Policy Research Working Paper 9574
Saving the American Dream?
Education Policies in Spatial General Equilibrium
Fabian Eckert
Tatjana Kleineberg
Development Economics
Development Research Group
March 2021
Policy Research Working Paper 9574
Abstract
Children’s education and economic opportunities differ on education outcomes and social mobility. The reform’s
substantially across US neighborhoods. This paper devel- direct effects improve education outcomes among children
ops and estimates a spatial equilibrium model that links from low-skill families. However, the effects are weaker in
children’s education outcomes to their childhood location. spatial general equilibrium because average returns to edu-
Two endogenous factors determine education choices in cation decline and residential and educational choices of
each location: local education quality and local labor market low-skill families shift them toward locations with lower
access. This paper estimates the model with US county-level education quality.
data and studies the effects of a school funding equalization
This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the
World Bank to provide open access to its research and make a contribution to development policy discussions around the
world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may
be contacted at tkleineberg@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Saving the American Dream?
Education Policies in Spatial General Equilibrium∗
Fabian Eckert† Tatjana Kleineberg ‡
Keywords: Intergenerational Mobility, Equality of Opportunity, School Access, Edu-
cation Reform, Regional Labor Markets, Economic Geography, Spatial Economics JEL
Codes: E24, E62, R12, R23,R75, I24, I28
∗ This article is a revised version of the ﬁrst chapter of Kleineberg’s PhD dissertation at Yale University,
which circulated under the title “Can We Save the American Dream? A Dynamic General Equilibrium Anal-
ysis of the Effects of School Financing on Local Opportunities.” We are indebted to Giuseppe Moscarini,
Samuel Kortum, Michael Peters and Fabrizio Zilibotti for their continued and invaluable support and guid-
ance in this project. In addition, we are very grateful to Joseph Altonji, Costas Arkolakis, Lorenzo Caliendo,
Ellora Derenoncourt, Ed Glaeser, Nathan Hendren, Joachim Hubmer, Ilse Lindenlaub, Costas Meghir, Pas-
cual Restrepo, Mark Rosenzweig, Tony Smith, Sharon Traiberman, Aleh Tsyvinski, and Conor Walsh for
helpful discussions and suggestions. We are also grateful to audiences at Yale, Harvard, Princeton, NYU,
NYU-Stern, IIES Stockholm, Philadelphia Fed, Wisconsin, the World Bank, as well as at the Penn State New
Faces in International Economics Conference, the Yale Cowles Macro Conference 2019, the SED 2019, and
the NBER Urban SI 2019. We owe special thanks to Rucker Johnson for providing additional estimation
results. The ﬁndings, interpretations, and conclusions expressed in this paper are entirely those of the au-
thors. They do not necessarily represent the views of the World Bank and its afﬁliated organizations, or
those of the Executive Directors of the World Bank or the governments they represent.
† Department of Economics; University of California, San Diego; Email: fpe@ucsd.edu
‡ Development Research Group; World Bank; Email: tkleineberg@worldbank.org
1. I NTRODUCTION
Neighborhoods in the United States have an important impact on children’s education
and economic outcomes. Policies to increase social mobility and equality of opportu-
nity could therefore try to improve disadvantaged locations, for example, through higher
school funding, or incentivize families to move to better-performing locations, for exam-
ple, through rent subsidies. However, the success of such policies depends on why certain
locations produce better outcomes and whether that changes in response to policies.
Childhood neighborhoods matter for children’s long-run outcomes for two reasons. First,
the place where children grow up determines their future wages and returns to education
because it is costly to move. Second, childhood neighborhoods differ in education envi-
ronments, which depend on local schools and other neighborhood characteristics. We
refer to these two channels as “local labor market access” and “local education quality.”
Importantly, both channels interact with each other and change in response to policies,
for example, through adjustments in local prices or local skill compositions.
In this paper, we therefore develop a spatial equilibrium framework that accounts for
these feedback effects by jointly modeling local labor markets, local education environ-
ments, and families’ education and residential choices. We use our estimated model to
evaluate an equalization of school funding and show that interactions in spatial equilib-
rium shape the long-run effects of the policy.
Seminal work that studies the link between residential choices, education outcomes, and
intergenerational mobility dates back to the 1990s and was mostly theoretical (cf. Benabou
(1993, 1996), Durlauf (1996a,b) and Fernandez and Rogerson (1996, 1997, 1998)). We use
recent advances in spatial economics (cf. Redding and Rossi-Hansberg (2017)) to study
these research questions by developing a quantitative spatial model with local education
quality and local education choices. Chetty and Hendren (2018b) provide causal effects of
childhood neighborhoods on children’s education outcomes for the entire United States,
which makes it possible to estimate our spatial model.
We begin by providing evidence that labor market access and education quality vary
across US locations. We show that individuals are more likely to stay in or near the lo-
cation in which they grow up and that wages and skill premia differ across locations.
These facts together imply that returns to education differ across childhood locations. We
further document that school funding–one important determinant of education quality–
varies substantially across locations.
We then develop a spatial equilibrium framework that formalizes these mechanisms. In-
1
dividuals live for two periods: childhood and adulthood. Children choose to remain
low-skill (high school) or to become high-skill (college), which is ﬁxed during adulthood.
Education choices depend on local education quality and local returns to education. Af-
ter choosing their education, individuals may have children themselves and then choose
their adulthood location. Parents’ residential choices take the utility that destinations
offer to their children into account. We call this utility destinations’ “child opportunity
values,” which depend on local education quality and local labor market access. Child
opportunity values vary by parental education because children from low- and high-skill
parents may beneﬁt differentially from local opportunities.
The model has a nested geography where larger “labor markets” nest smaller “neigh-
borhoods.” Labor market clearing determines local wages and skill premia. Children’s
future returns to education depend on their childhood locations because it is costly to
move. Neighborhoods differ in education quality, rents, and amenities. The model has a
dynastic structure in which each time period represents one generation. Residential and
education choices jointly determine how the distribution of workers across skills and lo-
cations evolves over generations. Local labor market access and local education quality
depend on the distribution of workers, making all of these objects equilibrium outcomes.
Our model can be used to study many research and policy questions. We focus on school
funding reforms and parameterize locations’ education quality as a function of endoge-
nous school funding and an exogenous component that captures all other determinants
of local education quality. To mimic the US school funding system, we include federal
and state income taxes and local taxes on rent (proxying property taxes). The reliance
on local taxes creates a direct link between local wages, rents, and school funding. This
interaction can generate inequality of opportunity because richer families live in more
expensive areas that have better-funded schools.
We estimate the model with census data using a two-step estimator. The ﬁrst step uses
data on residential choices to estimate the mean utility that each education and family
type attributes to each neighborhood. The second step identiﬁes how types’ mean utility
in a location depends on their preferences for regional characteristics. In the second step,
we use instruments to identify workers’ valuation of real wages. We then use residential
choices of non-parents to identify the general attractiveness (i.e., unobserved amenities)
of a location. Last, we exploit differences in residential choices between parents and non-
parents to estimate parents’ valuation of local child opportunity values.
We then use our estimated model to evaluate an equalization of school funding across
students. The reform raises average funding for low-skill families and reduces it for high-
skill families. We compare the reform’s direct effects, where only education choices adjust,
2
with its general equilibrium effects. Direct effects of equalizing school funding are large
for low-skill families: Their children’s probability of attending college increases by 3.15
percentage points (henceforth p.p.). Effects are smaller in general equilibrium (only +0.6
p.p.) because average education returns decline and low-skill families shift toward loca-
tions with lower exogenous education quality. For high-skill families, the reform leads
to a small reduction in their children’s probability of attending college (-0.5 p.p.). The
effect is similar in general equilibrium (-0.3 p.p.) because high-skill families shift toward
locations with better exogenous education quality which offsets the decline in average
education returns. Our ﬁndings are similar when allowing for peer effects in education.
We ﬁnd that the reform increases the geographic variation in education outcomes: Loca-
tions with lower exogenous education quality initially tend to have higher school fund-
ing. Equalizing funding therefore cuts resources in these locations, further deteriorating
their education outcomes. Local wage adjustments mitigate the direct effects of the fund-
ing cut because lower education outcomes reduce local skill supply, which increases local
skill premia and therefore children’s incentives to get educated. In the Appendix, we
further evaluate the effects of rent subsidies as an alternative policy to increase equality
of opportunity. Overall, our ﬁndings emphasize that interactions between local markets,
local education quality, and households’ education and residential choices are important
to evaluate the long-run effects of education policies.
Related Literature
Our paper relates to several strands of the literature. Seminal work that studies the link
between inequality, local human capital formation, and local school ﬁnancing goes back
to Benabou (1993, 1996), Durlauf (1996a,b), and Fernandez and Rogerson (1996, 1997).
Most of the work is theoretical with the exception of Fernandez and Rogerson (1998),
who develop and calibrate a stylized dynamic general equilibrium model with two loca-
tions to study the effects of school ﬁnance reforms on income inequality and intergenera-
tional mobility. Other quantitative work on the topics includes contemporaneous work by
Durlauf and Seshadri (2017), Fogli and Guerrieri (2019), and Zheng and Graham (2020).
Fogli and Guerrieri (2019) study the effects of a skill premium shock on inequality and
segregation in an overlapping generations model with two locations and local education
spillovers. Zheng and Graham (2020) develop a dynamic heterogeneous agent model
with three neighborhoods in which agents choose their residence location and human
capital investment. They use the calibrated model to study the effects of school fund-
ing reforms and housing vouchers on intergenerational mobility. Our paper embeds the
3
mechanisms highlighted by this literature into a quantitative spatial framework with an
arbitrary number of locations that allows us to evaluate policies while accounting for
interactions between local labor markets, local education environments, and families’ ed-
ucation and residential choices.
A large empirical literature studies the causal effects of neighborhoods and school fund-
ing on children’s education and economic outcomes. Altonji and Mansﬁeld (2018) ﬁnd
that schools and neighborhoods have large effects on children’s education and future
earnings. Chetty and Hendren (2018b) use administrative tax record data to estimate the
causal effects of US counties on children’s education and other adulthood outcomes. Re-
cent studies by Jackson et al. (2016) and Biasi (2019) estimate the causal effects of local
school funding on children’s education and future earnings. More generally, our paper
relates to a large literature that studies skill formation and optimal education policies,
including Durlauf (2004), Cunha et al. (2010), Fryer and Katz (2013), Abbott et al. (2019),
Daruich (2018), and many others. Our paper uses ﬁndings from the empirical literature
to quantify a spatial general equilibrium model which can evaluate policies and study
the macro implications of existing micro estimates. Our analysis intuitively decomposes
the causal neighborhood effects from Chetty and Hendren (2018b) into parts due to local
labor market access and local education quality. We use the elasticities estimated by Jack-
son et al. (2016) to incorporate endogenous local school funding as a determinant of local
education quality into our quantitative framework.
Another relevant literature studies how workers sort into locations based on local wages
or amenities (e.g., Berry and Glaeser (2005), Diamond (2016), Moretti (2013), and Bilal and
Rossi-Hansberg (2018)). Other papers study how parents additionally sort into neighbor-
hoods with good local education environments (e.g., Bayer et al. (2007) and Nechyba
(2006)). Parents’ residential choices are an important way of investing in their children’s
human capital. We incorporate both motives for residential choices in our model and
study their implications in general equilibrium.
To take our framework to the data, we utilize methods from the Quantitative Spatial
Economics literature (reviewed in Redding and Rossi-Hansberg (2017)). The dynamic
structure of our model relates in particular to Caliendo et al. (2019). This literature has
developed tractable frameworks that account for heterogeneity in locations’ exogenous
characteristics and endogenous interactions between agents’ choices and local markets.
A central contribution of this literature is to formalize the notion of labor market access
(e.g., Redding and Venables (2004), Redding and Sturm (2008), Tsivanidis (2018), and
Bryan and Morten (2019)). Loosely speaking, the local market access of an origin loca-
tion is the wage in all possible destinations weighted by the respective moving costs to
4
reach these destinations. Our paper highlights that local labor market access affects not
only the static sorting of workers, but also children’s returns to education and therefore
their educational and economic outcomes. We add to the quantitative spatial literature
by incorporating this channel into a dynastic model where local educational and residen-
tial choices jointly determine workers’ skill distribution across locations. Our framework
opens a new avenue to account for changes in both of these decisions when evaluating
policy counterfactuals.
