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Neighborhood Dynamics
D aniel A aronson

W orking Papers Series
Research Department
Federal Reserve Bank of Chicago
December 1998 (WP-98-20)

FEDERAL RESERVE BANK
OF CHICAGO

N eighborhood D yn am ics1

D aniel Aaronson
Federal R eserve Bank o f Chicago
daaronson @ frbchi .org

D ecem ber 1998

A b stract
Given accum ulating em pirical and theoretical evidence on the consequences o f
com m unity sorting, understanding neighborhood evolution appears to be an im portant but
understudied com ponent of this literature. Therefore, this paper reports descriptive
findings on census tract dynam ics in the U nited States between 1970 and 1990. T he
em pirical vector autoregression techniques allow a more com plete description o f
im portant system atic facts about neighborhood race, incom e, and housing dynam ics. A
num ber o f insights about neighborhood evolution em erge. First, tract racial com position
is extrem ely persistent. Tract incom e is persistent as well, especially at the high end o f
the incom e distribution. Taken together, the overw helm ing am ount o f evidence suggests
racial and incom e sorting are independent o f each other. Second, housing price dynam ics
m irror the dynam ics o f high-incom e households in the com munity; they are highly
persistent and have some im portant positive feedback effects on high-incom e fam ilies
and negative effects on fraction Black but not H ispanic residents. Third, there are
differences, but notably a striking am ount o f hom ogeneity, in the evolution o f
neighborhoods. Fourth, spillover effects from nearby neighborhoods and labor m arkets
are im portant. W ith respect to race and incom e dynam ics, the cum ulative effect o f
shocks are ordered in a m onotonic way. Im pulses within a tract are most im portant,
nearby neighborhoods m atter a little less, and counties m atter the least, although are still
statistically important. In fact, the size o f the county effect is not trivial. Furtherm ore,
there appears to be some heterogeneity in these county spillover effects. Positive county
incom e im pulses are particularly strong am ong high-incom e families, suggesting that
labor m arket conditions have a larger effect on w ealthier families. However, the im pact
o f labor m arkets on low -incom e fam ilies is im portant as well.

1 This paper i a work i progress. Comments are appreciated. My thanks t Joe Altonji and Dan Sullivan
s
n
o
f r helpful d s
o
i cussions. The views expressed are those of the author and are not nec s a i y those ofthe
esrl
Federal Reserve Bank ofChicago or t e Federal Reserve System.
h




I. In tro d u ctio n
A num ber o f theories in the social sciences seek to explain the dynam ic process o f
neighborhood developm ent, particularly the potential for a separating equilibrium based on
certain characteristics, such as race, ethnicity, incom e, and housing values. These m odels rely on
a variety o f sorting m echanism s, including governm ent redistributive policies (Epple and Rom er
1991), local com plem entarities in production (Benabou 1993), capital m arket im perfections
(B enabou 1994), differences in preferences (Schelling 1971), zoning and land use controls
(H am ilton 1975), and desired levels o f taxation and education spending (Fernandez and
R ogerson 1996, Tiebout 1956).1 W hile theory m ay suggest a separating equilibrium is feasible,
the consequences are m ore contentious. M any m odels conclude that individual outcom es are not
a function o f residential location. Others note possible benefits from sorting due to, for exam ple,
hom ogeneous tastes for public goods consum ption o r protection o f m inority businesses . 2
H ow ever, accum ulating em pirical evidence indicates there m ay b e im portant costs to
neighborhood sorting.

In particular, com pounded disparities in education arising from

neighborhood spillover effects and the role o f a com m unity’s resources in funding schools have
m otivated concern about income segregation . 3 T he consequences o f racial sorting are discussed
in research on the spatial m ism atch hypothesis, w here m inority em ploym ent problem s are linked

1 Atkinson and S i l t (1980), S i l t (1983), deBartolome (1990), Ioannides and Hardman (1997), and Frankel
tgiz
tgiz
(1998) introduce models where long-run i t g a i ncan r s l among communities.
nerto
eut
2 Borjas (1986) findsth tpartofthe immigrant d f e e t a i self-employment r t scan be a t i u e to an “enclave
a
ifrnil n
ae
trbtd
effect”
3 Jencks and Mayer (1990) give a comprehensive summary of the neighborhood e f c s l t r t r . For recent
f e t ieaue
evidence of such e f c s see Aaronson (1998a) and Borjas (1995). For c i i u s of the l t r t r , see Evans, Oates,
fet,
rtqe
ieaue
and Schwab (1992) and Manski (1993). The schooling argument can be generalized t a l neighborhood-specific
o l
public goods i s r i g would lead t l s access t higher qua i y s r i e . Furthermore, many argue t a
f otn
o es
o
lt evcs
ht
neighborhood income or r c a segregation could r s l i l s i c i a i n among the wealthy to support
ail
eut n es nlnto
r d s r b t v p l c e t t e poor.
eitiuie oiis o h




1

to urban residential segregation . 4 If these factors are im portant, the w ay society sorts can be a
com ponent o f incom e and education distributions across generations. In fact, B enabou (1994)
shows, w ith assum ptions about com plem entarities in the labor m arket, that w elfare effects o f
neighborhood incom e and education sorting can be harm ful in the long run to all fam ilies.
W hile theoretical m odels stress the pertinence o f com m unity sorting, the em pirical
literature docum enting neighborhood dynam ics and the persistence o f com m unity conditions is
som ew hat lim ited. Studies o f area dynam ics tend to concentrate on relationships at the city and
state level, exploring the persistence and R ed b ack effects o f changes to regional w ages,
em ploym ent, and prices . 5 l i ttl e w ork has system atically studied neighborhood dynam ics and the
relationships th at w ould b e relevant at this local level.
M uch o f w hat exists o n neighborhood dynam ics has grow n out o f the T iebout literature.
A n im portant im plication o f Tiebout is jurisdictional hom ogeneity . 6 Therefore, as a test o f the
theory, m any authors have m easured the integration o f neighborhoods along a variety o f
m easures. F or exam ple, in an early paper, G rubb (1982) analyzes the com position o f B oston
com m unities, concluding that com m unity incom e and age hom ogeneity increased, but
hom ogeneity in other dim ensions decreased (including racial hom ogeneity), betw een 1960 and
1970.

M ore recently, a num ber o f authors have presented evidence on spatial clustering,

particularly w ith regard to race and incom e, o f w hich W hite (1987), Persky (1990), M assey and

4 See Holzer (1991) for a summary. Cutler and Glaeser (1997) f nd t a outcomes are worse for Blacks who l v i
i ht
ie n
c t e with higher l v l of r c a segregation, and, using a v
iis
ees
ail
ariety of instruments t correct f r the endogeneity of
o
o
segregation, they conclude t a the c u a i y runs from segregation t outcomes.
ht
aslt
o
5 Bartik (1991) and Blanchard and Katz (1992) are p r i u a l good examples. Bartik’ book summarizes much of
atclry
s
ti ltrtr.
h s ieaue
6 More generally, a large t e r t c l l t r t r on club theory, which models the optimal formation ofconsumption
h o e i a ieaue
and production c u s has a i e . See Brueckner and Lee (1989).
lb,
rsn




2

D enton (1993), H eikkila (1995), and Ioannides and H ardm an (1997) are but a sm all but
w orthw hile sampling.

M any o f these studies find that clustering, especially due to race, is

declining over tim e but still an im portant phenom enon. O ther studies concentrate on specific
groups o f the population. For exam ple, G ram lich, Laren, and Sealand (1992) and Jargow sky and
Bane (1991) explore the m igration dynam ics o f p oor urban areas and the im plications they have
on income grow th in these com m unities.
This paper has tw o m ain goals.

First, I present estim ates o f the dynam ics o f

neighborhood com position in the U nited States betw een 1970 and 1990.

T he em pirical

techniques allow a m ore com plete, albeit atheoretical, description o f im portant system atic facts
about neighborhood race, incom e, and housing dynam ics.

W hile these estim ates allow som e

inference about w ithin-com m unity dem ographic dynam ics, it is also straightforw ard to analyze
relationships across com m unities.

Therefore, a second m ain goal is to docum ent betw een-

com m unity dynam ics and thus get a feel for the im portance o f spillovers from nearby
neighborhoods or labor m arket areas. These estim ates m ay b e helpful in m easuring the benefits
o f neighborhood developm ent program s.
To explore these issues, a panel o f m etropolitan neighborhood characteristics from the
1970,1980 and 1990 U.S. Censuses is constructed to estim ate vector autoregressions (V A Rs) o f
urban neighborhood income, racial, and housing distributions.

V ARs are useful tools w hen

theoretical guidance on the structural relationship betw een a system o f variables is absent. In this
application, the neighborhood V A R measures the persistence and feedback effects o f com m unity,
nearby com munity, and labor m arket characteristics. A num ber o f sim ple tim e-series techniques
are used to describe the resulting dynamics o f the system. T he V A R s include all m etropolitan




3

census tracts and block num bering areas. Consequently, neighborhoods largely ignored in the
em pirical literature, particularly those w ith high fractions o f m iddle-incom e and high-incom e
residents, but w hich play a vital role in theories o f incom e sorting can be studied.
A num ber o f insights about neighborhood evolution em erge.
com position is extrem ely persistent.

First, tract racial

A tem porary shock to the racial com position o f a

neighborhood dam pens very little tw enty years after the innovation. T ract incom e is persistent as
w ell, especially at the high end o f the incom e distribution. Taken together, w hile there are som e
negative feedback effects o f shocks to race on incom e and incom e o n race, the overw helm ing
evidence suggests racial and incom e sorting are independent o f each other.

Second, housing

price dynam ics m irror the dynam ics o f high-incom e households in the com m unity; housing
prices are highly persistent and have som e im portant positive feedback effects on high-incom e
fam ilies and negative effects on fraction B lack but not H ispanic residents.

Third, there are

differences, but notably a striking am ount o f hom ogeneity, in the evolution o f neighborhoods.
Fourth, spatial dependence m atters. S pillover effects from nearby neighborhoods are im portant,
and in one notable case, indistinguishable from ow n tract effects.

W ith respect to race and

incom e dynam ics, the cum ulative effect o f shocks are ordered in a m onotonic way. Im pulses
w ithin a tract are m ost im portant, nearby neighborhoods m atter a little less, and counties m atter
the least, although are still statistically im portant. T he one exception to this spatial ordering is
housing value dynam ics where the tract appears to b e too sm all a u n it to describe house value
evolution. Finally, county-level shocks play a role in tract evolution. W hile this m ay not be a
surprise, the size o f the im pact is not trivial.

Furtherm ore, there appears to b e som e

heterogeneity in these county spillover effects. Positive county incom e im pulses are particularly




4

strong am ong high-incom e families, suggesting that labor m arket conditions have a larger effect
on w ealthier families.

However, the im pact o f labor markets on low -incom e fam ilies is

im portant as w ell.
T he paper is organized as follows. Section tw o outlines the em pirical strategy em ployed
to describe neighborhood dynamics. V AR models o f neighborhood conditions are outlined and
m ethods to analyze the resulting dynamics are briefly discussed. Section three describes the data
used to im plem ent these models. The m ain findings are reported in section four. The results are
checked for robustness along a variety.of dim ensions, including the identification schem es used
and the possibility o f neighborhood and tim e heterogeneity. The final section concludes w ith
som e possibilities for future research.

II. N eighborhood Dynam ics: A Sim ple E stim ation S trategy Using Census D ata
O ne strategy for m odeling neighborhood com position dynamics is to develop a structural
m odel o f the relationship am ong the various characteristics o f the com m unity, nearby
com m unities, and the labor market.

However, such a structural m odel often results in

exclusionary restrictions that might be inconsistent across tim e and cross-sectional units.
Furtherm ore, in this application, there is little theoretical guidance as to how neighborhood
characteristics relate over time.

An alternative m ethod o f m odeling dynam ic relationships is

through a vector autoregression, which is based on the em pirical regularities o f the data rather
than on a structural m odel closely tied to econom ic theory.




