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Journal of Housing Economics 35 (2017) 13–25
Contents lists available at ScienceDirect
Journal of Housing Economics
journal homepage: www.elsevier.com/locate/jhec
Immigration and housing: A spatial econometric analysis
�
Abeba Mussa
a , Uwaoma G. Nwaogu
b , ∗, Susan Pozo
c
a Department of Economics, Farmingdale State College, 2350 Broad Hollow Rd, Farmingdale, NY 11735, USA b Economics, Accounting and Management Department, Central College, 812 University, Pella, IA 50219, USA c Department of Economics, Western Michigan University, 1903 West Michigan Ave, Kalamazoo, MI 49008, USA
a r t i c l e i n f o
Article history:
Received 1 July 2014
Revised 6 August 2016
Accepted 2 January 2017
Available online 3 January 2017
JEL classification:
F22
L85
R21
Keywords:
Immigration
Housing price
Housing rent
Spatial model
Spillover effect
a b s t r a c t
In this paper we examine the effect of immigration into the U.S. on the U.S. housing market, both in
terms of rents and single family house prices. We model the housing market in a spatial econometrics
context using the spatial Durbin model. This approach helps us exploit and capture both the direct and
indirect effects of immigration inflows on the U.S. housing market. We find that an increase in immi-
gration inflows into a particular MSA is associated with increases in rents and with house prices in that
MSA while also seeming to drive up rents and prices in neighboring MSAs. The patterns observed in the
rental and house price markets, along with the larger spillover effects, are consistent with native-flight
from immigrant receiving areas.
© 2017 Elsevier Inc. All rights reserved.
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. Introduction
For the last three decades, the United States has experienced
surge of immigration. Foreign-born households now account for
bout 14% of all U.S. households ( Trevelyan et al., 2013 ) and two
hirds of projected U.S. population growth from 1995 to 2050 is
xpected to be due to immigrants and their offspring ( National Re-
earch Council, 1997 ). Much of the analysis on the effects of immi-
ration on the U.S. economy has focused on its impacts on wages
nd has found mixed results (e.g. Ottaviano and Peri, 2012; Borjas,
003, Borjas and Katz, 2007 ). While labor market effects are of in-
erest, understanding how immigration affects other facets of the
conomy is also important. We focus on an area we know rela-
ively little about and provide a coherent framework for measuring
ow immigration influences housing markets in a spatial context.
n particular, we focus on the spillover effect of immigration on
ouse prices and housing rents.
We argue that immigration can be an important factor that
rives house prices and rents, in particular, given immigrant’s re-
� We are grateful to the suggestions of 2 referees and the editor for numerous
uggestions for improving this paper. ∗ Corresponding author.
E-mail addresses: [email protected] (A. Mussa), [email protected]
U.G. Nwaogu), [email protected] (S. Pozo).
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ttp://dx.doi.org/10.1016/j.jhe.2017.01.002
051-1377/© 2017 Elsevier Inc. All rights reserved.
ent and projected contributions to U.S. population growth. In
rinciple, new immigrant demand for housing coupled with an
pward-sloping housing supply in metropolitan areas (where im-
igrants tend to settle) would be expected to yield rising rents
nd prices ( Saiz, 2007 ). However, we need to also consider the pos-
ibility that immigration is associated with decreasing prices and
ents. There are a number of mechanisms by which this may take
lace. For example, if immigration is associated with driving down
ages and income in a given area ( Altonji and Card, 1991 ), it is
onceivable that we observe an adverse shift in housing demand.
his shift in the demand curve—a negative income effect—would
ikely depress housing values. An alternative mechanism that could
esult in downward pressure on housing values is if natives dislike
esiding in areas where immigrants tend to settle. This could lead
o offsetting out-migration of natives in response to immigration.
epending on the relative magnitudes of the in-migration of im-
igrants and out-migration of natives, we might observe a decline
n aggregate housing demand and in housing prices in immigrant
ettlement areas. The possibility that immigration into an area may
esult in additional population flows (e.g. out-migration of natives)
oints to the importance of accounting for geography and for pos-
ible spillover effects. In this paper we accomplish such by employ-
ng spatial econometric methods. We observe how inflows of new
mmigrants into an MSA influences the housing market, not only
n that MSA, but also in the surrounding MSAs
14 A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25
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A positive relationship between immigration and housing val-
ues in immigrant receiving areas has been estimated by a number
of researchers. Using a general equilibrium model calibrated to U.S.
conditions, Ottaviano and Peri (2007) conclude that immigrant in-
flows into the U.S. raise rents for natives. Using data on MSAs and
an IV based approach that relies on historical levels of immigration
into metropolitan areas, Saiz (2007) estimates that an immigration
inflow equal to 1 percent of a city’s population is associated with
increases in average rents and housing values of about 1%. Qual-
itatively similar results have been reproduced in other countries
as well. Akbari and Aydede (2012) examine the effect of immi-
gration on house prices in Canada. Their result indicates that a 1
percentage point increase in the immigrant share of the popula-
tion raises house prices in Canada, though, by only a fraction of
a percent. They suggest that the relatively modest effect of immi-
gration might be due to out-migration of local natives from the
areas where new immigrants settle or to increased housing sup-
ply taking place in response to projected increases in immigra-
tion. More dramatic price findings are reported by Gonzalez and
Ortega (2013) who conclude that immigration to Spain in the pre-
vious decade was responsible for a 52% increase in housing values.
In addition they attribute 37% of new construction due to immi-
grants and argue that by contributing to the stock of construction
workers, immigration also propelled an increase in housing supply
experienced by Spain.
While it seems most reasonable to expect that immigration
raises housing values, there are several arguments for expecting
the converse, justifying the findings of a number of researchers
who have found that immigration results in declining housing val-
ues instead. Accetturo et al. (2014) suggest that natives might per-
ceive a deterioration in amenities (e.g. over-crowding) due to the
inflow of immigrants, causing native-flight from immigrant-dense
districts, thus slowing down price appreciation. Using district level
data for a sample of 20 large Italian cities, they show that a 10%
increase in immigrant stocks leads to a fall in housing prices of
2 percentage points in districts affected by the inflow in com-
parison with the rest of the city. Similarly, Sá (2015 ) finds nega-
tive effects of immigration on housing prices using UK data. She
finds evidence that immigration generates a negative income ef-
fect on housing demand by driving out natives who are relatively
high wage earners. Her results also show that the negative effect
is mainly driven in local areas where immigrants have lower levels
of education.
The timing of immigration (immigration vintage effects) may
also influence relative housing values. For example, Akbari and
Aydede (2012) note that immigrants tend to buy housing after a
period of residency in their adopted homelands, while recent im-
migrants tend to rent. We might, therefore observe excess demand
for rental housing units driving up rental prices when immigrants
first move in. But over time, as immigrants move onto becoming
homeowners, they may apply upward pressure on prices for single
family homes. Hence the vintage of immigrants may affect differ-
ent segments of the housing market in different ways. Using the
Mariel boatlift natural experiment, Saiz (2003) concludes that this
population influx raised rents and depressed home values in immi-
grant receiving areas. The Mariel immigrants tended to rent, pos-
sibly propelling natives to purchase housing in other areas. Using
finer distinctions (census tracts instead of MSAs) Saiz and Wachter
(2011) conclude that housing appreciation was slower in immi-
grant neighborhoods, with natives moving out in response to the
in-migration of the newcomers.
The idea that natives may move out when immigrants move
in and that home prices and rental rates may be differentiated by
the timing of immigration, points to the importance of accounting
for the geography of immigration. In addition, we note that im-
migrant settlement patterns tend to be clustered with clustering
ikely due to immigration networks. By reducing the costs of infor-
ation gathering, immigrant networks help channel immigrant to
pecific areas. However, the impact of immigration network might
ot be limited to the cities or MSAs in which immigrants are liv-
ng, but also the surrounding metropolitan areas. Immigrants in
hicago (New York City) are likely to be relatively well informed of
pportunities for new immigrants in Gary, Indiana (Newark, New
ersey). On account of information networks or because new im-
igrants drive older residents out, immigration inflow and hous-
ng prices, in one MSA may be highly spatially correlated with the
ome prices and rents in neighboring MSAs. We, therefore argue
hat it is important to take into account spatial dependence across
pace (MSAs) in order to better understand the effects of immigra-
ion on the housing market. As such we believe it is important to
pply spatial techniques when studying the interaction of immi-
rants with the housing market. In the following section we intro-
uce spatial methods and review how they have been applied to
ousing markets.
. Spatial methods and their application to housing markets
Spatial regression methods are useful for estimating economic
elationship characterized by a data generating process with spa-
ial dependence among observations. For example, we might ex-
ect that house prices in NYC are all relatively high, exhibiting
ositive spatial dependence. Similarly, the price of a house in Kala-
azoo, is likely to be relatively similar to other house prices in
alamazoo (and considerably less than NYC house prices). In this
etting, spatial dependence (rather than spatial independence) bet-
er describes the relationship of one observation to another. There
re a number of ways by which spatial dependence may manifest
tself and a variety of econometric models have been proposed to
ccount for differing data generating processes. Two popular mod-
ls are the spatial error model (SEM) and the spatial autoregressive
odel (SAR). Each model contains only one type of spatial interac-
ion effect ( Elhorst, 2010 ). The SEM incorporates a spatial autore-
ressive process in the error term while the SAR contains a spa-
ially lagged dependent variable as an additional explanatory vari-
ble.