2. M OTIVATING E VIDENCE ON L OCAL D ETERMINANTS OF
E DUCATION O UTCOMES
This section documents large variation in education outcomes across US commuting zones
(henceforth “CZs”), which motivates our analysis. We present differences in skill premia
and school funding across CZs, which suggest that CZs differ in returns to education and
education quality. Online Appendix B contains a detailed description of data sources and
construction.
Geographic Variation in Education Outcomes Conditional on Parental Background.
A large literature emphasizes the importance of neighborhoods for children’s long-run
outcomes (see Durlauf (2004) for a review and Chetty et al. (2014), Chetty et al. (2016),
Altonji and Mansﬁeld (2018), and Chetty and Hendren (2018a,b) for more recent work). In
Figure 1, we present data from Chetty and Hendren (2018b) on the share of children who
attend college in each CZ, separately for families at the 25th (blue bars) and 75th (red bars)
percentile of the US income distribution. We order CZs by education outcomes of children
from low-income families. The share of children attending college varies substantially
across CZs, ranging from 0.35 to 0.8 for low-income families and from 0.7 to almost 1 for
high-income families. Chetty and Hendren (2018b) ﬁnd that a large part of this variation
is causal to children’s exposure to their childhood location.
Geographic Variation in Returns to Education. Children’s future returns to education
differ across childhood locations if skill premia vary across locations and moving across
locations is costly. With moving costs, childhood locations matter for future residential
choices which determine labor market access and returns to education. We provide evi-
dence for this channel using micro-data from the decennial census and the 2006-10 Amer-
ican Community Survey (ACS). We estimate college wage premia for each CZ by regress-
ing individuals’ log wages on CZ and education ﬁxed effects, controlling for a range of
5
F IGURE 1: C OLLEGE ATTENDANCE R ATES A CROSS US C OMMUTING Z ONES
1
.9
.8
Share of Family
Children .7 Income:
Attending High
College
.6 Low
.5
.4
.3
Commuting Zones Ordered by Share of
Children from Low-Income Families Attending College
Notes: This ﬁgure shows the geographic variation in the share of children attending college across US commuting zones. Blue (red)
bars show the share of children attending college whose families are at the 25th (75th) percentile of the US income distribution. We
order commuting zones by the college attendance share of children from low-income families. The source of the data is “Online Data
Table 4: Complete County-Level Dataset: Causal Effects and Covariates” from Chetty and Hendren (2018b).
demographic characteristics. The estimated college wage premia average 57 percent and
vary substantially across CZs with a standard deviation of 8 percent. Census data show
that childhood location matters for future moving choices. In particular, 50 percent of
workers between ages 35 and 50 years still live in their state of birth. Even conditional
on moving, workers are much more likely to move to locations that are close to their
childhood location.
Geographic Variation in Education Quality. Local education quality (i.e., the ease of
getting educated) can depend on different local factors, such as school funding, teacher
quality, infrastructure, role models, information, culture, peers or others. Local school
funding has received particular interest in the public and academic debate because of its
policy relevance. Figure 2 shows per student school funding in the ten best and worst
funded CZs using data from the National Center for Education Statistics (NCES). Vari-
ation is substantial with per student funding ranging from $7,000 to more than $25,000
across CZs. The composition of funding also differs across CZs, as seen in the color shad-
6
F IGURE 2: S CHOOL F UNDING PER S TUDENT A CROSS US C OMMUTING Z ONES
30
20 Source:
School
Funding Federal
per Student State
($1000)
Local
10
0
ke or C y, UT
C d ity T
Bo Bu ity City , ID
Z
. G vi y ty T
ea lev orge C ity, ID
of lan e C ty, T D
d ity N
To term ity UT
di TN
N on nta wn s
ew d C , ...
W ive ork Ci y, NY
N elli rto C ty, Y
t g C , R
Fo R uckton ity NY
ne Sto lin CDity, Y
rd B kto Cit , M X
H k C y, WA
en Ci y, Y
C ty, TX
P, T
A
O on te ...
Z
La aff llo it U
St oss Cit Ci y, U
D M
C se rle Cit , A
R Y on it W
an n n ity O
t aw et C W
P T
i I
M
C
,
lt S ate n C ty,
C ,
,
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av er it
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a
Po og o C
C eo To
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e
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a
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Notes: This ﬁgure presents per student school funding in the ten best- and worst-funded commuting zones using 2010 data from the
National Center for Education Statistics (NCES). The color shading of the bar graphs indicates the share of funding that is received
from federal, state, and local sources. The ﬁgure shows large geographic variation in per student school funding and substantial
differences in the composition of the funding sources.
ing of Figure 2. On average, better-funded CZs raise more of their resources locally. Re-
cent studies such as Jackson et al. (2016) show that local school funding has large causal
effects on children’s education outcomes.
3. A M ODEL OF L OCAL H UMAN C APITAL P RODUCTION
AND L OCAL L ABOR M ARKETS
Guided by these motivating facts, we now present a spatial equilibrium model that links
educational and residential choices to local labor markets and local education quality. In
this section, we introduce the core framework that highlights the model’s key mecha-
nisms. In the remainder of the paper, we extend and estimate the framework to evaluate
the effects of school funding reforms in spatial general equilibrium.
7
3.1 Environment
Geography. Locations n are separated by bilateral moving costs Cnn which we measure
in utils. These moving costs can reﬂect pecuniary or non-pecuniary costs, such as the
time of moving, information frictions, or the psychological cost of being away from one’s
family or childhood friends.1
Worker Characteristics and Preferences. Workers i are characterized by their education
e (skill level), which is either low or high, e = {l , h}, and their location of work n. Each
worker has one child and receives taste shocks over education levels and locations, which
we respectively denote by e i and i . We use the terms worker, parents, or families inter-
n
changeably. Workers value the consumption good on which they spend their entire wage
income. We denote the indirect ﬂow utility of workers with education e in location n by
Une . Parents are altruistic and discount their children’s utility by a factor β.
Local Labor Markets. Perfectly competitive ﬁrms produce a homogeneous, freely traded
consumption good with location-speciﬁc production technology Yn = Gn ( Ll h
n , Ln ). Low-
and high-skill labor, denoted Le n , are inputs into production and can be imperfect sub-
stitutes. Local labor market clearing endogenously determines local wages for each skill
type, which we denote by wn e.
Local Human Capital Production. Education quality Qe n represents the utility costs of
becoming high-skill relative to remaining low-skill. The cost depends on childhood lo-
cation n and parental education e. Education is a binary choice, so we can normalize
the cost of remaining low-skill to zero without loss of generality. Education quality can
depend on a variety of local factors. Some of the most important ones are likely endoge-
nous as they relate to a location’s skill composition (e.g., peer effects or role models) or
to local factor prices (e.g., local resources or tax revenues). We therefore deﬁne local ed-
ucation quality as a general function of the endogenous wage and worker distribution
across locations and skill levels: Qe e e e
n ≡ Qn ( { Ln }, { wn } ). An exogenous local component
can capture additional local factors that matter for education quality.
3.2 Location and Education Choice Problem
Timeline and Decisions. Individuals live for two periods: childhood and adulthood.
Children are born to parents with education e and are raised in childhood location n
1 Information frictions can be important because uncertainty about the economic conditions in other
locations can affect moving choices. See Porcher (2019) for a study of information frictions in a spatial
framework.
8
(which was chosen by their parents). They receive idiosyncratic education taste shocks,
i
e , and then choose their education e . Education choices additionally depend on local
returns to education and local education quality. After ﬁnishing their education, children
become young adults and have their own children. The previous adult generation dies.
Young adults then learn their idiosyncratic location taste shocks, n i , and choose their
adulthood location in which they work and raise their children. Parents are altruistic,
so their residential choices consider the utility that destinations offer to their children.
Residential and educational choices are forward-looking, so our model is dynastic and
each time period represents one generation.
Dynamic Decision Problem. Young adults with education level e and childhood location
n choose their adulthood location n by solving the following maximization problem:
e
(1) V ( n, e ) = E n
max Un − Cnn + n + βO ( n , e ) ,
n
where Un e is the ﬂow utility in each destination, C
nn is the bilateral moving cost, and
n is the idiosyncratic location taste shock. V ( n, e ) is the expected utility value of young
adults before moving, where the expectation is taken over their idiosyncratic location
taste shocks. O(n , e) is the expected utility of children who are born to parents of educa-
tion e and are raised in childhood location n . We call this utility local “child opportunity
value” and it is given by:
O(n , e) = E e max 1e =h Qe
n + e + V (n , e ) .
e
The expectation is taken over children’s idiosyncratic education taste shocks e . V (n , e )
is the expected continuation value that location n offers to young adults of the next gen-
eration who obtain education level e .
Solving Education and Location Choices. To solve education and location choices, we
make the following assumption, which is standard in the discrete choice literature:
Assumption 1. Idiosyncratic taste shocks over locations n and education levels e are drawn
i.i.d. from a Gumbel distribution with mean zero and dispersion parameters σN and σE .
Under this assumption, we can aggregate individuals’ choices into the shares of each
type that makes a given decision. We can also express expected value functions in closed
form. We solve families’ problem backwards, starting with children’s education choice.
The share of children in location n with parents of education e who choose education e
9
is:
1 e 1
exp σE 1e =h Qn + σE V ( n, e )
(2) Pr(e | n, e) = .
1 1
∑e exp e
σE 1e =h Qn + σE V ( n, e )
Child opportunity values for these children (before knowing education taste shocks) are:
1 1
(3) O(n, e) = σE log ∑ exp σE
1e = h Q e
n+
σE
V ( n, e ) .
e
Similarly, the share of young parents with education e who move from their childhood
location n to adulthood location n is:
1 e 1 β
exp σN Un − σN Cnn + σN O ( n , e)
(4) Pr(n | n, e) = .
1 e 1 β
∑n exp σN Un − σN Cnn + σN O ( n , e)
The expected utility of these young adults (before knowing location taste shocks) is:
1 e 1 β
(5) V (n, e) = σN log ∑ exp Un − Cnn + O(n , e) .
n
σN σN σN
3.3 Aggregation and Equilibrium
Aggregate Law of Motion. Individuals’ educational and residential choices determine
how the distribution of workers across education levels and locations evolves dynami-
cally over generations. The law of motion (with time subscripts) is given by:
(6) Le
n ,t = ∑ Prt (n | n, e ) ∑ Prt−1 (e | n, e) Le
n,t −1 .
n e
On the right, we start with workers Le from generation t − 1 who have education e and
n,t −1
who work and raise their children in location n. A fraction Pr(e | n, e) of these children
obtains education e . Summing across parental education e yields the mass of young
adults from generation t who have education e and grew up in location n. A fraction
Pr(n | n, e ) of these young adults then moves to adulthood location n . Summing across
childhood locations n yields generation t s distribution of adults across education levels
e and adulthood locations n . In the steady state, this distribution is constant across
generations, so that Le e
n ,t = Ln,t−1 holds for all t.
2
Market Clearing. Proﬁt-maximizing ﬁrms in each location n determine local labor de-
mand by skill type. Workers’ educational and residential choices determine local labor
2 In
the steady state, young adults can still move across locations. Education levels can also change
across generations within a given dynasty. In the stationary equilibrium, these changes balance so that the
aggregate adult population of each skill type remains constant in each location.
10
e adjust in each location to clear local labor markets.
supply. Wages for each skill type wn
Equilibrium. The exogenous parameters of our model consist of structural parameters
and time-varying “regional characteristics.” Given a path of these exogenous parameters
{Ωt }∞ e
t=0 and an initial distribution of workers Ln,0 , the recursive competitive equilibrium
is deﬁned by the paths of:
(i) families’ residential and education choices for each education type and location {Pr t (n |
∞
n, e),Pr t (e | n, e)}∞
t=0 , (ii) value functions for each education type and location {Vt ( n, e ) }t ,
∞
(iii) the distribution of workers across education types and locations Le n,t t=0 , and (iv)
e ∞
local factor prices wn ,t t=0 , such that:
1. Residential and education choices maximize families’ utility as derived in Equations
(2) and (4);
2. Value functions are consistent with Equations (3) and (5);
3. The distribution of workers across education levels and locations is consistent with
the law of motion in Equation (6);
4. Wages for each education level clear labor markets in each location and period.
3.4 Model Implications
The central equation of our model links children’s education outcomes to local educa-
tion quality and local returns to education (conditional on parental education e). We can
express the odds of becoming high-skill relative to remaining low-skill as (cf. Equation
2):
Pr(h | n, e) 1 1
(7) log = (V (n, h) − V (n, l )) + Qe e e
n ( { L n }, { w n } ) .
Pr(l | n, e) σE σE
High-Skill Odds Return to Education Education Quality
The ﬁrst determinant of local education choices is children’s future return to education.
