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Working Paper Series

Housing Externalities: Evidence from
Spatially Concentrated Urban
Revitalization Programs

WP 08-03

Esteban Rossi-Hansberg
Princeton University
Pierre-Daniel G. Sarte
Federal Reserve Bank of Richmond
Raymond E. Owens III
Federal Reserve Bank of Richmond

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

Housing Externalities: Evidence from Spatially
Concentrated Urban Revitalization Programs∗
Esteban Rossi-Hansberg
Princeton University
Pierre-Daniel Sarte and Raymond Owens III†
Federal Reserve Bank of Richmond
June 2008

Abstract
Using data compiled from concentrated residential urban revitalization programs
implemented in Richmond, VA, between 1999 and 2004, we study residential externalities. Specifically, we provide evidence that in neighborhoods targeted by the programs,
sites that did not directly benefit from capital improvements nevertheless experienced
considerable increases in land value relative to similar sites in a control neighborhood.
Within the targeted neighborhoods, increases in land value are consistent with externalities that fall exponentially with distance. In particular, we estimate that housing
externalities decrease by half approximately every 990 feet. On average, land prices
in neighborhoods targeted for revitalization rose by 2 to 5 percent at an annual rate
above those in the control neighborhood. These increases translate into land value
gains of between $2 and $6 per dollar invested in the program over a six-year period.
We provide a simple theory that helps us interpret and estimate these eﬀects.

∗

We thank Miklos Koren, Dan Tatar and David Sacks for many helpful discussions. We thank Brian
Minton and Kevin Bryan for outstanding research assistance.
†
The views expressed in this paper are those of the authors and do not necessarily reflect those of the
Federal Reserve Bank of Richmond or the Federal Reserve System.

Introduction

The existence of cities is a manifestation of the presence of agglomeration forces between
economic agents. While much has been written about the nature and characteristics of
these forces, most studies have focused on agglomeration forces between producers. As
a result, virtually all urban theories have these producer-based agglomeration economies at
their core.1 In fact, agglomeration eﬀects can also result from interactions between residents.
Specifically, they can take the form of housing externalities whereby improvements made to
a particular house can have an eﬀect on the value of nearby houses. To the extent that
these eﬀects decline with distance, this form of externalities can lead to the agglomeration of
residents and, potentially, the formation of cities. Moreover, because the presence of housing
externalities may justify government intervention, in that equilibrium allocations will diﬀer
from eﬃcient outcomes, assessing the importance of these externalities in practice is central to
urban policy. In this paper, therefore, we study the magnitude and characteristics of housing
externalities. We are interested in the eﬀects of housing externalities on average land prices
and in how fast these eﬀects decline with distance. These are the key characteristics that
lead to agglomeration.
The standard problem in measuring agglomeration eﬀects lies in the circular causation
present in all spatial concentrations of economic activity. People and firms locate in a specific area because that area is particularly productive or pleasant to live in, but the area
is particularly productive or pleasant to live in because others chose to reside or work at
that location. This implies that identifying agglomeration eﬀects in the data requires an
exogenous source of variation in the “attractiveness” of a given location. In this paper, we
exploit such a source of variation by taking advantage of an urban revitalization program
implemented in Richmond, Virginia, between 1999 and 2004: the Neighborhoods-in-Bloom
(NiB) program. We describe the program and its associated policies in detail in Section
2. For now, we note that this program represented federally funded housing investments
concentrated in a few disadvantaged neighborhoods. We know the location of homes that
obtained direct funding, and the amount that was received. We also have information on
housing prices and a comprehensive list of housing characteristics before and after the program was implemented. This information allows us, using a hedonic regression, to estimate
land prices before and after the policy was implemented. Taking into account city-wide time
eﬀects, we can calculate the eﬀects of the program in the various treated neighborhoods. Put
another way, we estimate the eﬀects of the policy on land values controlling for investments
1

See the theoretical survey in Duranton and Puga (2004) and the empirical survey in Rosenthal and
Strange (2004).

in observable housing characteristics. By carrying out this exercise only for houses that were
not directly targeted by the Neighborhoods-in-Bloom program, we ensure that the eﬀects
we measure are not the valuation of unobservable investments directly associated with its
policies.
We estimate changes in land prices, following the Neighborhoods-in-Bloom program, that
are consistent with the predictions of a simple theory of housing externalities. We present
this theory in Section 3. In particular, increases in the returns to land decline with distance
from the impact area. This eﬀect, which we measure nonparametrically in the data, emerges
clearly and corresponds to housing externalities that decline by half approximately every
990 feet. The theory also has predictions for the magnitude of the eﬀects induced by the
Neighborhoods-in-Bloom policies that are consistent with our measurements. Finally, we
use the findings from our estimation exercise to obtain parameter values for our model. This
step potentially allows the model to guide the design of urban policies, although we leave
this task to future research.
The exercise we have just described does not directly allow us to make statements regarding the total return to land associated with the Neighborhood-in-Bloom program. We
are able to assess whether changes in land prices are consistent with housing externalities
that decline with distance, and how fast they decline, but additional information is needed to
draw conclusions regarding the average increase in land values associated with these external
eﬀects. We use time eﬀects at the city level to control for any city-wide changes and, potentially, general equilibrium eﬀects induced by the Neighborhood-in-Bloom policies. That
said, as indicated in Section 2, the magnitudes of these policies are generally small enough
that they are unlikely to aﬀect land rents in the city as a whole. In order to identify the
eﬀects of the revitalization policies that arise by way of housing externalities, one needs to
take a stand on the scope of these externalities, and measure increases in land values over
and above those at the boundary of a selected neighborhood. This is, in principle, problematic since we have little information regarding the scope of housing externalities, nor do we
know whether other non-observables might have aﬀected land values at the boundaries of the
neighborhoods under consideration. Fortunately, a key feature of Neighborhoods-in-Bloom
oﬀers us an alternative approach.
One of the unique aspects of the study we carry out in this paper relates to the presence
of a neighborhood that shares almost identical physical and demographic characteristics as
those selected for urban revitalization. Although initially considered by the Neighborhoodsin-Bloom task force, this neighborhood did not ultimately receive funding for reasons that
were secondary and non-economic in nature. Hence, we use it as a control with which to
contrast our findings for neighborhoods explicitly targeted by the urban renewal program.
3

Two key results emerge: i) in contrast to the treated neighborhoods, our estimates of changes
in land rents in the control neighborhood do not fall with distance as we move away from
its centroid. This result is consistent with the idea that one cannot measure changes in land
valuations resulting from housing externalities in the absence of an exogenous source of variation in land prices, ii) we compute average land price increases in the control neighborhood
and show that they fall significantly short of those measured in the targeted neighborhoods.
We then use the findings associated with the control neighborhood to infer increases in land
values arising from externalities induced by the revitalization policies. We find land value
gains in the targeted neighborhoods that range between $2 and $6 per dollar invested in the
program over a six-year period.
To the best of our knowledge, there have been only few studies of housing externalities
that rely on a policy experiment with individual housing transaction data, and none where
the experiment was spatially concentrated to the degree of Neighborhoods-in-Bloom. In
Section 5, we compare our findings with other work that exploit parametric approaches to
measure the decline in externalities across space. In general, we find housing externalities
that decrease somewhat slower with distance. Ioannides (2002) finds important residential
neighborhood eﬀects using neighborhood clusters in U.S. cities. These neighborhood eﬀects,
which have received some theoretical and empirical attention in the literature, are broader
than the housing externalities considered in this paper as they include other forms of social
interactions. See for example Benabou (1996) for an insightful theoretical model describing
these types of social interactions and their eﬀects. There are several studies, both theoretical
and empirical, that have analyzed urban renewal projects. Davis and Whinston (1961),
Rothenberg (1967), and Schall (1976) are notable early examples. None, however, include
the type of detailed empirical work we perform in this paper. On a theoretical level, Strange
(1992) provides an informative discussion of policy in the presence of strong interactions
across neighborhoods.2
The rest of the paper is organized as follows. Section 2 describes the Neighborhoodsin-Bloom program. Section 3 presents the model and the eﬀects of housing subsidies on
equilibrium outcomes. Section 4 discusses our empirical methodology and Section 5 presents
our findings. Section 6 oﬀers concluding remarks.
2

Durlauf (2004) provides a survey of the literature on neighborhood eﬀects.