5

C onsider a country w ith c counties and i neighborhoods. Let Y jcj b e a j x l vector o f the
incom e characteristics o f residents in neighborhood i and county c at tim e t Let the vector R . ^
.
index r racial categories, for exam ple, the fraction o f the population that is W hite, B lack, and
Hispanic. Finally, H .^ in c lu d e s h dim ensions o f the housing stock. Suppose that Y jcf ^ R jC(

and H .cj are influenced by lag values o f the neighborhood incom e, racial, and housing
com position. If the lag length is assum ed to b e one period, the, dynam ics o f Y, R , and H can be
m odeled by a norm ally distributed vector autoregression

Yict
(1)

aY

^Y Y

[[R ict 1 = ta R l + [P r y
H ict

aH

Ph Y

Py

r

Py H

Y* c t- 1

^Y

eYt

P r R P r h 1[Rict - 1 1+ [9 R lYct _ ! + [®Rt ]
Ph r Ph H

H ic t-1

9H

eHt

eYt
w here [ e R t ] is a (j+ r+ h)xl vector o f serially uncorrelated error term s that are distributed
eHt

N ( 0 ,£2 ) ,

aY
pY Y
[[a R ] is a (j+r+h)xl vector o f intercept term s, and [P r y
a H

Ph Y

Py R P y H
P r r P r j j ] is a
Ph r P h H

(j+r+h)x(j+r+h) m atrix o f lag coefficients. T o allow for possible effects o f labor m arket shocks,

<Y
P
the lag o f county incom e, employment, and race, Yc t _ j»

3 16

allow ed to en ter the m odel; [ ^ r ]

<H
P
is the vector o f county coefficients. Equation (1) is an atheoretical w ay to describe feedback
effects o f incom e, housing, and racial distributions on future neighborhood conditions. So long




6

as the error term is uncorrelated w ith all lags o f Yjct R jct and H jct ? the m axim um likelihood
estim ator o f the a , P, (p’s and its standard errors are asym ptotically the sam e as OLS estim ates o f
Y icjt on the lags in the system . *7
T here are a num ber o f assum ptions em bedded in equation (1). Som e o f these restrictions,
such as the absence o f serial correlation and neighborhood heterogeneity, relate to the
specification o f the error term . O ther constraints are on the inclusion and specification o f the
system variables, including lag length, stationarity o f the lag coefficient m atrices, nonlinearities
betw een neighborhood characteristics, and contagion effects from nearby neighborhoods.
R obustness tests o f these restrictions are described next.
Som e o f the restrictions, m ost notably lag length, arise due to data lim itations. Lag length
is constrained to b e one period because only three data points (1970, 1980, and 1990) are
observed in the census data set.

This constraint assum es that the single lag is sufficient to

sum m arize the dynam ic correlation betw een Y jct R jcj , and H jct- However, this restriction is
not as lim iting as it first appears since a single lag already encom passes ten years o f inform ation.
It is certainly possible to include a second lag but given the frequency o f the data, the second lag
is m ost likely picking up unobserved individual effects rather than a real im pact o f the second
lag. R esults that use alternative m ethods to m odel fixed effects are discussed below.
A second constraint due to the sm all num ber o f tim e periods is that the coefficients are
restricted to be stationary.

Generally, for ease o f presentation, the coefficients are assum ed

invariant over tim e in m ost o f the results presented. B ut it m ight be reasonable to assume that

7 See, for example, Hamilton (1994). A seemingly unrelated regression model t a accounts for the nonzero
ht
covariance associated with t e er o terms may seem l k an appropriate way of estimating equation ( ) However,
h rr
ie
1.
when the s tof independent variables i i e t c l across e
e
s dnia
quations, SUR and OLS estimation ar the same.
e
7




neighborhood persistence and feedback effects changed betw een the 1970s and 1980s, especially
given the dram atic divergence in incom e during the 1980s. The im plication o f grow ing incom e
inequality is highlighted in the next section. I ‘d eal’ w ith this problem in tw o ways. First, I
include a 1990 dum m y variable to account for com m on secular trends in the data.

Second, I

present results using 1970-80 and 1980-90 data separately to allow som e interpretation on
w hether changes in neighborhood feedback effects betw een the tw o decades are im portant.
A particularly im portant restriction on equation (1) is the structure o f the feedback from
other neighborhoods.

F or neighborhoods outside the county, the effects are set to zero, an

innocuous assum ption. But for neighborhoods w ithin the county, the effects are all set equal to
<p, the coefficient on the county measure. This assum ption m ay be unrealistic if it is im portant to
consider geographic proxim ity at a m ore detailed level than the county. If spatial dependence
exists, then adjoining neighborhoods, for exam ple, m ay exert a strong influence, perhaps as
strong as the 'own' neighborhood, on future conditions. G entrification program s, w here several
neighborhoods are sw ept up b y the invigoration o f the local econom y, exem plify these spillovers.
Therefore, I experim ent w ith adding incom e, race, and housing stock controls from
nearby neighborhoods. G eographic proxim ity is calculated using the longitude and latitude o f
census tracts.

I find the five closest neighborhoods w ithin ten m iles o f a neighborhood and

calculate the unw eighted average o f incom e, housing values, housing com position, and fraction
B lack and H ispanic o f these com m unities. U sing such a m easure still introduces restrictions on
the contagion feedback measures. For exam ple, it is possible that there is som e heterogeneity in
how these proxim ity effects w ork that is related to the location or characteristics o f a
neighborhood. Perhaps neighborhoods w ith few er resources or located in denser parts o f a city




8

w ill be m ore influenced by the evolution o f adjacent com m unities. H ow ever, this five closest
neighborhood average should pick up first-order concerns about spatial dependence.
Finally, as already alluded to, equation (1) includes im portant restrictions on the error
term. In particular, the possibility o f an individual error com ponent is ignored, im plying that the
tim e-series relationship betw een the variables is the sam e for all cross-sectional units. H ow ever,
it is a reasonable conjecture that characteristics o f an area, such as proxim ity o f the neighborhood
to a lake o r a toxic w aste dum p, m ight affect the decision o f all households to m ove in or out.
A dding fixed effects at the state, county, or neighborhood level can control heterogeneity. A t the
neighborhood level, the m odel w ould then look like

Yict
(2)

aY

^Y Y

[[R ict ] = [a R 1+ [P r y
H ic t

a H

Ph Y

Py

r

Py h

Pr R Pr

h

Ph r Ph H

Yi c t - 1

9Y

YY

eYt

HR ict - 1 1+ [^ R ]Yct _ J + [YR * iic + [e R t ]
H ic t-1

9H

YH

where |X.c is a neighborhood-specific error term w ith a stationary coefficient vector,

eH t
7

.

O ne com m on m ethod to correct the individual effect bias is to transform the V A R into a
sim ple difference equation (Holtz-Eakin, Newey, and R osen 1988).

B u t the identification

conditions require that enough instrum ental variables be available to satisfy orthogonality
conditions betw een the error term and the lagged variables. In a three-period m odel, this m ethod
cannot b e identified.

Fortunately, A rellano and B over (1995) present an alternative m ethod.

Their idea is to apply predeterm ined, but not necessarily exogenous, variables in the level
equation as first difference instrum ents. If the model is stationary and the correlation betw een
the predeterm ined variables and the individual effect is tim e invariant, these variables are valid
instrum ents. T he m ain assum ptions are




9

(3)

E(Xjt|X|)= E(Xjsn.) and E(x.^ e.s)= 0 for all time t and s

w here x is the predeterm ined variable(s). If (5) holds, then E ( ( u .+ e .j) A x .j)= 0 and A x.^ can
act as an instrum ent. Furtherm ore, if there is no autocorrelation in the error term , then the lagged
dependent variable m ay act as the differenced instrum ent. A t the end o f the paper, I report IV
estim ators using a set o f first difference instrum ents. I also present results that m odel the fixed
effect at the state and county level.
D escribing the System Dynamics
T he V A F s are used in tw o w ays to describe neighborhood dynam ics. First, I look at the
ability o f the statistical m odels to forecast incom e, race, and housing characteristics. T he V A Rs
are estim ated o n 1970 and 1980 data, and used to forecast 1990 data. Theil statistics and other
m easures o f forecasting accuracy are used as test statistics.

Forecasting errors are presented

separately for low , m iddle, and high-incom e neighborhoods. Second, I use the V A R to describe
and sim ulate the dynam ics o f the system o f equations. T o this end, I use tw o com m on m ethods
introduced in Sim s (1980) to analyze the im pact o f innovations to variables: im pulse response
functions and forecast variance decom position.
T he im pulse response function m easures the consequence o f a one-tim e, one un it shock to
a variable’s error term on the rest o f the m odel w ith all else held constant. This is done for each
o f the j+ r+ h error term s in the system. B ecause every lagged endogenous variable appears in
every equation, each o f the shocks has contem poraneous and future effects on the endogenous
variables. H ence, the effect o f the innovation slow ly propagates throughout the system. A fter s




10

periods, the impulse response function traces through the cumulative effect of the initial one
standard deviation increase in ekt on all other variables at date t+s.
A fundam ental identification problem w ith the im pulse response m ethodology arises
because the error term s are collinear; that is the vector o f residuals is not contem poraneously
uncorrelated.

Thus shocks to, say, ey w ill have a com m on com ponent w ith eR and en and,

consequently, it m ay not be clear how to identify innovations.

Therefore, the variance-

covariance m atrix o f the residuals m ust be orthogonalized into a set o f uncorrelated com ponents
in order to calculate the im pact of a particular innovation. U nfortunately, com m on m ethods to do
this, such as the Choleski decom position, are sensitive to the ordering o f variables.

T he

assum ption is all com m on com ponents o f the innovations betw een variables are attributed to
w hichever variable appears first in the system.
Typically, researchers have a particular recursive ordering in m ind w hen m aking
forecasts. H owever, in this case, there is little theoretical justification for any ordering o r crossequation restrictions. Instead, m ost o f the results that I present do the factor ordering in a very
specific way. W hen describing each variable’s shock, I order that variable first in the system .
This im plies that all com m on com ponents o f the error covariance m atrix are given to the shock
being analyzed. Therefore, the cum ulative effects o f that shock are upper bound estim ates.
W hy do I do this? First, since each variable is placed first in the ordering, no ad hoc
decision about ordering has to be m ade beyond the first slot. Second, this setup answ ers a very
specific question: w hat is the impact o f an w ell-identified shock that only initially im pacts one
particular variable in the system. There are many exam ples o f such shocks. C ard (1990) studies
the im plications o f the M ariel Boatlift, w hich shocked the share o f H ispanics in Southern Florida




11

(although even this may not be clean since it probably shifted the income distribution as w ell).
Examples o f housing price shocks could be a cleanup o f a local toxic waste site, the arrival or
departure o f a star school principal, or other sudden changes to neighborhood amenities. Income
shocks could result from the arrival o f a new employer who is a large hirer o f high or low-incom e
workers. Nevertheless, to show the importance o f ordering, I also report results that provide one
internally consistent ordering system for all impulse response functions.
O f course, if the covariance o f the error structure is small, ordering is not an issue. A
useful way to understand these issues and learn more about the persistence and feedback between
the variables is through the variance decomposition. The variance decomposition gives the
portion o f a variable’s forecast error variance that is attributable to each o f the endogenous
variables in the model. Essentially, this statistic decomposes the mean squared error o f a speriod ahead forecast o f variable k into the proportion that is due to each o f the disturbances eu in
the system. Therefore, a variable that explains none o f the system’s forecast error variance is
considered exogenous. In the next section, I report variance decompositions where each o f the
variables are ordered last, resulting in a lower bound estimate o f the fraction o f forecast variance
that is due to its own innovations. If the proportion o f variance due to own innovations is large,
even after ordering the variable last and thus assigning no common error component, it suggests
that the variable is independent o f others in the system. In such a case, ordering does not matter.

III.

T he C ensus D ata
The census data are derived from extracts created at the Panel Study o f Income

Dynamics, the Princeton University data library, and CEESIN, an environmental data




12

clearinghouse in Michigan. From these different sources, roughly 200 variables are pulled from
the 1970, 1980, and 1990 STF3A census data files. The three censuses are merged using two
Census Bureau files that match geographic areas across decennial years. The STF3A database
contains information on demographics, income, housing, mobility, and employment for a number
o f geographic levels, the smallest o f which are census tracts, block numbering areas (BNAs), and
enumeration districts (EDs). The primary unit of analysis in this study is the census tract or
BNA, the basic statistical reporting unit in metropolitan areas.8 Taking into account natural and
manmade boundaries and population homogeneity, local committees design tracts to represent
"neighborhoods." On average, tracts consist of about 4,000 people, but may range between 2,500
and 8,000 people. EDs, the rural version o f a tract, are excluded from the metropolitan sample.
Finally, the census tract database is merged with a database on county income, race, and labor
force participation characteristics.
M ost o f the variables used in this study are directly from the census, including the
fraction o f a tract’s population that is Black or Hispanic, average housing value, the average
number o f rooms in a housing unit, and the age distribution o f the housing stock. The age and
average number o f rooms variables are meant to capture the quality of the housing stock.
County-level variables included in the analysis are average family income, adult labor force
participation rates, fraction Black, and fraction Hispanic. The regressions also include a dummy
that equals one for 1990 observations to account for secular trends and differences in variable
definitions across time. The next section makes clear the importance o f this 1990 dummy.

8 From here on, t a t mean census t a t and BNAs.
rcs
rcs




1
3

The tract-level income data requires some description. The census summarizes income in
numerous ways: average and median family income, percentage o f persons under the federal
poverty level, and in detailed brackets across the distribution.9 Because o f interest in income
persistence and feedback effects at different points o f the income distribution, I compute each
tract’s 10th, 50th, and 90th family income percentile using the detailed income bracket data To
compute these deciles, I assume that the cumulative distribution function of individuals within an
income bracket is linear. This assumption is generally innocuous because the bands o f the
income categories are narrow. However, topcoding is a problem, especially in the calculation o f
the 90th income percentile. In these cases, I use information on the total aggregate fam ily income
o f the neighborhood and fit a linear curve on the aggregate income that remains after accounting
for those families that fit into the non-topcoded categories.
Table 1 reports descriptive statistics o f the main sample. Panel A show the total number
o f metropolitan area census tracts and BNAs that remain after matching across years.10 O f the
roughly 54,000 tracts, approximately 58 percent can be traced from 1970 to 1990. Slightly over
30 percent o f the tracts show up only once in the three years. The majority o f the remaining
tracts are found in the 1980 and 1990 censuses but not the 1970 census. Because metropolitan
areas are growing over this time, many areas became tracted in 1980 or 1990 for the first time.