In each childhood location, local education returns are equal to the difference in contin-
uation values for high- versus low-skill young adults. Continuation values depend on
education level and childhood location because it is costly to move and locations differ in
wages and skill premia. Continuation values in each childhood location therefore capture
the ability of young local workers to access labor markets where wages for their educa-
tion level are high. We refer to this determinant interchangeably as “local labor market
access” or “local returns to education”.
11
Local education quality is the second determinant of education choices. It captures chil-
dren’s utility cost of becoming high-skill relative to remaining low-skill in each location.
To study speciﬁc policy questions, local education quality can be parameterized as a func-
tion of different exogenous or endogenous model moments, such as local factor prices or
local skill composition.
An important feature of our model is that locations’ education returns, education qual-
ity, prices, and the distribution of workers across locations and education levels are all
endogenous and interact with each other through families’ residential and educational
choices. To evaluate policies, our framework therefore accounts for the direct effects of
policies and the indirect ones that operate through the feedback effects in spatial general
equilibrium.
4. R EFORMING THE US E DUCATION S YSTEM IN S PATIAL
G ENERAL E QUILIBRIUM
We now extend and estimate our core framework to study the effects of school funding
reforms on local education outcomes and social mobility in the aggregate and across lo-
cations. Schools in the US are funded from federal, state, and local taxes. Differences
in local school funding are large (cf. Figure 2), and they have been the subject of a long
and ﬁerce political debate. The reliance on local tax revenues creates a feedback between
local prices and local school resources. Locations with higher rents have higher tax rev-
enues and therefore better-funded schools. Better schools can attract more high-income
families, which further increases rents, tax revenues, and school funding. Poor families
cannot afford the rent in these locations, depriving their children of access to high-quality
schools. We formalize this relationship between local prices and local school quality in
our model and study its implications in our counterfactual analysis.
4.1 Quantitative Model: Additional Ingredients and Assumptions
We enrich our core framework to incorporate local school funding, taxes, and other ele-
ments that allow us to take the model to the data.
Family Types. We now allow workers to differ not only by education e but also by parent
status k. We indicate workers who have children by k = 1 and those who do not by
k = 0. Fertility is exogenously determined by probabilities Pr(k |e), which can differ across
12
education types. Parents of education e have 1/ Pr(k = 1|e) children to keep population
constant.
Nested Geography. We consider a nested geography with multiple local labor markets,
indexed by m ∈ M. Each labor market consists of several neighborhoods, indexed by n ∈
Nm . Moving across labor markets incurs a cost Cmm
ek , which can differ across education
and family types ek.
Neighborhood Housing Markets and Amenities. Neighborhoods have a ﬁxed housing
supply Hn . Rental markets clear in each neighborhood, which determines local rents rn .
We reimburse aggregate rent payments to workers in proportion to their wage income.3
Neighborhoods differ in amenities Aekn , which capture regional characteristics that make
a neighborhood more or less desirable for each education and family type ek.
Neighborhood Education Quality. We specify local education quality Qe n as a function
of endogenous per student school funding f n and an exogenous local component Kn e as:
(8) Qe e e
n = γ log ( f n ) + Kn ,
where γe is the causal effect of school funding on education quality. The exogenous
component captures all remaining factors that are important for local education envi-
ronments.
School Funding and Taxation. School funding is raised through federal and state income
taxes and local rent taxes, which we denote by τg w , τ w , and τ r . School funding therefore
s n
depends on local prices and the distribution of workers across skills, family types, and
locations. Federal and state governments distribute their tax revenues to neighborhoods
g s . Each neigh-
n according to school funding allocation rules, which we denote by δn and δn
borhood allocates its entire tax revenue to local schools.
Functional Forms for Production Technology and Preferences. Production technologies
differ across labor markets and have a constant elasticity of substitution over low- and
high-skill labor, so that:
1
ρ ρ ρ
(9) Gm ( Ll h
m , Lm ) = l
Zm Sm Ll
m
h
+ Sm h
Lm ,
e
where ρ determines the elasticity of substitution, Zm is total factor productivity, and Sm
h + S l = 1.
are factor shares that add to one across skill types: Sm m
3 Each e , where the dividend D equals the ratio between the econ-
worker receives a payment of Dwm
omy’s total rent payment and total wage income. This reimbursement can mimic dividends that house-
holds would receive from investing an amount proportional to their wage income in a national real estate
portfolio.
13
Families have Cobb-Douglas preferences over the consumption good C and housing H .
Amenities Aek
n enter the utility function additively, so families’ utility is given by:
αek 1−αek
H C
(10) U= Aek
n + log ,
αek 1 − αek
where αek is the housing expenditure share.
4.2 Solving the Quantitative Model
The model solution is similar to the core model that we presented in Section 3. We sum-
marize the most important solution steps here and provide the full set of equations in
Online Appendix A.
Static Choice between Housing and Consumption Goods. In each period, families of
type ek in location n choose housing units H and consumption good C to maximize their
utility (Equation (10)) subject to a budget constraint. This derives the following indirect
utility where Yne is disposable income:
ek
(11) Un = Aek e ek
n + log (Yn ) − α log(rn ).
Dynamic Decision Problem. To express families’ education and residential choice prob-
lem, we must now adjust indices to the nested geography and family types k. Families
learn whether or not they have children after ﬁnishing their education and before moving
to their adulthood location. Value functions of young adults with education e, family type
k, and childhood labor market m before moving are given by:
ek ek
V ( m, e, k ) = E n
max Un − Cmm + σN n + 1k=1 βO(n , e) ,
n ∈N
where we now multiply the continuation value with an indicator that is equal to one
if the family has children and zero otherwise. Parents’ residential choices are dynamic
because they value destinations’ child opportunity values. Non-parents do not value
child opportunity values so their residential choices are static. Wages wme , moving costs
ek and value functions V ( m, e, k ) vary across labor markets, while rent r , education
Cmm n
e
quality Qn and child opportunity values O(n, e) vary across neighborhoods. 4
4 Value functions vary across childhood locations due to bilateral moving costs. It follows that value
functions only depend on labor markets (and not neighborhoods) because we assume that moving is costly
across labor markets but not within.
14
Children’s likelihood of becoming high-skill relative to remaining low-skill is given by:
Pr(h | n, e) 1 1 e γe
(12) log = ( R(m, h) − R(m, l )) + K + log( f n ),
Pr(l | n, e) σE σE n σE
High-Skill Odds Return to Education Exog. Educ. Quality Funding
As before, education returns in each childhood location are given by the difference in ex-
pected continuation values for high-skill versus low-skill young adults. We deﬁne young
adults’ expected continuation values before knowing their fertility shocks as: R(m, e) ≡
∑k Pr(k | e)V (m, e, k). Local education quality Qe n consists of endogenous local school
funding f n and the local exogenous component Kn e.
4.3 Market Clearing and Recursive Equilibrium
Law of Motion. Individuals’ education and residential choices and their exogenous fer-
tility shocks determine how the distribution of workers evolves dynamically across neigh-
borhoods, education levels, and family types.
e .
Market Clearing. Labor market clearing determines local wages for each skill type wm
Rental market clearing in each neighborhood determines local rents rn .
Equilibrium. Exogenous parameters include structural parameters, tax rates, school fund-
ing allocation rules from federal, state, and local governments, and time-varying regional
characteristics. Conditional on these exogenous parameters, the deﬁnition of equilibrium
is similar to that of our core framework presented in Section 3. Endogenous factor prices
are now local wages and rents {wmt e , r }.
nt
5. C ALIBRATION AND E STIMATION
When taking our model to the data, we interpret labor markets m as commuting zones
(following Tolbert and Sizer (1996)) and neighborhoods n as counties.5 There are 741
commuting zones (CZs) and 3,100 counties in the United States. CZs are constructed to
have strong commuting ties within and weak commuting ties across their boundaries.
This deﬁnition is in line with our model in which labor markets are separated by moving
costs. Individuals whose highest education level is high school are considered low-skill.
All others are considered high-skill. Households in which a child under 18 is currently
5 Ouranalysis focuses on counties, instead of smaller units such as school districts, because causal effect
estimates from Chetty and Hendren (2018b) are only available at the county level.
15
present are considered parents.6
The estimation of our model relies on six key data moments: moving ﬂows across CZs,
residential choices within CZs, CZ-level wages, and at the county level rents, education
choices for children from high- and low-skill families, and per student school funding
by funding source (federal, state, local). We provide more information about the data
construction and summary statistics in Online Appendix B.
We identify the model’s structural parameters with a mix of calibration and estimation
strategies. As a last step, we follow the Quantitative Spatial Economics (QSE) literature
and infer regional characteristics as structural residuals by ﬁtting our model predictions
to regional data moments. In this section, we describe the calibration, estimation, and
inference of regional characteristics. Online Appendix C provides additional information
and derivations.
5.1 Calibrated Parameters
We now discuss the calibration of the parameters that relate to local school funding. Table
1 describes our calibration strategy and presents results for additional calibrated param-
eters.
Effects of School Funding on Education Outcomes. We use estimates from the literature
to identify the causal effect of per student school funding on the probability of attending
college. In particular, we rely on Jackson et al. (2016), who use exogenous variation in
school funding from court-mandated reforms to estimate the effects of school funding on
children’s probability of attending (and graduating from) college. Effects are separately
estimated for children from low- and high-skill families.7 We map the authors’ linear
2SLS estimates to our model by taking the derivate of Equation 12 with respect to school
funding so that:
(13)
∆ Pr(h|n,e) |m in Jackson et al. (2016) and
γ e,2SLS
= ∂∆ log( f n )
e
Pr(h|n,e) | = γ Pr(h | n, e) (1 − Pr(h | n, e)) in our model.
∂ log( f ) m
n σE
6 Iffamilies had a child in the past, we consider them to be “non-parents” if the child no longer lives in
the household. This classiﬁcation is reasonable because only households where a child is currently present
value local education environments at that moment of time.
7 The authors kindly provided us with these estimates, since their published paper does not include this
exact model speciﬁcation that best maps to the structural parameters of our model. We are very grateful to
the authors and in particular Rucker Johnson for their time and effort in providing these results.
16
TABLE 1: O VERVIEW OF C ALIBRATED PARAMETERS
Parameter Calibration Data or Source Results
Wage and Rent Tax Wages, rents, and school fund- τgw = 1.6%,
ing (Decennial Census, ACS, τsw = {6.1%, 1.7%},
and NCES). r = {14.9%, 9.8%}
τn
(mean, std)
Effect of School Funding Causal 2SLS estimates from γl /σE = 2.43,
Jackson et al. (2016). γh /σE = 2.25
Housing Expenditure Share Microdata on expenditure αl 0 = 0.34, αh0 = 0.33,
(CEX 2011). αl 1 = 0.38, αh1 = 0.36
Probability of Having a Child Share of individuals with chil- Pr(k=1 | l) = 0.56
dren by skill (Decennial Cen- Pr(k=1 | h) = 0.63
sus, ACS).
Skill Substitutability Estimates from Ciccone and ρ = 1/3
Peri (2005).
Notes: This table documents calibrated parameters using our baseline sample from 2010, which re-
stricts population to ages 35 to 44 years. The ﬁnal sample consists of 2,840 counties. We trim local
tax rates on rent at the 1st and 99th percentile. NCES denotes the "National Center for Education
Statistics," CEX is the "Consumer Expenditure Survey," and ACS the "American Community Survey."
The 2SLS estimation controls for location ﬁxed effects, so that we hold regional character-
istics constant and assume ∂ R(m, e)/∂ f n = 0 when taking the derivative.
Jackson et al. (2016) ﬁnd that a 10 percent increase in school funding increases children’s
probability of attending (and graduating from) college by 7 (4.6) percentage points for
low-skill parents. For high-skill parents, children’s probability of graduating from college
increases by 3.2 percentage points and effects on the probability of attending college are
not signiﬁcant. Averaging these values, we set γl ,2SLS = 0.58 and γh,2SLS = 0.29. Using
the relationship in Equation 13 and data on the national average of college-attendance
probabilities from Chetty and Hendren (2018b), we ﬁnd that γe /σE = {2.43, 2.25} for
children from low- and high-skill families.
Tax Rates. We calibrate tax rates to county-level data on school funding from federal,
state, or local governments. All tax revenue in our model is used for school funding and
each level of government balances its budget. Governments’ budget constraints therefore
directly link school funding to tax rates and local wages or rents. We use this mapping
to calibrate federal and state income taxes and local rent taxes. Table 1 shows the results.