The Neighborhoods-in-Bloom Urban Revitalization
Program

The Neighborhoods-in-Bloom (NiB) program was an outgrowth of the observation by Richmond city oﬃcials that during the previous 25 years, investment programs undertaken to
revitalize areas within the city had demonstrated only limited success. They noted that
the programs had often improved small areas—such as a city block— but in many instances,
measurable improvement in the surrounding neighborhoods remained elusive.
In evaluating the features of previous programs, oﬃcials noted that investment activity–
in most cases using federal funding sources— had often been targeted in a scattered fashion.
This approach had the advantage of reaching a large number of city neighborhoods that
qualified under federal guidelines, but available funding per area was necessarily limited. The
resulting constraints on investment activity led to impacts on home prices in surrounding
areas that were diﬃcult to gauge. Because city oﬃcials’ objective was to visibly raise the
values of surrounding homes, an idea developed that investment concentrated in fewer areas
might yield more measurable eﬀects. This approach, they reasoned, might lead to a more
noticeable revitalization of the city’s housing stock than had the previous, more scattered
approach.
To carry out this experiment, city oﬃcials began to identify potential areas for investment, determine the number of sites to target and source funding. As had historically been
the case, the City of Richmond had numerous areas that qualified for revitalization funding
through the Department of Housing and Development’s (HUD) Community Development
Block Grant (CDBG) and Home Investment Partnership (HOME) programs. Additional
funding was made available through other federal monies as well as through the non profit Local Initiatives Support Corporation (LISC), a community development corporation (CDC).
The CDBG and HOME funding was attractive to the city, in part, because it was outside
money. Simply put, these funds come from the federal government, and the resulting investments benefit the city without reducing local spending on consumption or investment
that would otherwise occur if the funds were raised through local taxes. Interestingly, LISC
funding also has this advantage. Founded by the Ford Foundation, LISC is a national organization headquartered in New York and is funded by nationwide donations. Because of
this structure, funds that flow from the organization to Richmond are eﬀectively exogenous
as well in that they do not necessarily originate from local sources.
The selection process of investment sites was a multiple step process. Past scattered
approaches to investment had been driven in part by political pressures to fund areas within
nearly all city council members’ districts. Aware that a more concentrated approach would
5

likely fund fewer sites than the number of districts, broad support of a small number of sites
was a primary objective. To achieve that support, in mid 1998, Richmond administrators established an internal planning task force composed of the acting city manager, the assistant
city manager, and representatives from a variety of city departments associated with housing and economic development. Several members within the group developed indicators of
neighborhood conditions and data that served as comparative portraits of the neighborhoods
that qualified to receive CDBG or HOME funds. Throughout 1998 and into early 1999, staﬀ
from the city’s Community Development Department met with community groups to explain
and gather feedback on the approach. In particular, city staﬀ and members of the groups
also toured the potential sites, and support for both the concept and for a small group of
neighborhoods had come together by February 1999. Later that year, the city community
development department recommended four broad neighborhoods. These were Church Hill
Central, Southern Barton Heights-Highland Park-Southern Tip, Jackson Ward-Carver, and
Blackwell. The locations and size of these neighborhoods relative to the city of Richmond
are shown in Figure 1.
Table 1A. Demographics of selected neighborhoods
Neighborhood

Total
Housing Percent
Percent
Persons Units
Non-White Below Poverty

Church Hill
Blackwell
Highland Park-Barton
Jackson Ward-Carver
Bellemeade
City of Richmond

1505
1376
2763
1975
2742
197790

822
651
1227
1332
947
92282

94.8
97.0
97.2
81.7
90.2
61.5

27.2
35.8
26.3
29.5
31.6
20.3

These four neighborhoods share many common characteristics. All had been selected
according to criteria developed by the city’s community development staﬀ and had concentrations of vacant structures, substantial poverty, and low home ownership rates. In
addition, the capacity of the areas to revitalize absent NiB investment was viewed as low.
The neighborhoods also had active nonprofit Community Development Corporations (CDCs)
in place. This was an important feature in that funds from the HUD programs are generally
disbursed through these organizations which perform new home construction, rehabilitation,
and renovations that comprise the vast majority of investment activity in the neighborhoods.
Although the selected NiB neighborhoods share many similarities, one important distinction
must be made in that Blackwell was subject to an additional urban program, known as
HOPE VI, alongside NiB. HOPE VI was a program designed to raze unfit homes, without at
6

the time creating new construction in their place. Tables 1A and 1B provide a summary of
basic demographic and housing characteristics of the selected neighborhoods using the 2000
census and our housing data before the start of the program in 1998.
Table 1B. Characteristics of the housing stock in NiB neighborhoods
Neighborhood
Church Hill
Blackwell
Highland Park-Barton
Jackson Ward-Carver
Bellemeade
City of Richmond

Percent Percent Average
Median Price
Vacant Owned Plot Acreage Pricea
St. Dev.
21.7
23.2
18.3
31.5
10.8
8.4

35.7
32.6
40.5
36.0
51.4
46.1

0.07
0.09
0.14
0.06
0.16
0.17

14,861
17,368
33,223
37,914
33,881
74,394

29,244
16,705
24,740
46,548
15,643
121,539

a : expressed in 2000 constant dollars
As shown in Figure 1, the selected neighborhoods all fall in the eastern part of the city and
share a heritage dating to Richmond’s origins. The city was founded because of its location
at the fall line of the James River, the farthest inland point navigable to ship traﬃc. Early
development began in this area, but as factories emerged, the neighborhoods in the eastern
portion of the city gradually fell into disfavor and declined over time. This process led to
changes in the demographic makeup of these areas, with higher poverty rates and lower
average home prices, as well as higher percentages of crime relative to citywide averages.
Aside from their similarities in terms of demographics, homes in the selected neighborhoods,
because of their historical ties, also share many elements of style and construction. In
particular, homes in all selected areas consist mostly of row houses of similar sizes, many
constructed of brick. A slight exception is Blackwell and Highland Park, where some homes
are of detached Queen Anne and Victorian styles.
With funding sources in place and neighborhoods identified, NiB began operations in
July 1999. Prior to start up, teams were formed comprised of city staﬀers, community group
representatives, and CDC representatives to review neighborhood redevelopment plans, identify precise boundaries of investment, known as “impact areas”, and identify specific homes
for renovation and sites for new home construction. Once specific home projects within
individual impact areas were determined, the CDCs operating in those areas applied for
funds to carry out the projects. Nearly all investment activity consisted of acquisition, demolition, rehabilitation, and new construction of housing within NiB impact areas. The
work carried out by the various CDCs varied in impact, reflecting in part the comparative
7

strengths of individual organizations, in that specific CDCs had unique relationships with
their home neighborhoods and specialized experience in some categories of construction or
rehabilitation.
Spending under the NiB program began in 1999 (although a small fraction preceded the
oﬃcial start date of the program) and continued through 2004. Over this period, approximately $14 million was spent in total. Slightly over $11 million came through CDBG and
HOME programs, smaller federal programs and Commonwealth of Virginia monies. LISC
added nearly $3 million. Around $1 million came from other sources, with approximately
half that amount from undocumented sources. Most of the spending took place in the 1999
through 2001 period, with yearly expenditures trailing oﬀ in the later years of the program.
Finally, one of the unique aspects of the study we carry out in this paper relates to the
presence of a neighborhood that was almost included in the NiB program but that did not,
ultimately, received funding. Specifically, the neighborhood of Bellemeade lies in the eastern
portion of the city, south of the James River (see Figure 1). Its makeup and location are
typical of NiB neighborhoods and, according to a former city oﬃcial closely involved with
the NiB selection process, “absolutely matched” the selected neighborhoods in physical and
demographic terms. This is in fact also clear from Tables 1A and 1B. The reason that
Bellemeade did not make the final cut, he suggests, is that the area did not have active
enough CDCs, so that the channel used to direct NiB investment dollars was mostly absent.
This distinction, however, makes Bellemeade close to an ideal control neighborhood. In
particular, because no NiB investment took place in that neighborhood, and given that its
demographics and housings stock closely match that of the selected NiB neighborhoods, it is
natural to use Bellemeade as a benchmark in gauging changes in neighborhood land values
arising from the NiB program.

A Model of Housing Externalities

This section provides a framework that oﬀers insight into the types of urban renewal policies
we have just described. More importantly, it helps underscore the importance of housing externalities in determining the eﬀects of these revitalization policies. Consider a neighborhood
represented by N = [−R, R], where R denotes the neighborhood’s edge, with density of land
equal to one. All agents living in the neighborhood work at location 0.3 We assume that all
agents are endowed with one unit of time, and that some of this time is spent commuting to
work. Thus, an agent commuting from location ∈ N only works e−τ | | time units, τ > 0.
3

This simplifying assumption ensures symmetry but is otherwise unimportant for the questions we shall
be asking.