A number of studies have explored the use of spatial methods
n the context of housing markets. DeSilva et al. (2012) examine
he impact of Blacks and Hispanics on house prices in a small ur-
an housing market in the U.S. Using simple OLS they find that
he presence of Blacks in a neighborhood is associated with lower
ouse prices while Hispanic neighborhoods seem to enjoy house
rice premiums. However, when employing, instead, spatial meth-
ds (SEM and SAR) the effect of Blacks in a neighborhood, while
till negative, is smaller and Hispanics do not appear to have a sta-
istically significant impact on housing prices. Basu and Thibodeau
1998) model housing using the SAR model. In their view, hous-
ng prices are autocorrelated spatially because values of properties
n a given neighborhood capitalize on shared location amenities.
ocation amenities such as the quality of the police department,
ssessment of the public schools, percent of the population with
college degree, distance to employment, availability of shopping
r transportation may affect house prices more generally in the
rea. Using data from a region in Norway, Osland and Thorsen
2013) use the SDM to examine how travel time from the central
usiness district and how labor market accessibility affect hous-
ng prices. Fernández-Avilés et al. (2012) examine the impact of air
ollution on housing prices in Madrid, Spain. Employing SDM they
orroborate other studies that fail to find a link between air pollu-
ion and housing prices.
Focusing on the negative externalities, Cohen and Coughlin
2008) note that houses located near noisy areas such as rail-
ay tracks and airports sell for lower prices. They use a spatial
A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25 15
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ramework to examine the impact of airport-related noise on hous-
ng prices in the neighborhoods near Atlanta’s Harsfield-Jackson
nternational Airport. Based on a noise contour map, they cate-
orized houses into two zones; in one, noise does not disrupt
ormal activities while in the other it does. Employing a gen-
ral spatial econometrics model they show that houses located
n vicinities where noise disrupts normal activities sold for 20.8%
ess than houses located where noise does not disrupt normal
ctivities.
Presently, many spatial econometrics studies have shifted to
model with more than one spatial interaction called a spatial
urbin model (SDM). This model, introduced by LeSage and Pace
2009) , nests both the SAR and the SEM models by including spa-
ial lags of both the dependent variables and explanatory variables.
n addition to being more flexible in accommodating different as-
ects of spatial dependence, the SDM is attractive for its ability to
btain direct, indirect and total marginal effects for the explanatory
ariables, providing us with a more complete understanding of the
elationships we wish to explore. The SDM has only recently been
mployed in the context of housing markets. 1
Given the importance of immigration networks and the spa-
ial relationships we discussed earlier, we surmise that it might be
orthwhile to explore the impact of immigration on housing mar-
ets using the SDM methodology. Given its flexibility in account-
ng for the two models of spatial dependence, and given its abil-
ty to uncover both direct and indirect (or spillover) effects, the
DM is well positioned to model the complexities that follow im-
igration flows and housing prices. Spatial econometrics, however,
s not without its limitations. According to Gibbons and Overman
2012) while spatial econometrics provides a good description of
patial data, techniques for addressing causality in spatial models
ave not been well developed. For the question on hand—how does
mmigration impact house prices and rents—establishing causality
s key. 2 Therefore, in addition to employing spatial techniques, we
ollow Saiz (20 03, 20 07) and Saiz and Wachter (2011) and first
ttempt to achieve identification by modeling the first difference
f the log of rents and prices. We follow this specification with
ne that employs two stage instrumental variables with bootstrap-
ing to obtain unbiased coefficient values with correct standard
rrors.
.1. Marginal effects—spatial Durbin models
The spatial Durbin model can be specified as:
= αI n + X β + ρW y + W X ∅ + ε (1)
here I n denotes the identity matrix and Wy captures spatial in-
erdependence of the dependent variable in the model (see LeSage
nd Pace, 2009 ). The reduced form of the SDM model and implied
ata generating process can be written as:
= ( I n − ρW ) −1
( αl n + X β + W X ∅ ) + ( I n − ρW )
−1 ε with ε ∼ N
(0 , σ 2 I n
)(2)
The direct (feedback) effect estimate is captured by X β while
X captures the indirect (spillover) effect estimate. The total ef-
ects of the explanatory variables are the sum of direct (feedback)
nd indirect effect (spillover) estimates. According to LeSage and
1 See Fernández-Avilés et al. (2012 ) and Osland and Thorsen, 2013 . 2 According to Gibbons and Overman (2012) , natural experiments, IV techniques
nd differencing are alternative measures for dealing with identification although
ach has drawbacks. The IV technique can be used effectively if applied care-
ully with attention to the identification of specific causal parameters. Alternatively,
patial differencing removes relevant omitted variables, eliminating time-invariant,
rea-specific factors that simultaneously affect immigration and the level of house
rices and rents.
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ace (2009) , the SDM model has several advantages over the SEM
nd SAR models. The model produces unbiased estimates even
hen the true data-generating process is simply a spatial lag or a
patial error process. Also, SDM does not impose any prior restric-
ions on the magnitude of spillover effects ( Elhorst, 2014 ). In de-
iving the marginal effects of the explanatory variables in the SDM,
lhorst (2010) provides the following matrix of partial derivatives
f the dependent variable in the different units with respect to
he k th explanatory variable in the different units (e.g., x ik for
= 1,…, N ) at time t :
∂y
∂ X 1 k
. . . ∂y
∂ X Nk
]t
=
⎡
⎢ ⎢ ⎣
∂ y 1 ∂ X 1 k
· · · ∂ y 1 ∂ X Nk
. . . . . .
. . . ∂ y N ∂ X 1 k
· · · ∂ y N ∂ X Nk
⎤
⎥ ⎥ ⎦
= ( I n W ) −1
⎡
⎢ ⎢ ⎣
βk w 12 ∅ k · · · w 1 N ∅ k w 21 ∅ βk w 2 N ∅ k
. . . . . .
. . . . . .
w N1 ∅ k w N2 ∅ k · · · βk
⎤
⎥ ⎥ ⎦
(3)
Three different marginal effects are obtained when estimating
patial models: direct (feedback) effects, indirect (spillover) effects,
nd total effects ( LeSage and Pace, 2009 ). In the context of the
ousing model, the direct effect records the impact of a housing
rice determinant, (e.g. immigration into that particular MSA) on
ousing prices in that MSA. The indirect (spillover) effect, in con-
rast, measures the effect of the housing price determinant (e.g.
mmigration into a particular MSA) on housing prices in surround-
ng MSAs. LeSage and Pace (2009) point out that the average of the
iagonal elements of the matrix on the right-hand of Eq. (3) is the
irect effect while the indirect effect is given by either the average
f the row or the average of the column (see Elhorst, 2010 ).
Given that the SDM nests both the SEM and the SAR models,
lhorst (2010) shows how one can obtain marginal effects for the
EM or SAR model by imposing restrictions on the matrix on the
ight-hand side of Eq. (3) . In the case of the SEM, the matrix above
educes to a diagonal matrix with βk on the main diagonals. As a
esult, the direct effect of the k th explanatory variable for the spa-
ial error model is βk , while the indirect effect will be zero. For the
patial lag model, ∅ k = 0. Elhorst (2010) notes that even though all
he off-diagonal terms of the right hand side matrix of Eq. (3) be-
ome zero, the marginal effects—direct and indirect effects—in the
patial lag model does not reduce to one single coefficient or zero
s in the spatial error model.
. Data and methodology
The availability of data at the MSA level determined both the
ependent variable and the time period for this study. Our panel
ata consist of 275 MSAs for the rent equation and 282 for the
ome price equation over the 2002–2012 period. Our housing rent
ata are from the Department of Housing and Urban Development
HUD) Fair Market Rent Series (FMR). The FMR corresponds to the
ctual (nominal) dollar price of a vacant 0 bedroom to 4 bedroom
ental unit at the 50% percentile (or median) of the MSA’s distri-
ution. It is calculated annually by HUD using data from the Cen-
us and American Housing Survey (AHS). Data on home prices are
btained from the Federal Housing Finance Agency (FHFA). Under
HFA, the Office of Federal Housing Enterprise Oversight (OFHEO)
stimates and publishes quarterly home price indexes for single-
amily detached properties. The OFHEO use the data on conven-
ional conforming mortgage transactions obtained from the Federal
ome Loan Mortgage Corporation (Freddie Mac) and the Federal
ational Mortgage Association (Fannie Mae). These are converted
16 A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25
Table 1
Descriptive statistics.