9 The number of income brackets varies across census years. In 1970, the income categories from $0 to 10,000 are
delineated by $1,000. Above $10,000, t e categories are $10-12,000, $12-15,000, $15-25,000, $25-50,000, and
h
$50,000 p u . In 1980, the income categories from $0 to $30,000 are delineated by $2,500. Above $30,000, the
ls
categories are $30-35,000, $35-40,000, $40-50,000, $50-75,000, and $75,000 p u . In 1990, the categories are $0ls
5.000, $5-10,000, $10-50,000 delineated by $2,500, $50-55,000, $55-60,000, $60-75,000, $75-100,000, $100125.000, $125-150,000, and $150,000 p u . I also experimented with share of families i s a e s e i i income
ls
n tt-pcfc
deciles as an a t r a i e method f rdescribing the income d s r b t o . These r s l s areavailable upon request
lentv
o
itiuin
eut
10 In 1970, there were 33,672 metropolitan t a tcodes. The number oft a t grew s e d l , reaching 40,694 i 1980
rc
rcs
taiy
n
and 44,567 i 1990.
n




1
4

The final three rows o f panel A report the sample o f neighborhoods used in this study. The
sample includes all tracts and BNAs that can be linked to at least two census years and which
include the relevant neighborhood data. The final sample includes 37,461 tracts, o f which almost
85 percent are matched to all three census years. Roughly 69,239 tract-year observations can be
used in a lag one vector autoregression.
Panel B reports means, standard deviations, minimums, and maximums for the tract-level
variables. A ll income and housing value measures are transformed into 1990 dollars using the
CPI. For the analysis, income and housing variables are in logs, and the race, housing age and
room size data are in levels. The standard deviations are particularly useful for the impulse
response analysis since all reported statistics are in standard deviation units.

IV . R esults
The Predictive Power o f the Simple Equations
Before presenting the VAR results, table 2 reports some evidence on the forecasting
success o f the individual equations that make up the VAR system. This is done for two reasons.
First, statistics on forecasting errors provide some interpretation on the statistical validity o f the
model. Second, the forecasting statistics point out a basic problem with the results; given the
lim ited data available, it is difficult to pick up structural changes in the data, such as the rise o f
incom e inequality in the 1980s.
As a true test o f simulation accuracy, out-of-sample forecasts are necessary. To
accomplish this, tract data from 1970 and 1980 is used to forecast 1990 values. The 1990
forecasts are compared to actual 1990 values and synthesized in various forecasting statistics that




1
5

are reported in columns 2 to 7. Column 2 displays Theil’s U-statistic, a root mean square error
measure that is scaled to fall between 0 and 1. The U-statistic is

, where Y * and Y* are the simulated and actual values o f the

variable Y for neighborhood i.* The numerator is simply the root mean square error. The
11
denominator is the root mean square error when ‘naive’ forecasts are extrapolated to allow for no
change in the dependent variable. If U is one, the model provides no new information beyond
the naive model. This happens in two cases: when either Y‘ or Y* is always zero or when
aY ‘+bY*=0 for all i and a>0 or b>0, both o f which suggest, in the words o f Henri Theil, “very
bad forecasting.” On the other hand, a value o f zero means perfect predictive power (i.e.
Y* = Y* ). As shown in panel A, among the key income, race, and housing variables, the Ustatistic seems reasonable, falling between 0.117 (fraction Black) and 0.187 (the 90th percentile
o f family incom e).12

IX \

i

11 This i the formulation from Theil (1961). In Theil (1966), the denominator i I
s
s —
(Y,a)2 .
|N i i
=
12 Given concern about e t r a i i s associated with r c a and income s r i g i i of some i t r s to know how
xenlte
ail
otn, t s
neet
well race or income f r c s housing p i e . I tu n out lagged r c , income, and housing stock add very l t et the
oeat
rcs t r s
ae
id o
f r c s . Race i only marginally successful a predicting house v l e , and i p r i u a l poor a r
oeat
s
t
aus
s atclry
t eplicating the
v r a i i yof future house p i e . The U s a i t c i 0.437, the mean simulation error i almost -$40,000 and the
aiblt
rcs
-ttsi s
s
mean absolute simulation er o i roughly $60,000. Income measures are s i h l more successful a forecasting
rr s
lgty
t
house prices but silmiss much ofthe variance and seem t be systematically biased downward.
tl
o
16




One advantage o f the U-statistic is that it can be decomposed into the fraction o f the error
due to the mean, variance, and covariance terms.13 The mean term is a measure o f the extent to
which average values o f the simulated and actual series diverge. The variance proportion
measures the extent to which the simulated series reproduces the variability o f the actual series.
The covariance term indicates the extent o f unsystematic error. Again, the results axe
encouraging. There appears to be little systematic bias; the worst case appears to be the 10th
percentile o f income where nine percent o f the error arises from being off on the mean. In five
out o f the six cases reported, the simulations replicate much o f the variance in the actual series as
w ell. The one exception is the 90* percentile o f income, where 57 percent o f the forecast error is
due to the variance term. This is primarily because o f topcoding.
Finally, the last two columns report two common measures o f forecasting error: mean
simulation errors and mean absolute simulation errors. The absolute error measure is cumulative
so that negative and positive errors do not cancel out. Note that the root mean error statistics
show an interesting trend. The models overpredict growth at the bottom of the income
distribution (hence the high bias proportion o f the U-Statistic) and underpredict growth at the top
o f the distribution. This points to a cautionary note. There are structural changes in the
evolution o f race, income, and housing statistics. In the 1980s, income inequality grew. The
tract data suggest that the ratio o f the 90* percentile o f income to the 10* percentile o f income

N
13 Decompose the numerator in o — ^X ( - Y.“ )* _/vs. Y* )+(ag - a g ■+2(l-p)<is< a . Divide through
t
Y?
= (Y? J
by t e l ft-hand side t get the proportion ofer o due t the mean, variance, and covariance (Theil 1961).
h e
o
rr
o
17




was 6.2. But the forecast of this 1990 ratio is 4.5. Panels B, C, and D show that this error also
occurs in subsamples of low, middle, and high-income tracts.14
Dealing with nonstationarity in data with only three time periods is d ifficult.15 One
common solution is to difference the data, which Sim s (1980) and others have argues throws
away information about common movements in the data. Instead, I account for common secular
changes in the variables across decades by including a dummy variable that equals one if the

I

observation is in 1990 and zero otherwise. I also present some o f the findings using the 1970-80
and 1980-90 data separately to show how this effects the results.
The VAR Parameter Estimates
The VAR estimates for the baseline specification are presented in table 3. These tables
include the coefficients and standard errors from OLS regressions o f each logged neighborhood
variable on lags o f all other logged neighborhood and county variables. Each column o f table 3
represents a separate regression.

The results allow some inferences about persistence and

feedback effects, although the coefficients must be cautiously interpreted due to the interactions
between the variables within the system.
Looking first at the family income variables (columns 1 to 6), the results suggest that
neighborhood income is fairly persistent, especially at the high end o f the distribution.
Combining the three lagged income variables, the sum o f the income AR(1) coefficients is 0.581,

14 The t a t are s r t f e by median income i 1970. Forecasts are derived from regressions t a include the f l
rcs
taiid
n
ht
ul
sample oft a t ,but the r s l s are si i a i a subsample of t a t i used to estimate the forecasting parameters.
rcs
eut
mlr f
rcs s
15 Although Dickey-Fuller and Phillip-Peron t s s of s a i n r t of the income, r c , and housing value variables
et
ttoaiy
ae
e s l r j c the hypothesis of a u i r o . The t s uses the following two regression equations to calculate an F t s
aiy eet
nt ot
et
-et
of the hypothesis t a p = 0
ht




AY„ = a + P Y H + 4 .4 Y „ _ ,+ e 1„
_l
AY„ = a+(|>AY1
,_1+ e 2i,

18

0.584, and 0.729 for the 10th, 50th, and 90th income percentile. Most o f this contribution comes
from the lagged dependent variable, particularly at the 90th percentile. Racial feedback effects
are, not surprisingly, much smaller, although these racial effects remain significant and negative.
The racial feedback is strongest at the low end o f the income distribution (column 1) and weakest
at the high end (column 5). Labor market feedback effects, as reported in the rows labeled
‘county,’ are smaller than the tract effects but still statistically important.
The racial composition o f neighborhoods is very persistent, particularly among Blacks
(column 7).

The AR(1) coefficient in the fraction Black equation is 0.953 (0.002).

The

corresponding number for the Hispanic equation (column 9) is 0.969 (0.002). When the fraction
Black and Hispanic equations are run without the income terms, the lagged dependent variables
are 0.936 (0.002) and 0.979 (0.002). The similarity o f the findings with and without the income
terms suggests that racial segregation is independent o f income segregation in metropolitan
neighborhoods. This inference appears again in the forecast diagnostics reported below.
Column 11 reports the coefficients from the average house value regression.

House

values appear to have the same level o f persistence as income; the lagged dependent variable for
the average housing value regression is 0.736 (0.005). The high end o f the income distribution is
the largest driver o f housing values. The magnitude o f the 90th percentile coefficient is 0.401
(0.009), compared to a median income coefficient o f -0.049 (0.008) and a 10th percentile
coefficient o f -0.011 (0.006). Racial feedback is negative and significant. Past characteristics o f
housing stock are significant but enter the regressions with negative signs. Finally, higher house
values, larger homes, newer housing stock, fewer minorities, and higher income at the top o f the
income distribution lead to more new home building (columns 13 to 16).




19

However, because o f the way in which the equations and variables interrelate in the
model, it is difficult to conclude much from the reduced form estimates o f a single equation in
the VAR. This is because even if variable x is insignificant in directly helping to forecast the
one-step ahead estimate o f variable y, it may still affect variable y through other equations in the
system s.16

Therefore, we next turn to the variance decompositions and impulse response

functions to more fully describe the dynamics o f neighborhood evolution.
The Variance Decomposition
Table 4 reports the decomposition o f the two step forecast variance. Each cell gives the
share o f the two period (or 20 year) forecast variance for each variable that is attributable to its
own innovations and to innovations from the other variables in the system. It is important to
stress that the results in table 4 are not from a single decomposition but rather each row signifies
a separate analysis. As already noted, each variable is listed last in its own decomposition to
allow for a lower bound estimate o f the share o f forecast variance due to a variable’s own
innovations and an upper bound estimate o f the share due to all other variables. The rest o f the
system is ordered as reported in the table reading from left-to-right. The county variables are
ordered first, the housing variables second, the race variables third, and the income variables last.
I also report two orderings o f the three income variables for each decomposition and a third
ordering that places the county variables near last, just ahead o f the variable being analyzed and

16 This i best seen from r s l sofGranger causality t s st a determine i lag variables or blocks of lag variables
s
eut
et h t
f
enter the equations f rthe remaining v r a l s Given the high number of s g i i a tvariables across equations, i i
o
aibe.
infcn
ts
not surprising t a the n l of block exogeneity i rejected a the one percent s g
ht
ul
s
t
i nificance l v l i every case. In
ee n
other words, a lelements of the income, housing, and r c a d s r b t o help t improve the forecast of a lother
l
ail itiuin
o
l
elements i the system. Block exogeneity ofthe county-level c a a t r s i s a i rejected a the one percent
n
h r c e i t c lso s
t
significance l v l
ee.




20

its directly related components (e.g. all three income variables are placed last when analyzing any
o f the income measures). The orderings are denoted in column (14).
The notable feature o f the two race variance decompositions is about 80 (Hispanic) to 83
(Black) percent o f forecast variance two periods out is explained by race’s own innovations.
Approximately 88 to 93 percent o f forecast variance is explained by racial innovations o f the
neighborhood or county.

There is little evidence that income distribution, housing

characteristics, or other county labor market characteristics matter to future racial composition o f
a neighborhood, suggesting independence between income and racial neighborhood sorting.
For the three income variables, approximately 50 to 60 percent o f the forecast variance
are explained by innovations to the income distribution, with the majority o f the variance coming
from direct innovations at the point in the income distribution being analyzed. For example, o f
the 57.7 percent o f the 10th percentile o f income’s forecast variance that is explained by all three
income innovations, roughly three-quarters is due to innovations at the 10th percentile. Likewise,
approximately 90 percent o f the 90th income percentile’s forecast variance that is explained by
income innovations is due to innovations at the 90th percentile. Depending on ordering, tract
average house values and average room size explain an additional 13 to 37 percent o f income
forecast variance, with the high end o f this estimate resulting from the 90th percentile
decomposition. Innovations in tract racial composition explain seven percent o f the low-income
distribution’s forecast variance but only 1.5 percent o f the high-income forecast variance. Even
when ordered near the end of the Choleski decomposition, shocks to county income are
important throughout the income distribution but seem to explain more forecast variance at the
high end than the low end of the income distribution.