The production technology is linear, and transforms one unit of time into w units of a final
good.
Agents’ preferences are defined over housing services enjoyed at a given location, denoted
e ) for an agent living at , and other types of consumption, c( ). The only good in the
by H(
economy can be allocated to either investment in housing or consumption. All agents live on
a lot of size one, which they rent from absentee landlords at rate q( ). Housing services at a
location are obtained from owning a piece of land and directly improving it, as well as from
the amount of housing services produced nearby. The fact that housing services produced
at a given location aﬀect housing services enjoyed elsewhere defines a housing externality.
Formally, if H( ) denotes investments in housing undertaken by an individual living at ,
then
Z R
e
H( ) = δ
e−δ| −s| H(s)ds + H( ).
(1)
−R

Hence, aside from home improvements they make at a given location, individuals also benefit
from having nearby housing owned by others that is well-maintained. In particular, housing
services enjoyed at location reflect in part a weighted average of housing services produced
at neighboring sites, with weights that decline with distance at an exponential rate δ > 0.
Agents living at location spend their income, we−τ | | , on the unit of land they rent at
rate q( ), housing investments, H( ), and consumption, c( ). We assume that individuals
order consumption baskets according to a Cobb-Douglas utility function. Hence, an agent
living at some location solves
e )1−α , 0 < α < 1,
e )) = c( )α H(
max u(c( ), H(

(P )

c( ) + q( ) + H( ) = we−τ | | ,

(2)

c( ), H( )

subject to
and

e )=δ
H(

e−δ| −s| H(s)ds + H( ),

−R

where housing services produced at other locations, H(s), are taken as given. The optimality
conditions associated with problem (P ) imply that
e ).
(1 − α)c( ) = αH(

(3)

Substituting this condition into the agent’s budget constraint (2), and using the equation
describing the externality from housing (1), immediately yields an expression for housing
services obtained at that depends only on prices and housing services produced elsewhere,
½
¾
Z R
−τ | |
−δ| −s|
e
H( ) = (1 − α) we
− q( ) + δ
e
H(s)ds .
(4)
−R

3.1

The Neighborhood Equilibrium

There are two key conditions that determine equilibrium allocations in the neighborhood.
First, all agents are identical and can choose freely where to live, including in another
neighborhood if their utility falls below some reservation utility, u. In equilibrium, therefore,
individuals obtain utility u at all locations, which immediately implies that
¶α
µ
1−α
e
.
(5)
H( ) ≡ H = u
α
That is, housing services enjoyed at any location are the same throughout the neighborhood.
It follows from Equation (1) that the function describing housing investments at diﬀerent
sites is a fixed point of the following functional equation,
Z R
H( ) = H − δ
e−δ| −s| H(s)ds, ∈ [−R, R].
(6)
−R

The second condition needed to determine equilibrium allocations involves a boundary condition for land rents at either edge of the neighborhood, which we denote by qR > 0. From
equations (4) and (5), land rents in the neighborhood are given by
−τ | |

q( ) = we

+δ

−R

e−δ| −s| H(s)ds −

1
H.
1−α

At the boundary, therefore, we have that R implicitly solves
Z R
1
e−δ| −s| H(s)ds =
H + qR − we−τ R .
δ
1
−
α
−R

(7)

(8)

To summarize, an equilibrium for the neighborhood is a function describing housing investments at all locations, H( ), a function describing land rents, q( ), a level of housing services
H, and a boundary for the neighborhood, R, such that equations (5), (6), (7) and (8) are
satisfied.
The solid curves in Figure 2A and 2B depict typical equilibrium housing investment allocations, H( ), and land rents, q( ), respectively.4 Housing investments are highest near
the boundaries of the neighborhood where externalities from housing are lowest. With lower
externalities from housing at locations away from the neighborhood center, individuals living
at those locations must spend a greater share of their income on direct home improvements in
order to obtain the constant level of housing services H. The fact that housing externalities
are lowest near the neighborhood boundaries also implies that land rents are lowest at those
4

The parameter values used in this example are: u = 13.25, δ = 0.001, R = 3500, A = 1190, σ = 0.368,
w = 25, α = 0.6, and τ = 0.00001.

locations. On a more practical level, observe in Figure 1 that the highlighted neighborhoods
are indeed often bounded by major roads, such as interstates or highways, and other landmarks that eﬀectively reduce externalities from housing potentially located outside those
boundaries. The neighborhood of Blackwell, for instance, is bounded by highways to the
west, north, and east, as well as by an industrial railway station in part to the south. Similarly, the neighborhood of Jackson Ward-Carver is bounded by Interstate 64 to the north and
Highway 250 to the south, and adjoins an industrial zone to the east. Although not bounded
by main roads, the land surrounding Highland Park-South Barton Heights is largely free of
housing, composed of a large cemetery to the south, warehouses to the west, and vacant
grounds to the east and north.

3.2

The Neighborhoods-in-Bloom Program

Consider a federally funded neighborhood revitalization program that aims to increase housing investments at all locations in an area A = [−r, r] ⊆ N by some fixed amount σ > 0.
Throughout the paper, we refer to A as an ‘impact area.’ Let Hp ( ) denote the new equilibrium housing investment function that emerges after implementation of the policy. Similarly,
e p ( ) describe housing services enjoyed at location following the program. Because the
let H
reservation utility from living in some other neighborhood is unchanged, and agents can
freely move between neighborhoods, housing services are still given by Equation (5) so that
e p ( ) = H. Then, for ∈ N \A, Hp ( ) solves
H
H = Hp ( ) + δ

−δ| −s|

Hp (s)ds + σδ

−R

e−δ| −s| ds,

(9)

−r

where the last term in (9) captures externalities generated by the program and obtained at
a location outside the impact area. For locations ∈ A that are directly aﬀected by the
revitalization policy, we have that
µ Z r
¶
Z R
−δ| −s|
−δ| −s|
H = Hp ( ) + δ
e
Hp (s)ds + σ δ
e
ds + 1 ,
(10)
−R

−r

where the last term now reflects the fact that those locations are also the direct recipients
of capital improvements σ.
Since H remains unchanged following the urban development program, it follows that
H( )p − H( ) < 0 for all ∈ [−R, R]. To see this, note from equations (6) and (9), and

abstracting from the direct subsidy, that for ∈ N \A,
Z

e
[Hp (s) − H(s)] ds − σδ
e−δ| −s| ds
−R
−r
½ Z r
Z R
Z r
= σδ −
e−δ| −s| ds + δ
e−δ| −j|
e−δ|j−s| dsdj
−r
−R
−r
¾
Z R
Z R
Z r
2
−δ| −j|
−δ|j−k|
−δ|k−s|
−δ
e
e
e
dsdkdj + ...

H( )p − H( ) = −δ

< 0

since
δ
Rr

R
−δ| −s|

ds = δ

−R

−δ| −s|

−R

−δ|j−s|

−R

−r

(11)

¯2R
e−δs ds = − e−δs ¯0 = 1 − e−δ2R < 1,

so that −r e
ds < 1 as well. The direct eﬀect of subsidies, of course, only serves
to amplify this eﬀect in the impact area. Put another way, Equation (11) implies that
investment in housing decreases everywhere in the neighborhood, and this decrease is more
pronounced the closer the locations are to the impact area. In this framework, therefore, the
neighborhood revitalization program crowds out private investment in housing. The subsidy
to home improvements in eﬀect allows agents to enjoy housing services without having to
spend on those services themselves. The implied relaxation of their budget constraint leads
individuals to bid up the price of land so that, in the new equilibrium, higher land rents,
qp ( ), prevail throughout the neighborhood.
The diﬀerence in land rents created by the implementation of the policy, net of the direct
capital improvement σ, is given by
∙Z R
¸
Z r
−δ| −s|
−δ| −s|
e
[Hp (s) − H(s)] ds + σ
e
ds > 0.
(12)
qp ( ) − q( ) = δ
−R