Rent equation Observations Mean Std. Dev. Min Max
Housing rent 3024 767.3 222.5 416.2 2049.6
Immigration inflows 3025 3313.5 13,536.9 11 224,4 4 4
Immigrant t /Pop t −1 2750 0.002061 0.001911 0.0 0 0 035 0.02267
Income per capita (chained 2005 $s) 3005 36905.9 10191.1 15619 90,528
Land per capita 3025 0.00795 0.01156 0.0 0 034 0.154655
Murder (per 10 0,0 0 0) 2687 4.72 3.36 0 28.2
Burglary (per 10 0,0 0 0) 2664 809.2 329.0 219.5 2179
Population 3025 808,391 1,763,195 67,371 19,837,753
Permit 2949 3612.2 7901.1 17 74,007
Unemployment rate (%) 3020 6.54 2.64 2.42 27.2
Population density 2731 2.28801 0.38930 0.8148 3.4296
Price equation
Housing price index 3102 174.2 35.9 102.9 363.1
Immigration inflows 3102 3398.9 13476.1 11 224,4 4 4
Immigrant t /Pop t −1 2821 0.002127 0.002398 0.0 0 0 0 0479 0.02266
Income per capita (chained 2005 $s) 3092 37,004.9 10,334.9 15,619 90,528
Land per capita 3102 0.00788 0.01145 0.0 0 034 0.154655
Murder (per 10 0,0 0 0) 2749 4.70 3.34 0 28.2
Burglary (per 10 0,0 0 0) 2725 806.51 327.96 219.5 2179
Population 3099 821,412 1,757,445 67,371 19,837,753
Permit 3026 3652.5 7860.2 17 74,007
Unemployment rate (%) 3101 6.55 2.63 2.5 27.2
Population density 2731 2.28801 0.38930 0.8148 3.4296
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to an index that measures the movement of single-family home
prices.
The specific data source and some descriptive statistics for
home prices, rents and the other variables incorporated into our
price and rent equations are displayed in Table 1 and Appendix
Table A. Our main right hand side variable of interest, immigra-
tion inflows as a share of the MSA’s population, is derived with
information from the Department of Homeland Security (DHS) on
immigration and this is scaled by census estimates of population
by MSA. DHS reports on the number of “immigrants admitted to
the United States by MSA” specifically admission of foreign-born
individuals as permanent residents into the United States for the
year. 3 Average immigrant inflow for the housing sample is 3399,
slightly higher than the average inflow in the rent sample, 3314.
Nonetheless, the standard deviation is very high, pointing to the
wide dispersion in immigration inflows by geography with some
MSAs experience very large inflows while others receive very small
inflows. Once scaled by MSA population we find that there con-
tinue to be large variations in the immigrant inflows across the
United States with at least one MSA with immigration inflows as
a share of the population reaching 2 and a quarter percent. While
we might expect that immigration will have a positive impact on
rents and house prices, alternative scenarios are also possible. If
natives have a distaste for immigrant neighbors, we might instead
see offsetting outmigration that, to the contrary, depresses hous-
ing values. Or if immigrants impact labor markets by depressing
wages, housing values could instead fall due to a negative income
effect.
We assume that housing rents and housing prices are also in-
fluenced by wealth, land per capita, crime rates, availability of jobs
3 The timing of the admission of a foreign person as a permanent resident does
not necessarily coincide with the actual date of entry into the U.S. The data, also,
do not account for illegal immigrants or foreign-born individuals who stay in the
U.S. temporarily such as tourists and students. Undocumented and temporary im-
migrants usually rent rather than buy houses. The exclusion of these immigrants
would tend to cause us to overstate the effect of immigration on the rental mar-
ket. The housing price market, however, is less likely to be directly affected by the
nflow of illegal or temporary immigrants.
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nd potential housing supply and therefore need to incorporate
hese controls in our estimation. Since wealth at the MSA level is
ifficult to obtain, we proxy for it using data on personal income
er capita. These are obtained from the Bureau of Economic Analy-
is (BEA) Regional Information System (REIS). According to the BEA,
his value is the income received by all persons from all sources.
n average, income per capita in our sample is around $37,0 0 0.
and per capita is defined as the MSA’s land area in square miles
ivided by total population of the MSA. Land per capita is indica-
ive of the availability of space and is postulated to have a neg-
tive impact on house prices and rents. We measure crime using
urglary and murder rates. These were obtained from FBI uniform
rime report and are expected to have negative impacts on both
ent and house prices as these characteristics make the MSA a less
esirable area in which to reside.
As we would anticipate, murder rates are much lower than bur-
lary rates. Finally, unemployment and housing permit rates at the
SA level are obtained from the Bureau of Labor Statistics and the
ensus Bureau respectively. Increases in the unemployment rate
re expected to reduce house prices and rents. On average the un-
mployment rate was about 6.5% over the time period in these
SAs. Housing permits are simply the number of new privately
wned housing units authorized by each MSA. As more houses are
uilt, all other things equal, rent and house prices are expected to
ecline.
Table 2 follows up on Table 1 and identifies the different MSAs
ssociated with the highest and lowest values for the variables
n the model. New York-Northern New Jersey-Long Island Consoli-
ated Metropolitan Area (CMSA) has the highest immigration rate
nd population, but the lowest land per capita. Santa Fe, New Mex-
co and the New Orleans-Metairie-Kenner, Metropolitan Statistical
reas have the highest burglary and murder rates respectively. Res-
dents of San Jose-Sunnyvale-Santa Clara, California pay the high-
st rents, while residents of Naples-Marco Island, Florida pay the
teepest housing prices. Las Vegas-Paradise, Nevada has the low-
st home prices and St. Joseph, MO-KS renters are charged the
east. In El Paso, Texas and San Jose-Sunnyvale-Santa Clara, Califor-
ia unemployment rates are highest and income per capita lowest
espectively among the MSAs.
A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25 17
Table 2
MSA with minimum and maximum values for each explanatory and dependent variable.
Variable MSA with maximum value MSA with minimum value
Housing price index Naples-Marco Island, FL Las Vegas-Paradise, NV
Rent San Jose-Sunnyvale-Santa Clara, CA St. Joseph, MO-KS
Immigration rate New York-Northern New Jersey-Long Island, NY-NJ-PA Cheyenne, WY
Immigrant as a share of MSA
population
Charlottesville, VA Charleston-North Charleston, SC; Riverside-San
Bernardino-Ontario, CA
Murder (per 10 0,0 0 0) New Orleans-Metairie-Kenner, LA Wausau, WI; Bangor, ME; Billings, MT; Fargo, ND-MN
Burglary (per 10 0,0 0 0) Santa Fe, NM Bismarck, ND
Population New York-Northern New Jersey-Long Island, NY-NJ-PA Casper, WY
Land per capita Flagstaff, AZ New York-Northern New Jersey-Long Island, NY-NJ-PA
Income per capita San Jose-Sunnyvale-Santa Clara, CA McAllen-Edinburg-Mission, TX
Permit Atlanta-Sandy Springs-Marietta, GA Wheeling, WV-OH
Unemployment El Paso, TX Fort Walton Beach-Crestview-Destin, FL
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5 The spatial weight matrix W can also be column normalized. The interpretation
for column and row normalized matrix is different. For row normalized weight ma-
trix, the row gives the impact on a given unit by all other units. An element of a
column normalized matrix gives the impact of a given unit on all other units. 6 We use MATLAB code written by Paul Elhorst and James LaSage. See Elhorst’s
.1. Model
The study estimates the following SDM to obtain the marginal
ffects of rent and house price determinants.
ln ( H mt ) = ρW l n ( H mt ) +
Immigrant s m t
P opul ation m t−1
. δ1 + X mt β1
+ W
Immigrant s m t
P opulation m t−1
. δ2 + W X mt β2 + �μmt (4)
The dependent variable is the annual change in the log of rent
house prices) in MSA m at time t . Following the housing literature,
e model the first difference of the log of prices and rent. By dif-
erencing the price (rent) variable and employing panel methods,
e help control for time-invariant, area-specific factors that could
imultaneously affect immigration and the level of house prices
nd rents, helping remove a potential source of endogeneity. 4 This
s a conservative solution for achieving identification, given the
tate of spatial econometrics. GMM and 2SLS estimation are not
asily applied in the context of a spatial Durbin model according
o Pace et al. (2012 ) who note that the combination of correlated
egressors and the SDM specification provides a challenging en-
ironment for instrumental variable techniques. In spite of these
hallenges, in a final specification, we employ a two-step instru-
ental variables procedure to more fully account for endogeneity
nd we follow up with corrected standard errors via bootstrapping.
The coefficient ρ , in Eq. (4) and associated with the spatial
eight matrix, W , reflects inherent spatial interdependence in the
ata measuring the impact of rents (house prices) in a particular
SA on rents (house prices) in surrounding MSAs. The indepen-
ent variable of interest is the annual inflow of immigrants into
SA m divided by the MSA’s lagged population while the X matrix
ncludes all the other control variables. As noted in Saiz (2007) , the
arameter, δ1 , associated with the immigrant population ratio, is
nterpreted as the percentage change in rents (house prices) corre-
ponding to an annual inflow of immigrants equal to one percent
f the city’s population. In our case, δ1 and β1 correspond to the
irect effect estimates of immigration on house prices (rents) while
2 and β2 are the parameters for the indirect effect estimates of
mmigration on house prices (rents).