The federal income tax rate is 1.6 percent. State income taxes average 6.1 percent with
17
a standard deviation of 1.7 percent. Local tax rates on rent average 14.9 percent with a
standard deviation of 9.8 percent. Local tax rates have a large variation because counties
differ in school funding and in the extent to which their schools are funded from the
federal, state, or local government (cf. Figure 2).
TABLE 2: O VERVIEW OF E STIMATION S TRATEGY
Description Symbol Estimation Strategy
Panel A: Auxiliary Terms and Model Objects
(Step 1 of Estimation, Used in Step 2)
Moving Cost cek ek
mm ≡ Cmm / σN Parameterized and estimated from moving
ﬂows across CZs.
CZ-Utility ek ek
um ≡ Um /σN Estimated from moving ﬂows across CZs.
County-Utility ek ≡ X ek / σ
xn n N Estimated from CZ-utility and county popula-
tion stocks.
Value Function v(e, k, m) ≡ Estimated from CZ-utility and moving costs.
V (e, k, m)/σN
Panel B: Model Parameters
(Step 2 of Estimation)
Dispersion of σN Identiﬁed from relationship between changes
County Taste in county-utility and exogenous variation in
Shock changes of real income.
Altruism β Identiﬁed from the extent to which parents sort
more into neighborhoods with higher child op-
portunity values than non-parents.
Dispersion of σE Identiﬁed from relative weight that parents
Education Taste place on local education probabilities compared
Shock to local continuation values.
Notes: Panel A of this table describes the ﬁrst step of our estimation, which estimates model objects
and auxiliary terms. Panel B describes the second step, in which we decompose types’ county-utilities
into the preference weights that each type places on different regional characteristics.
School Funding Allocation Rules. We set funding allocation rules to approximate the
current distribution of per student school funding across counties. For the federal (and
each state) government, we deﬁne the allocation rule to each county n as the relative
amount of funding that a student in county n receives compared to the average student
in the nation (state). Conditional on tax rates and school funding allocation rules, each
18
county’s per student funding is endogenously determined by wages and rents.
5.2 Estimated Parameters
To estimate the remaining model parameters, we use a two-step estimator that was devel-
oped in the empirical industrial organization literature (cf. Berry et al. (2004)) and used
in many relevant applications (e.g., Artuç and McLaren (2015) and Diamond (2016)). We
interpret the data to reﬂect a transitional period in our model instead of its steady state.8
The ﬁrst step of the estimator uses individuals’ residential choices to estimate the average
ek . In this step,
utility that each type attributes to each county. We denote this utility by xn
we additionally estimate value functions and moving costs (i.e., all objects listed in Table
2, Panel A). The second step decomposes mean county utilities into the weights that each
education-family-type places on local rents, wages, and child opportunity values. These
weights correspond to the dispersion of location and education taste shocks (σN , σE ) and
parental altruism β. In this estimation, we normalize utility by the dispersion of neigh-
borhood taste shocks σN and we denote normalized terms in small caps (cf. deﬁnitions
in Table 2). Online Appendix C contains the derivations of all expressions used in the
estimation.
Step 1: Estimation of Mean County-Utility
ek for each family-education type as:
We deﬁne average county-utility xn
ek ek 1 ek
(14) xn ≡ an + I + 1k =1 β o ( n , e ),
σN n
where an ek are local amenities, I ek is real income, and o ( n, e ) are child opportunity values.
n
Individuals of a given education-family type value these regional characteristics equally.
Model objects and regional characteristics that are measured in utils (such as amenities
and child opportunity values) are now re-normalized. The ﬁrst step estimates average
county-utilities from observed residential choices. This approach relies on revealed pref-
erences and requires no assumptions on expectations. In our nested geography, moving is
costly across CZs but not within them. We therefore ﬁrst estimate average CZ-utilities and
moving costs from observed moving ﬂows across CZs. We then identify relative county-
utilities within each CZ from the population stocks in each county. We now provide more
8 We do so because data from 1990, 2000, and 2010 show that the economy is not in the steady state.
In particular, we observe positive net moving ﬂows across CZs and educational deepening, (i.e., more
children go to college compared to their parents’ generation). In the steady state, population size and skill
composition are constant in each CZ.
19
details on this estimation strategy.
Estimation of CZ-Utilities and Moving Costs. For a given education-family type, our
model predicts that moving ﬂows from childhood CZ m to destination CZ m are given
by:
ek − c ek )
exp(um
(15) Lek
mm = ek
mm
ek
˜ ek
L m,
∑m ∈M exp(um − cmm )
where um ˜ ek
ek are average CZ-utilities, c ek are bilateral moving costs, and L
m denotes the
mm
number of young adults of type ek in location m before making their moving decision.
We parameterize moving costs as a function of type-speciﬁc coefﬁcients λek and origin-
destination-speciﬁc data moments Xmm : cmm ek = λek Xmm . For these data moments, we
use distance, distance squared, and dummies that indicate whether a move between two
CZs changes states, geographic divisions, urban status or coast status. Using this param-
eterization, we write Equation (15) as:
(16) Lek ek ek ek
mm = exp destm − λ Xmm + origm + mm ,
where destination ﬁxed effects destek ek
m correspond to CZ-utilities um . CZ-utilities capture
ek absorb
the attractiveness or the pull-factor of each destination. Origin ﬁxed effects origm
the outside option and origin labor stocks. We use data on moving ﬂows across CZs to
estimate Equation (16) separately for each education and family type via Poisson pseudo-
maximum likelihood (PPML).9 The estimation simultaneously identiﬁes each type’s CZ-
utilities and moving costs up to a constant of normalization. We normalize the cost of
staying to zero without loss of generality.
Construction of County-Utilities. Due to perfect mobility within CZs, we can identify
relative county-utilities within each CZ from data on counties’ population stocks as fol-
lows:
ek Lek
n ek
(17) exp(xn )= exp(um ),
Lek
m
where average county-utility xn ek depends on CZ-utility u ek and the share of that CZ’s
m
population that lives in county n ∈ m.
9 PPML estimates the equation in levels and not logs, so the estimator can account for moving ﬂows
that are zero. This is important in our context, since we observe only a subset of all movers and observed
moving ﬂows are zero between many locations. Other advantages of PPML are discussed in Silva and
Tenreyro (2006).
20
Construction of Value Functions. We further use our estimates of CZ-utility and moving
costs to construct value functions for each education-family type, which are given by:
(18) v(m, e, k ) = log ∑ ek
exp um ek
− cmm .
m ∈M
This equation shows that young families’ value functions depend on the utility offered
by all possible destinations and the cost that these families have to pay to reach these
destinations from their childhood location m.10
Step 2: Estimation of Model Parameters
In the second step of the estimation, we identify the remaining model parameters (σN ,σE , β)
by decomposing the estimated county-utilities into the weights that each type places on
regional characteristics.
To identify the dispersion of location taste shocks, σN , we use county-utilities of non-
parents, which are given by:
e0 e0 1 e0
(19) xn = an + I ,
σN n
where In ek is real disposable income, which is known from the data. It is challenging
to identify σN because local amenities an ek are unobservable and correlate with local real
income. To overcome this challenge, we follow Diamond (2016) and use exogenous varia-
tion in changes in real income from Bartik-like local labor demand shocks and local hous-
ing supply elasticities. The intuition behind the local labor demand shocks is that national
changes in industry productivity differentially affect locations based on their initial indus-
trial composition (Bartik (1991)). To construct these labor demand shocks, we compute
national changes in industry-level wages and weigh them by locations’ industry-level
employment in 1980. We do this separately for low- and high-skill workers. We proxy
local housing supply elasticities with land-use regulation from Gyourko et al. (2008). Lo-
cations’ housing supply elasticities provide additional variation because they affect how
local wages, rents, and population stocks respond to exogenous labor demand shocks.
We use these instruments and their interaction to estimate Equation 19 in changes. We
present the estimation results in Panel A of Table 3 and we ﬁnd an estimate of σN = 0.2.11
ˆ N , we can infer local amenities as a structural residual
Conditional on this estimate of σ
10 To see this, recall the deﬁnition of expected value functions in Equation 5 or Equation OA.2 and note
ek ≡ log ek ) .
that average CZ-utilities relate to county-utilities through: um ∑n∈Nm exp(xn
11 This value is comparable to the literature. Diamond (2016) ﬁnds, for example, a value of 0.24 for low-
skill workers and 0.18 for high-skill workers for moves across MSAs using the same data sources and the
same deﬁnitions of low- and high-skill.
21
from Equation (19).
TABLE 3: E STIMATION OF M ODEL PARAMETERS
Implied
Variable Name Coefﬁcient Parameter
Panel A: GMM Estimation of Equation 19
Change in Real Income (∆ In
e0 ) 5.248** σN = 0.19
(2.569)
Observations 1,142
Panel B: OLS Estimation of Equation 20
Amenity e)
(an 0.784*** θ = 0.78
(0.005)
Value of Low-Skill Young Adult ( R(m, l )) 0.389*** β= 0.39
(0.012)
Probability of Staying Low-Skill (Pr(l | n, e)) -0.085*** σE = 0.043
(0.016)
Observations 5,744
R-Squared 0.905
Notes: Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1. This table presents
the results from the second step of our estimation, which decomposes types’ county-
utilities into the preference weights that each type places on different regional charac-
teristics. Panel A estimates Equation 19 in changes via GMM. The dependent variable
is the change in non-parents’ county-utility between 2000 and 2010. We pool data from
low- and high-skill non-parents and include education ﬁxed effects. We instrument for
changes in locations’ real income with Bartik-like labor demand shocks, housing supply
elasticities, and their interaction. Data availability of housing supply elasticities reduce
our sample size. We restrict the sample to individuals between ages 25 and 64 years,
which is possible in the 2000 and 2010 data. Panel A shows results where variables
are constructed from individual-level data. We estimate the same GMM speciﬁcation
with variables constructed from household-level data and obtain a coefﬁcient of 4.813**
(2.248). We use σN = 1/5 = 0.2 as the middle value between these two estimates. Panel
B estimates Equation 20 by OLS. The dependent variable is parents’ county-utility. We
pool data from low- and high-skill parents, include education ﬁxed effects, and weigh
counties by their population size. We restrict the sample to individuals between ages 35
and 44 years, which is possible only in the 2010 data. When causal effects of counties on
local college-attendance probabilities are missing or out of the (0, 1) bound, we use data
on local college-attendance probabilities instead. We obtain both data moments from
Chetty and Hendren (2018b).
To identify the remaining parameters ( β, σE ), we use parents’ county-utilities and make
the following identifying assumption:
22
Assumption 2. Local residential amenities differ between education types, but not between par-
ek = a e .
ents and non-parents, so that an n
We write parents’ county-utilities as:
e1 1 e1 1 σE
(20) xn − In = θ e1 an
e
+ β o ( e , n ) = θ e1 an
e
+β R ( m, l ) − log (Pr(l | n, e)) ,
σN σN σN
where we allow parents to place a different weight on amenities than non-parents, which
we denote by θ e1 . We express local child opportunity values o (n, e) as a function of lo-
cal continuation values R(m, l ) and local education probabilities Pr(l | n, e). All regional
characteristics in Equation (20) are known from the data or previous estimates.12 We
can therefore estimate the equation by OLS. Assumption 2 allows us to explicitly include
the amenity estimates from non-parents in the regression. According to our model, these
amenities absorb all unobserved variation (i.e., the entire regression residual) which could
otherwise bias our estimation. Intuitively, we use county-utilities of non-parents to iden-
tify the general attractiveness (i.e., unobserved amenities) of locations that is independent
of local child opportunity values. We then use differences in county-utilities between par-
ents and non-parents to identify parent-speciﬁc valuations. The value that parents place
on child opportunity values identiﬁes altruism β. The value they place on local education
probabilities compared to local continuation values identiﬁes the dispersion in education
taste shocks σE . Restricting amenities to be the same for parents and non-parents is neces-
sary to relate differences in parents’ residential choices to local child opportunity values.
The model provides a good ﬁt of the data despite this restriction and the OLS regression
of Equation (20) has an R-squared of 0.91. To estimate the OLS regression, we further have
to make assumptions about parents’ expectations over their children’s continuation val-
ues as young adults Rt+1 (m, l ). We assume that parents are naive and expect local values
to remain the same in the next generation, so that Rt (m, e) = Rt+1 (m, e). We present the
regression results in Panel B of Table 3. We ﬁnd that parents place a weight of θ 1 = 0.78
on amenities, compared to a value of 1 for non-parents. For the dispersion of education
taste shocks we ﬁnd a value of σE = 0.043 and for altruism β = 0.39.13
12 In particular, we have measures of county-utilities x ˆn
ek from step 1, real disposable income I
ˆn ek from the
data and calibrated parameters, the dispersion of location taste shocks σ ˆ N from step 2, amenities a e from
ˆn
ˆ
step 2, education probabilities Pr(l | n, e) from the data, and expected continuation values R(m, l ) from step
1 and data on fertility probabilities.