−r

We have already argued that the first term in square brackets is negative. The second
term captures positive externalities generated by the capital improvement policy. In this
respect, the size of the exogenous increase in housing investment at each targeted location,
σ, and the extent of the impact area, A, have a first order positive eﬀect on land prices.
In contrast, because commuting costs, τ , and income, w, aﬀect land rents in the same way
in (7), both before and after the introduction of the policy, these features are essentially
diﬀerenced out and only aﬀect land prices through changes in H(.) in Equation (12). Note
that since qp ( ) − q( ) in (12) is simply the negative of the change in land rents Hp ( ) − H( )
in (11), it immediately follows that qp ( ) − q( ) > 0. Hence, our assumption of CobbDouglas preferences with elasticity of substitution equal to one (which implies an unchanged
H following the policy) ensures that the implementation of the revitalization program is
12

associated with higher land rents. This choice of preferences stems from empirical work on
cities which has found the Cobb-Douglas specification with respect to land and consumption
to fit the data well (see Davis and Ortalo-Magne, 2007).
In the end, as a result of the revitalization program, housing investments fall and land
prices rise throughout the neighborhood. Agents consume a constant fraction of housing,
and now that nearby homes oﬀer additional housing services, they prefer to invest less where
they live. The revitalization policy increases the value of location and, therefore, land prices.
We summarize these results in the following proposition:
Proposition 1 Following the positive housing subsidy on a set of locations A, housing investments decrease at all locations, H( )p − H( ) < 0 ∀ ∈ [−R, R], and land rents
increase at all locations, qp ( ) − q( ) > 0 ∀ ∈ [−R, R].
The new equilibrium land rents, qp ( ), are described by the dashed curve in Figure 2B. As
we have just argued, these new land rents are everywhere higher in the neighborhood, and
especially when close to the impact area. Figure 2C shows the percentage or log diﬀerence
between post-policy and pre-policy land rents on either side of the center of the impact area,
net of the direct capital improvements brought about by the renewal program. This diﬀerence, therefore, reflects only the propagation of housing externalities across space induced
by the federal housing investment increase.
Given that externalities fall exponentially with distance in this model, increases in land
value in Figure 2C will generally mimic a diﬀusion process as they level out with distance from
the impact area. The rise in land rents is more pronounced over the impact area because a
typical location in that area is mainly surrounded by other locations that received funding for
capital improvements. Hence, a location in A benefits from externalities generated by many
similarly aﬀected locations nearby. Note, in particular, the steep drop oﬀ in land returns
once we move outside the impact region. At locations near the boundary, diﬀerences in land
rents become mostly flat near zero in Figure 2C. This eﬀect arises because any one location
near the boundary, contrary to a location in A, is mainly surrounded by other locations that
did not benefit from the revitalization program. External eﬀects from the policy, therefore,
are negligible at those locations. Because externalities generate a two-tier eﬀect on land rents
across space, changes in land rents produced by the revitalization program will generally be
characterized by a bimodal distribution. This is shown in Figure 2D. Keep in mind, from
Equation (12), that this bimodal aspect of land returns arises independently of the direct
eﬀect related to capital improvements in A.

The Empirical Framework

This section sets up an empirical framework whose aim is to help us identify the extent to
which the eﬀects of the NiB programs, in practice, propagated to non-targeted sites. We
are also interested in whether we can establish empirically that these external eﬀects decline
with distance in a way suggested by Figure 2C. If so, we also wish to a gauge how far the
eﬀects of NiB programs were able to extend in this case.
We denote a location in the city of Richmond by = (x, y) ∈ R2 , where x and y are
Cartesian coordinates. Let p represent the (log) price of a home per square foot of land in
the city of Richmond. Our analysis begins with the following semiparametric hedonic price
equation,
p = Zβ + q( ) + ε,
(13)
where Z is a k−element vector of conditioning housing attributes such that cov(Z| ) = Σz| ,
q( ) is the component of home prices directly related to location, and ε is a random variable
such that E(ε| , Z) = 0 and var(ε| , Z) = σ 2ε . While this semi-log specification is standard
in the analysis of real estate data, we diﬀer somewhat in that we try to remain flexible with
respect to the form of q( ). In particular, we do not assume that q( ) lies in given parametric
family.5
We are interested in assessing the eﬀects of NiB policies on the component of prices
related to location, q( ), in the various targeted neighborhoods described previously. This
suggests estimating Equation (13) both before and after the NiB policies come into eﬀect.
Because our concern is with assessing the extent of residential externalities, we omit observations on homes that directly benefited from NiB funding in our estimation. Although our
model predicts that the types of renewal programs considered here generally crowd out of
private investment, it is conceivable that these programs induced a reshuﬄing of heterogenous populations across neighborhoods, consistent with gentrification, that is not captured
in our framework. In particular, a higher income household that decided to relocate to an
impact area and further invested in home improvements would have very likely used some
NiB funding (since the program aimed to precisely subsidize this type of investment). As
such, simply subtracting public home improvements at that location would overstate the
external eﬀect of the policy on land prices. Because we have no way of measuring any additional private spending on home improvements at locations that received NiB funding, a
conservative strategy is to omit the observation altogether.
Some key questions that the analysis will attempt to uncover are: i) How did the price
5

See Ho (1995), and Anglin and Gencay (1996), for early applications of the semiparametric hedonic
pricing model to the real estate market.

of land change in each of the neighborhoods in Figure 1, say from q( ) to qp ( ), at sites not
directly targeted by the NiB revitalization projects? ii) Can we relate this change to some
notion of distance from a focal point in a given impact area? In particular, do the findings
related to the neighborhoods targeted for revitalization indicate external eﬀects that dissipate
with distance? Conversely, given the absence of an impact area in the control neighborhood
of Bellemeade, are land price changes in that neighborhood more uniform across space?

4.1

Data Description

Our dataset stems from two sources. First, the city of Richmond collected records of all
properties that benefited from NiB funding between 1999 and 2004. These records include
the geo-coded location of those properties as well as the amount and type of funds that it received. Second, we also obtain from the city of Richmond a geo-coded listing of all properties
sold between 1993 and 2004 that includes information on condition and age, construction descriptors (e.g. exterior materials, type of heating, etc.), and various dimensional attributes
(e.g. lot size, size of living area, etc.). Since the NiB revitalization programs specifically
targeted residential properties, we remove from our sample all non-residential properties,
mainly commercial buildings. We also delete listings that were likely incorrectly recorded,
including homes listed as being built before 1800 and homes whose living area is recorded
as less than 250 square feet. Because all of our data is geo-coded, we are able to cross-check
our two datasets and remove any property that directly benefited from NiB funding. In this
sense, we aim to measure only the external eﬀects associated with the NiB programs. In all,
we have 44, 412 sales observations.
Descriptive statistics of the housing characteristics for all years are reported in Table 2.
These characteristics include the furnished square footage of a house, the number of years
since the house was first built, its plot acreage, and the number of bathrooms available (with
half baths counting as one half). We also include binary variables that indicate whether the
house has central air conditioning, whether its exterior is brick or vinyl, and whether it is
heated using gas or hot water. The city of Richmond also assigns condition grades to each
house, which we capture using binary variables to indicate whether a house was assessed
in good condition, poor condition, or very poor condition. Finally, we include among our
conditioning variables, Z, a set of time dummies that capture secular city-wide increases
in home prices driven by aggregate factors such as city population growth or interest rates
changes.

Table 2. Data Summary
Variable

Mean

St. dev. Min.

Sales Pricea
1122281 136327
Air Conditioning
0.5716
0.4949
Brick Exterior
0.4611
0.4985
Vinyl Exterior
0.0404
0.1970
Gas Heating
0.1267
0.3326
Hot Water Heating
0.2167
0.4120
Square Footage
1664.9
1190.3
Age (in years)
63.78
26.46
Acreage
0.2337
0.3506
Good Condition
0.1789
0.3833
Poor Condition
0.0196
0.1385
Very Poor Condition 0.0137
0.1162
No. Bathrooms
1.546
1.245

Max.

0.93 8946680
0
1
0
1
0
1
0
1
0
1
319
63233
0
205
0.012
37.67
0
1
0
1
0
1
0
1

a : Expressed in constant 2000 dollars.

4.2

Estimation of the Parametric Eﬀects

In order to estimate the non-parametric component of Equation (13), q( ), we must first
address the estimation of the parametric eﬀects, β. Let n denote the number of observations
on home prices and k the number of variables in Z. A popular approach, pioneered by
Robinson (1988), proceeds in two steps. In the first step, non-parametric (kernel) estimates
of E(p| ) and E(Z| ) are constructed. Since Equation (13) implies that
p − E(p| ) = [Z − E(Z| )]β + ε,

(14)

the second step involves replacing the conditional means in (14) by these non-parametric
functions and estimating β by least squares. Robinson (1988) shows that estimates of β
√
obtained in this way are n consistent. Because of the size of our dataset, and given that
separate non-parametric regressions are required for each housing attribute in Z, this method
proves onerous in our case. To circumvent this problem, Yatchew (1997, 2001) proposes a
diﬀerencing approach that we adopt in this paper.
The basic idea behind Yatchew’s (1997, 2001) estimation strategy is to re-order the data,
(p1 , Z1 , 1 ), (p2 , Z2 , 2 ), ... , (pn , Zn , n ) so that the ’ s are close, in which case diﬀerencing
tends to remove the non-parametric eﬀects. In particular, first-diﬀerencing of (13) gives
pi − pi−1 = (Zi − Zi−1 )β + q( i ) − q(
16

i−1 )

+ εi − εi−1 .