The spatial weight matrix, W , is a block diagonal matrix de-
cribing the arrangement of the spatial units (neighbors). The defi-
ition of neighbors used in the weights matrix is based on the idea
f borders or adjacent areas. The weights matrix assigns weights to
SAs m = i and m = j based on the following criteria:
i j =
⎧ ⎪ ⎨
⎪ ⎩
1 i f MSA i and j are in the same state or in states
that share a border
0 otherwise
4 See Saiz (2007) .
w
w
The diagonal elements of the matrix are set to zero and row el-
ments are standardized such that they sum to one. 5 For any year,
∈ [2002, 2012], W is defined as
=
⎡
⎢ ⎢ ⎢ ⎣
0 w i j · · · w ik
w
ji . . .
0 w
jk . . .
w ki w k j · · · 0
⎤
⎥ ⎥ ⎥ ⎦
(5)
here w ij defines the functional form of the weights between any
air of host MSAs i and j. We use maximum likelihood (MLE), the
echnique that has been adopted in spatial econometrics when es-
imating the SDM. 6
. Empirical results
Before discussing and comparing estimation results, we need to
rst determine the appropriate model specification that describes
ur data. In Section 2 of this paper, we noted that there are a vari-
ty of spatial models (SEM, SAR) but the incorporation of both into
single model (SDM) has not been commonly used to capture spa-
ial dependence in housing studies. Elhorst (2010 ) provides guide-
ines for determining the appropriate model specification and we
ollow them. We employ the Lagrange Multiplier (LM) test to de-
ermine whether a non-spatial model (OLS), the spatial lag model
r the spatial error model is appropriate. The LM test is based on
he residuals of the OLS model. 7 If the non-spatial model is re-
ected in favor of the spatial lag model, the spatial error model,
r in favor of both models, then the spatial model is the appro-
riate model to use. Table 3 presents the test results (LM classic
nd robust tests) for the different panel model specifications. Us-
ng the classic and robust LM tests, the hypothesis of no spatially
utocorrelated error term and the hypothesis of no spatially lagged
ependent variable were both rejected at the 1% significance lev-
ls (except for the rent equation with MSA and time period fixed
ffects, which was rejected at the 6% level). Overall these results
uggest that a spatial model rather than a non-spatial model is the
ppropriate model to use.
We also test whether unobserved heterogeneities (spatial and
ime period fixed effects) are jointly significant by performing like-
ihood ratio (LR) tests. The test results for the hypothesis that the
patial fixed effects are not jointly significant cannot be rejected
ebsite, http://www.regroningen.nl/elhorst/software.shtml and LaSage’s website
ww.spatial-econometrics.com/ . 7 See Matlab software for spatial panels by Elhorst (2010) .
18 A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25
Table 3
Test results for choosing between spatial and non-spatial models.
ln rent log house price
MSA fixed effect Time-period fixed
effect
MSA and
time-period fixed
effect
MSA fixed effect Time-period fixed
effect
MSA and
time-period fixed
effect
LM spatial lag(classic) 5304.443 156.404 138.530 5027.875 6 882.4 94 6203.984
[0.0 0 0] [0.0 0 0] [0.0 0 0] [0.0 0 0] [0.0 0 0] [0.0 0 0]
LM spatial error (classic) 5330.378 146.788 130.442 8742.024 7616.052 7167.980
[0.0 0 0] [0.0 0 0] [0.002] [0.0 0 0] [0.0 0 0] [0.0 0 0]
Robust LM SAR 29.238 19.212 11.551 316.018 39.091 143.922
[0.0 0 0] [0.013] [0.001] [0.0 0 0] [0.0 0 0] [0.0 0 0]
Robust LM SEM 55.174 9.596 3.464 4030.167 772.650 1107.918
[0.0 0 0] [0.002] [0.063] [0.0 0 0] [0.0 0 0] [0.0 0 0]
LR tests for the joint 246.713 258.831
Significance of spatial fixed effects [0.889] [0.8353]
LR tests for the joint 838.063 11545.834
Significance of time-period fixed effects [0.0 0 0] [0.0 0 0]
Notes : Probability values are in square brackets: ∗significant at 10%; ∗∗significant at 5%; ∗∗∗significant at 1%.
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for both housing rent (246.7, p > 0.01) and house price (258.8,
p > 0.01) estimations. To the contrary, the test results for the hy-
pothesis that the time-period fixed effects are not jointly signif-
icant is rejected for both rent (838.1, p < 0.01) and house price
(11545.8, p < 0.01) estimations. These test results seem to justify
the extension of the model with only time period-fixed effects.
Since the OLS specification is rejected in favor of spatial mod-
els we proceed by estimating the SDM model. Recall that the SDM
nests both the SEM and the SAR models. We determine whether
or not the SDM can be simplified to one or the other (spatial lag
or spatial error model) using a Wald test ( Elhorst, 2010 ). Based on
the Wald test as well as the LR test result shown at the bottom
of column II of Tables 4 and 5 , the spatial lag and the spatial er-
ror model were rejected in favor of the SDM. We therefore use the
SDM model to describe rents and house prices.
The novelty of the SDM method is its ability to disaggregate the
marginal (total) effects into direct and indirect effects as displayed
in Tables 4 and 5 . The first column of each specification records
the direct effect – the impact of changes in determinants on rents
or house prices in a particular MSA. The indirect or spillover effect,
displayed in the second column of each specification, measures the
impact of rent (or price) determinants in a particular MSA on rents
(prices) in surrounding MSAs. The total effect is the sum of both
direct and indirect effects.
4.1. Rents
Table 4 presents the results for the rent equation with specifica-
tions I and II displaying the SDM results prior to and after control-
ling for unobserved fixed heterogeneities. One might further ques-
tion whether one should incorporate business cycle effects. The
problem is that there are no known model specification tests that
can attest to the appropriateness of their inclusion. We, nonethe-
less, report and discuss on a model incorporating business cycle
effects as displayed in Appendix Tables B and C for the rent and
house price models respectively. 8 Inspection of the business cycle
estimates reveal that the main results are very similar to specifi-
cations I and II. Given, therefore, the inability to assess the appro-
8 In the regional business cycle specification displayed in the Appendix, we in-
clude regional effects, and the interaction of such regional effects with a dummy
for the last 5 years in our sample. A quinquennial dummy separates the 20 02–20 07
boom period from the 2007–2012 bust period. In other words, we controlled for un-
observable trends that varied across regions and in two distinct periods of time. The
interaction term based on the four regions (Northeast, Midwest, West, and South),
and the housing boom (20 02–20 07) and housing bust (2008–2012) periods are in-
cluded and displayed in Appendix Tables B and C .
p
(
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riateness of Business Cycle specification, we simply report these
esults and note that they are very similar to the results obtained
n specifications I and II—specifications we can formally evaluate.
The spatial coefficient, ρ , on ( W
∗rent), displayed in the first row
f Table 4 , is highly significant in all specifications suggesting that
ur estimation strategy is appropriate. When rents in one MSA rise
fall), the rents in surrounding MSAs tend to rise (fall) as well.
urning now to the explanatory variables, the methodology splits
he “total effect” into two—the “direct effect” and “indirect effect.”
onsidering first, the direct effect in specification I, the results sug-
est that immigration is positively associated with housing rents at
he MSA level. Specifically, the coefficient on immigration is inter-
reted as the percentage change in rents corresponding to an an-
ual inflow of immigrants equal to 1% of the MSA’s prior period’s
opulation. Before controlling for unobserved heterogeneities (Spa-
ial Durbin Model I), our results suggest that rent in an MSA in-
reased by 1.18% with an inflow of immigrants equal to 1% of the
SA’s population. A similar result holds after we control for time-
eriod fixed effects (specification II). Immigrant inflows equivalent
o 1% of the MSA’s population is associated with a 1.165% rise in
ents. A similar result is found in the Business cycle model dis-
layed in Appendix Table B . These results are intuitive as they sug-
ests that immigrant arrivals put pressure on rents as individuals
eed to secure places to live, positively affecting housing rents in
hose MSAs. Similar empirical results were obtained by Saiz (2003,
007) , and Susin (2001) , who find that rents are higher in cities
ith increased immigration.
The indirect effect results across the different model specifica-
ion (I and II and the Business Cycle model) indicate that immi-
rant arrivals into a particular MSA are associated with a positive
pillover (indirect) effect on surrounding MSAs and the effect ap-
ears to be larger relative to the direct effect. Prior to controlling
or unobserved heterogeneities, rent is found to increase by 12%
ith an immigration inflow of immigrants equal to 1% of the sur-
ounding MSAs population. A more modest impact, roughly 8%, is
bserved when we control for time-period fixed effects as we do
n model II while the business cycle model suggests a 7% rise.