13 Our estimate of altruism is comparable to the literature. Daruich (2018) ﬁnds, for example, an estimate
of 0.475, while Abbott et al. (2019) ﬁnds parameters of 0.518 for males and 0.470 for females. Compared
to these papers, we do not model children’s utility and consumption during childhood, so our altruism
parameter only captures parental preferences over their children’s utility during adulthood. This could ex-
plain why our estimates are slightly lower. It is also possible that parents have imperfect information about
neighborhoods’ effects on their children’s future utility, which would bias our altruism estimate downward.
23
TABLE 4: I NFERRING R EGIONAL C HARACTERISTICS AS S TRUCTURAL R ESIDUALS
Regional Characteristic Symbol Description of Identiﬁcation
Productivity and e
Zm , Sm Labor market clearing and data on local
Skill Intensity wages and labor supply by skill type.
Housing Supply Hn Rental market clearing and data on local
rents and housing expenditure.
Amenity e ≡ Ae /σ
an Non-parents’ county-utilities and data on
n N
local wages and rents.
Exog. Component of e
Kn Data on local education choices, estimated
Education Quality education returns, and school funding.
Notes: This table summarizes how we infer regional characteristics as structural residuals by ﬁtting
model predictions to regional data moments. This approach follows the Quantitative Spatial Economics
(QSE) literature.
5.3 Inferring Regional Characteristics as Structural Residuals
We infer regional characteristics as structural residuals to ﬁt model predictions to regional
data moments. This approach follows the Quantitative Spatial Economics literature, re-
viewed in Redding and Rossi-Hansberg (2017). To infer the exogenous component of
local education quality Kn e –which is at the heart of our analysis and a novel ingredient
in the spatial literature–we rearrange educational choice probabilities (cf. Equation 12) in
the following way:
e Pr(h | n, e)
(21) Kn = R(m, h) − R(m, l ) + γe log( f n ) − σE log .
1 − Pr(h | n, e)
We can compute exogenous education quality from this equation because all terms on the
right-hand side of the equation (i.e., education returns, school funding, and educational
choice probabilities) are known from the data or previous estimates.
Amenities for each education type are identiﬁed from the residential choices of non-
parents. These residential choices are invariant to an additive increase or decrease in
utility across all locations, so amenities are identiﬁed only up to constant of normaliza-
tion. We can normalize amenities for each skill type without loss of generality because the
residential choices of parents as well as children’s education choices are also invariant to
amenity levels (as we show in Online Appendix C). Normalizing amenity levels for each
skill type additively shifts value function levels and therefore the level of education re-
turns. To ﬁt observed education outcomes, our model offsets the shift in education returns
by inversely adjusting the level of exogenous local education quality Kne (cf. Equation 21).
24
The level of skill-speciﬁc amenities ane and the level of exogenous education quality K e are
n
therefore jointly, but not separately, identiﬁed.
Table 4 describes how we infer the remaining regional characteristics by following the
Quantitative Spatial Economics literature.
6. D ECOMPOSITION AND P OLICY C OUNTERFACTUALS
We now use the estimated model for our counterfactual analysis. First, we decompose
the geographic variation in education outcomes into variation due to differences in ed-
ucation quality versus returns to education. Second, we study a counterfactual school
funding reform, which equalizes funding across students. We analyze the effects of this
reform on education outcomes, intergenerational mobility, and child opportunity values
in the aggregate and across locations. In Appendix A, we further analyze a rent subsidy
program as an alternative policy to improve social mobility and equality of opportunity.
In all counterfactuals, we evaluate the long-run effects of policies by comparing the steady
states of a baseline economy and counterfactual economies. We ﬁrst solve for the baseline
steady state because our estimation interprets the data as a transitional period. To solve
for the baseline steady state, we ﬁx regional characteristics, tax rates, and school funding
allocation rules at their estimated values.
6.1 Decomposing the Geographic Variation in Education Outcomes
A key equation of our model links children’s education outcomes to local education re-
turns and education quality (cf. Equation 7):
Pr(h | n, e) 1 1 e
(22) log = ( R(m, h) − R(m, l )) + Q .
Pr(l | n, e) σE σE n
ˆn
College Odds ≡ E e ˆm
Education Return ≡ R ˆe
Education Quality ≡Q n
To study the importance of these two factors in explaining the large variation in education
outcomes across locations, we implement the following variance decomposition:
(23) ˆn
var( E e
) = var( R ˆe
ˆ m ) + var(Q ˆ ˆe
n ) + 2covar( Rm , Qn ),
ˆn
where we denote the local odds of attending college by E ˆ m,
e , local education returns by R
ˆe
and local education quality by Q n.
Rows 1 and 2 of Table 5 present this decomposition for the baseline steady state, sepa-
rately for children from low- and high-skill families. Education quality and education
25
TABLE 5: D ECOMPOSING THE G EOGRAPHIC VARIATION
IN E DUCATION O UTCOMES
Variances Covariance
College Education Education Education
Parental Odds Returns Quality Return & Quality
Skill ˆ e
( En ) ˆ m)
(R ˆe
(Q n)
ˆe
ˆ m, Q
(R n)
Baseline Low 0.84 4.52 5.19 -4.44
Steady State High 0.96 4.62 6.03 -4.85
Equalized Low 0.23 0.23 0 0
Education Quality High 0.20 0.20 0 0
Equalized Expected Low 5.93 0 5.93 0
Education Returns High 4.24 0 4.24 0
Notes: This table decomposes the geographic variation in education outcomes into variation due to dif-
ferences in local education quality versus local education returns. Columns present the "simple" variance
decomposition for a given steady state of the general equilibrium model. Rows present the baseline steady
state (rows 1 and 2) and then the full decomposition in general equilibrium, where we ﬁrst equalize educa-
tion quality (rows 3 and 4) and then education returns (rows 5 and 6), solving each time for the new steady
state of our model. All terms are population-weighted.
returns vary substantially across locations. Their covariance is negative so childhood
locations with lower education quality have on average higher education returns. A pos-
sible explanation for the negative covariance could be that low education quality makes
it hard for the local population to become educated, which lowers local skill supply and
increases skill premia and education returns.
We then perform a model-based decomposition that accounts for interactions between
education quality and education returns in general equilibrium. In two separate counter-
factuals, we solve for the new steady state by ﬁrst equalizing education quality and then
education returns across locations, respectively by setting them to their average value.
Rows 3 and 4 of Table 5 show that an equalization of education quality across locations
substantially reduces the geographic variation in education outcomes. The only driver of
this variation now is variation in local education returns. Variation in education returns
itself decreases substantially because locations with higher initial education returns had
lower initial education quality, i.e., these two objects covary negatively in the baseline.
Equalizing education quality therefore improves it in locations with initially higher edu-
cation returns, which increases local education outcomes and skill supply and therefore
decreases local skill premia. The opposite happens in locations with low initial education
returns. This mechanism drives skill premia and education returns to become more sim-
ilar across locations. This endogenous response of local education returns ampliﬁes the
26
direct effect of equalizing education quality, leading to a substantial drop in spatial dif-
ferences in education outcomes. These results hold for children from low- and high-skill
families.
Rows 5 and 6 of Table 5 show that an equalization of education returns instead increases
the geographic variation in education outcomes. The only driver of this variation now
is variation in local education quality. Local education quality can adjust endogenously
through changes in local school funding. However, this channel does not lower the vari-
ation in education quality, which remains large and even increases slightly for children
of low-skill families. The geographic variation in education outcomes increases because
local education quality and local education returns are negatively correlated in the base-
line. Equalizing education returns therefore reduces them in locations where education
quality is low, which further deteriorates education outcomes in these low-performing
locations.
These results emphasize the importance of local education quality to explain spatial dif-
ferences in education outcomes. We now study the role of local school funding as an
important and policy-relevant component of local education quality.
6.2 Effects of Equalizing School Funding
We now use our model to study a budget-neutral school funding reform, which allocates
funds equally across students and raises all revenues through federal wage taxes. We
analyze the effects of this reform on education outcomes, intergenerational mobility, and
child opportunity values.
6.2.1 Equalizing School Funding and the Geographic Variation in Education Out-
comes
We study the effects of equalizing school funding on the geographic variation in educa-
tion outcomes by extending the variance decomposition of Equation 22 in the following
way:
ˆn
var( E e
) =var( R ˆn
ˆ m ) + var(K e
) + var( fˆn )
ˆ m, K
+ 2covar( R ˆne
) + 2covar( R ˆ ) + 2covar(K
ˆ m, fn ˆne ˆ
, fn ) .
in baseline (-) in baseline (+) in baseline (-)
Local education quality is now expressed as a function of endogenous local per student
school funding and an exogenous local component. We denote terms related to local
ˆn
odds of attending college by E ˆ m , the exogenous component of
e , education returns by R
27
TABLE 6: E FFECTS OF E QUALIZING S CHOOL F UNDING ON THE
G EOGRAPHIC VARIATION IN E DUCATION O UTCOMES
Variances Covariances
College Education Education Education Return & Return & Quality &
Parental Odds Return Quality Funding Quality Funding Funding
Skill ˆn
(E e) ˆ m)
(R ˆn
(K e) ( fˆn ) (R ˆn
ˆ m, K e) (Rˆ m , fˆn ) ˆn
(K e , fˆ )
n
Baseline Low 0.84 4.52 6.11 0.37 -4.76 0.32 -0.64
Steady State High 0.96 4.62 6.95 0.33 -5.13 0.28 -0.62
Equal Funding Low 1.11 4.52 6.11 0 -4.76 0 0
Direct Effect High 1.31 4.62 6.95 0 -5.13 0 0
Equal Funding Low 0.89 5.25 6.12 0 -5.24 0 0
GE Effect High 1.01 5.37 6.98 0 -5.67 0 0
Notes: This table documents the effects of equalizing school funding on the geographic variation in education outcomes. Columns
present the "simple" variance decomposition of local education outcomes E ˆn ˆ m , local exogenous
e into parts due to local education returns R
education quality K e , and local school funding fˆ for a given steady state. Rows present the baseline steady state (rows 1 and 2) and
ˆn n
then the effects of equalizing school funding on the geographic variation in education outcomes. We ﬁrst present the direct effects where
all objects except education choices are held constant (rows 3 and 4) and then the full general equilibrium effects where all margins of
our model adjust (rows 5 and 6). All terms are population-weighted.
ˆn
education quality by K e , and school funding by fˆ . We ﬁrst consider the direct effects of
n
equalizing school funding by holding all model objects besides funding and education
choices constant.14 We then implement the full general equilibrium (GE) effects where all
margins adjust endogenously. This approach allows us to evaluate the importance of
endogenous responses to the reform.
Rows 1 and 2 of Table 6 present the variance decomposition for the baseline steady state.
Education returns and exogenous education quality vary substantially across locations,
while school funding has a smaller variance. Local exogenous education quality and
education returns have a negative covariance. Local school funding covaries positively
with education returns but negatively with exogenous education quality. School funding
is therefore on average higher in locations that face other education frictions.
The direct effects of equalizing school funding holding all else constant substantially in-
crease the geographic variation in education outcomes (Rows 3-4 of Table 6). Locations
with initially higher school funding have on average lower exogenous education qual-
ity since these two objects negatively covary in the baseline. Equalizing school funding
therefore reduces funds in locations where exogenous education quality is low, further
deteriorating the low education quality. The opposite applies to locations with high ex-
ogenous education quality that now receive more school funding. Spatial differences in
14 Inparticular, we ﬁx local population stocks, education returns, rents, wages, and continuation values.
This counterfactual can be thought of as a one-period change in school funding that is announced after
families have made their residential choices, but before they have chosen their children’s education.
28
education outcomes therefore increase, which holds for children from low- and high-skill
families.
Equalizing school funding in general equilibrium again increases the geographic varia-
tion in education outcomes (Rows 5-6) but much less than the direct effects. In general
equilibrium, skill premia now increase in locations where school funding cuts decrease
education outcomes and skill supply. Higher skill premia create incentives for children to
get educated, which mitigates the direct effects of funding cuts on education outcomes.
The opposite applies to locations where school funding increases. General equilibrium
responses and the interactions between the funding changes and regional characteristics
are therefore important to evaluate the reform’s long-run effects.