(15)

Assuming that a Lipschitz condition holds for q, |q( a ) −q( b )| ≤ L|| a − b ||, the diﬀerence in
non-parametric component in (15) vanishes asymptotically.6 Yatchew (1997) shows that the
OLS estimator of β using the diﬀerenced data (i.e. the projection of pi −pi−1 on Zi −Zi−1 ) is
√
also n consistent. This estimator of β, however, achieves only 2/3 eﬃciency relative to the
one produced by Robinson’s method. This can be improved dramatically by way of higherorder diﬀerencing. Specifically, define ∆p to be the (n − m) × 1 vector whose elements are
P
Pm
[∆p]i = m
s=0 ds pi−s , ∆Z to be the (n − m) × k matrix with entries [∆Z]ij =
s=0 ds Zi−s,j ,
and similarly for ∆ε. The ds ’s denote constant diﬀerencing weights and m governs the order
of diﬀerencing. We thus estimate a more general version of Equation (15),
∆p = ∆Zβ +

m
X

ds q(

i−s )

+ ∆ε, i = m + 1, ..., n,

(16)

s=0

where the following two conditions are imposed on the diﬀerencing coeﬃcients, d0 , ..., dm :
m
X

ds = 0 and

s=0

m
X

d2s = 1.

(17)

s=0

The first condition ensures that diﬀerencing removes the non-parametric eﬀect in (13) as
the sample size increases and the re-ordered ’s become “close”. The second condition is a
normalization restriction that implies that the transformed residual in (16) has variance σ 2ε .
When the diﬀerencing weights are chosen optimally, the diﬀerence estimator, β∆ , obtained
by regressing ∆p on ∆Z approaches asymptotic eﬃciency by selecting m suﬃciently large.7
We use m = 10 which produces coeﬃcient estimates that are approximately 95 percent
eﬃcient when using optimal diﬀerencing weights. Note that, as a practical matter, the initial
re-ordering of the ’s is not unambiguous here since ∈ R2 . We re-order locations using a
path created by a Hamiltonian nearest neighbor algorithm and, for our dataset, this yields
P
a mean distance between locations, 1/n || i − i−1 |, that is 24 to 28 times smaller than
that obtained by simply re-ordering locations according to their x or y coordinate (i.e. the
wrap-around method)8 .
6

Suppose that locations constitute a uniform grid on the unit square (the re-scaling is without loss of
generality). Each point may then be thought of as residing in an area of 1/n, and the distance between
√
re-odered adjacent observations, || i − i−1 ||, is 1/ n.
P
P
7
2
Optimal diﬀerencing weights, d0 , ..., dm , solve min δ = m
k=1 ( s ds ds+k ) subject to the constraints in
(16). See Yatchew (1997).
8
The starting point when using the nearest neighbor approach is arbitrary but has little implications for
our results.

4.3

Non-Parametric Kernel Estimation of q( )

Denote by Y the price of a home “purged” of its contribution from housing characteristics,
b ∆ , and construct the data (Y1 , 1 ),
where Y is obtained using first stage estimates, Y = p−Zβ
b ∆ is a consistent estimator of β, standard kernel estimation
(Y2 , 2 ),...,(Yn , n ). Because β
methods applied to purged home prices yield consistent estimates of q( ).
The Nadaraya-Watson kernel estimator of q at location j is given by
−1

q( j ) = n

n
X

Whi ( j )Yi .

(18)

i=1

In other words, the component of home prices directly related to location, j , is a weightedaverage of the Y ’s in our data sample. The weight Whi ( j ) attached to each price Yi is given
by
Kh ( j − i )
Whi ( j ) = −1 Pn
,
(19)
n
i=1 Kh ( j − i )

where

u
Kh (u) = h−1 K( ),
h
R
R
and K(ψ) is a symmetric real function such that |K(ψ)|dψ < ∞ and K(ψ)dψ = 1.
Thus, we may choose to attach greater weight to observations on prices of homes located
near j rather than far away by suitable choice of the function K. In particular, as in much
of the literature, our estimation is carried out using the Epanechnikov kernel. The distance
between location j and some other location i in the city is simply measured as a Euclidean
distance in feet. An implication of the Epanechnikov kernel is that prices of homes located
more than a distance of h feet from j will receive a zero weight in the estimation of q( j ).
In that sense, the bandwidth h has a very natural interpretation in this case.9
The NiB programs were first implemented in 1999 and nearly phased out by 2004. Consequently, we estimate Equation (13) over two subsamples, 1993 − 1998, the period prior to
NiB coming into eﬀect, and 1999 − 2004, the post revitalization period for which we have
data. The first and second subsamples contain 18102 and 26310 observations respectively.
Ultimately, we wish to capture increases in the price of land at diﬀerent locations between
1998 and 2004. Hence, we set the base year for the time dummies in Z as the last year in
each subsample period. All prices are measured in 2000 constant dollars, and we estimate
land prices using observations over the entire city of Richmond.
9

In practice, the estimation of q( ) is aﬀected to a greater degree by the choice of bandwidth rather than
the choice of kernel. See diNardo and Tobias (2001) for a detailed discussion. In this case, the bandwith is
Pn
chosen by means of Cross-Validation. Hence, we select h so that it solves minh CV (h) = n−1 j=1 [Yj −
Pn
qeh ( j )]2 , where qeh ( j ) = n−1 i6=j Whi ( j )Yi .

Empirical results

This section reviews our findings. We present estimates of the semiparametric hedonic price
regression (13) and illustrate what they imply for city-wide land prices prior to the implementation of NiB. This allows us to compute changes in land values for the neighborhoods
targeted for revitalization and describe how these changes vary as we move away from the
impact area. We then compare our findings for the targeted neighborhoods with those in our
control neighborhood. This comparison lets us compute the total eﬀect of the NiB program
relative to a benchmark where no such public investment took place. Finally, we use this
evidence to calibrate the model of housing externalities presented in Section 3.
Table 3 presents estimates of the parametric components of Equation (13). Virtually all
housing characteristics in Table 3 are statistically significant at the 5 percent critical level,
and the large majority of these attributes is significant at the 1 percent level in both samples.
In addition, both specifications achieve a surprisingly good fit for cross-sectional data.10
Coeﬃcients associated with the sale date are significant over and above prices being
measured in constant dollars. In the post 1998 period, in particular, our findings suggest
a considerable real run up in home prices in the city of Richmond (as with many other
U.S. cities over the same time period). We estimate separate semiparametric hedonic price
specifications over the pre and post 1998 period to account for possible changes to the
valuation of housing attributes triggered by the implementation of the revitalization policy
or any other city policy or shock. The housing coeﬃcients shown in Table 1, however, tend
to be relatively similar across subsamples. Alternative estimates that hold the coeﬃcients on
housing attributes constant across subperiods have immaterial implications for the results
we present below.
Of central interest are the nonparametric estimates of land prices, q( ), in both the
targeted neighborhoods and the control neighborhood.11 Prior to the start of the NiB project,
we estimate land prices that in 1998 averaged $5.97 per square foot in the neighborhood of
Church Hill, $6.38 in Highland Park-South Barton Heights, and $5.17 in Blackwell. In
contrast, we estimate higher land prices for the city as a whole, with a mean of $8.29 per
square foot, and land prices that are as high as $100 per square foot in the more aﬄuent parts
of Richmond. The large majority of these highly priced sites form part of a historical district
known as the Fan located in the center of Richmond. Because the neighborhood of Jackson
Ward-Carver adjoins the Fan district, the local averaging implied by kernel estimation gives
Pn
b )2 →P σ 2 . Hence, we compute R2 as 1 − s2 /s2 .
It can be shown that s2∆ = n1 i=1 (∆pi − ∆Zi β
∆
ε
∆ p
11
Land prices are estimated on a grid containing the coordinates of home sales in our pre-policy sample.
Using the grid corresponding to post-policy home sales instead does not change our findings.
10

land prices that have a mean of $12 per square foot in that neighborhood. In contrast,
estimated land prices in the control neighborhood of Bellemeade fall well within the range
of the other three NiB neighborhoods, with a slightly lower mean at $4.71 per square foot.
Table 3. Estimates of the parametric eﬀects on home prices
Variable