Our result so far only tangentially account for endogeneity. The
anel structure along with the transformed dependent variable
percent change in price/rent)) helps correct for endogeneity by
weeping away fixed unobservable variables that could be corre-
ated with immigration and rents/home prices. However, an ad-
itional source of endogenity could nonetheless still be present
n account of reverse causality. It is logical that immigrants are
riven by housing costs, for example, moving to areas that offer
ower prices and rents. To further address endogeneity we use an
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Table 4
Housing rent estimation.
Dependent variable �ln( Rent mt )
Spatial Durbin model I Spatial Durbin fixed effects model II SDM instrumental variables model III
Direct effect Indirect effect Total effect Direct effect Indirect effect Total effect Direct effect Indirect effect Total effect
ρ 0.801 ∗∗∗
(0.023)
0.412 ∗∗∗
(0.050)
0.467 ∗∗∗
(0.003)
Immigration t /Pop t −1 1.184 ∗∗
(0.546)
12.495 ∗
(7.216)
13.680 ∗
(7.308)
1.165 ∗∗
(0.536)
8.200 ∗∗∗
(2.907)
9.364 ∗∗
(2.897)
0.792 ∗∗∗
(0.072)
1.612 ∗∗
(0.777)
2.404 ∗∗∗
(0.728)
Murde t −1 0.0 0 0
(0.0 0 0)
0.004
(0.005)
0.004
(0.005)
0.0 0 0
(0.0 0 0)
0.004 ∗∗
(0.002)
0.004 ∗
(0.002)
0.0 0 0 ∗∗∗
(0.0 0 0)
0.002 ∗∗∗
(0.0 0 0)
0.003 ∗∗∗
(0.0 0 0)
ln Burglary t −1 0.002
(0.002)
0.015
(0.026)
0.017
(0.027)
0.002
(0.002)
−0.007
(0.013)
−0.005
(0.013)
−0.001 ∗∗∗
(0.0 0 0)
−0.005 ∗∗∗
(0.001)
−0.006 ∗∗∗
(0.001)
Land per capita −0.031
(0.083)
−0.615
(0.978)
−0.646
(0.992)
−0.004
(0.081)
−0.358
(0.358)
−0.398
(0.356)
−0.046 ∗∗∗
(0.002)
−0.206 ∗∗∗
(0.001)
−0.252 ∗∗∗
(0.010)
ln Income per capita 0.003 ∗∗
(0.001)
0.002
(0.011)
0.004
(0.011)
0.003 ∗∗
(0.001)
−0.001
(0.008)
0.001
(0.009)
0.001 ∗∗∗
(0.0 0 0)
−0.004 ∗∗∗
(0.001)
−0.003 ∗∗∗
(0.001)
ln Permit −0.003 ∗∗∗
(0.001)
−0.016
(0.012)
−0.019
(0.012)
−0.003 ∗∗∗
(0.001)
−0.010 ∗
(0.006)
−0.013 ∗∗
(0.006)
−0.002 ∗∗∗
(0.0 0 0)
0.003 ∗∗∗
(0.001)
0.001
(0.001)
Unemployment t −1 0.0 0 0
(0.001)
−0.006 ∗
(0.003)
−0.006 ∗
(0.003)
0.0 0 0
(0.001)
−0.004 ∗∗
(0.002)
−0.004 ∗∗
(0.002)
−0.0 0 0 ∗∗∗
(0.0 0 0)
−0.0 0 0
(0.0 0 0)
−0.001 ∗∗∗
(0.0 0 0)
Observation 2750 2750 2750
Log-likelihood 4715.537 4780.716 4831
Time fixed effect No Yes Yes
Wald test, spatial lag 14.681 [0.040] 5.658 [0.580]
Wald test, spatial 16.476 [0.021] 6.106 [0.5274]
LR test, spatial lag 14.792 [0.039] 5.654 [0.5806]
LR test, spatial 16.644 [0.020] 6.126 [0.5251]
Notes : Standard errors are in parentheses. The probability values for the various tests are in square brackets. Probabilities smaller than 0.05 point to significance of Wald or LR test. The dependent variable is the annual change
in the ln of rent in MSA m at time t . ∗ Significant at 10%. ∗∗ Significant at 5%. ∗∗∗ Significant at 1%.
20
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Table 5
Housing price estimation.
Dependent Variable is �log ( Price mt )
Spatial Durbin model I Spatial Durbin FE model II SDM instrumental variables model III
Direct effect Indirect effect Total effect Direct effect Indirect effect Total effect Direct effect Indirect effect Total effect
ρ 0.906 ∗∗∗
(0.012)
0.881 ∗∗∗
(0.015)
0.877 ∗∗∗
(0.003)
Immigrant t /Pop t −1 −0.875 ∗∗∗
(0.183)
−24.470 ∗∗∗
(6.205)
−25.345 ∗∗∗
(6.300)
−0.700 ∗∗∗
(0.186)
−11.753 ∗
(6.086)
−12.452 ∗∗
(6.189)
0.810 ∗∗∗
(0.047)
9.594 ∗∗∗
(0.520)
10.404 ∗∗∗
(0.539)
Murder 0.0 0 0
(0.0 0 0)
0.002
(0.006)
0.002
(0.006)
0.0 0 0
(0.0 0 0)
0.003
(0.005)
0.002
(0.005)
0.0 0 0 ∗∗∗
(0.0 0 0)
−0.001 ∗∗∗
(0.004)
−0.001 ∗∗∗
(0.0 0 0)
log Burglary −0.006 ∗∗∗
(0.002)
−0.173 ∗
(0.071)
−0.180 ∗
(0.072)
−0.006 ∗∗∗
(0.002)
−0.129 ∗∗
(0.060)
−0.135 ∗∗
(0.061)
−0.002 ∗∗∗
(0.0 0 0)
−0.046 ∗∗∗
(0.003)
−0.049 ∗∗∗
(0.003)
Land per capita 0.136 ∗∗∗
(0.032)
0.480
(0.824)
0.617
(0.835)
0.128 ∗∗∗
(0.032)
0.201
(0.679)
0.329
(0.690)
0.148 ∗∗∗
(0.001)
−0.265 ∗∗∗
(0.023)
−0.117 ∗∗∗
(0.023)
log Income per Capita 0.001
(0.001)
0.010
(0.035)
0.011
(0.035)
0.0 0 0
(0.002)
−0.029
(0.083)
−0.030
(0.084)
−0.003 ∗∗∗
(0.0 0 0)
−0.151 ∗∗∗
(0.004)
−0.154 ∗∗∗
(0.004)
log Permit 0.004 ∗∗∗
(0.0 0 0)
0.153 ∗∗∗
(0.024)
0.157 ∗∗∗
(0.024)
0.003 ∗∗∗
(0.001)
0.104 ∗∗∗
(0.031)
0.107 ∗∗∗
(0.032)
0.0 0 0
(0.0 0 0)
0.031 ∗∗∗
(0.001)
0.031 ∗∗∗
(0.001)
Unemployment −0.001 ∗∗∗
(0.0 0 02)
0.006 ∗∗
(0.003)
0.906
(0.012)
−0.002 ∗∗∗
(0.0 0 02)
−0.003
(0.003)
−0.005
(0.004)
−0.002 ∗∗∗
(0.0 0 0)
−0.012 ∗∗∗
(0.0 0 0)
−0.014 ∗∗∗
(0.0 0 0)
Observation 2820 2820 2820
Log-likelihood 7445.497 7433.129 7447
Time Fixed Effect No Yes Yes
Wald test, spatial lag 20.194 [0.005] 17.23 [0.016]
Wald test, spatial error 20.214 [0.005] 19.35 [0.007]
LR test, spatial lag 20.218 [0.005] 17.11 [0.017]
LR test, spatial error 20.348 [0.005] 18.93 [0.008]
Notes : Standard errors are in parentheses. The probability values for the various tests are in square brackets. Probabilities smaller than 0.05 point to significance of Wald or LR test. The dependent variable is the annual change
in the log of housing prices in MSA m at time t . ∗ Significant at 10%. ∗∗ Significant at 5%. ∗∗∗ Significant at 1%.
A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25 21
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ability values reported under specification III are not corrected and cannot properly
interpret the fit of the model. 10 The “peso problem” refers to the idea that low probability events might not be
properly reflected in the price of an asset ( Sill, 20 0 0 ). 11 A procedure, comparable to that used in the rent estimation, was used to obtain
an instrument for immigration in the case of the house prices and subsequently
estimate the spatial model for house prices. However given the slightly different
availability of data for house price and rent series, (the house price series is avail-
able for 282 MSAs while the house rent series for 275 MSAs) the house price first
stage estimation required a new set of 150 replications for immigration inflows in
order to obtain appropriate standard errors. The far right two columns of Appendix
nstrumental variable approach that focuses on year to year
hanges in immigration inflows. As in Saiz (2007) , we construct a
shift-share” prediction of the inflow of immigrants into each MSA.
he prediction of immigration into MSA m at time t is based on
he total number of new immigrants in the United States in year t
immigrants US,t ) multiplied by the share of all US immigrants resid-
ng in that specific MSA in 1990:
hi f t share _ im m mt = ϕ m 1990 × immigrant s USt (6)
here shi f t share _ im m mt is the estimated number of new immi-
rants in metropolitan area m in year t and ϕm 1990 is the share
f all U.S. immigrants who resided in MSA m in 1990. The idea
ehind this variable is that immigration flows are propagated and
nfluenced by networks. Immigrants are likely to flow to areas that
lready house large numbers of immigrants.