21

Finally, approximately one half o f average housing value forecast variance is due to own
innovations. County average income is especially important to house values, explaining over 11
percent o f forecast variance even when ordered last. Slightly less than 27 percent o f house value
forecast variance is due to income innovations, with most o f this due to innovations at the high
end o f the income distribution. Racial composition explains less than three percent o f housing
value forecast variance.
Generally, the results o f the variance decomposition point to four conclusions. First, race
appears to be independent o f income and housing characteristics. Second, income and house
values are highly correlated with each other. Therefore, the impulses arising from income and
housing value data are somewhat sensitive to the ordering o f the system. Third, despite the
coiTellation between income and house values, all variables are fairly persistent, even when
ordering allows lower bound estimates o f the share o f own innovations on forecast variance.
Finally, an important part o f forecast variance, especially house value and racial composition,
arises from common shocks to county characteristics.
Impulses
Table 5 reports impulse response results. Each row lists the cumulative effect o f a one­
tim e, one standard deviation shock to the key income, race, and housing variables in the system
on the other variables in system, keeping eveiything else constant at time t. Unlike the variance
decomposition results from table 4, in this exercise, each row’s variable is ordered first in the
system.

Therefore, it receives all common innovations to tract and county measures.

But

because common components between correlated residuals w ill be attributed to this innovation,




22

these impulse responses are upper bound estimates o f the cumulative effect from a shock. The
next section reports some sensitivity checks on the VAR ordering.
The first four categories describe the cumulative effect of a one standard deviation shock
to county income, labor force participation, and racial composition on tract composition.

A

county income shock increases tract income throughout the income distribution, but more
substantially at the high end o f the distribution. After twenty years, tract income at the 10th
percentile increases by 0.37 standard deviations, at the 50th percentile by 0.38 standard
deviations, and at the 90* percentile by 0.52 standard deviations. This implies that a $8,680
increase in county mean income leads to a $2,600 increase in income among the poorest fam ilies
o f the average census tract, a $5,600 increase among the median family, and a $20,500 increase
among the wealthiest families. County income shocks lead to a slight decline o f 0.06 standard
deviations (or 1.4 percent) in the share o f Blacks and a slight increase o f 0.08 standard deviations
(1.1 percent) in the share o f Hispanics. The positive shock to local labor market incom e also
leads to an increase in average house value o f 0.53 standard deviations or $37,800 and a
temporary increase in new home building that disappears by the second step. Similar but muted
reactions occur from a one standard deviation shock to county labor force participation.
The next two rows report the impact o f a one standard deviation shock to county racial
composition. An one standard deviation or 11.8 percent shock to a county’s share o f Black
residents leads to a drop in tract income o f 0.06 to 0.10 standard deviations (or $700 at the 10*
percentile and $3,100 at the 90* percentile) and a drop in home values o f 0.10 standard
deviations or $7,100. New home building declines as w ell. A similar one standard deviation or
10.6 percent shock to Hispanic share in the county increases income by 0.04 to 0.10 standard




23

deviations (or $300 at the 10th percentile and $3,900 at the 90th percentile) and housing values by
0.20 standard deviations or $14,300. The Hispanic shock has no effect on new home building.
The next two rows describe the effects that arise from a one standard deviation shock to
community racial composition. As noted in the variance decomposition, innovations to racial
composition are persistent. This is quantified by the cumulative effect from a shock to itself. In
the case o f fraction Black, an initial one standard deviation or 23.7 percent shock diminishes to
only 0.97 standard deviations in the second period. An initial one standard deviation or 14.5
percent shock to fraction Hispanic even grows to 1.02 standard deviations by the second step. A
consequence o f this permanent increase to minority share is a reduction in tract income. For the
fraction Black shock, the impact is particularly strong at the 10th percentile. The innovation leads
to a 0.30 standard deviation or $2,100 drop in income, roughly three times the size o f the county
fraction Black shock. The median and 90th percentile o f income and average house value drops
by approximately 0.17 standard deviations (or $2,400 at median income, $7,000 at the 90th
percentile o f income, and $12,000 at the average housing value). A shock to fraction Hispanic
leads to a 0.10 standard deviation decline in income that is independent o f the point in the
distribution analyzed and, notably, has no effect on house values. New home building arising
from shocks to tract racial composition decline by approximately the same as one standard
deviation shocks to county racial composition.
The next three categories report impulses due to shocks to the 10th, 50th, and 90th
percentile o f tract income. There are several differences between the three incom e levels that are
worth noting. First, persistence is highest at the upper end o f the distribution. The second step
impulse declines only slightly to 0.91 standard deviations for the 90th percentile o f incom e,




24

whereas the second step effect from a shock to median income falls to 0.38 standard deviations
and the corresponding result for the 10th percentile is 0.61 standard deviations. Income shocks
lead to a decline in minority representation, with the largest effect resulting from impulses at the
10th income percentile.
A one standard deviation shock to income at the 90th percentile has the largest effect on
housing value, increasing values by 0.53 standard deviations. By comparison, a one standard
deviation innovation to median income increases average house value by roughly 0.33 standard
deviations, and a one standard deviation innovation to the 10th income percentile increases house
value by 0.32 standard deviations. However, since moving up the income distribution increases
the variance o f income, the dollar-for-dollar effects look larger for poorest members o f the tract.
For example, a one standard deviation shock at the 90th percentile is equivalent to roughly
$39,405 and leads to a $37,800 increase in average house values.

A similar one standard

deviation shock at median income would equate to a $14,780 increase in income and a $23,500
increase in housing values. Finally, a shock at the 10th percentile o f income would result in a
$6,944 increase in income and a $22,800 increase in average house values.
Finally, responses to house value shocks are similar to high-income impulses. Housing
values are persistent, as 85 percent of the one standard deviation or $71,353 shock remains after
two periods. The house value shock increase income at the 10th, 50th, and 90th percentiles, with
the largest effect occurring at the high end. Fraction Black declines by 0.22 standard deviations
or 5.2 percent, but there is no effect on fraction Hispanic. Home building increases temporarily.
In sum, the basic VAR model gives a number o f insights about the evolution o f
neighborhoods in a simple Markov process world. First, both the variance decomposition and




25

impulse responses suggest that county-level shocks play an important role in tract evolution.
County average income innovations explain a share o f forecast variance in tract income and
house values, although the exact amount is sensitive to ordering. The spillover effects from
impulses to county income are particularly strong among high-income fam ilies in a tract,
suggesting that labor market conditions have a larger effect on wealthier fam ilies. However, the
impact o f labor markets on low-income families is quite important as w ell. Second, tract racial
composition is highly persistent with very little, if any, dampening twenty years after an initial
one standard deviation shock. Third, tract income is also persistent, especially at the high end o f
the income distribution. There is some feedback effects o f shocks to race on income and income
on race. But to some degree, racial and income sorting are independent o f each other; the vast
majority o f forecast variance in tract racial composition is due to its own innovations, as w ell as
innovations to county racial composition. Likewise, tract racial composition explains less than
10 percent o f the forecast variance in income. Finally, house values are also highly persistent
and have important positive feedback effects on high-income families and negative effects on
fraction Black but not Hispanic residents.
Two Caveats: Ordering and Stationaritv
Before presenting results on neighborhood heterogeneity and spatial dependence, two
important caveats need to be explored. Table 6 report results on the importance o f system
ordering. For each variable, two sets o f second step impulses are reported. The first row, labeled
‘Order,’ shows the cumulative effect o f an impulse where the order o f variables is consistently
maintained throughout the table. In particular, the variables are ordered first-to-last as fraction
Black, fraction Hispanic, 50th income percentile, 90th income percentile, 10th income percentile,




26

house value, housing age distribution, average room size, county average income, county labor
force participation, county fraction Black, and county fraction Hispanic. The second row, labeled
‘first,’ reports the second step impulses from table 5.

The results differ in how the

orthogonalization o f common components o f the error terms is distributed.
Two important implications arise. First, ordering makes no difference to the race results.
As has already been argued, race appears to be independent o f other neighborhood
characteristics. Consistent with this observation, the negative racial feedback effect from shocks
to income seems to be somewhat sensitive to ordering. Second, because o f the collinearity o f the
income and house value measures, the effects from income and house price shocks are generally
smaller. However, note that the persistence o f the 90th income percentile and average house
value remains fairly undisturbed.

Overall, these results point to some obvious caution in

interpreting the findings. Results from table 5 pertain to a very specific question; what happens
if the entire shock can be attributed to one variable. If there is a shock that affects more than one
variable, ordering matters and some results may be sensitive to the Choleski framework.
A second caveat is related to the time-series analyzed. The results presented thus far
depend on cross-sectional and time-series variation in the data. But as noted already, the timeseries is limited to the 1970s and 1980s. Given the important changes in income and racial
dynamics over this time, it is important to ask how similar the impulse responses are over the two
decades. Table 7 reports two step impulse responses using 1970-80 and 1980-90 data separately.
The second column, labeled “year,” notes which o f the two time periods is used. There are some
critical differences across decades that wind up being averaged out in table 5. In particular, in
virtually every case, the income effects that arise from the 1980-90 regressions are larger than




27

those that arise from the 1970-80 analysis. For example, using the 1970-80 data, a one standard
deviation shock to county income results in a 0.19, 0.11, and 0.26 standard deviation increase in
the 10th, 50th, and 90th percentile o f income. The comparable figures for the 1980-90 data are
0.51, 0.69, and 0.68 standard deviations, over two and a half times larger.

A similar story

appears with regard to shocks to tract income and house value. But the cumulative effects that
arise from impulses to racial composition are similar across decades. These findings suggest
critical differences between decades. Income and housing values were much more persistent in
the 1980s than the 1970s, although there appears to be little change in racial dynamics between
the decades. The results also suggest that the forecasts o f neighborhood characteristics that rely
on a single decade (or even two decades) must be cautiously interpreted.
High-Minoritv. Low-Income, and High-Income Neighborhoods
Given particular policy interest in the dynamics o f high-minority and low-incom e
neighborhoods, tables 8 to 10 report the impulse responses in subsamples o f such tracts. Table 8
reports impulses from a subsample o f tracts where the Black population is at least 20 percent in
one o f the three census years. Table 9 is an analogous table for tracts with at least 20 percent
Hispanic, and table 10 reports results from tracts that are in the bottom and top quartile o f their
state’s income distribution in 1970.
Many o f the results are similar across neighborhood types, particularly those related to
racial composition. A few notable differences do emerge. Perhaps o f most interest is that shocks
to county average income have smaller effects on housing values and income in tracts with over
20 percent Black residents or are poorer, although neighborhoods with a high share o f Hispanic




28

residents look identical to the average tract. These results suggest that positive labor market
shocks do not have as large an impact in mostly Black or poor neighborhoods.
Generally, though, it is the similarity o f the results across neighborhood types that is most
striking. It is difficult to point to substantial heterogeneity in tract impulses by minority status.
There is some mild evidence that income shocks to the 10th and 50th percentile are stronger in
high-minority neighborhoods, seeming to point to a stronger tie between median and low-income
residents in these communities. This shows up in two ways: in larger feedback effects from
shocks to the 10th percentile income on median income and conversely from median income on
10th percentile income. Additionally the results in tables 8 and 9 point to weak evidence that
additional segregation (e.g. shock to fraction Black in high Black neighborhoods and fraction
Hispanic in high Hispanic neighborhoods) has more negative consequences on income than in
the all neighborhood sample, but it is important to emphasize that these results are not strong.
Furthermore, there is virtually no difference in the housing price effect o f additional segregation
relative to the full sample results from table 5.
The Feedback Effects from Nearby Neighborhoods
In the previous section, it was assumed that all neighborhoods in a county have an equal
feedback effect on an individual community’s evolution.

However, it is likely that nearby

neighborhoods have stronger feedback effects on the composition o f a neighborhood due to the
clustering o f similar residents in areas of a city. Therefore, the basic VAR model is reevaluated
after controlling for the income, housing, and racial composition o f close communities. The




29

nearby communities are defined as the unweighted average of the five closest neighborhoods that
are within ten miles of the tract’ center.17
s
Separate likelihood ratio tests o f the nearby neighborhood average income, income
shares, and racial composition variables reject the null at the one percent level that these
variables are equal to zero in the VAR specification.

In fact, the impact o f spatially close

neighborhoods appears to be large. These results are summarized in table 11. They suggest that
lagged racial composition o f nearby neighborhoods is important for the current and future racial
distribution o f a neighborhood. A one standard deviation shock to the fraction o f the five nearby
neighborhoods that is Black or Hispanic has a 0.50 to 0.60 standard deviation impact on the
fraction o f minorities in the neighborhood o f interest which is not shocked. By comparison, table
5 shows that the impact o f an innovation on a tract’s own minority share is close to one at the
second step.