6.2.2 Equalizing School Funding and Children’s Outcomes by Family Background
Education Outcomes by Family Background. We now document the effects of equaliz-
ing school funding on social mobility by comparing changes in children’s education out-
comes between low- and high-skill families. In the baseline, average per student school
funding is higher for children from high-skill families because they live on average in
better-funded counties.15 Equalizing school funding increases average per student fund-
ing by 1.8 percent for low-skill families and reduces it by 1.4 percent for high-skill fam-
ilies. Table 7 shows the reform’s effect on the average probability of attending college
for children from low- and high-skill families, where we take population-weighted aver-
ages across all locations. We again consider the direct effects of equalizing school funding
(where only education choices adjust) and the full general equilibrium case (where all
margins adjust). The direct effects increase children’s probability of attending college by
3.15 p.p. for low-skill families. However, these effects are mitigated to a 0.57 p.p. increase
in general equilibrium. For high-skill families, direct effects decrease children’s probabil-
ity of attending college by 0.47 p.p., which is similar in general equilibrium with a 0.33
p.p. decrease.
Mechanisms. We now investigate how school funding, education returns, and exoge-
nous education quality contribute to the effects in general equilibrium (Panels B-D of Ta-
ble 7). School funding changes have a net positive effect on children’s education outcomes
for low-skill families and a negative effect for high-skill families (cf. Panel B and direct-
effect scenario). Returns to education and skill premia decrease on average due to the re-
form, which lowers children’s incentives to get educated for low- and high-skill families
(Panel C). Differences in exogenous education quality contribute negatively to changes
15 We assume that school funding is equally available to all students in the same county.
29
TABLE 7: E FFECTS OF E QUALIZING S CHOOL F UNDING ON
E DUCATION O UTCOMES BY FAMILY B ACKGROUND
General
Parental Skill Direct Effect Equilibrium Fixed Wages
Panel A: Probability of Attending College (p.p. change)
All 1.15 0.11 0.793
Low 3.15 0.57 -0.75
High -0.47 -0.33 1.51
Panel B: Effect from School Funding
Low (+) (+) (+)
High (−) (−) (−)
Panel C: Effect from Education Returns
Low None (−) (+)
High None (−) (−)
Panel D: Effect from Exogenous Education Quality
Low None (−) (−)
High None (+) (+)
Notes: Panel A of this table documents the effects of equalizing school funding on the
probability of attending college for children from low- and high-skill families. Num-
bers in Panel A represent percentage point changes in population-weighted averages
relative to the baseline steady state. Column 1 shows the direct effects of equalizing
school funding where all objects except education choices are held constant. Column 2
documents the full general equilibrium effects where all margins of our model adjust.
Column 3 allows all margins to adjust except local wages, which are held constant.
Panels B-D analyze the mechanisms behind the results by documenting how school
funding, education returns, and exogenous education quality contribute to the pol-
icy’s effects on education outcomes.
30
in children’s education outcomes for low-skill families and positively for high-skill fam-
ilies (Panel D). Exogenous education quality in each location is constant by deﬁnition. It
nevertheless matters for changes in education outcomes because children’s exposure to
locations changes in response to policies. In particular, changes in families’ residential
and educational choices shift more low-skill (and fewer high-skill) families into locations
with lower exogenous education quality compared to the baseline. The shift happens
in the following way: First, the equalization of school funding reduces funds in locations
where exogenous education quality is low because initial funding is negatively correlated
with exogenous education quality. The funding cut reduces education outcomes which
increases the share of low-skill families in these low-education-quality locations. Lower
skill supply in these locations increases skill premia. These local wage changes mitigate
the reduction in the local skill composition by increasing children’s incentives to get ed-
ucated and by changing young adults’ residential choices. In particular, the decline in
low-skill wages decreases net inﬂows of low-skill young adults and the rise in high-skill
wages increases net inﬂows of high-skill young adults. Changes in net moving ﬂows
therefore weaken the link between children’s local education outcomes and adults’ local
skill supply. Wage changes offset the direct effects of the funding cut only partially, so the
equalization of school funding increases the share of low-skill families and decreases the
share of high-skill families in locations with low exogenous education quality.
The effects of wage changes and resulting moving ﬂow changes are nevertheless impor-
tant: If we hold wages constant, we ﬁnd a much larger shift of low-skill families into
locations with low exogenous education quality (Column 3 of Table 7). Remarkably, un-
der constant wages this effect is so strong that children’s education outcomes decrease
for low-skill families despite an increase in average school funding. Similarly, children’s
education outcomes increase for high-skill families despite a reduction in average school
funding.16
Expected Income and Child Opportunities by Family Background. Table 8 shows the
effects of equalizing school funding on children’s expected income and child opportunity
values for low- and high-skill families. We compute children’s expected income for each
parental education level and childhood location by taking expectations over children’s
future education level, family type, and moving decision. Equalizing school funding
16 Inthis counterfactual, local wages and local skill premia are ﬁxed, so changes in average education
returns are small and mostly driven by shifts of low- and high-skill families across locations that differ in
education returns. School funding and education returns are positively correlated in the baseline (cf. Table
6). Equalizing school funding therefore reduces funds in locations where initial education returns are high.
The reform therefore shifts low-skill (high-skill) families toward locations with higher (lower) education
returns compared to the baseline.
31
TABLE 8: A DDITIONAL E FFECTS OF E QUALIZING S CHOOL F UNDING
Parental Skill Changes from Baseline
Expected Low 0.32%
Income High -0.35%
Child Opportunity Low 0.42%
Value High 0.10%
Notes: This table documents the effects of equalizing school funding on ex-
pected income and child opportunity values (i.e., expected utility at birth)
for children from low- and high-skill families. All numbers are percent-
age changes in population-weighted averages relative to the baseline steady
state.
increases expected income by 0.3 percent for children from low-skill families. These chil-
dren are now more likely to become high-skill and their average wage is higher if they
remain low-skill. Expected income for children from high-skill families decreases by 0.35
percent because they are less likely to become high-skill and their average wage is lower
if they become high-skill. Child opportunity values–the expected lifetime utility of chil-
dren at birth–increases for children from low- and high-skilled families, albeit more for
low-skill families with an increase of 0.4 percent compared to 0.1 percent for high-skill
families. Expected utility at birth increases for children from high-skill families (despite
lower expected income) for two reasons. First, utility is now higher for children who re-
main low-skill. Lower inequality in the economy therefore serves as an insurance against
the possibility of receiving low education taste shocks. Second, more high-skill families
now live in locations with better education quality, which lowers their children’s utility
cost of accumulating skills.
Discussion and Summary of Results. Our decomposition shows that equalizing educa-
tion quality across locations substantially reduces the geographic variation in education
outcomes because effects are further ampliﬁed through an endogenous decrease in the ge-
ographic variation in education returns. However, equalizing education returns or school
funding increases the geographic variation in education outcomes by further deteriorat-
ing outcomes in locations with low exogenous education quality and by shifting more
low-skill families into these locations.
Comparing effects by family background, we ﬁnd that equalizing school funding has
large direct effects on children’s education outcomes for low-skill families. Effects are
substantially reduced in general equilibrium because of a decrease in average education
32
returns and a shift of low-skill families into locations with lower exogenous education
quality. For high-skill families, the equalization of school funding has negative but small
effects on their children’s education outcomes. Direct effects and full general equilibrium
effects are similar for high-skill families because lower returns to education are offset
by a shift of high-skill families toward locations with better exogenous education qual-
ity. Overall, the equalization of school funding has positive but modest effects on social
mobility. Our results and the analysis of the mechanisms emphasize the importance of
accounting for interactions between local education quality, local labor markets, and fam-
ilies’ education and residential choices when evaluating the long-run effects of education
policies. Appendix A shows that our results are robust to the inclusion of peer effects in
education and to different sample selections.
C ONCLUSION
Neighborhoods in the United States shape children’s educational and economic oppor-
tunities, putting at risk the equality of opportunity at the heart of the American dream.
Recent work by Chetty and Hendren (2018b) provides the ﬁrst estimates of the causal
effects of each US county on its children’s education and economic outcomes. They doc-
ument large differences in opportunities across counties which create an urgent need to
understand the determinants behind these effects and formulate policies that promote
equality of opportunity.
Our paper advances these objectives by developing a quantitative spatial equilibrium
model that generates neighborhood effects through local education quality and local la-
bor market access. Our framework bridges the gap between an early theoretical literature
and recent empirical work. To estimate our model, we use the county-level neighborhood
effects from Chetty and Hendren (2018b), elasticity estimates from the applied micro liter-
ature, and data on regional outcomes and characteristics from multiple census data sets.
Our framework can be used to analyze education policies in spatial equilibrium taking
into account how local education quality and education returns interact and respond to
policy. In this paper, we focus on an equalization of school funding: an intensively de-
bated policy. We ﬁnd large differences between direct and general equilibrium effects
highlighting the importance of accounting for interactions between local markets, local
education quality, and families’ educational and residential choices.
Our model can be extended to study many applications and policy questions for which lo-
cal education outcomes are important. Future research should extend the model to study
33
additional endogenous local factors that characterize local labor markets and local edu-
cation quality. A key challenge to the inclusion of additional endogenous factors is the
identiﬁcation of the structural parameters that measure the direct effect of each local fac-
tor on education outcomes. The estimation of such micro-elasticities and the inclusion of
additional endogenous determinants into our framework are promising future research
applications. Of particular interest is the role of peers in shaping children’s education out-
comes. We show in the Appendix how peer effects can be integrated into our framework
in a straightforward way but leave a thorough analysis for future research.
Our uniﬁed framework of local human capital production, local labor markets, and costly
migration can be further used to study the persistence of regional inequality, rural-urban
wage gaps, and low migration rates in advanced or developing countries. Other inter-
esting applications could study the effects of policies on local development by targeting
either local skill supply (e.g., investing in education or attracting skilled workers) or local
skill demand (e.g., subsidizing companies or creating industrial zones).
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38
A. A PPENDIX : A DDITIONAL R ESULTS
In this Appendix, we present two additional exercises. First, we analyze the school fund-
ing equalization in an extended version of our model that features peer effects as an
additional endogenous component of local education quality. Second, we evaluate rent
subsidies to low-skill parents as an alternative policy to increase social mobility by incen-
tivizing them to move to locations with better child opportunity values.
A.1 Peer Effects in Education and Equalizing School Funding
Peer effects can be an additional important determinant of local education quality. A large
literature studies peer effects in education, emphasizing that the presence of high-skill
children or families in a school or neighborhood can have positive spillovers on educa-
tion outcomes of other children (c.f. Benabou (1993), Benabou (1996), Durlauf (1996b),
Fogli and Guerrieri (2019), and Agostinelli (2018)). Importantly, the skill composition of
local peers can change in response to education policies if they induce low- and high-skill
families to move across neighborhoods. In our model, the skill composition of neighbor-
hoods is endogenously determined by families’ residential and educational choices. We
can therefore incorporate peer effects simply by specifying local education quality as:
(A.1) Qe e ˜n
¯n ) + γe log( f n ) + K
n = µ log( e
e
,
where e ˜n
¯n is the local share of high-skill families, f n is local school funding, and K e is the
exogenous component of local education quality that corresponds to this model speciﬁca-
tion. The parameters µe and γe respectively measure the causal effects of peers and school
funding on education quality.
Identifying the strength of peer effects µe is challenging and there is no clear consensus on
the size of this parameter in the literature. Most empirical studies focus on peer effects in
classrooms and not at the neighborhood level. Agostinelli (2018) ﬁnds, for example, large
peer effects in classrooms that are stronger for children from disadvantaged backgrounds.
Fogli and Guerrieri (2019) estimate the strength of local skill spillovers by targeting mo-
ments from the causal effect estimates from Chetty and Hendren (2018a). On the other
hand, Carrell et al. (2018) ﬁnd that exposure to disruptive peers has particularly large neg-
ative effects on children’s future income. Given the wide range of estimates in the litera-
ture, we consider three cases with weak (µe /σE = {1.5, 1}), medium (µe /σE = {2, 1.5}),
and strong (µe /σE = {4, 3}) peer effects. The ﬁrst number indicates the parameter for
children from low-skill families, the second for high-skill families. Following Agostinelli
A-1
(2018), we assume that peer effects are larger for children from low-skill families.
For each parameter set, we implement the counterfactuals that equalize school funding in
the following way: First, we re-estimate the exogenous component of education quality
from Equation A.1 to ensure that each extended model ﬁts observed education choices.17
Next, we solve for the respective baseline steady state while holding all parameters con-
stant at their estimated values. Finally, we equalize school funding in the same way as in
the main part of our paper and we solve for the counterfactual steady state.