1993-1998 Period
Coeﬀ. t-statistics

1993
1994
1995
1996
1997
Air Cond.
Brick Exterior
Vinyl Exterior
Gas Heating
Hot Water Heating
Sq. Ft.a
Ageb
Acreage
Good Cond.
Poor Cond.
Very Poor Cond.
No. Bathrooms
No. obs.
R2

-0.059
-0.039
-0.048
-0.036
-0.029
0.094
0.152
-0.290
0.092
0.101
0.055
-0.007
-0.815
0.095
-0.510
-0.867
0.003
18102
0.64

1999-2004 Period
Coeﬀ. t-statistics

-3.453
-2.381
-2.924
-2.203
-1.874
7.752
11.386
-8.636
5.610
6.624
6.237
0.218
-37.652
6.524
-11.864
-17.327
0.479

1999
2000
2001
2002
2003
Air Cond.
Brick Exterior
Vinyl Exterior
Gas Heating
Hot Water Heating
Sq. Ft.
Age
Acreage
Good Cond.
Poor Cond.
Very Poor Cond.
No. Bathrooms
26310
R2

-0.428
-0.380
-0.303
-0.232
-0.129
0.078
0.186
-0.187
0.154
0.066
0.027
0.149
-0.423
0.137
-0.375
-0.613
0.010

-30.206
-27.401
-22.513
-17.316
9.718
7.900
16.173
8.250
10.317
5.210
5.496
5.972
-34.920
11.087
12.990
-17.449
2.251

0.68

a : measured in 1000 sq. ft.; b : measured in 100 years.
A contour map of the price of land per square foot for the city of Richmond before NiB is
shown in Figure 4. It is clear from the figure that the NiB neighborhoods are associated with
some of the lowest land prices in the entire city. Despite its relatively small area of 60 square
miles, Figure 4 suggests considerable variation in land prices throughout Richmond. Because
lot sizes are relatively homogenous throughout Richmond at around 0.1 acres, our estimates
suggest lot prices that vary from $20,000 in the neighborhoods targeted by NiB to $435,000
in the more well-oﬀ districts. Table 4 focuses on the NiB neighborhoods more specifically
and gives estimated land prices per square foot at diﬀerent percentiles in comparison to the
city as whole.
20

Table 4. Pre-NiB land price per square foot
Neighborhood
Church Hill
Blackwell
Highland Park-Barton
Jackson Ward-Carver
Bellemeade
City of Richmond

5.1

10th
25th
50th
75th
90th
Percentile Percentile Percentile Percentile Percentile
0.81
0.76
1.29
2.22
1.87
3.09

1.84
1.84
2.61
4.85
2.89
5.11

5.21
3.83
5.22
11.77
4.71
8.29

13.32
7.04
8.05
21.66
6.42
14.94

21.02
12.15
11.59
31.36
8.13
27.40

The Return to Land in the Neighborhoods Targeted by NiB

To relate our empirical findings to the theory in Section 3 more closely, we now explore
several key aspects of the data. First, we explore whether changes in land value in the four
selected neighborhoods decrease with distance in a way suggested by Figure 2C? Second,
given the absence of an impact area in the control neighborhood of Bellemeade, we ask
whether changes in land value in that neighborhood are both lower and more uniform across
space?
To answer these questions, there are two aspects of the empirical framework that we must
first reconcile with the theory presented in Section 3. First, in contrast to our model, targeted
neighborhoods in practice generally have more than one impact area that lie in R2 . Second,
for ease of presentation, we must tackle the issue of how to present our estimates for ∆q( ),
where ∈ R2 , in terms of distance from a focal point, ∆q(d), where d ∈ R, analogously to
Figure 2C. By way of example, we use the neighborhood of Blackwell to discuss our approach
to both issues, and proceed similarly in the other targeted neighborhoods.
Figure 3 shows the targeted neighborhood of Blackwell, denoted by N . Within N , let
Ai represent the cluster of locations that were the direct recipient of NiB funding. There are
2 such clusters shown in Figure 3, which essentially constitute impact areas. Formally, the
partitioning of directly targeted locations into separate clusters satisfies a K-means criterion.
Specifically, our partitioning of those locations into 2 disjoint subsets, A1 and A2 , satisfies
P P
minK K
i=1
n∈Ai | n − μi |, where n and μi are a location and the geometric centroid of Ai
12
respectively. We define the funding center of an impact area as a convex combination of
the locations that received NiB funding within that cluster. These are shown as c1 and c2 in
12

Although this problem potentially yields multiple solutions, the clusters of funded locations are suﬃciently separated in our case that this is not an issue.

Figure 3. The weights in that combination are given by the relative amounts of NiB funds
spent at the diﬀerent locations. In that sense, this funding center represents a focal point of
the revitalization policy in a given impact area.
In general, it is possible that a location in between two impact areas, such as between
A1 and A2 in Figure 3, benefit from externalities related to both sets of funded locations
simultaneously. In that case, for simplicity, we attribute any measured external eﬀect on land
values to the closest impact area. Thus, for each location in N , we compute the distance
from to the center of the closest cluster, d( ) = mini {|| − ci ||}, where ci is the center of
Ai . We can then rank these distances from smallest to largest. In particular, the variable
d( ) represents a convenient mapping from R2 to R that, despite the existence of several
impact areas in a given neighborhood, captures some notion of distance from a central point
of the policy experiment. It also allows us to plot land price changes with respect to distance
from this focal point, ∆q(d), and to examine whether changes in land value indeed fall as we
move away from the policy experiment (i.e. as d increases). In order to capture any external
eﬀects that potentially exist beyond the targeted neighborhoods in Figure 1, we extend each
neighborhood to encompass locations such that d( ) covers a radius of 3500 feet. In doing
so, however, we are careful not to cross natural boundaries such as highways, railroad tracks,
industrial zones, etc. that often arise before reaching 3500 feet. In practice, therefore, this
radius generally represents the broadest definition of a neighborhood that does not infringe
on other neighborhoods with distinctly diﬀerent demographics or housing characteristics.
Figure 5 illustrates (kernel-smoothed) distributions of estimated land price changes,
∆q( ), in each of the NiB neighborhoods. Recall that q( ) is estimated from log prices
so that ∆q( ) measures percent changes which we express at an annual rate. The distribution of estimated changes in land value generally depicts positive returns in all four cases,
although the spread and mean of these distributions vary. The question is whether, as in
Figure 2C, these land price increases become smaller as one moves further away from the
impact area.
Figure 6 illustrates the behavior of estimated changes in land prices per square foot with
respect to distance from the impact area, ∆q(d). It is apparent that in all four cases, the
returns to land fall as the distance from the policy experiment increases.13 Externalities
are more pronounced close to the funding center and fall steeply as one moves away from
locations in the impact area. In the neighborhood of Church Hill (Figure 6A), most of the
13

The curves shown in each panel of Figure 6 are Nadaraya-Watson kernel estimates computed as described
in section q
4. The 95 percent confidence bands are based on standard errors at each distance, d, computed
R
Pn
b σ 2ε
di −d
1
as s(d) = hepK(d)n
, where pb(d) = hn
K(u)du, and n is the number of observations in
i=1 K( h ), bK =
each panel.

returns to land are concentrated around the upper tier, which explains a mode annual return
of around 12 percent in Figure 5A. In contrast, in the neighborhood of Blackwell (Figure
6B), most of the returns to land are located near the lower tier so that the mode return in
Figure 5B is around 4.5 percent. Both Figures 5 and 6 suggest perceivable diﬀerences in the
way that each neighborhood was aﬀected by the NiB program, with mean annualized returns
that vary from 5.93 percent in Blackwell to 9.71 percent in Church Hill. Thus, we examine
more closely below the relationship between the size of the capital improvement program
in a particular neighborhood and its overall gain in value from externalities. Recall from
Equation (12) that both the size of the impact area and the amount of funding for home
improvements have a first-order eﬀect on price changes. It remains that in all four cases, the
neighborhoods targeted for revitalization appear to have fared appreciably better than the
control neighborhood of Bellemeade whose mean return of 3.88 percent is shown as the flat
solid line in Figure 6. Strikingly, observe that land returns in the targeted neighborhoods
tend to level out at the control neighborhood mean as the distance from the center of the
impact area reaches 2500 to 3500 feet.
Figure 7 shows contour maps of the returns to land in each of the NiB neighborhoods. In
each neighborhood, distinct land return ‘hills’ are clearly visible. Furthermore, the locations
we identify as centers of the policy experiment (i.e. the convex combination of funded
locations) tend to be situated near the peaks of those ‘hills’. In some cases one center tends
to dominate; as in Church Hill where the southern policy center is located right at the top
of the highest hill in land returns. Given the absence of an impact area in Bellemeade, a
key question then is: are changes in land value in the control neighborhood lower and more
uniform across locations unlike those shown in Figure 6 and 7?