Most o f the nearby neighborhood effect occurs in the first period, but little

dampening follows in the second period. Variance decompositions (not shown) indicate that
approximately 26 to 28 percent o f the forecast variance o f neighborhood racial composition is
due to nearby neighborhoods; by comparison, five (14) percent is due to county fraction Black
(Hispanic) and 55 to 60 percent is due to own racial composition.
The impact o f nearby neighborhood racial shocks on own neighborhood income levels is
negative and smaller than own tract racial shocks. The income spillover effects are larger from

17 Longitude and latitude data is available for 1990. Therefore, this analysis only includes tracts in 1970 and 1980
that can be traced to 1990.
The distance between tract i and tract j is approximated as
^(lonj - Ionj)2+(latj - latp2*69.1, where Ion, lat are the longitude and latitude of the center of the census tract and
69.1 is the constant used to convert longitude/latitude degrees to miles. See Van Nostrand (1977). This formula is
not entirely accurate because of the spherical nature of the earth. However, it is accurate enough for my purposes
since I am primarily interested in the ordinal properties of this distance calculation and because the distances
calculated are relatively short (i.e. lessening the spherical bias).
30




innovations to nearby neighborhood’s fraction Black than fraction Hispanic, and appear to have a
larger impact at the low end o f the own neighborhood income distribution. Average house value
and new home building drops due to a shock in the fraction Black o f a nearby neighborhood but
increase slightly from a shock in fraction Hispanic and are generally o f the same magnitude as
shocks to a tract’s own racial composition.
Similar to racial composition, the spatial dependence o f nearby neighborhood income
conditions on own neighborhood income conditions appears to be o f some importance. Variance
decompositions (not shown) indicate that approximately 22 to 28 percent o f the forecast variance
o f neighborhood income composition are due to nearby neighborhoods.

An one standard

deviation innovation to the nearby neighborhood's median income has a cumulative two period
effect on neighborhood median income o f 0.32 standard deviations, almost as much as the 0.38
standard deviation impact from a neighborhood’s own median income innovation. Impulses
from nearby neighborhood shocks to the 10* and 90th percentile o f income are smaller than
comparable impulses from the tract’s own innovation. For example, the two step impulse from a
one standard deviation shock to nearby neighbor’s 90th income percentile leads to a 0.35 standard
deviation increase in a tracts own 90th income percentile, quite a bit lower than the 0.91 standard
deviation impulse from a shock to own tract’s 90th income percentile. Additionally, shocks to
nearby neighborhood income has a negative impact on the fraction o f a neighborhood that is
Black, but no discernible effect on the fraction that is Hispanic. In particular, the largest impulse
arises from a positive one standard deviation shock to the 10th income percentile, which leads to
a fall in the fraction o f black residents by 0.13 standard deviations. A comparable result arising
from the same shock in the tract reduces fraction Black by 0.20 standard deviations. Housing




3
1

value impulses arising from nearby neighborhood income shocks are relatively similar to own
tract shocks, although shocks at the high end o f the income distribution appear to be a bit smaller
when they com e from nearby communities.
Finally, shocks to house values and home building are o f similar magnitude whether they
arise within the tract or from nearby tracts that are within five miles. Therefore, the tract appears
to be too narrow a definition o f neighborhood when exploring the impact o f shocks to
demographics on house value and shocks to house value on demographics.
Overall, it appears that there are contagion effects from innovations to nearby
neighborhood characteristics. It is estimated that nearby neighborhoods account for roughly onequarter o f the forecast variance in a neighborhood’s racial or income composition. Thus, in most
cases, especially those related to race, nearby neighborhoods exert an important but clearly
smaller impact on tract composition than innovations to own tract composition. But in some
cases, particularly those related to house value, the impact from impulses to nearby neighborhood
characteristics is roughly the same magnitude as own tract impulses, suggesting perhaps that the
tract is too narrow a geographic unit for analysis.
Adding Fixed Effects
Since much o f the variation used to estimate the statistical models is cross-sectional, there
is clear concern about neighborhood heterogeneity. As currently constructed, the possibility o f
an individual error component in the VAR is ignored, implying that the tim e-series relationship
between the variables is the same for all cross-sectional units.

However, it is a reasonable

conjecture that characteristics of an area, such as proximity o f the neighborhood to a lake or a




32

toxic waste dump or statewide policies that impact migration dynamics,18 might affect the
migration decisions o f households.
Adding fixed effects at the state or county level can control some o f this heterogeneity.
Table 12 reports second step impulses with such fixed effects. The results are reasonably similar
to those reported in table 5. Perhaps the most important difference is that the Hispanic results
look more like the Black results when county or state fixed effects is introduced. A lso, the
county income and employment shocks are muted when county fixed effects is included.
But, in all likelihood,

alteration does not control for the local heterogeneity issues

that might be more important to neighborhood evolution. To control for neighborhood fixed
effects, a method introduced in Arellano and Bover (1995) is employed. These authors show that
first difference stationary variables are valid instruments if they are constantly correlated with the
individual effect and are uncorrelated with the white noise error term. Table 13 uses the vector
o f lagged first difference county and tract income and race measures as instruments. The table
reports two figures for each cell. The top number in a cell, labeled ‘FE,’ gives the cumulative
two step effect from a one standard deviation shock to a variable on each o f the other variables in
the system using the individual effects specification. The bottom number, labeled ‘Basic,* gives
the second step impulse from a basic VAR that uses a comparable sample o f tracts. The second
lag used for the instruments requires that the basic model’s sample be trimmed to include only
tracts available in all three census years.
Although the signs o f the impulses are usually the same across the models, the
magnitudes o f the impulses are often different. M ost importantly, the results suggest larger

1 For example, see Aaronson (1999) on the effect of school finance reform on school district income sorting.
8




33

incom e effects due to tract and county income shocks and a larger negative effect on fraction
minority from low and median income shocks. On the housing side, the results are essentially
the same across the models except that the relationship between fraction Hispanic and housing
values, which was essentially zero in the basic model, is large and negative in the fixed effect
version. Thesrefore, with some notable exceptions, I conclude that the results are reasonably
robust to heterogeneity issues, but remain cautious due to the sensitivity o f the results to the form
o f the instrumental variable specification.

V.

Conclusions
This paper reports descriptive findings on the evolution o f census tracts in the United

States between 1970 and 1990.

The empirical techniques allow a more complete, albeit

atheoretical, description o f important systematic facts about neighborhood race, income, and
housing dynamics. A number o f insights about neighborhood evolution emerge.
First, tract racial composition is extremely persistent. A temporary shock to the racial
composition o f a neighborhood dampens very little twenty years after the innovation. Tract
incom e is persistent as w ell, especially at the high end o f the income distribution.

Taken

together, the overwhelming amount o f evidence suggests racial and income sorting are relatively
independent o f each other. Second, housing price dynamics mirror the dynamics o f high-income
households in the community; they are highly persistent and have some important positive
feedback effects on high-income fam ilies and negative effects on fraction Black but not Hispanic
residents. Third, there are differences, but notably a striking amount o f homogeneity, in the
evolution o f neighborhoods. Fourth, spatial dependence matters. Spillover effects from nearby




34

neighborhoods are important, and in one notable case, indistinguishable from own tract effects.
With respect to race and income dynamics, the cumulative effect o f shocks are ordered in a
monotonic way. Impulses within a tract are most important, nearby neighborhoods matter a little
less, and counties matter the least, although are still statistically important. The one exception to
this spatial ordering is housing value dynamics where the tract appears to be too small a unit to
describe house value evolution.

Finally, county-level shocks play a role in tract evolution.

W hile this may not be a surprise, the size o f the impact is not trivial. Furthermore, there appears
to be some heterogeneity in these county spillover effects. Positive county income impulses are
particularly strong among high-income fam ilies, suggesting that labor market conditions have a
larger effect on wealthier families.

However, the impact o f labor markets on low-income

fam ilies is important as well.
Given the growing evidence on the importance o f communities, understanding
neighborhood dynamics appears to be an important but understudied component o f the literature.
In future work, I plan to study persistence and feedback effects o f other important demographic
characteristics o f communities, including ethnicity, education, age, and single household headed
fam ilies, as w ell as study the implications o f county and neighborhood amenities such as air
quality or distance to center city on future growth. An important enhancement to the current
analysis w ill be to study specific shocks that might be plausibly identified to particular
community demographics.

Possible avenues include changes in neighborhood and county

amenities, school finance reform, state revenue and expenditure limitation laws, or neighborhood
development programs.

Identifying shocks w ill improve understanding o f neighborhood

dynamics and help to characterize any heterogeneous impact o f these shocks.




35

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38

Table 1
Composition of Metropolitan Tract/BNA Sample

Panel A: Decom position of tract sam ple
Total number of metropolitan tracts/BNAs, 1970-901

53,998
58.7
0.1
10.8
0.1
5.6
24.6

Fraction in 70,80,90
Fraction in 70,80 only
Fraction in 80,90 only
Fraction in 70 only
Fraction in 80 only
Fraction in 90 only

37,461
84.7
15.3

Number in final sample
fraction in all three years
fraction in two years

Panel B: Descriptive statistics on final sam ple 2
Average family income On 1990$)
10th percentile of family income On 1990$)
50th percentile of family income (in 1990$)
90th percentile of family income (in 1990$)
Fraction Black
Fraction Hispanic
Average house value (in 1990$)
Average number of rooms in house
Fraction of houses less than 1 year
Fraction of houses 2-5 years
Fraction of houses 5-10 years
Fraction of houses 10-20 years
Fraction of houses 20-30 years
Fraction of houses more than 30 years
County average income
County labor force participation rate
County fraction Black
County fraction Hispanic

Mean
Std dev. Minimum Maximum
42,263
17,566
3,976
423,804
14,251
6,944
301
136,566
14,780
1,506
38,612
185,900
77,216
39,405
10,096
934,812
23.7
0
100
11.6
6.9
0
14.5
100
98,325
71,353
1,544
607,500
5.3
0.9
1.0
9.7
2.6
0
4.4
100
0
8.4
9.4
100
10.5
0
100
10.0
20.4
0
100
14.6
16.5
0
12.0
100
41.5
28.5
0
100
42,511
62.3
12.0
7.0

8,680
5.4
11.8
10.6

20,773
18.4
0
0

81,846
80.4
72.1
93.9

Notes:
1 D oes not include tracts with missing income, race, and housing data. Tracts with greater
income growth above 500 percent between census years are also not Included.
2 Income and race variables are weighted by familes in tract. Housing variables are weighted
by total housing units in tract.




Table 2
Theil Statistics and Mean Simulation Errors of Key Variables

Unweighted
Mean in 90
(1)
A. A ll census tracts
10th pictl of family income
50th prctl of family income
90th prctl of family income
Fraction Black
Fraction Hispanic
Average house value
90/10 income ratio: actual
90/10 income ratio: predicted

Theil U
Statistic
(2)

13,230
36,914
81,757
15.97
8.81
114,845
6.18
4.50

0.131
0.143
0.187
0.117
0.140
0.182

6,346
22303
54374
35.33
16.71
78,772
8.60
7.29

0.196
0.164
0.154
0.089
0.128
0.247

C. Middle income tracts in 1970 ( l
10th prctl of family income
50th prctl of family income
90th pictl of family income
Fraction Black
Fraction Hispanic
Average house value
90/10 income ratio: actual
90/10 income ratio: predicted

12,729
35,720
73,794
14.27
9.43
108,920
5.80
5.38

0.153
0.141

D. Hieh income tracts in 1970 Cl
10th prctl of family income
50th pictl of family income
90th prctl of family income
Fraction Black
Fraction Hispanic
Average house value
90/10 income ratio: actual
90/10 income ratio: predicted

21331
54,985
131,160
7.27
435
182,329
6.09
5.04

B. Low income tracts in 1970 (1
10th prctl of family income
50th prctl of family income
90th prctl of family income
Fraction Black
Fraction Hispanic
Average house value
90/10 income ratio: actual
90/10 income ratio: predicted

0.122
0.130
0.142
0.191

0.123
0.103
0.230
0.188
0.215
0.159

Decomposition of Theil U
Mean
Variance
Covariance
(3)
(4)
(5)

0.090

0.012
0.050
0.038
0.056

0.000

0.092
0.123
0.008
0.023
0.060

0.001

0.047
0.052
0373
0.016
0.041

3,286
485
-7,361
1.45
1.30
51

7,909
3,252
15,196
4.87
3.35
37346

0.007
0.008
0.244
0.042
0.044
0.030

0.901
0.869
0.748
0.935
0.896
0.969

934
2,970
-1336
1.41
1.91
-1,513

2,253
6,061
9,972
6.06
4.92
30,085

0.904
0.839
0.624
0.943
0.938
0.944

434
4,438
-3,022
1.67
1.31
-1,864

3,259
8,129
10,871
5.00
3.38
35,915

0.966

-732
-1,238
-26,322
1.34
1.41
-4,108

4,116
8,429
31,689
4.15
2.71
51,899

0.001

0.010

0.086

0.000

0.001

0.055

0.017

0.017
0.303
0382
0.054
0.038
0.036

0.183
0.046
0.119
0.004

0.348
0.007

0.001

0.686
0.235
0.900
0.843
0.960

Notes:
1) Low, middle, and high income tracts are those with median income in the bottom, middle two, and top
quartile of their state.