Table A.1 presents the differences in probabilities of college attendance and child oppor-
tunity values between each of the three counterfactual steady states and the correspond-
ing baseline steady states. For comparability, we include our benchmark results without
peer effects. We ﬁnd that the estimated effects of equalizing school funding are similar
with none, weak, medium, or strong peer effects. Despite the similarities in the results,
we nevertheless see some differences. For children from low-skill families, we ﬁnd that
peer effects slightly increase effects on education outcomes and child opportunity values.
However, these improvements are very small, with increases in children’s probability of
attending college ranging from 0.57 p.p. without peer effects to 0.65 p.p. with strong
peer effects. Results are even more similar for children from high-skill families for whom
college-attendance probabilities decrease by 0.33 p.p. without peer effects and by 0.36 p.p.
with strong peer effects. The inclusion of peer effects has small effects on the results be-
cause the school funding equalization does not substantially change the skill composition
in neighborhoods. This is partly due to non-parents, who contribute to local peer effects
but whose residential choices do not directly respond to changes in school funding.
A.2 Subsidizing ”Moves to Opportunity”
Many academic studies and policy experiments consider rent subsidies or rent vouch-
ers as tools for improving social mobility and education opportunities for children from
disadvantaged backgrounds (e.g., Bergman et al. (2020), Katz et al. (2001), Chetty et al.
(2016) and many others). A well-known example is the Moving to Opportunity (MTO)
study, which offered housing vouchers to randomly selected families if they moved from
high-poverty housing projects to lower-poverty neighborhoods. Katz et al. (2001) found
in an initial study that these moves had no signiﬁcant effects on the earnings and em-
ployment rates of adults who accepted the voucher. In a recent study, Chetty et al. (2016)
17 We can re-estimate the exogenous education quality without re-estimating any other model parameters
due to the sequential structure of our estimation strategy, in which these regional characteristics are inferred
as structural residuals in the last step of the estimation procedure.
A-2
TABLE A.1: E FFECTS OF E QUALIZING S CHOOL F UNDING WITH P EER E FFECTS
Strength of Peer Effects
Parental Skill None Weak Medium Strong
Panel A: Probability of Attending College (p.p. change)
Low 0.57 0.60 0.61 0.65
High -0.33 -0.34 -0.35 -0.36
Panel B: Child Opportunity Value (% change)
Low 0.42 0.44 0.45 0.48
High 0.10 0.11 0.12 0.14
Notes: This table shows the effects of equalizing school funding on the probability
of attending college and child opportunity values when allowing for peer effects in
education. We consider different sets of parameters that imply weak, medium, and
strong peer effects. All numbers represent percentage or percentage point changes in
population-weighted averages relative to the respective baseline steady state which
we recompute for each peer effect level.
estimate the effects of these moves on children’s long-run outcomes. They ﬁnd signiﬁ-
cant improvements in college attendance and earnings for children who moved to better
neighborhoods at young ages.18 However, the MTO study offered rent vouchers only to a
small number of families, so that the moves did not generate general equilibrium effects.
If rent subsidies would instead be implemented as an economy-wide and permanent pol-
icy, then widespread moves could affect local skill compositions, local rents, and local
wages. We use our model to study the effects of a large-scale rent subsidy program which
allows us to account for general equilibrium effects and interactions between local labor
market outcomes, local education quality, and families’ education and residential choices.
Speciﬁcally, we consider a policy that reimburses 20 percent of total rent expenditure to
low-skill parents conditional on living in locations that are in the top quartile of the base-
line distribution of education outcomes. We fund the rent subsidy through a lump-sum
tax on all workers. Table A.2 shows that the rent subsidy has moderate effects on edu-
cation outcomes. Children’s probability of attending college increases by 0.35 p.p. for
low-skill families and decreases by 0.4 p.p. for high-skill families. Despite the small ef-
18 Our model framework is consistent with these ﬁndings. Families in the MTO study moved between
close-by neighborhoods so that they stayed in the same labor market. In that case, our model predicts
that adults’ earnings remain unchanged, but that children’s education outcomes and their future income
improve if families moved to neighborhoods with better education quality.
A-3
TABLE A.2: E FFECTS OF S UBSIDIZING R ENT OF L OW-S KILL PARENTS
Parental Skill Change from Baseline
Probability of Low 0.35 p.p.
Attending College High -0.41 p.p.
Child Opportunity Low -0.27%
Value High -0.04%
Notes: This table presents the effects of subsidizing rent of low-skill parents on
children’s probability of attending college and on average child opportunity
values for low- and high-skill families. The rent subsidy is funded through a
lump-sum tax and reimburses 20 percent of total rent expenditure to low-skill
parents conditional on living in locations with good education outcomes in
the baseline. All numbers represent percentage or percentage point changes
in population-weighted averages relative to the baseline steady state.
fects, the subsidy successfully increases the share of low-skill parents who live in eligible
locations (by approximately 20 percent), so more children from low-skill families have
access to high education quality. The subsidy increases rents in eligible locations, which
pushes low-skill non-parents and high-skill families out of these locations. Overall, the
share of low-skill workers increases in eligible locations, which lowers low-skill wages
and raises high-skill wages. Despite the increase in local skill premia, returns to educa-
tion measured in utils nevertheless decline due to the eligibility rules of the policy. Only
low-skill parents are eligible to receive the subsidy, which raises their utility and makes it
more attractive for children to remain low-skill. The redistributive nature of the policy
therefore has unintended effects which lower children’s incentives to become educated
for children from low- and high-skill families.
The child opportunity values decrease by 0.27 percent for children from low-skill fami-
lies and by 0.04 percent for high-skill families. Child opportunity values are children’s
expected utility at birth where the expectation is taken over all possible future education
and family types. The child opportunity values decrease because the subsidy increases
the welfare of low-skill parents but decreases it for all other education and family types
who are not eligible for the rent subsidy but face higher rents and have to pay the lump-
sum tax to fund the subsidy.
A-4
A.3 Robustness of Results to Samples and Imputations
To test the robustness of our results, we re-compute the decomposition and policy coun-
terfactuals in a variety of different samples. We re-estimate regional characteristics each
time by inferring the structural residuals that perfectly ﬁt our model predictions to re-
gional data moments (as described in Section 5.3). We do not re-estimate the structural
and time-invariant parameters (cf. Section 5.1 and 5.2). In the main analysis of our pa-
per, we use 2010 data and restrict the sample to workers between 35 and 44 years.19 We
test the robustness of our results to other sample selections by using data for all workers
above 25 years. For this age group, we implement all counterfactuals with data from 1990
and 2010.
We further test the robustness of our results to different county samples. A key data mo-
ment for our quantitative analysis are the causal effects of childhood counties on chil-
dren’s education choices which we obtain from Chetty and Hendren (2018b). In the
main analysis of our paper, we complement these data with information on local college-
attendance probabilities (also obtained from Chetty and Hendren (2018b)) when causal
effect estimates are missing or out of the admissible (0,1) bounds for probabilities. We
test whether this imputation affects our results by re-computing all counterfactuals in a
smaller county sample for which causal effect estimates are available. In addition, we
re-compute all counterfactuals in a sample of counties for which the causal effects are
most precisely estimated. In particular, we exclude counties for which standard errors
of estimated causal effects lie in the top 25 or top 50 percentiles. This exercise addresses
potential concerns about the robustness of the causal effect estimates from Chetty and
Hendren (2018b) (as discussed, for example, in Mogstad et al. (2020)).
For all of these different data samples, we ﬁnd that our results and the underlying mech-
anisms are qualitatively unchanged and quantitatively very similar. This ﬁnding holds
for the decomposition and the equalization of school funding.
19 This age group best maps to the timing in our model which assumes that adults move after ﬁnishing
their education and after knowing whether they have children or not, but before joining the labor market.
A-5
O NLINE A PPENDIX FOR
S AVING THE A MERICAN D REAM ?
E DUCATION P OLICIES IN S PATIAL G ENERAL E QUILIBRIUM
BY FABIAN E CKERT AND TATJANA K LEINEBERG
FOR ONLINE PUBLICATION ONLY
A. M ODEL S OLUTION AND D ERIVATIONS
This section provides all equations that characterize the solution of our extended quanti-
tative model (described in Section 4). The equations are closely related to the solution of
our core framework (described in Section 3).
Static Choice between Housing and Consumption Goods. Workers of education and
e
family types ek live in a neighborhood n. They spend their entire disposable income Yn
on housing H and the homogeneous consumption good C by solving the following utility
maximization problem:
αek 1−αek
H C
max log exp(Aek
n) ,
C, H αek 1 − αek
subject to the budget constraint:
e w
Yn = (1 − τg e
)(1 − τsw )wm e
+ Dwm = rn H + C,
where Aek e ek
n denotes amenities, wm wages, rn rents, and α housing expenditure shares. τg
w
and τsw denote federal and state wage taxes. Dwme is the reimbursement of aggregate rent
payments.
The utility maximization yields the following indirect utility function:
ek
(OA.1) Un = Aek e ek
n + log(Yn ) − α log(rn ).
Dynamic Decision Problem. The expected utility of young adults with education e, fam-
ily type k and childhood location m before moving is given by:
ek ek
Vt (m, e, k) = E n
max Un t − Cmm t + σN nt + 1k=1 βOt (n , e) ,
n ∈N
where expectations are taken over young adults’ location taste shocks n . Cmm ek are mov-
ing costs, σN is the dispersion of location taste shocks, and β is the altruism parameter.
O(n, e) denotes the child opportunity value (i.e., the expected utility) of children who
are born to parents of education e and raised in childhood location n. Child opportunity
values can be expressed as follows:
Ot (n , e) =E e max 1e =h Qe
n t + σE et + ∑ Pr t (k | e )Vt+1 (m , e , k ) ,
e k
where expectations are taken over children’s education taste shocks e . Qen denotes local
education quality, σE is the dispersion of education taste shocks, and Pr(k | e) are fer-
tility probabilities. We deﬁne continuation values before knowing fertility as R(m, e) =
OA - 1
∑ Pr(k |e)V (m, e, k ). We assume that location and education taste shocks are extreme value
k
distributed. This assumption allows us to express value functions and child opportunity
values in closed form as:
1 ek 1 ek β
(OA.2) Vt (m, e, k ) = σN log ∑ exp
σN
Un t −
σN
Cmm t + 1k=1 Ot (n , e)
σN
and
n ∈N
1 1
(OA.3) Ot (n, e) = σE log ∑ exp
σE
1e = h Q e
nt +
σE
R t +1 ( m , e ) .
e
The share of young adults with education e and family type k that move from childhood
location m to adulthood location n is given by:
1 ek 1 ek
exp σN Un t − σN Cmm t + 1k=1 σβ
N
Ot ( n , e )
(OA.4) Pr t (n | m, e, k) = ,
1 ek 1 ek
∑n ∈N exp σN Un t − σN Cmm t + 1k=1 σβ
N
Ot ( n , e )
and the share of children in location n with parents of education e who choose education
e is:
1 e 1
exp σE 1e =h Qnt + σE Rt+1 ( m, e )
(OA.5) Pr t (e | n, e) = .
1 e 1
∑ exp σE 1e =h Qnt + σE Rt+1 ( m, e )
e
These analytical expressions are standard in the literature under the assumption of ex-
treme value distributed shocks. A useful reference for the derivations is Redding and
Rossi-Hansberg (2017).
Law of Motion
Individuals’ residential and educational choices and their exogenous fertility probabilities
determine how the distribution of workers evolves dynamically across locations, skill
levels, and family types. The resulting law of motion is given by:
Le 1
(OA.6) Le
nt
k
= ∑ Pr t (n | m, e , k ) Pr t−1 (k | e ) ∑ ∑ Pr t−1 (e | n, e) nt−1
,
m ∈M e n ∈Nm Prt−1 (k | e)
where Le 1
nt−1 denotes the number of parents with education e who live in neighborhood n
at time t − 1.
OA - 2
Market Clearing
Rental market clearing in each neighborhood determines the local rental rate rn as a func-
tion of local ﬁxed housing supply Hn and residents’ local housing demand:
1
(OA.7) Hnt =
rnt ∑ ∑ αek Ynt
e ek
Lnt .
e k
e which equalize ﬁrms’ local
Labor market clearing determines wages for each skill type wm
labor demand and residents’ local labor supply:
1
e e ρ −1 ρ ρ ρ −1
(OA.8) wmt = Smt ( Le
mt ) Zmt h
Smt h
Lmt l
+ Smt Ll
mt .