5.2

Comparisons with the Control Neighborhood of Bellemeade

Figures 8A and 8B illustrate the behavior of changes in land value in the control neighborhood
of Bellemeade. Figure 8A shows changes in the return to land as a function of distance from
the centroid of the neighborhood (since Bellemeade does not contain an impact area), while
Figure 8B gives a contour map of the returns. It is clear from both panels in Figure 8 that
the returns to land are more uniform across the neighborhood in this case. These returns
are also more concentrated around the mean (the solid line in Figure 8A) than those in the
neighborhoods in bloom and, in some cases, are even negative.
It seems clear from Figure 6 and Figure 8A that the neighborhoods targeted for revitalization generally performed better than the control neighborhood in terms of changes in
land value. On average, land prices increased by 3.88 percent at an annual rate between
23

1998 and 2004 in Bellemeade. This roughly implies a 24 percent increase over this six-year
period. In contrast, mean annual land prices increased by 9.71 percent in Church Hill, 5.93
percent in Blackwell, 6.60 percent in Highland Park-South Barton Heights, and 8.65 percent
in the neighborhood of Jackson Ward-Carver. Moreover, Figure 6 indicates that sites near
the (funding) center of the impact area experienced returns on land of 12 to 15 percent in
each of the NiB neighborhoods. At the upper end, therefore, these returns represent almost
a doubling of land prices over the period 1998 to 2004 compared to just a 24 percent increase
in Bellemeade. Finally, observe that consistent with the absence of any targeted programs in
our control neighborhood, changes in land values in Bellemeade display much less variation
than in the NiB neighborhoods.
Given the size of the land returns estimated in the NiB neighborhoods relative to Bellemeade, it is natural to ask whether these external gains may have been driven not only by
the revitalization policies put in place but also by simultaneous increases in private investments triggered by the renewal program. Several aspects of the analysis suggest that this
consideration plays a limited role in this case.
Under the assumptions maintained in Section 3, recall that the model predicted a crowding out of private investments following the renewal program rather than a corresponding
increase in private home improvements. This result stems from agents being able to move
freely between neighborhoods but also from the assumption that they are identical (and have
Cobb-Douglas preferences). In practice, of course, the revitalization policies may have produced a reshuﬄing of population across neighborhoods such that higher income households
moved into the targeted areas and bid up the price of land. This process, in fact, often
precisely describes gentrification. If these higher income households also carried out home
improvements, the estimated returns on land shown in Figure 6 overstate the external eﬀects
induced by the revitalization policies. However, accounting for a simultaneous increase in
income, w, (to reflect a changing population) in addition to public investments, σ, would
shift the entire land return gradient, qp ( ) − q( ), in Figure 2B upwards. Returns to land
near the boundary of the neighborhood, R, in Figure 2B would also shift upward if the
new population invested in housing outside the impact area. In contrast to these predictions, what is striking in Figure 6 is that changes in land value in the NiB neighborhoods
eventually level out to match the returns estimated in Bellemeade. Recall, in particular,
that land returns in the control neighborhood are relatively even around the mean in Figure
8A. Nothing in our estimation procedure forces these results. Finally, anyone moving into
a targeted neighborhood after 1998, and privately investing in home improvements, would
likely have taken advantage of the NiB program since the program would have subsidized
the investment. As such, the observation would have been omitted from our sample.
24

5.3

Calibration and the Rate of Decline in Housing Externalities

In order to determine more directly what Figure 6 implies for the speed at which externalities
dissipate with distance, we now proceed with a calibration of the model in Section 3 that
gives us some sense of the size of the parameter δ. In accordance with CPI weights, we set
the share of income spent on housing, 1 − α, to 0.32. Analogously to the rate of interest
in a dynamic framework, the level of wages in our model determines the time period tied
to the flow of consumption services and housing investments. Thus, we set a daily wage of
w = 80 which corresponds to ten dollars an hour and would be typical for residents of an
NiB neighborhood. We set the radius of each neighborhood, R, to 3500 feet consistent with
Figure 6. To calibrate the radius of the impact area, r, we estimate the total size of impact
p
areas in each neighborhood, A, and set r = (A/π). This yields an impact area radius of
1085 feet in Church Hill, 1190 feet in Blackwell, 1365 feet in Highland Park-South Barton
Heights, and 1400 feet in Jackson Ward-Carver. If R is measured in feet, then the parameter
σ in Section 3 refers to the amount of spending per foot in the impact area. Note, however,
that only some of each neighborhood is composed of residential land. To compute residential
area in a given impact region, therefore, we first multiply the number of residential units in
the corresponding neighborhood by their mean acreage, which gives us an estimate of total
residential acreage in that neighborhood. To obtain residential acreage within an impact
area, we then multiply total residential acreage by the ratio of the size of an impact area,
πr2 , to total neighborhood area, πR2 . We have available the amount of NiB funds disbursed
in each neighborhood. Hence, we can approximate σ in a given neighborhood as
σ=

Total Funding in Neighborhood
No. of Units × Mean Unit Acreage ×

πr2
πR2

However, since NiB residents generally live on one-tenth acre plots (which correspond to 4356
square feet), and funding took place over a six-year period (or 6×365 days), an appropriately
4356
scaled value for σ is σ
e = σ × ( 6×365
). This calculation yields NiB spending per unit area of
$6.48 in Church Hill, $5.61 in Blackwell, $2.46 in Highland Park-South Barton Heights, and
$5.96 in Jackson Ward-Carver. Finally, because each neighborhood is small relative to the
city as a whole, we assume that all residents in a neighborhood face the same commuting
costs. Thus, we set τ = 0 and interpret w as a wage net of commuting. This leaves only the
parameter u, which we set to 33. The implied land rent at the edge, qR , is then around 26
dollars per day per acre, or equivalently 780 dollars a month for a typical lot.
The solid curves in Figure 9 depict land returns predicted from our model in each neighborhood when δ = 0.0007. Given this value of δ, the model does relatively well in replicating
the nonparametric estimates from Figure 6, with the exception of Blackwell. Aside from
25

diﬀerences in the geography of each NiB neighborhood, the discrepancy in Blackwell likely
reflects diﬀerences in the eﬀectiveness of CDCs across neighborhoods. As indicated in Section
2, variations across CDCs often result in disparities in the quality of capital improvements,
in particular home renovations, generated by a dollar of NiB funding. These disparities, in
particular, arise from ties between a given CDC and specific contractors or input suppliers.
In addition, recall from Section 2 that Blackwell is unique relative to the other neighborhoods
in that, simultaneously with NiB, the Hope VI program in that neighborhood was actively
engaged in eradicating housing stock deemed “unfit” but without, at the time, replacing
it with new construction. Interestingly, Figure 9 suggests that any diﬀerences in the way
CDCs operate seem of second order in the other three neighborhoods. In Blackwell, the
amount of NiB funding per square foot comes to $5.61 per square foot. Assuming that this
funding translated instead into $3.10 of eﬀective home improvements relative to the other
three neighborhoods (i.e. a ratio of 1 to 1.81), the model would have produced the dotted
curve in Figure 9B. Put another way, we think of the negative externalities generated by
the simultaneous destruction of housing stock in Blackwell by the HOPE VI program as
oﬀsetting the eﬀectiveness of an NiB dollar by about 45 cents. More generally, a value of
0.0007 for δ implies external eﬀects from housing services that fall by half approximately
every 990 feet. Note that the model accurately predicts the total magnitude of the eﬀect
arising from externalities, namely the diﬀerence between land rent returns at the center of
the neighborhood and its boundary.
Our findings, therefore, suggests externalities that dissipate somewhat more slowly with
distance than estimated in previous work. In particular, Schwartz, Ellen, Voicu, and Schill
(2006), using data from a ten-year residential investment program in New York City, find
residential externalities lasting out to 2000 feet from a project site, with stronger eﬀects in
poor neighborhoods similar to those in this study. Santiago, Galster and Tatian (2001) find
eﬀects on house prices at 1000 to 2000 feet from a project site, though the investments in that
paper are specific to public housing, not simply housing investment. Ding, Simons and Baku
(2000), and Simons, Quercia and Maric (1998), examining CDC investments in Cleveland,
find price eﬀects that dissipate between 300 and 500 feet from a project site, though their
methodology indicates that distances further than 500 feet were not investigated. In contrast
to our investigation, all of these papers estimate house prices (rather than land values) using
parametric hedonic regressions rather than the nonparametric approach adopted in this
paper.