Mean abs.
simulation
error
(7)

0.863
0.936
0.377
0.961
0.928
0.959

0.161
0.028
0.050
0.061

0.011

Mean
simulation
error
(6)

Table 3
Vector Autoregression Coefficients Using Basic Model
family Income: 10th prctl
(2)
(1)
10th prctl of family income
50th prctl of family income
90th prctl of family income
Fraction Black
Fraction Hispanic
Average house value
Average number of rooms
Fraction homes < year
1
Fraction homes 2-5 years
Fraction homes 10-20 years
Fraction homes 20-30 years
Fraction homes >30 years
County average family income
County adult LF participation rate
County fraction Black
County fraction Hispanic
Constant
Year is 1990
R-bar squared

0.349
0.177
0.055
-0.005
-0.004
0.214
0.144
0.001

0.000
o.ooo
0.001
-0.001
0.014
0.003

0.000
0.001
-2.628
-0.092

0.004
0.006
0.007

0.000
0.000
0.004
0.002

0.000
0.000
0.000
0.000
0.000
0.011

0.000
0.000
0.000
0.103
0.003




-0.546
0.013
-1.759
•0.036
0.969
-0.315
-0.768
-0.016
-0.031
-0.009
-0.005
-0.007
7.290
0.017
0.025
0.271
-59.599
-1.005

nor
t*

0.155
0.156
0.273
-0.003
-0.003
0.140
0.075

0.003
0.005
0.005

0.000

0.000
0.000
0.000
0.000
0.000

-0.001

0.000
0.000
0.000
0.001
0.001
0.001
0.002
-0.491
-0.102

0.000
0.000
0.003
0.002

0.009

0.000
0.000
0.000
0.079
0.002

0.698

0.750
Fraction Hispanic
(10)
(9)

10th prctl of family income
50th prctl of family income
90th prctl of family income
Fraction Black
Fraction Hispanic
Average house value
Average number of rooms
Fraction homes <1 year
Fraction homes 2-5 years
Fraction homes 10-20 years
Fraction homes 20-30 years
Fraction homes >30 years
County average family income
County adult LF participation rate
County fraction Black
County fraction Hispanic
Constant
Year is 1990

family Income: 50th prctl
(4)
(3)

0.082

0.111
0.128
0.001
0.002
0.066
0.037
0.006
0.005
0.003
0.003
0.002
0.209
0.006
0.002
0.004
1.893
0.055

0.000
0.010
-1.310
0.034

r
y

-0.016
0.019
0.726

0.003
0.004
0.004

0.000

0.000
0.000

-0.001
0.164
0.051

0.000
0.000
0.000
-0.001

0.000
0.006
-0.001
0.001
0.002
-0.957
0.051

0.002
0.001

0.000
0.000
0.000
0.000
0.000
0.007

0.000
0.000
0.000
0.061
0.002

0.775

Average house value
(12)
(i d
-0.011
-0.049
0.401
-0.002
-0.001
0.736
-0.036
-0.004
-0.004
-0.001
-0.003
-0.002
0.327
-0.003

family income: 90th prctl
(6)
(5)

0.006
0.008
0.009

0.000
0.000
0.005
0.003

0.000
0.000
0.000
0.000
0.000
0.015

0.000
0.000
0.000
0.131
0.004

0.000
15.269
-1.056

r 4do
\

1.445
1.505
-1.183
0.953
-0.023
-2.340
-0.745
-0.014
-0.025
-0.011
0.012
-0.004
4.609
-0.007
0.203
0.007
-20.494
-1.229

0.125
0.169
0.195
0.002
0.004
0.100
0.056
0.009
0.007
0.005
0.004
0.004
0.319
0.010
0.003
0.006

2.888
0.084

0.895

Fraction homes <1 year
(14)
(13)
-0.902
-0.272
-0.383
-0.009
0.003
0.538
0.429
0.105
0.013
-0.031
-0.030
-0.037
-1.390
0.015
-0.011

_______Fraction Black
(7)
(8)

0.045
0.060
0.070

0.001
0.001
0.036
0.020
0.003
0.003
0.002
0.002
0.001
0.114
0.003
0.001
0.002
1.031
0.030

Fraction homes 2-5 years
(15)
(16)
-2.206
-0.744
-1.163
-0.029
0.002
1.086
1.323
0.302
0.052
-0.103
-0.118
-0.128
-5.112
0.095
-0.036
-0.002
57.531
-0.272
ry o e rn

0.092
0.124
0.143
0.001
0.003
0.073
0.041
0.006
0.005
0.004
0.003
0.003
0.234
0.007
0.003
0.004
2.115
0.061

Table 4
Variance Decomposition of VAR Using the Basic Mo 'el

Relative
variance in (1

Fraction Black in Tract

Share of forecast variance in second step due to
County County County Housing Average Average Tract
Tract
County
Tract
Tract
Tract
age number of house
fraction fraction income at income at income at Ordering of
Standard average lbr force fraction fraction
error
value Hispanic Black lQ-pgre. 5Qperc. 90 perc. variables (2
ingoing participtn Black Hispanic iJistributior rooms
(10)
(6)
(7)
(9)
(12)
(4)
(5)
(2)
(3)
(8)
(13)
(14)
(11)
a)
12.26

0.3

Tract income at 50th percentile

Tract income at 90th percentile

Average house value

0.1

1.2

0.2

3.7

2.0

83.1

5.7

0.0

2.0

0.0

13.6

0.3

0.1
1.2

3.0
0.7

79.5

0.1
0.0

0.2

2.1

0.1

2.3

6.9

0.1
8.8

79.5
0.9

2.5

0.39

0.1
0.0

13.2

17.2

0.0
0.0

0.2
0.0

0.1
0.2

5.0
1.3

7.5
5.2

19.7

0.29

3.3
18.8

0.8
1.0

5.6
3.0

0.0
0.0

0.1
0.1

0.2

3.8

0.5

0.8

5.8
5.3

21.0

0.26

4.0
24.0

13.7

0.8
0.6

0.8

0.53

4.1
33.0

0.0
0.0

0.1
0.1

5.9
0.5

31.3
51.3

0.5
0.5

8.28

0.3

1.0
Tract income at 10th percentile

5.6

0.0
0.0

1.2
Fraction Hispanic in Tract .

0.0

0.1

3.2

4.2

0.8

8.6

2.0

83.1
2.5

6.1

2.5

2.8
3.4
2.4
0.5
0.9
0.4
44.6
44.6
44.6
10.9
14.3
10.9

0.6

0.1
1.6
0.1

2.3

0.3

1.1
2.2

3.22

11.4
1.7

0.0

0.2

3.9

0.3

0.5

0.0

3.6
95.1

0.5
0.3

51.3
0.5

0.0
0.1

2.4
0.5

0.7

0.3

Fraction of homes < 1 year

0.3

0.4

0.0

95.1

0.3

0.8

0.0

0.8

0.8
1.0

0.0
0.0
0.0
0.1
0.1
0.0
10.8
12.9

10.8
41.8
41.8
41.8
5.3
3.8
5.3

0.1
0.1
0.5

0.1
0.1
0.1

0.9 90,10,50
0.4 10,90,50
0.5 county last
1.1 90,10,50
0.8 10,90,50
0.8 county last
2.4 90,50,10
0.2 50,90,10
2.4 county last
9.2 90,10,50
5.8 10,90,50
9.2 county last
48.8 50,10,90
48.8 10,50,90
48.8 county last
7.0 90,10,50
6.2 10,90,50
24.0 county last
0.2 90,10,50
0.1 10,90,50
0.9 county last

Notes:
1) Share of forecast variance in the 2nd step.
2) Column (14) refers to the ordering of the variabless used in the Choleski factorization to orthogonalize the innovations. Three different orderings are reported. Each is based
on the following general ordering: county average income, county labor force participation rate, county fraction Black, county fraction Hispanic, housing age distribution,
average number of rooms, house value, tract fraction Black, tract fraction Hispanic, and the three income variables. However, each variable is ordered last when the its own
variance is decomposed. In the first two subrows of each row, the income variables are switched in order. *90* is the 90th percentile, *50* is the 50th percentile, and *10’ is
the 10th percentile. So 90,10,50 implies that the 90th percentile is ordered first, then the 10th percentile, and finally the median income level. In the subrows
labeled ’county last,’ the county variables are ordered next to last, with the group of variables, say the three income variables, being decomposed still last.



Table 5
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Basic Model

One std dev shock to

County avg income
County labor force
participation rate
County fraction Black
County fraction Hispanic

Fraction Black in tract
Fraction Hispanic in tract

Tract income at 10th ptct
Tract income at 50th prtc
Tract income at 90th prct

Average house value
Fraction of homes
< l year




Step

1
2
1
2
1
2
1
2

Tract income at
10th prot 50th prot 90th prct
(2)
(3)
(1)
0.35
0.37

0.02

0.02

0.45
0.52
0.25
0.28
-0.08
-0.08
0.03

0.04

0.06

0.10

0.26
-0.03
-0.05

1
2
1
2

-0.24
-0.30
-0.10
-0.11

-0.13
-0.16
-0.08
-0.08

-0.15
-0.18
-0.09
-0.10

0.97
-0.10
-0.11

t

1.00

2
1
2
1
2

0.61
0.38
0.37
, 0.39
0.43

0.38
0.35

0.39
0.42
0.46
0.51

1
2
1
2

0.34
0.50
0.13
0.14

0.20
0.23
-0.07
-0.10

0.34
0.38
0.17

Cumulative effect on
Avg. house
Tract
Tract
< 1 vears
Black
value
Hispanic
(4)
(5)
(6)
(7)

0.20
-0.07
-0.06

1.00
0.38
0.46
0.52

1.00
0.91

0.32
0.44
0.09

0.11

0.10

0.14

0.46
0.70

-0.06
-0.06
-0.04
-0.05

0.01

0.55
0.53
0.31
0.29
-0.08
-0.10

-0.09
-0.03

0.20
0.20

0.02
0.01

-0.10
-0.13

-0.16
-0.17

1.00
1.02

0.00
0.01

-0.24
-0.20
-0.13
-0.12
-0.15
-0.17

-0.10
-0.11
-0.08
-0.09
-0.09
-0.11

0.34
0.32
0.32
0.33
0.46
0.53

-0.16
-0.22
-0.09
-0.10

0.00

1.00

0.03
-0.02
-0.03

0.85
0.13

0.22

1.00

0.08

0.02
0.07
-0.02
-0.04
0.33
0.42

0.10

0.13

0.00
0.12
0.02

Fraction of homes
2-5 years 10-20 year? 2Q-3Q
(10)
(8)
(9)
0.19
-0.01
0.13
0.04
-0.11
-0.05
-0.01

-0.11

0.12
-0.08
0.09
0.05
-0.12

-0.07
-0.07
-0.05
-0.06
0.08
0.07

-0.10
-0.05
-0.08
-0.08
0.09
0.14

0.00
0.01

0.00

-0.03

0.02
0.01

-0.09
-0.03
-0.02

-0.10
-0.05
-0.03

0.07
-0.05

0.09

0.02

0.10

0.06

0.01

0.00

-0.01

0.03
0.03

-0.02

0.13
-0.05
0.09
-0.02

0.19
-0.05

-0.11

0.12

-0.06
0.09
-0.06

-0.07
-0.06
-0.05
-0.03
-0.06
-0.05

-0.07
0.03
-0.08
-0.01
-0.10
-0.04

-0.05
-0.06
-0.31
-0.42

-0.12
-0.10
-0.31
-0.54

0.11
-0.01
0.13
0.05

1.00
0.18

-0.03
0.16
-0.01
0.18
0.05
0.49
0.29

0.01

>30 years
(11)

0.02

0.10

0.10
-0.06

0.10
-0.35
0.30

0.02

Table 6
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
The Effect of an Ordering System on the Second Step Impulse (1

One std dev shock to

Tract income at
Order 10th prct 50th prct 90th prct
(2)
(1)
(3)

Cumulative effect on
Tract
Avg. house
Tract
< 1 vears
value
Hispanic
Rlask
(6)
(5)
(4) .
(7)
-0.17
-0.17
-0.01

Order
First
Fraction Hispanic in tract Order
First

-0.24
-0.30
-0.13
-O.ll

-0.30
-0.16
-0.14
-0.08

-0.18
-0.18
-0.11
-4 .1
30

0.97
0.97
-0.02
-0.11

-0.13
-0.13

Tract income at 10th ptct Order
First
Tract income at 50th prtc Order
First
Tract income at 90th prct Order
First

0.20

0.33
0.35
0.45
0.38
0.19
0.52

0.03
0.42
0.48
0.51
0.75
0.91

0.03
-0.20
0.03
-0.12
-0.04
-0.17

-0.02
-0.11
-0.01
-0.09
-0.03
-0.11

0.08
0.32
0.32
0.33
0.41
0.53

0.24
0.44

0.30
0.70
0.14

0.04
0.03
-0.01
-0.03

0.66

0.02
0.10

•0.08
-0.22
-0.01
-0.10

Fraction Black in tract

Average house value
Fraction of homes
< 1 year

Order
First
Order
First

0.61
0.45
0.37
0.30
0.43

0.20
0.50

0.01
0.14

0.01

1.01
1.02

0.01

0.85
-0.02

0.10

Fraction of homes
2.-5. years 10-20 years 20-30 years >39 years
(8)
(10)
(9)
(ID

-0.03
-0.03

-0.05
-0.05

0.00
0.01

0.00
0.00

-0.05
-0.05
-0.03
-0.02

-0.05
-0.05
-0.03
-0.03

-0.05
-0.05
-0.02
-0.01
0.04

0.10

0.00

0.00

0.09
0.09
0.05

-0.01

-0.01

0.10

0.06
0.05
0.09
0.18

0.07
0.05

0.04

0.12

-0.25
0.30

0.29

0.10

0.10
0.10
0.04
0.03
-0.01
-0.06
-0.04
-0.03
-0.01
-0.05

-0.01
-0.04
-0.04

-0.03
-0.06
-0.08
-0.42

-0.10
-0.10
-0.05
-0.54

Note:
1) The rows labeled ’Order* are ordered from first to last in the following way: fraction Black, fraction Hispanic, 50th income percentile, 90th income percentile,
10th income percentile, house value, housing age distribution, average room size, county average income, county labor force participation, county Black,
and county Hispanic. The rows labeled ’First* order the variable listed in the first column first.