After constructing the “shift share” variable for each period and
ach MSA, we estimate the model with the “shift share” variable
sing a 2SLS procedure. However, since an appropriate estimator
as not been worked out in the context of the Spatial Durbin
odel, we manually employ 2SLS to obtain coefficient estimates
nd follow up by obtaining bootstrapped standard errors. In order
o construct the immigration IV (first stage regression), we gener-
ted predictions for immigration to each MSA by estimating the
ollowing equation:
( ln immigration in f low ) mt = α0 + α1
( shi f t share _ im m mt
)+ α2 ( Murde r mt ) + α3 ( l nBurgl ar y mt )
+ α4 ( Land per Capit a mt ) + α5 ( lnIncome per Capit a mt )
+ α6 ( lnP ermi t mt ) + α7 ( unemploymen t mt )
+ t ime f ixed e f f ect s + e mt . (7)
Using the estimated coefficients from Eq. (7) along with actual
alues for all the explanatory variables, predicted ln(annual immi-
rant inflow) mt for all 275 MSAs in each time period is obtained.
hese values are transformed to immigrant t /population t −1 and in-
orporated into the spatial model for rent—part two of the 2-step
rocedure.
Appendix Table D displays the first stage coefficients along with
he corrected (bootstrapped) standard errors for the first stage re-
ression. The standard errors were obtained by generating 150 sep-
rate random samples without replacement of approximating 80%
f the 275 MSAs we work with. The standard deviation of the re-
ulting sampling distribution for each coefficient is the reported
bootstrapped) standard error in the first stage regression. Inspec-
ion of the first stage results suggest that the natural log of immi-
ration in an MSA is positively related to the share of immigrants
n that MSA in 1990, to per capita income, the issuance of build-
ng permits and to unemployment in the MSA. By contrast, murder
ates, burglary activity and land area per capita are all negatively
elated to the natural log of immigration. All of the explanatory
ariables are statistically significant at conventional levels for the
rst step in the rent estimation.
The second step of our estimation requires that we incorporate
he results of the first stage regression—predicted immigration in-
ows as a share of the population—into the SDM model and esti-
ate it. The standard errors in the SDM model are also obtained
ia bootstrapping. That is, the SDM model (4) is estimated 150
imes employing the predicted (immigrant t /population t −1 ) vector
erived from each of the 150 iterations of ( 7 ). In this way we ob-
ain sampling distributions for the coefficients in Eq. (4) , the SDM
odel with which to compute appropriate standard errors. 9
9 While we obtain corrected standard errors for the coefficients in the IV-SDM
odel, we cannot assess the probability value for the Wald and LR tests. The prob-
T
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Inspection of the instrumented results, while a bit different in
agnitude, are similar in “spirit” to the earlier model specifications
ith respect to the main explanatory variable of interest, immigra-
ion inflows. A one percent rise in immigration to an MSA is asso-
iated with a 0.8% rise in rents. The indirect effect is about doubled
ith a 1% increase in immigration to an MSA raising rents by 1.6%
n surrounding areas. This result is somewhat more tempered than
n the case of the non-instrumented models. The other explana-
ory variables in the IV SDM model are somewhat intuitive. With
espect to the direct effects, burglary, land per capita, supply of
ousing (permits), and unemployment are associated with lower
ents, while income is associated with higher rents. The positive
oefficient on murder is not intuitive. Given that murder is a low
robability event perhaps this is reflective of a “peso problem” in
he case of housing markets with respect to some forms of crime. 10
Overall then, we have found that inflows of immigrants into
particular MSA are not only associated with increasing rents in
hat MSA, but also rents in surrounding MSAs. Also of note is that
he size of the immigration coefficients is quite different in mag-
itude with the spillover (indirect) effects appearing to be much
arger. These are interesting patterns that beg an explanation. Be-
ore further discussing these results in context, we examine the
ouse price market to see whether similar patterns are observed.
.2. House prices
The empirical results for the housing price equations are dis-
layed in Table 5 . Similar to rent, the spatial coefficient, ρ , on
∗rent, is highly significant suggesting that house prices in one
SA are positively affected by prices in surrounding MSAs and cor-
oborates the choice of a spatial model. Inspection of the main
o-variate of interest (immigration as a share of the MSA’s pop-
lation) across models reveals that, unlike in the case for rents,
he results of the non-IV and IV models do not coincide in spirit. 11
hile immigration is associated with increases in prices in the IV
odel, they are associated with decreases in prices in the non-IV
pecification. The difference in results in the case of IV and non-
V specifications, underscores the need to account for endogeneity.
he differential results may be the result of coefficient bias intro-
uced on account of the use of an endogenous regressor in models
, II, and in the Business Cycle model. For this reason we center
he remaining discussion on the instrumented results. According
o specification III, immigration inflows have a direct effect elas-
icity of 0.8. This implies that housing prices in a particular MSA
ncrease by about 0.8% following an inflow of immigrants equal to
% of the MSA’s population. This result is in keeping with rents
hich saw a similar increase. As in the rent model, the indirect or
pillover effect is larger than the direct effect. But the magnitude
f the difference is much larger. An increase in immigration inflows
quivalent to 1% of an MSA’s population increases house prices in
able D display the coefficient values along with the corrected standard errors. The
oefficient values for price are similar in sign though with somewhat different val-
es. As with the rent sample, all the coefficients are significant, with the exception
f burglary, which does not seem to be associated with immigration flows in the
ouse first stage regression.
22 A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25
Table 6
Native, immigrant estimation—spatial model.
Dependent variable �log( natives mt )
Time fixed effect Spatial and time fixed effect
Direct effect Indirect effect Total effect Direct effect Indirect effect Total effect
ρ 0.127 ∗
(0.066)
0.124 ∗
(0.066)
log Immigration t −1 −0.053 ∗∗∗
(0.005)
0.075 ∗∗∗
(0.018)
0.020 ∗
(0.018)
−0.053 ∗∗∗
(0.005)
0.081 ∗∗∗
(0.017)
0.028 ∗
(0.018)
log Income per capita 0.023
(0.028)
0.035
(0.102)
0.058
(0.013)
0.028
(0.028)
0.168
(0.100)
0.196 ∗∗
(0.096)
Murder 0.0 0 0
(0.0 0 0)
−0.003 ∗
(0.001)
−0.002
(0.002)
0.0 0 0
(0.0 0 0)
−0.002 ∗
(0.002)
−0.001
(0.002)
log Burglary −0.002
(0.006)
0.020
(0.021)
0.018
(0.019)
−0.002
(0.006)
0.019
(0.028)
0.017
(0.029)
Unemployment t −2 −0.001 ∗
(0.001)
0.001
(0.002)
−0.0 0 0
(0.002)
−0.001 ∗
(0.001)
0.003 ∗
(0.002)
−0.002
(0.001)
Population Density −0.044 ∗∗∗
(0.007)
0.064
(0.047)
0.021
(0.780)
−0.043 ∗∗∗
(0.007)
0.090 ∗
(0.049)
0.047
(0.049)
Observation 2730 2730
Log-likelihood 6343.92 6360.196
Wald test, spatial lag 63.377 [0.0 0 0] 33.973 [0.0 0 0]
Wald test, spatial 44.653 [0.0 0 0] 27.127 [0.0 0 0]
LR test, spatial lag 68.879 [0.0 0 0] 37.969 [0.0 0 0]
LR test, spatial 55.551 [0.0 0 0] 34.392 [0.0 0 0]
Notes : Standard errors are in parentheses. The probability values for the various tests are in square brackets. Probabilities smaller than 0.05 point
to significance of Wald or LR test. ∗ Significant at 10%. ∗∗ Significant at 5%. ∗∗∗ Significant at 1%.
�
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surrounding areas by close to 10%, quite a bit more in comparison
to the rental market.
4.3. Explanation for larger indirect effect
The estimates are suggesting that the indirect effect of immi-
gration on rents and house prices is much larger than the di-
rect effect. There are a number of plausible explanations for the
large spillover. A strong network effect may operate. When immi-
grants settle in a particular MSA, they may draw additional im-
migrant relatives and friends to settle in surrounding MSAs in or-
der to be close by and as such may explain the larger indirect ef-
fect. An alternative mechanism that could be at play is that im-
migrants moving to one MSA “push out” older residents. Perhaps
this is a manifestation of distrust of immigrant neighbors. Frey
(1995) , found that immigration plays an important role in the re-
distribution patterns of the U.S. population by influencing inter-
nal migration which is selective on race and socio-economic sta-
tus. Using 1990 Census data, Frey argues that natives, especially
whites, move-out from high-immigration areas. Similarly, Borjas
(2006) used census data from the 1960–2000 decennial censuses
to examine the impact of immigration on internal migration be-
havior of native-born workers. His result shows that “for every ten
immigrants who enter a particular MSA, between three and six na-
tives will choose not to live in that locality.”(p. 255).