5.4

Urban Revitalization Programs and Gains in Land Value

This section examines more closely the relationship between the size of the NiB program
implemented in a specific neighborhood and its overall gain in land value. In particular,
while we have the amount of funding received in each of the concerned neighborhood between
1998 and 2004, we wish to arrive at an estimate of overall land gains over that period for
comparison.
Table 5A Neighborhood land values in 1998
Neighborhood

No. of units Median plot value Neighborhood value

Jackson Ward
Highland Park
Church Hill
Blackwell

2913
3471
2520
1411

33,338
42,170
21,136
31,081

97,113,594
146,372,070
53,262,720
43,855,291

From the city of Richmond, one can obtain the number of residential units in each of
the targeted neighborhoods. These are shown in the first column of Table 5A. Although
consistent data on lot sizes for each of these units is unavailable, we can compute the median
land value of a lot in each of the neighborhoods from our dataset. In particular, we have lot
sizes for homes that have sold in each neighborhood which we can multiply by our estimated
price per square foot land, q( ), at each corresponding location. Multiplying the number of
units in a given neighborhood by its median plot value then gives us an estimate of total
neighborhood value in 1998. These are shown in the last column of Table 5A. Note that
there are considerable variations in neighborhood values. The median plot value in Highland
Park-South Barton Heights, for instance, is roughly twice as expensive as in Church Hill prior
to the revitalization policy, with roughly 1.4 times the number of units.
Table 5B Overall land gains and the size of urban revitalization programs
Neighborhood
Jackson Ward
Highland Park
Church Hill
Blackwell

Excess Return Neighborhood Gain NiB Funding Gain:Funding Ratio
4.77
2.72
5.84
2.05

27,793,911
23,887,922
18,663,257
5,394,201

4,127,636
4,261,211
3,129,187
2,533,243

6.73
5.61
5.96
2.13

To compute overall land gains in the targeted neighborhoods, the first column of Table
5B gives the (annualized) mean excess return to land in each neighborhood relative to Bellemeade. Given the value of land shown in Table 5A for each neighborhood, we can readily

compute its overall gain between 1998 and 2004. These gains are shown in the second column of Table 5B. The last column in Table 5B then shows the ratio of this overall land gain
to the amount of NiB funding received for each neighborhood. Surprisingly, these ratios
are quite close in three of the four neighborhoods at about 5.5 to 6. The ratio in Blackwell is considerably lower, however, which explains the diﬃculty in matching the returns for
that neighborhood in the calibration exercise carried out earlier. As indicated previously,
variations in CDC’s across neighborhoods and the fact that the Hope VI program was in
the process of razing unfit homes in Blackwell, without at the time replacing it with new
construction, made that neighborhood somewhat unique. In any case, it remains that total increases in land value in each neighborhood (Table 5B, column 2) generally reflect the
intensity of the NiB program in that neighborhood (Table 5B, column 3).
At this stage, it is absolutely crucial to recognize that our results, both in terms of theory
and the empirical work, depend importantly on the exogeneity of NiB funding. Specifically,
it matters critically that NiB expenditures were financed from sources exclusively outside
Richmond. One cannot, therefore, expect the ratios of land gains to funding shown in
Table 5B to obtain more generally as the size of revitalization programs increases. Broader
programs are less likely to be funded solely from external sources. Moreover, when the funds
that finance revitalization policies are raised from local taxes, externalities will be positive
in the targeted neighborhoods but negative in areas where higher taxes lead to a reduction
in housing investments. In practice, this reduction often arises by way of population moving
outside the city boundaries to escape the increase in taxes. In that sense, the ratios of gains
in land value to funding in Table 5B are best interpreted as upper bounds.
As a final thought experiment, we can compare the results shown in the last column of
Table 5B with a more direct implication of the model in Section 3. Specifically, consider the
eﬀects generated by $1 of capital improvements spent at the center of an impact area. If
externalities from housing services decline exponentially with distance in the way described
in Equation (1), the external eﬀect obtained a distance s away from that location is given
by δe−δs . Thus, the aggregate externality obtained within a radius R of where the dollar is
spent is given by
Z Z
R

2π

ρ=δ

e−δs dsdθ = 2π(1 − e−δR) ),

(20)

which is bounded between 0 and 2π for given δ and R. When R is 3500 feet, as suggested
by Figure 6, and δ = 0.0007, as suggested by our calibration exercise, ρ = 5.74. This result
coincides well with the magnitudes calculated in Table 5B for the three neighborhoods that
were not simultaneously subject to additional housing programs.

Concluding Remarks

In this paper we presented and interpreted evidence of housing externalities. Our findings
suggest that housing externalities are large, fall by half approximately every 990 feet, and
considerably amplify the eﬀects of revitalization programs. The evidence we uncover in this
paper can be used, in conjunction with a model of the type we provide, to evaluate and design
urban renewal policies. More generally, having estimates of the size and rate of decline of
housing externalities is central to the results of any such policy exercise.
We estimate that a dollar of home improvement generated between $2 and $6 in land
value by way of externalities in the neighborhoods of interest. The type of revitalization
policies considered here, therefore, appear to have been an excellent investment for the city
of Richmond. However, a word of caution is in order. First, as argued earlier, the returns
to renewal projects may decrease rapidly with the size of the program. Second, to the
extent that the returns computed here include private investment in unobservable housing
characteristics, our findings may overstate the eﬀects of the program. Finally, given our
findings, a natural question arises: Could a developer have instead privately internalized (a
portion of) the external eﬀects associated with the NiB program? In principle, this would
have been possible but to capture these externalities, the developer would have had to incur
the fixed cost of purchasing (parts of) the neighborhood. The return on total investment,
therefore, would have been well within the norm of other standard investment vehicles.
For example, abstracting from structures, we estimate that the neighborhood of Jackson
Ward-Carver would have cost around $97 million. Our work then suggests that spending an
additional $4 million in capital improvements yielded about $28 million from externalities
over 6 years. Hence, the return from external eﬀects alone would have come to roughly 4.1
percent at an annual rate. While this represents a reasonable rate of return, it is not one
that obviously dominates other investment opportunities given the initial investment of $97
million. Moreover, obtaining this return may involve a degree of community participation
that would be diﬃcult for private developers to elicit.
Evidently, the results we obtain in this study are to a degree particular to the NiB
program and to the city of Richmond. It is not clear that they can be generalized or used in
other contexts. That said, although the magnitude of housing externalities may vary across
settings, the evidence we uncover points to a general feature of residential neighborhoods:
The existence of significant housing externalities. In light of this evidence, it would be
misleading to omit this feature of residential neighborhoods in standard urban theories used
to design urban policy.

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Figure 1: Overview of the Neighborhoods-in-Bloom Program, Richmond VA

A. Housing Investment

B. Land Rents

6.5

6
7
q(l) and qp(l)

H(l) and Hp(l)

5.5
5
4.5
4
3.5

6
5
4

Impact Area

2.5
-R

-r

Impact Area
r

3
-R

-r

distance

C. Changes in Land Rents

D. Distribution of land returns

0.5

5
Percent land return

r
distance

0.4

4
0.3
3
0.2
2
0.1

1
Impact Area
0

r
distance from center of impact area

2
3
percent land return

Figure 2: A model of housing externalities

6000

5000

distance in feet

4000

3000

2000

1000

2000
distance in feet

3000

Figure 3: Funding locations and impact areas in Blackwell

4000

Figure 4: Pre-NiB land prices per square foot in Richmond
35

Figure 5: Distribution of changes in land value in the neighborhoods targeted by NiB

Figure 6: Change in the return to land with distance from the impact area

Figure 7: NiB returns to land
38

Figure 8: Returns to land in the control neighborhood
39

A. Church Hill

B. Blackwell

8
6

4
4
2
2
0
0

0
0

500

1000

1500

2000

2500

3000

3500

500

C. Highland Park and South Barton Heights

1500

2000

2500

3000

3500

D. Jackson Ward and Carver

1000

-2

1
2
0
0

500

1000

1500

2000

2500

3000

3500

-1

0
0

500

1000

1500

2000

2500

3000

Figure 9: Calibrated model and nonparametric estimates of land returns

3500

Full text of Working Papers (Federal Reserve Bank of Richmond) : Housing Externalities : Evidence From Spatially Concentrated Urban Revitalization Programs, Working Paper 08-03

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