0.06
0.06
-0.01
-0.02
0.05
0.03

0.01

Table 7
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Second step impulses using 1970-80 and 1980-90 data separately (1

One std dev shock to

Year

Tract income at
10.lh.BlSl SOthprot 90th prct
(2)
(3)
O)

0.11

0.26

0.69
0.07
0.39
-0.09

0.68

Cumulative effect on
Avg. house
Tract
Tract
value
Hispanic
<Ll-ycats
Black
(4)
(5)
(6)
(7)
0.05
0.16
0.06

0.21

0.01

0.01

0.12

0.74

0.06

0.04

0.08

0.20

0.02

0.02

0.11

0.10

0.37
-0.17

0.02

0.04
-0.04
-0.01

0.05
-0.06
-0.02

0.23
0.26

0.01
0.02

0.01
0.01

0.03
-0.10
-0.07
-0.04

-0.04
-0.02
-0.01
0.03

0.18
0.36
-0.13

-0.08
-0.08
-0.04
-0.03
0.26

0.02

0.22

0.17

0.06
0.18

-0.06
-0.05

-0.36
-0.25
-0.14
-0.07

-0.24
-0.25
-0.11
-0.09

-0.19
-0.17
-0.08
-0.09

0.98
0.96
-0.12
-0.15

-0.14
-0.17

-0.22
-0.15

1.02
1.04

0.01
0.02

Tract income at 10th prct 70-80
80-90
Tract income at 50th prct 70-80
80-90
Tract income at 90th prct 70-80
80-90

0.48
0.81
0.62
0.72
0.33
0.51

0.33
0.84
0.65
0.89
0.29
0.81

0.26
0.55
0.51
0.79
0.74
1.08

-0.24
-0.21
-0.02
-0.18
-0.21
-0.17

-0.18
-0.04
-0.15
-0.06
-0.13
-0.10

0.13
0.47
0.07
0.61
0.31
0.67

Average house value

0.39
0.62
0.17

0.21

0.52

1.02

0.83

0.11

0.15

0.07
-0.05

0.91
0.05

0.21

0.12

0.13

0.11

-0.29
-0.22
-0.10
-0.07

0.02

0.86

0.01

0.10

0.15

70-80
80-90
70-80
County labor force
participation rate
80-90
County fraction Black 70-80
80-90
County fraction Hispanic 70-80
80-90

0.19
0.51
0.14
0.30
-0.15

0.01
0.00
0.12

Fraction Black in tract

70-80
80-90
Fraction Hispanic in traci 70-80
80-90

County avg income

Fraction of homes
< 1 year

70-80
80-90
70-80
80-90

0.02
0.00

-0.06
-0.05
0.44
0.39

-0.03
-0.07
-0.03
-0.06
0.09
-0.01

-0.13
-0.05
-0.12
-0.05
0.14
0.08
0.03
-0.02

0.00

0.00
0.01

-0.07
-0.03
-0.01

-0.02
-0.04
-0.02

0.14
0.03
0.05

0.05
0.05

0.02

0.00

0.02

-0.04

-0.04

-0.03

0.01

0.00

0.12
0.02

-0.07
-0.05

-0.09

-0.10

0.01

0.02

0.01

0.08
0.04

-0.02
0.03
0.13

0.03

0.03

0.10

0.01

0.00

0.08

-0.06
-0.07
-0.03

-0.10
-0.04

0.06
0.08

0.11

0.04
0.09
0.30
0.27

-0.05
-0.06
-0.54
-0.25

-0.18
-0.09
-0.62
-0.47

Note:
1) Includes tracts that are matched between the three census years, approximately 85 percent of the total sample.




Fraction of homes
2-5 years .10-20 vears 20-30 vears >30vears
(10)
(8)
(9)
(11)

0.06
0.31
0.26

0.01

0.00

Table 8
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Basic Model
Tracts with Black population greater than 20 percent between 1970 and 1990 (1

One std dev shock to

Step

1
2
County labor force
1
participation rate
2
1
County fraction Black
2
County fraction Hispanic 1
2
County avg income

1
2
Fraction Hispanic in tract 1
2
Fraction Black in tract

Tract income at
H tfa.BIgJ 50th prct SOtlLPlCl
O
(2)
(3)
(1)
0.37
0.35
0.23

0.21

0.22

-0.07
-0.09

-0.09
-0.09

0.02

0.00

0.04

0.05

-0.07
-0.05
-0.01
0.04

-0.27
-0.27

-0.22
-0.26
-0.03
-0.01

-0.22
-0.21
-0.05
-0.02

0.63
0.56

0.42
0.44
0.56
0.56

0.00
-0.01

1.00

-0.11
-0.05
-0.06
-0.05
0.26
0.26
-0.04
-0.06

0.03
0.09
-0.02
0.03
-0.06
-0.12

0.45
0.35
0.28
0.23
-0.08
-0.08

0.22

1.00
0.81
-0.27

0.71

1
2
1
2

0.34
0.46
0.15
0.17

0.35
0.50
0.15
0.16

0.41
0.56
0.13
0.15

-0.19
-0.21
-0.18
-0.21

Average house value
Fraction of homes
< 1 year

1.00

-0.02
-0.04

0.32

0.14

0.01

0.02

0.02

-0.27
-0.33

-0.19
-0.19
0.04
0.08

-0.18
-0.05

-0.25
-0.10

-0.17

0.18
0.13

0.06
0.17

0.00
0.02

0.01
0.02

0.00
0.01

0.00
0.02

0.00

0.34
0.30
0.35
0.31
0.41
0.43

0.15
-0.04
0.15
-0.03
0.13
-0.02

0.19
-0.04
0.17

-0.08
0.09
-0.06
0.04
-0.04
0.07

-0.08
-0.05
-0.07
-0.05
-0.07
-0.05

1.00

0.15
0.04

-0.03
0.08
-0.23
0.35

-0.04
-0.04
-0.23
-0.28

1.00

-0.03
-0.06
-0.05
-0.09
0.04
0.07

0.00
0.01

0.76
0.15
0.13

0.02

0.16

1.00

0.17
0.06
0.46

0.13

0.21

0.11

Note:
1) The sample consists of tracts with at least 20 percent of the population that is Black in one of the three census years. Sample size is 9,691 tracts.




0.00
0.00

0.10

0.12
0.00

o
o
i

0.63
0.56
0.59

1.00

-0.10
-0.02
-0.07
-0.06
0.09

-0.13
-0.04
0.03

0.00
0.00

0.56
0.63
0.56
0.42
0.44

-0.04
-0.03
-0.04
-0.01
0.07
0.04

-0.10
-0.02
0.03

0.97

-0.27
-0.12
-0.23
-0.11
-0.22
-0.16

0.15
-0.03
0.09

-0.05
0.08
-0.02
0.06
0.03
-0.13
-0.01

-0.29

1
2
Tract income at 50th prct 1
2
Tract income at 90th prct 1
2
Tract income at 10th prct

0.14
-0.02

Fraction of homes
3
2-5 rears l&2Q.y«H52Q:■0years >30vears
(8)
(10)
(9)
(ID

o
o
*

0.20
0.20

0.36
0.32
0.23

0.34
0.29

Cumulative effect on
Avg. house
Tract
Tract
value
<1 years
Hispanic
Blask
(6)
(7)
(5)
(4)

0.12

-0.05
-0.07

0.00
-0.08

0.02
-0.08

0.00
-0.11
-0.10
-0.29
-0.44

Table 9
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Basic Model
Tracts with Hispanic population greater than 20 percent between 1970 and 1990 (1

One std dev shock to

Step

1
2
County labor force
1
participation rate
2
County fraction Black
1
2
County fraction Hispanic 1
2
County avg income

Tract income at
10th prct 50th prct 90th prct
(2)
(3)
(1)

-0.08
-0.07

0.43
0.42
0.30
0.28
-0.11
-0.07

0.02

0.01

0.01

0.05

0.04

0.07

0.24
-0.05
-0.08

1
2
Fraction Hispanic in tract 1
2

-0.20
-0.20
-0.14
-0.15

-0.14
-0.16
-0.15
-0.16

-0.14
-0.14
-0.18
-0.18

0.92
-0.19
-0.21

1
2
Tract income at 50th prct 1
2
Tract income at 90th prct 1
2

1.00
0.55
0.56
0.50
0.43
0.45

0.56
0.50

0.43
0.42
0.52
0.51

1
2
1
2

0.34
0.52
0.14
0.15

Fraction Black in tract

Tract income at 10th prct

Average house value
Fraction of homes
< 1 year

0.35
0.35

0.22
0.23
-0.11
-0.10

0.37
0.35
0.24

Cumulative effect on
Avg. house
Tract
Tract
value
< 1 vears
Hispanic
filaek
(4)
(5)
(7)
(6)

0.22

1.00
0.52
0.52
0.55
0.36
0.50

0.12
0.13

0.00

0.15
-0.02

0.16
-0.01

-0.08

0.11

0.11

0.20

-0.02
-0.12
-0.02
0.03

-0.02
-0.11
-0.06
-0.01

0.18

0.00

0.01

-0.07
0.08
0.03
-0.13
0.03
-0.04

-0.07
-0.02
-0.06

0.91

-0.14
-0.12
-0.05
-0.04

-0.07
-0.04
-0.10
-0.02

-0.14
-0.14
-0.15
-0.16
-0.18
-0.25

0.34
0.34
0.36
0.35
0.45
0.50

0.14
-0.05

0.80

-0.20
-0.14
-0.14
-0.08
-0.14
-0.12

0.45
0.64
0.13
0.14

-0.14
-0.19
-0.07
-0.08

-0.05
-0.08
-0.06
-0.09

0.89
0.13
0.08

1.00

-0.07
-0.10
-0.05
-0.10

0.04

0.21

0.01
-0.01
0.28
0.31

1.00

-0.19
-0.21

Fraction of homes
2-5 vears IQbfflLysan 20-30 years >30 year;
(10)
(8)
(9)
(ID

0.05

0.00

1.00

0.50
0.49
0.35
0.29
-0.09
-0.09

1.00

0.00

0.12
-0.03
0.13
-0.01
0.13
0.04

1.00
0.17

0.10

-0.05
-0.04
-0.03
-0.02

0.10

0.10

0.06
0.06
0.03

0.16
-0.03

0.06
-0.01
0.05
-0.06

0.08
0.09
0.08
0.08

-0.03

0.15
-0.04
0.14
-0.02
0.15
-0.01

-0.11
0.07
-0.09
0.05
-0.06
0.09

-0.07
-0.04
-0.06
-0.06
-0.06
-0.05

-0.05
0.04
-0.07
0.04
-0.09
-0.03

0.13
0.06
0.45
0.28

-0.07
0.04
-0.35
0.24

-0.01
-0.05
-0.30
-0.39

-0.08
-0.04
-0.28
-0.51

Note:
1) The sample consists of tracts with at least 20 percent of the population that is Hispanic in one of the three census years. Sample size is 9,245 tracts.