Following Frey (1995) and Borjas (2006) , we explore the “native
out-migration” channel to see whether immigrants moving to one
MSA displace or “push out” older residents. If so, we can argue that
finding a larger indirect effect over the direct effect is consistent
with a displacement explanation. The native out-migration channel
is considered by estimating the following SDM equation: 12
12 Rather than estimating separate “native out-migration” equations for rent and
house price samples, we estimate one equation by using all the MSAs that are in
both rent and price equations. The MSA overlap is almost complete with only nine
MSAs in the rent sample not included in the house price sample and two MSAs in
house price sample that are not in housing rent sample. In total the equation we
estimate contains 273 MSAs.
5
e
p
log ( Nati v e mt ) = ρW l n ( Nati v e mt ) + l ogImmi g m t−1 . δ1 + X mt β1
+ W logImmi g m t−1 . δ2 + W X mt β2 + �μmt (8)
The dependent variable is the change in the log of native popu-
ation in MSA m at time t , while the main independent variable is
he log of immigrants. In addition to the immigration variable, we
lso controlled for GDP per capita, the unemployment rate, murder
ates, burglary rates and population density. Population density is
efined as the ratio of the number of people in MSA m divided by
he land area of the MSA.
Table 6 provides the result of the native, immigrant estimation.
n Specification I we controlled for MSA fixed effect while in spec-
fication II, we controlled for both MSA and time fixed effects. The
egative direct effect in conjunction with the positive indirect ef-
ect is consistent with the notion that inflows of immigrants cause
ative-flight. While the negative direct effect indicates that inflow
f immigrants in a particular MSA reduces the number of natives
esiding in that area the positive indirect effect shows an increase
n the number of natives in surrounding MSAs. A 1% increase in
mmigration inflows is associated with a 0.05% fall in the growth
ate of the native population. The indirect effect coefficient value
s positive and a tad higher at 0.08. This implies that the same 1%
ise in immigration inflows into an MSA is associated with a 0.08%
ncrease in native population growth in the surrounding MSAs. If
atives are moving from larger population areas to smaller popula-
ion areas, the larger indirect effect is plausible. Native-flight might
ie behind one of our main findings, a stronger indirect effect rel-
tive to direct effect estimate of immigration on rents and house
rices.
. Conclusions and discussion
Using data that span from 2002–2012, we find, as have oth-
rs, that immigration inflows are associated with rising rents and
rices. In our final specification, where we employ IV techniques
A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25 23
t
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Table B
Spatial Durbin business cycle model for rent.
Dependent variable �ln( Rent mt )
Direct effect Indirect effect Total effect
P 0.412 ∗∗∗
(0.052)
Immigrant t /Pop t −1 1.108 ∗∗
(0.556)
7.261 ∗∗
(3.401)
8.369 ∗∗
(3.431)
Murder 0.0 0 0
(0.0 0 0)
0.004
(0.003)
7.261 ∗∗
(3.401)
ln Burglary 0.001
(0.002)
−0.019
(0.018)
0.004
(0.003)
Land per capita −0.048
(0.080)
−0.336
(0.595)
−0.019
(0.018)
ln Income per capita 0.003 ∗∗∗
(0.001)
0.007
(0.012)
−0.336
(0.595)
ln Permit −0.003 ∗∗∗
(0.001)
−0.014 ∗
(0.007)
0.007
(0.012)
Unemployment 0.0 0 0
(0.001)
−0.003
(0.003)
−0.014 ∗
(0.007)
Northeast 0.003
(0.010)
−0.014
(0.019)
−0.010
(0.017)
Midwest 0.001
(0.007)
0.010
(0.014)
−0.009
(0.014)
West −0.001
(0.007)
−0.003
(0.016)
−0.004
(0.014)
Northeast ∗Bust −0.002
(0.005)
−0.002
(0.016)
−0.004
(0.012)
Midwest ∗Bust −0.012
(0.013)
0.004
(0.019)
−0.008
(0.012)
West ∗Bust 0.008
(0.012)
0.001
(0.016)
0.009
(0.010)
Observations 2750
Log-likelihood 4786.735
Time fixed effect Yes
Wald test, spatial lag 11.387 [0.578]
Wald test, spatial error 12.635 [0.476]
LR test, spatial lag 11.287 [0.587]
LR test, spatial error 12.721 [0.470]
Notes : Standard errors are in parentheses. The probability values for the various
tests are in square brackets. Probabilities smaller than 0.05 point to significance of
Wald or LR test. Bust is a dummy variable equaling 0 from 20 03–20 07 and 1 from
2008–2012. ∗ Significant at 10%. ∗∗ Significant at 5%. ∗∗∗ Significant at 1%.
o account for potential endogeneity, we find that a rise in immi-
ration inflows, equivalent to one percent of an MSA’s population,
s associated with an approximate eight-tenths of a percent rise
n rents. More importantly, the SDM methodology that we employ
hows, in addition, that the rent effects of immigrant inflows into
ne MSA spillover to neighboring MSAs. Immigrant inflows equiv-
lent to one percentage point of an MSA’s population are associ-
ted with a 1.6% increase in rents in surrounding MSAs. A similar
attern is found in house prices. The same increase in immigrant
nflows appears to drive house prices up by 0.8%. However, in the
ase of house prices the spillover is much larger, leading to a 9.6%
ncrease in home prices in the surrounding MSAs.
Furthermore, we find that immigrant inflow into an MSA seem
o be driving natives out and into surrounding MSAs. Hence our
ndings are suggestive of increase in rents and prices in sur-
ounding areas as being driven by native population movements
n response to immigrant inflows. Immigration appears to induce
ative-flight, possibly explaining the pattern in rents and prices
hat we observe across geography.
We find it curious that while the direct effects of immigra-
ion on rents and house prices in an MSA are similar in magni-
ude, the spillover effects in the house price market are so much
arger. A rise in immigration inflows, equivalent to one percent-
ge point of an MSA’s population raises rents in neighboring MSAs
y 1.8% while house prices rise by 9.6%. What might be driving
he larger spillover effect in the house price market relative to the
ental market? A number of reasons could explain the differen-
ial spillovers. One possibility is that the immigration inflows that
ead to native flight result not only in natives moving into rental
ousing in neighboring MSAs, but also a good percentage of those
witching into the house market from the rental market. Native
ight might provide an opportune time for those leaving a rental
nit in an immigrant receiving area to switch from being a renter
o a homeowner. Those higher demand pressures in the housing
arket might explain the larger indirect impacts for house prices
elative to rentals. Overall, these results point to complex dynamics
n housing markets following immigration.
ppendix
Table A
Variable definitions and data source.
Variable Description Source
Housing rent Fair market rent corresponds to the price of a vacant 0
bedroom to 4 bedroom rental units
Department of Housing and Urban Development (HUD)
http://www.huduser.org/portal/datasets/50per.html
House price index (HPI) The HPI is a broad measure of the movement of
single-family house prices
Federal Housing Finance Agency
http://www.fhfa.gov/DataTools/Downloads/Pages/
House- Price- Index- Datasets.aspx#qpo
Immigration Number of immigrants admitted to the United States by
MSA
Department of Homeland Security
http://www.dhs.gov/yearbook-immigration-statistics
Personal income per capita Personal income is the income received by all persons
from all sources
Bureau of Economic Analysis (BEA)
http://www.bea.gov/regional/
Population Population estimate by MSA U.S. Census https://www.census.gov/popest/data/historical/
20 0 0s/vintage _ 20 08/metro.html
Burglary rate Rates are the number of reported burglary offenses per
10 0,0 0 0 population
FBI Uniform Crime Report http:
//www.fbi.gov/about- us/cjis/ucr/ucr- publications#Crime
Murder rate Rates are the number of reported murder offenses per
10 0,0 0 0 population
FBI Uniform Crime Report http:
//www.fbi.gov/about- us/cjis/ucr/ucr- publications#Crime
Unemployment Civilian unemployed as percent of total civilian labor force Bureau of Labor Statistics http://www.bls.gov/lau/
Housing permit Number of new privately owned housing units authorized
by each MSA
U.S. Census https://www.census.gov/construction/bps/
historical _ data/index.html
Land Land area in square miles U.S. Census http:
//www.census.gov/population/metro/data/pop _ data.html
Land density MSA’s land area in square miles divided by total
population of MSA
Constructed by the authors
Shift share to construct
immigrant IV
(Foreign-born population in 1990 census in the MSA)/Total
foreign born population in the U.S. in 1990
Obtained from the 1990 U.S. Census 5% IPUMS sample:
https://usa.ipums.org . Steven Ruggles et al. (2010 )
24 A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25
Table C
Spatial Durbin business cycle model for house price.
