 30 consistently defined census tracts between 1980 and 1990.
For the specifications in columns 3 - 5, we also trim the top and bottom 1 percent of the house price growth and the
income growth distributions. See text for additional details. Robust standard errors clustered at the city level are in
parentheses.
38
Table 6: Measures of Gentrification and Proximity to High Income Neighborhoods: Descriptive
Analysis 1980 - 1990 and 1990 - 2000
Gentrification Measure:
Neighborhood Income Growth During Time Period
Greater than 50%
Greater than 25%
(1)
(2)
(3)
(4)
1980 - 1990 1990 - 2000 1980 - 1990
1990 - 2000
Dummy: High-Price Neighborhood
Within 0 - 0.5 Miles
0.070
(0.017)
0.057
(0.028)
0.083
(0.036)
0.110
(0.041)
Dummy: High-Price Neighborhood
Within 0.5 - 1 Miles
0.014
(0.007)
0.016
(0.009)
0.094
(0.020)
0.062
(0.020)
Dummy: High-Price Neighborhood
Within 1 - 2 Miles
0.006
(0.008)
0.018
(0.007)
0.076
(0.020)
0.028
(0.014)
Dummy: High-Price Neighborhood
Within 2 - 3 Miles
-0.005
(0.007)
0.002
(0.005)
0.023
(0.019)
0.018
(0.014)
Fraction of Neighborhoods that Gentrified
11.0%
5.9%
30.2%
19.8%
Sample Size
4,253
7,955
4,253
7,955
Note: Table shows the results from a linear probability regression of a dummy variable indication of whether a
neighborhood gentrified between t and t + k on the proximity of that neighborhood to an existing rich neighborhood.
We define rich neighborhoods as those census tracts within a city that are in the top quartile of the period t house
price distribution. The samples in columns 1 and 3 (columns 2 and 4) are the same as column 7 (column 6) of Table
3. All regressions include city fixed effects. Robust standard errors, clustered at the city level, are in parentheses.
Table 7: Estimation of Measures of Gentrification and Proximity to High Income Neighborhoods,
Census Data 1980 - 1990
Dependent Variable: Measure of Neighborhood Gentrification
(1)
(2)
(3)
Growth in
Change in
Change in
Median Income Poverty Rate
Fraction of Residents
with Bachelor’s Degree
Log Dist. to Nearest High-Price
Neighborhood
0.09
(0.05)
-0.04
(0.02)
0.03
(0.01)
Log Dist. to Nearest High-Price
Neighborhood * Bartik Predicted City-Wide Income Shock
-0.55
(0.26)
0.22
(0.11)
-0.23
(0.08)
Mean: Dependent Variable
0.149
0.029
0.028
Sample Size
4,253
4,253
4,253
Note: Table reports the results from the regression specified by Equation (21) from the text. The sample is the same
as that used in Table 3, column 7. Standard errors bootstrapped. First stage is re-sampled from IPUMS, second
stage from census tract tabulations, and stratified by city (2,500 repetitions).
39
Table A1: MSA Level House Price Appreciation for Case-Shiller Covered MSAs
Akron
Atlanta
Boston
Charlotte
Chicago
Cincinnati
Columbus (OH)
Denver
Fresno
Jacksonville
Las Vegas
Los Angeles
Memphis
Miami
New York
Oakland
Philadelphia
Phoenix
Portland (OR)
Raleigh
Sacramento
San Francisco
San Diego
San Jose
Seattle
St. Paul
Tampa
Toledo
Washington DC
In MSA Sample,
City Sample, or Both
MSA Price
Appreciation
2000 - 2006
MSA Price
Appreciation
1990 - 2000
Both
Both
MSA Only
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
Both
MSA Only
Both
Both
Both
Both
Both
Both
MSA Only
3.6%
13.8%
49.0%
9.2%
36.8%
7.4%
7.4%
10.6%
124.1%
69.4%
88.8%
121.7%
6.0%
125.6%
72.4%
76.7%
59.1%
82.8%
47.0%
8.1%
96.0%
52.1%
93.5%
44.0%
46.7%
38.2%
88.6%
4.7%
98.3%
22.8%
14.6%
12.5%
12.7%
14.4%
15.4%
16.8%
65.9%
-8.5%
11.2%
-0.3%
-20.9%
8.7%
15.3%
0.0%
9.0%
-10.4%
20.8%
53.4%
14.5%
-11.7%
18.9%
-0.7%
30.6%
22.9%
29.9%
7.0%
19.7%
-8.5%
Notes: Table shows the MSA level house price appreciation rates for each MSA for the 2000-2006 period (column
2) and the 1990-2000 period (column 3) using the FHFA MSA level house price indices. Column 1 is an indicator
whether the data from these cities or MSAs are included in our MSA samples or in our main city only samples. The
data from Boston, San Francisco, and Washington DC are not included in our main city sample because there are
not 10 zip codes within the city that have a reliably computed price index.
40