-0.10
-0.05
-0.06
-0.03

0.00

0.01
0.04
0.03

Table 10
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Basic Model
Second step impulses in 1970 high income and low income tracts (1

One std dev shock to

Tract income at
Sam
pj< lOtfLcrei 50th nrct SQlhjtrc.t
(2)
(3)
(l)

County avg income

Low
High
County labor force
Low
participation rate
High
County fraction Black
Low
High
County fraction Hispanic Low
High

0.30
0.51

0.20

0.26
0.38
0.17

0.21

0.32
0.53

0.20

Cumulative effect on
Avg. house
Tract
Tract
value
Black
<Ll years
Hispanic
(4)
(5)
(6)
(7)
-0.07
-0.05
-0.07
-0.01
0.23
0.27
-0.15
-0.02

0.26
-0.08
-0.07
0.07
0.13

-0.10
-0.07
0.07
0.06

0.27
-0.06
-0.09
0.08
0.16

Low
High
Fraction Hispanic in tract Low
High

-0.26
-0.20
-0.05
-0.15

-0.27
-0.28
-0.04
•0.18

•0.18
•0.18
-0.05
-0.11

0.94
1.14
-0.23

Tract income at 10th prct Low
High
Tract income at 50th prct Low
High
Tract income at 90th prct Low
High

0.61
0.69
0.50
0.55
0.58

0.56
0.51
0.50
0.60
0.44
0.36

0.54
0.70
0.38
0.41
0.98

-0.22
-0.18
-0.25
-0.26
-0.16
-0.19

0.49
0.73
0.15
0.09

-0.24
-0.25
-0.13
-0.07

Fraction Black in tract

Average house value
Fraction of homes
< 1 year

Low
High
Low
High

0.66
0.48
0.17

0.43
0.48
0.18

0.10

0.10

0.66

0.66

0.02

0.18
0.03

0.10
0.06
-0.07

0.00
0.45
0.37
-0.25
-0.02

1.00
1.01
-0.04
-0.14

0.01
-0.22
-0.08
-0.09
0.14
-0.07
-0.04

0.02

0.38
0.53
0.25
0.26
-0.08
•0.10
0.19
0.25
-0.19
-0.16
0.07
-0.06

Fraction of homes
2-5 years IQ^Lyfiars 20-30 years >30 vears
(9)
(10)
(8)
(ID

0.01

0.02

0.11

-0.01
-0.01

-0.01

0.15
0.06

0.02

0.03
-0.04
-0.04
0.03
-0.01

-0.04

-0.07
-0.03
-0.01

-0.08
-0.02
-0.03

0.01

0.00

0.06
0.07
-0.02

-0.02
-0.02

0.02
0.00
-0.03
-0.02

0.00
0.02
0.00

0.32
0.50
0.28
0.31
0.40
0.52

-0.07
0.04
-0.02

0.76
0.81
0.13
0.04

0.05
0.04
0.13
0.18

-0.04

0.01

0.02

0.03
-0.04
0.03
-0.07
0.08
-0.02
0.09

0.01
0.25
0.27

-0.04
-0.03

0.01

-0.06
-0.12
-0.05
-0.13

0.11

-0.08

-0.12
-0.08

0.06

0.10
0.12

0.02
0.00

-0.04
0.07

0.10

0.07
0.04
-0.01
-0.03

0.00

0.02

0.16

-0.06

0.12

0.01

0.15

-0.06
-0.01
-0.09

0.11
0.12
0.10
0.15
0.06
0.42
0.23

-0.08
-0.05
-0.07

0.02

0.01

-0.10
-0.09

-0.02
-0.03
-0.22
-0.51

-0.16
-0.07
-0.48
-0.60

Note:
1) The low (high) income sample consists of tracts that have a median income in 1970 that is among the bottom (top) quartile in their state. Sample sizes are 8,478 (1
<
8,493 (high) tracts respectively.



Table 11
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Nearby Neighborhood Characteristics

One std dev shock to
5 nearest neighborhoods’ Step

Fraction Black
Fraction Hispanic

Income at 10th percentile
Income at 50th percentile
Income at 90th percentile

Average house value
Fraction of homes
< 1 year




Tract income at
50th prct 90th prct
(2)
(3)

IQth prct
0)

Cumulative effect on
Tract
Tract
Avg. house
Black
value
< 1 vears
Hispanic
(7)
(4)
(5)
(6)

Fraction of homes
2-5 years 10-20 vears 20-30 vears >30 vears
(10)
(9)
(8)
(11)

1
2
1
2

-0.14
-0.19
-0.03
-0.03

-0.09
-0.15
-0.02
-0.03

-0.09
-0.12
-0.03
-0.02

0.55
0.59
-0.06
-0.09

-0.07
-0.09
0.57
0.69

-0.13
-0.15
0.04
0.06

-0.06
-0.03

-0.07
-0.04

0.04
-0.04

0.06
0.07

0.01
0.01

0.00
0.01

0.00
0.00

0.01
0.01

0.05
-0.02
-0.04

1
2
1
2
1
2

0.42
0.44
0.30
0.34
0.27
0.30

0.33
0.37
0.39
0.32
0.30
6.32

0.30
0.35
0.31
0.35
0.48
0.55

-0.15
-0.13
-0.09
-0.08
-0.08
-0.10

-0.04
-0.03
-0.02

0.36
0.37
0.34
0.34
0.38
0.43

0.11

0.15

-0.06
-0.06
-0.06
-0.05
-0.04
-0.05

-0.06
-0.01
-0.07
-0.04
-0.07
-0.04

1
2
1
2

0.31
0.46

0.32
0.43

0.37
0.56

0.03
0.07

0.12

0.11
0.12

0.10

-0.11
-0.17
-0.08
-0.11

-0.04
-0.06
-0.15
-0.23

-0.05
-0.08
-0.13
-0.28

0.15

0.13

0.01
-0.04
-0.04

0.01
0.00

0.76
0.82
0.13

0.11

-0.01

0.01

0.10
0.00

0.14

0.09

0.13

0.01

0.00

-0.08
0.08
-0.07
0.09
-0.06
0.08

0.11

0.15
0.05
0.26
0.17

-0.07
0.08
-0.16
0.13

0.03
0.35
0.13

0.01

0.02

Table 12
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Second Step Impulses from Model with State and County Fixed Effects

One std dev shock to

Step

Tract income at
lOthprct 50th prct 90th prct
(2)
(3)
0)
0.27
0.31
0.15

Cumulative effect on
Tract
Avg. house
Tract
value
Black
:$_Lyears
Hispanic
(6)
(5)
(7)
(4)
-0.05
-0.03
-0.03
-0.03
0.24
0.23
-0.05

0.23
0.30

0.40
0.46

0.12
0.20

0.20

0.21
-0.09
-0.10
-0.01
-0.03

-0.12
-0.08
-0.03
-0.01

County
State
Fraction Hispanic in tractCounty
State

-0.23
-0.29
-0.13
-0.14

-0.30
-0.23
-0.14
-0.13

•0.18
-0.17
-0.14
-0.13

0.95
0.96
-0.10
-0.09

-0.13
-0.12
0.98

Tract income at 10th prctCounty
State
Tract income at 50th prctCounty
State
Tract income at 90th prctCounty
State

0.41
0.57
0.43
0.47
0.46
0.41

0.41
0.46
0.50
0.46
0.35
0.49

0.44
0.39
0.36
0.48
0.82
0.90

-0.11
-0.20
-0.21
-0.12
-0.15
-0.16

-0.16
-0.14
-0.17
-0.13
-0.19
-0.16

County
State
County
State

0.33
0.45

0.32
0.43
0.13
0.13

0.53
0.67

-0.19
-0.19
-0.09
-0.09

•0.18
-0.12
-0.06
-0.05

County
State
County
County labor force
State
participation rate
County fraction Black County
State
County fraction Hispanic County
State
County avg income

Fraction Black in tract

Average house value
Fraction of homes
< 1 year

0.11
0.16

0.27
-0.07
-0.08

0.02
0.00

0.12
0.14

Note: County = County fixed effects. State = State fixed effects.




0.00

-0.07
-0.01
-0.02
0.04
-0.03

0.02
0.36
0.32

1.00

0.28
0.40
0.16
0.27
-0.08
-0.08
0.04
0.03

Fraction of homes
2-5 years 10-20 vears 20-30 vears >30vears
(10)
(8)
(9)
(H )

-0.04
-0.01
-0.04

-0.05
-0.01
-0.04

0.01
0.00

0.02

-0.03

-0.01
-0.05

-0.05

0.11
-0.04
0.08
-0.03
-0.11
-0.04
-0.04

0.00
0.00

-0.01

-0.17
-0.16
-0.07
-0.06

-0.02
-0.03

-0.04
-0.05

0.00
0.00

-0.01

0.23
0.26
0.29
0.46
0.53

-0.03
-0.04
-0.05
-0.02
-0.02
-0.01

-0.02
-0.03
-0.04
-0.01
-0.02
-0.01

0.03
0.09

0.45

0.01

0.01

0.04

0.66
0.10
0.12

0.04
0.15
0.17

0.05
0.26
0.28

0.11

0.21

0.00

0.00

-0.04
-0.05
-0.02
-0.02
0.04

0.10
0.06

0.10

0.29
0.30

-0.10
-0.08
-0.04
-0.06

0.00
0.07
-0.04
0.03
0.08

0.14
-0.05

0.10
-0.07
0.03
0.13
0.06

0.02

0.11

0.04
0.06

0.03
0.05

-0.01

0.01

-0.09
-0.08
-0.08
-0.08
-0.07
-0.05

-0.04

-0.10
-0.07
-0.38
-0.42

-0.01
-0.13
-0.49
-0.54

0.04

0.01
0.03
-0.02

0.02

Table 13
Cumulative Effects on Income, Racial, and Housing Composition from an One Standard Deviation Shock to Neighborhood and County Characteristics
Second step impulses from Basic Model and Individual Tract Effects Model

One std dev shock to

Tract income at
Model lQthprct 50th prct 90th prct
(3)
(2)
0)
0.40
0.34
0.13

0.64
0.36
0.19

0.20

0.22

0.08
-0.08
0.08
0.05

0.09
-0.10
0.18
0.04

FE
Basic
Fraction Hispanic in traci FE
Basic

-0.41
-0.23
-0.16
-0.11

-0.32
-0.30
-0.22
-0.12

Tract income at 10th prct FE
Basic
Tract income at 50th prct FE
Basic
Tract income at 90th prct FE
Basic

0.78
0.49
0.71
0.49
0.89
0.50

1.05
0.51
0.97
0.61

Average house value

County avg income

FE
Basic
County labor force
FE
Basic
participation rate
County fraction Black FE
Basic
County fraction Hispanic FE
Basic
Fraction Black in tract

Fraction of homes
< 1 year

FE
Basic
FE
Basic

0.72
0.49
0.26
0.28
0.08
-0.08

-0.09
-0.06
-0.11
-0.04
-0.14
0.25

0.22
0.10

-0.05

-0.08
-0.18
-0.22
-0.09

1.05
0.97
-0.15
-0.11

-0.36
-0.14
0.98

-0.27
-0.17
-0.34

1.02

0.00

1.12

-1.57
-0.13
-0.64
-0.21
0.19
-0.17

-0.48
-0.09
-0.34
-0.11
-0.16
-0.11

0.65
0.33
0.76
0.31
1.09
0.52

-0.22
-0.22
-0.10
-0.10

-0.30
0.03
-0.02
-0.03

0.85
0.84
0.05
0.09

0.43

0.50
0.91
0.40
0.76
0.91

0.51
0.47
0.08

0.77
0.50

0.68

0.12

0.14

1.11

0.11

Cumulative effect on
Avg. house
Tract
Tract
value
< 1 years
Hispanic
Black
(4)
(5)
(6)
(7)

0.81
0.13
0.13

0.20

-0.13
0.09
0.17
0.08
0.38
-0.04
-0.04
0.42

0.69
0.50

0.22
0.29
0.13
-0.10
0.34

0.21

Fraction of homes
2-5 years 10-20 years 20-30 years >30 vears
(10)
(9)
(8)
(ID

0.07

0.08

0.00
0.00
0.01

0.00
0.00

-0.04
-0.03

0.03
-0.10
-0.05

0.00
0.01

0.00
0.01

0.00
-0.03

0.03
-0.05

0.00
0.01

0.00
0.00

0.00

-0.05
0.06
-0.01

0.06
-0.02
0.05
-0.05
0.03
-0.01

0.07
0.05
0.17
0.18

0.06
0.05
0.31
0.29

-0.02

0.02

Note: FE= tract fixed effects model (see text for details). Basic = basic model using tracts matched across 1970,80, and 90 census.



0.03
0.13

0.20
0.10
0.02

-0.12
-0.05
-0.06
-0.06

-0.04
-0.07
-0.11
-0.09

0.02

0.10

-0.12
-0.05
-0.03

0.07
-0.01

0.13
0.06

0.00

0.01

-0.09
-0.05
-0.02
-0.01

-0.01

0.02

0.11
0.00

0.06
-0.02
-0.02

0.00
0.10

-0.19
-0.06
-0.12
-0.06
0.07
-0.04

0.08
-0.05

-0.09
-0.05
-0.29
-0.43

-0.09
-0.11
-0.62
-0.56

-0.02

0.11
-0.15

0.10
0.09

0.10
0.44
0.31

0.03

0.09

0.00
0.05

0.02