Dependent variable �log( Price mt )
Direct effect Indirect effect Total effect
ρ 0.874 ∗∗∗
(0.015)
Immigrant t /Pop t −1 −0.787 ∗∗∗
(0.192)
−15.267 ∗∗
(5.940)
−16.055 ∗∗∗
(6.054)
Murder 0.0 0 0
(0.0 0 0)
−0.001
(0.004)
−0.001
(0.005)
log Burglary −0.004
(0.003)
−0.056
(0.079)
−0.060
(0.081)
Land per capita 0.137 ∗∗∗
(0.042)
0.567
(1.281)
0.704
(1.309)
log Income per capita 0.001
(0.002)
0.002
(0.091)
0.003
(0.093)
log Permit 0.003 ∗∗∗
(0.001)
0.098 ∗∗∗
(0.032)
0.101 ∗∗∗
(0.032)
Unemployment −0.001 ∗∗∗
(0.0 0 0)
0.001
(0.005)
−0.001
(0.005)
Northeast 0.006
(0.004)
0.036 ∗
(0.018)
0.041 ∗∗
(0.017)
Midwest 0.0 0 0
(0.002)
0.037
(0.032)
0.037
(0.033)
West 0.0 0 0
(0.003)
0.015
(0.026)
0.017
(0.026)
Northeast ∗Bust 0.004
(0.005)
−0.061 ∗∗∗
(0.021)
−0.056 ∗∗∗
(0.021)
Midwest ∗Bust −0.002
(0.003)
−0.071 ∗∗∗
(0.021)
−0.073 ∗∗∗
(0.021)
West ∗Bust 0.003
(0.004)
−0.053 ∗∗∗
(0.016)
−0.050 ∗∗∗
(0.015)
Observations 2820
Log-likelihood 7459.956
Time fixed effect Yes
Wald test, spatial lag 36.0 04 [0.0 0 0]
Wald test, spatial error 36.663 [0.0 0 0]
LR test, spatial lag 35.815 [0.0 0 0]
LR test, spatial error 37.497 [0.0 0 0]
Notes : Standard errors are in parentheses. The probability values for the various tests are in square
brackets. Probabilities smaller than 0.05 point to significance of Wald or LR test. Bust is a dummy vari-
able equaling 0 from 20 03–20 07 and 1 from 2008–2012. ∗ Significant at 10%. ∗∗ Significant at 5%. ∗∗∗ Significant at 1%.
Table D
First stage regression for immigration inflows IV.
Immigration IV for rent estimate Immigration IV for price equation
Coefficient Bootstrapped SE Coefficient Bootstrapped SE
ln(share1990) 0.37 ∗∗∗ 0.027 log(share1990) 0.663 ∗∗∗ 0.016
Murder −0.015 ∗∗∗ 0.006 murder −0.005 ∗∗∗ 0.002
ln(burglary) −0.188 ∗∗∗ 0.070 log(burglary) −0.049 0.052
Land per capita −29.33 ∗∗∗ 4.163 Land per capita −7.97 ∗∗∗ 1.852
ln(percapita Y) 0.783 ∗∗∗ 0.050 log(percapita Y) 0.415 ∗∗∗ 0.030
ln(permit) 0.665 ∗∗∗ 0.025 log(permit) 0.372 ∗∗∗ 0.017
unemployment 0.111 ∗∗∗ 0.011 unemployment 0.010 ∗∗∗ 0.004
Observations 1812 2321
R -squared 0.827 0.899
Notes : Year effects incorporated but not shown. Coefficient values obtained from a first-stage regression with
corrected standard errors derived from 150 replications. See text for details.
B
C
D
References
Accetturo, A. , Manaresi, F. , Mocetti, S. , Olivieri, E. , 2014. Don’t stand so close to me:
the urban impact of immigration. Reg. Sci. Urban Econ. 45, 45–56 . Akbari, A.H. , Aydede, Y. , 2012. Effects of immigration on house prices in Canada.
Appl. Econ. 44 (13), 1645–1658 . Altonji, J.G. , Card, D. , 1991. The effects of immigration on the labor market outcomes
of less-skilled natives. In: Abowd, J.M., Freeman, R.B. (Eds.), Immigration, Tradeand Labor. University of Chicago Press, pp. 201–234 .
Basu, S. , Thibodeau, T.G. , 1998. Analysis of spatial autocorrelation in house prices. J.
Real Estate Finance Econ. 17 (1), 61–85 .
orjas, G.J. , 2003. The labor demand curve is downward sloping: reexamining the
impact of immigration on the labor market. Q. J. Econ. 118 (4), 1335–1374 . Borjas, G.J. , 2006. Native internal migration and the labor market impact of immi-
gration. J. Human Resour. 41 (2), 221–258 . Borjas, G.J. , Katz, L.F. , 2007. The evolution of the Mexican-born workforce in the
United States. In: Borjas, G. (Ed.), Mexican Immigration to the United States.
National Bureau of Economic Research Conference Report, Cambridge, MA . ohen, J.P. , Coughlin, C.C. , 2008. Spatial hedonic models of airport noise, proximity
and housing prices. J. Reg. Sci. 48 (5), 859–878 . eSilva, S. , Pham, A. , Smith, M. , 2012. Racial and ethnic price differentials in a small
urban housing market. Housing Policy Debate 22 (2), 241–269 .
A. Mussa et al. / Journal of Housing Economics 35 (2017) 13–25 25
E
E
F
F
G
G
L
N
O
O
O
P
S
R
S
S
S
S
S
T
lhorst, J.P , 2010. Matlab software for spatial panels. In: Paper presented at the IVthWorld Conference of the Spatial Econometrics Association (SEA). Chicago .
lhorst, J.P. , 2014. Spatial Econometrics: From Cross-Sectional Data to Spatial Panels.Springer, Berlin, New York, Dordrecht, London .
ernández-Avilés, G. , Minguez, R. , Montero, J.-M. , 2012. Geostatistical air pollutionindexes in spatial hedonic models: the case of Madrid, Spain. J. Real Estate Res.
34 (2), 243–274 . rey, W.H. , 1995. Immigration and internal migration ‘flight’ from US metropoli-
tan areas: toward a new demographic balkanisation. Urban Studies 32 (4–5),
733–757 . ibbons, S. , Overman, H.G. , 2012. Mostly pointless spatial econometrics. J. Reg. Sci.
52 (2), 172–191 . onzalez, L. , Ortega, F. , 2013. Immigration and housing booms: evidence from Spain.
J. Reg. Sci. 5 (1), 37–59 . eSage, J.P. , Pace, R.K. , 2009. Introduction to Spatial Econometrics. CRC Press Taylor
and Francis Group, Boca Raton, U.S .
ational Research Council, 1997. The New Americans: Economic, Demographic andFiscal Effects of Immigration. National Academy Press, Washington .
sland, L. , Thorsen, I. , 2013. Spatial impacts, local labour market characteristics andhousing prices. Urban Studies 50 (10), 2063–2083 .
ttaviano, G. I.P. and Peri, G. 2007. “The effects of immigration on U.S. wages andrents: a general equilibrium approach,” CReAM Discussion Paper 13/07, Center
for Research and Analysis of Migration.
ttaviano, G.I.P. , Peri, G. , 2012. Rethinking the effects of immigration on wages. J.Eur. Econ. Assoc. 10 (1), 152–197 .
ace, R.K. , LeSage, J.P. , Zhu, S. , 2012. Spatial dependence in regressors and its effecton performance of likelihood-based and instrumental variable estimators. In:
Terrell, D., Millimet, D. (Eds.). In: 30th Anniversary Edition (Advances in Econo-metrics), 30. Emerald Group Publishing Limited, pp. 257–295 .
ill, K. 20 0 0. “Understanding asset values: stock prices, exchange rates and the“peso problem.” Business Review, Federal Reserve Bank of Philadephia, Septem-
ber/October 20 0 0, pp. 3–13. uggles, S. , Alexander, T. , Genadek, K. , Goeken, R. , Schroeder, M.B. , Sobek, M. , 2010.
Integrated Public Use Microdata Series: Version 5.0. University of Minnesota,
Minneapolis [Machine-readable database] . á, F. , 2015. Immigration and house prices in the UK. Econ. J. 125 (587), 1393–1424 .
aiz, A. , 2003. Room in the kitchen for the melting pot: immigration and rentalprices. Rev. Econ. Stat. 85 (3), 502–521 .
aiz, A. , 2007. Immigration and housing rents in American cities. J. Urban Econ. 61(2), 345–371 .
aiz, A. , Wachter, S. , 2011. Immigration and the neighborhood. Am. Econ. J. Econ.
Policy 3 (2), 169–188 . usin, S. 2001. “The Impact of the Mariel Boatlift on the Miami Housing Market,”
Washington DC: U.S. Bureau of the Census. revelyan, E.N. , Acosta, Y.D. , De La Cruz, P. , 2013. Homeownership among the for-
eign-born population: 2011. Census Bureau. U.S. Department of Commerce .