Recursive Equilibrium
The recursive equilibrium is deﬁned conditional on a list of exogenous parameters. Struc-
tural parameters are housing expenditure shares (αek ), altruism ( β), dispersion of location
and education taste shocks (σE , σN ), causal effects of school funding on the probability
of attending college (γe ), the elasticity of substitution between low- and high-skill work-
ers in production (ρ), and probability of becoming a parent, conditional on education
(Pr(k |e)). We denote the collection of these parameters by Υ ≡ {αek , β, σE , σN , γe , ρ, Pr(k |e)}.
Other parameters are tax rates and school funding allocation rules from federal, state, and
local governments, which we denote by: Γt ≡ {τgt w , τ w , τ r , δ g , δs }. Last, time-varying re-
st nt nt nt
gional characteristics include productivity, skill intensity, moving costs, amenities, hous-
ing supply, and the exogenous component of education quality, which we denote by:
Θt ≡ {Zmt , Smte , C ek , Aek , H , K e }.
mm t nt nt nt
Conditional on these exogenous parameters, the equilibrium deﬁnition is similar to that
of our core framework presented in Section 3. Endogenous factor prices are now local
e , r }.
wages and rents {wmt nt
B. D ATA C ONSTRUCTION AND S UMMARY S TATISTICS
The estimation of our model relies on the following key data moments: moving ﬂows
across commuting zones (CZs), wages by education level and CZ, and at the county level
population stocks, education choices for children from low- and high-skill families, per
student school funding and rents. We now describe the sources and construction of our
data sets. Table OA.3 provides summary statistics.
OA - 3
B.1 Data Construction
Moving Flows by Education and Family Type across Commuting Zones. We construct
moving ﬂows across CZs for each education and family type using individual-level data
from the decennial census in 1990 and 2000 and the American Community Survey (ACS)
in 2006-2010. We obtain the data from the Integrated Public Use Microdata Series (IPUMS)
(see Ruggles et al. (2017)). In our model, we assume that individuals move only once in
their life, after ﬁnishing their education and before joining the labor market. To capture
such moves in the data, we restrict the sample to young adults who are between ages
35 and 50 years. The data provide information on respondents’ current and past Public
Use Microdata Area (PUMA) of residence. The 1990 and 2000 census reports PUMAs of
residence 5 years ago, the 2006-2010 ACS 1 year ago, which allow us to construct 5-year
moving ﬂows for 1990 and 2000 and 1-year moving ﬂows for 2010. We then adjust the
1-year moving ﬂows by simulating them forward to construct a consistent panel of 5-year
moving ﬂows across all three decades (more detail below). We use a crosswalk to map
PUMAs to CZs.
Adjusting 1-year Moving Flows. To construct consistent 5-year moving ﬂows across all
three decades, we make the following adjustment to the 1-year moving ﬂows that we
observe in the 2006-2010 data. We start with the accounting identity:
Lm ,t = Bmm ,t,t−1 Lm,t−1 ,
where Lm,t−1 is the population in origin m before moving and Lm,t is the population in
destination m after moving. Bmm ,t,t−1 denotes the 1-year moving matrix, i.e., the popu-
lation share that moves from origin m to destination m between years t − 1 and t. These
objects are observed in the data. We simulate the 1-year moving matrix forward ﬁve times
to construct 5-year moving ﬂows as:
Lm ,t = Bmm ,t,t−5 Lm,t−5 ≈ (Bmm ,t,t−1 )5 Lm,t−5 .
We use this procedure separately for each education and family type.
Robustness of the Moving Flow Adjustment. In our model estimation, we use moving
ﬂows to identify bilateral moving costs across CZs and the utility levels offered by each
CZ. To verify how the adjustment procedure affects these results, we exploit the fact that
we observe 1-year and 5-year moving ﬂows for 2000 because the ACS and the decennial
census overlap in this year. For 2000, we can therefore compare estimates of moving costs
and utilities that we obtain from observed 1-year moving ﬂows (ACS), observed 5-year
moving ﬂows (census), and simulated 5-year moving ﬂows. We estimate moving costs
OA - 4
and utility levels by PPML from Equation (16) separately for each of the three sets of
moving ﬂows. Due to a small sample size, we use moving ﬂows across states (excluding
Alaska, Hawaii and DC) and we pool all family and education types who are older than 25
years. Table OA.1 shows that the level and dispersion of estimated moving costs are very
similar when using the observed or simulated 5-year moving ﬂows. CZ utility levels are
identiﬁed from destination ﬁxed effects up to a constant of normalization. The variation
of utility across CZs is therefore the statistic of interest, which is similar for estimates from
observed and simulated 5-year moving ﬂows (cf. Table OA.1). These ﬁndings suggest
that the adjustment of 1-year moving ﬂows does a good job at replicating the patterns of
observed 5-year moving ﬂows.
TABLE OA.1: M OVING C OST AND CZ-U TILITY
WITH S IMULATED AND O BSERVED M OVING F LOWS
Data Sample Mean Std. Dev.
Panel A: Moving Cost
1-yr observed ﬂows 7.16 1.33
5-yr simulated ﬂows 5.55 1.06
5-yr observed ﬂows 5.82 1.09
Panel B: CZ-Utility (Fixed Effects)
1-yr observed ﬂows 0.20 0.32
5-yr simulated ﬂows 0.21 0.33
5-yr observed ﬂows 0.14 0.33
Notes: This table presents estimates of moving
cost and CZ-utility obtained from estimating Equa-
tion 16 by Poisson pseudo-maximum likelihood
(PPML). The estimation is done separately with
2000 data from observed 1-year moving ﬂows
(ACS), observed 5-year moving ﬂows (census), and
simulated 5-year moving ﬂows. The sample in-
cludes bilateral moving ﬂows across 33 states, so
N = 332 = 1, 089. Estimates of moving costs and
the dispersion of CZ-utilities are similar when us-
ing observed or simulated 5-year moving ﬂows.
Population Stocks by Education and Family Type in Each County. We obtain data on
local population stocks by education and family type from the Education Demographic
and Geographic Estimates (EDGE). The data are special tabulations of census data and
OA - 5
are provided by the National Center for Education Statistics (NCES).20 For 1990, 2000,
and 2010, we obtain information on the number of households by education level and by
“presence of children” for each school district. In 2010, the data are further disaggregated
into age groups. We aggregate population stocks to the county level, which provides our
empirical measure of population by education and family type in each county.
Wages by Education Level for Each Commuting Zone. We use data on annual labor
income from the 5 percent microdata samples from the 1990 and 2000 decennial census
and the 2006-2010 ACS from IPUMS. We restrict the sample to full-time workers between
35 and 50 years where we deﬁne full-time work to be at least 48 weeks per year and on
average between 36 and 60 hours per week. We use the individual-level data to esti-
mate Mincer regressions. We control for a range of worker characteristics to isolate the
variation of wage income that is due to locations and education levels. We estimate the
following regression across individuals i in the data:
log(wi ) = Di, f emale + Di,black + α1 expi + α2 exp2 3 4
i + α3 expi + α4 expi + De Dm + i ,
where wi is annual gross wage income, D f emale is a dummy that indicates if the worker
is female, Dblack indicates if the worker is black, and expi are years of experience. The re-
gression speciﬁcation includes the full set of interactions between location and education
ﬁxed effects De Dm . These ﬁxed effects estimate wages by education level and location
up to a constant of normalization. We use a crosswalk to map PUMAs to CZs, applying
population weights if borders overlap.
Education Outcomes by County. We obtain data on education outcomes by childhood
county from Chetty and Hendren (2018b). For each childhood county in the US, the au-
thors provide children’s college attendance rates and the causal effects of the county on
children’s college attendance rates for families at the 25th and 75th percentiles of the na-
tional income distribution. Causal effects are estimated with quasi-experimental evidence
from movers. We map our model to the causal effect estimates because our model pre-
dicts that all differences in local education outcomes are causal to the childhood county
(conditional on parental education).21 We use families’ income percentile as proxies for
low and high education levels. Causal effects are estimated relative to the average county,
so that their level is not identiﬁed. We therefore adjust the levels to match the aggregate
20 The data are available at https://nces.ed.gov/programs/edge/.
21 Inour model, children’s education choices depend on parental education, childhood location and id-
iosyncratic education taste shocks. Education taste shocks are i.i.d. distributed and realized only after
families chose their adulthood neighborhood. Families therefore can not sort into neighborhoods based on
the realization of education taste shocks, so that average taste shocks do not differ across neighborhoods.
Future research could extend our model to study the effects of this type of sorting.
OA - 6
college enrollment rate respectively for children from low- and high-income families.
School Funding by County. We obtain school funding data at the school-district level
from the NCES. The annual Finance Survey (F-33) provides information on school dis-
tricts’ funding from federal, state, and local sources. In addition, we obtain information
on the number of students in each school district from the Common Core of Data (CCD)
ﬁles. We aggregate the data to the county level.
Rental Rates by County. We estimate county rental rates from tabulations of US census
data provided by the National Historical Geographic Information System (NHGIS). The
NHGIS provides information on median rent and several housing characteristics at the
block-group level. Block groups are small geographic units. Each county nests multiple
block groups. We use these data to estimate hedonic price regressions, following Eeck-
hout et al. (2014). We control for a range of each block group’s housing characteristics to
isolate the variation in rents across counties. We regress block group j’s median rent on
housing characteristics and county ﬁxed effects so that:
(OA.9) log rent j = log year j + rooms j + unit j + Tn + j ,
where j indexes each block group, r j is median gross rent in each block group, year j is the
median year of construction, rooms j is the median number of rooms, and unit j is a dummy
that indicates the most common type of structure in each block group. Tn are county ﬁxed
effects. These ﬁxed effects identify counties’ rental rates per quality-adjusted housing unit
up to a constant of normalization. We estimate the hedonic price regressions separately
for each decade and weigh block groups by their number of renters. Table OA.2 shows
the regression results.
Bartik Labor Demand Shocks by Commuting Zone. We compute Bartik-like local labor
demand shocks using US census data from 1980, 1990, 2000, and ACS data from 2006-
2010 provided by IPUMS. To compute changes in industries’ national wages for each skill
type, we restrict the sample to full-time workers between 35 and 50 years and we drop
observations with weekly wages below 150 USD. We deﬁne industries by the 2-digit SIC
codes provided in the census data. To avoid endogeneity issues, we compute national
changes in industry wages for each CZ by excluding the respective CZ from the data. We
then weigh each industry’s national wage changes by CZs’ industry-level employment
in 1980. We implement the procedure separately for low- and high-skill workers. The
census data provide PUMA identiﬁers that we map to CZs with a crosswalk.
Variables to Parameterize Moving Costs across Commuting Zones. We obtain CZ char-
acteristics from the 1990 and 2000 US census and the 2006-2010 ACS. For each CZ, we
OA - 7
TABLE OA.2: H EDONIC P RICE R EGRESSIONS FOR R ENTED H OUSING
Log Median Gross Rent
1990 2000 2010
2 Rooms 0.190*** 0.382*** 0.371***
(0.012) (0.013) (0.023)
3 Rooms 0.278*** 0.487*** 0.504***
(0.011) (0.012) (0.022)
4 Rooms 0.356*** 0.545*** 0.534***
(0.011) (0.012) (0.022)
5 Rooms 0.468*** 0.641*** 0.602***
(0.011) (0.012) (0.022)
6 Rooms 0.578*** 0.738*** 0.694***
(0.011) (0.012) (0.022)
7 Rooms 0.664*** 0.821*** 0.763***
(0.012) (0.013) (0.022)
8 Rooms 0.756*** 0.908*** 0.833***
(0.014) (0.014) (0.023)
9+ Rooms 0.815*** 1.029*** 0.895***
(0.024) (0.021) (0.026)
1-family house, attached -0.038*** -0.024*** -0.032***
(0.003) (0.004) (0.004)
2-family building -0.009*** -0.004 -0.056***
(0.003) (0.003) (0.003)
3-family building -0.020*** -0.029*** -0.088***
(0.002) (0.002) (0.003)
5-family building -0.047*** -0.043*** -0.114***
(0.002) (0.002) (0.002)
10-family building -0.016*** -0.014*** -0.102***
(0.002) (0.003) (0.002)
20-family building -0.037*** -0.046*** -0.129***
(0.002) (0.003) (0.003)
50-family building -0.079*** -0.056*** -0.150***
(0.002) (0.002) (0.003)
Log Median Construction Year 10.483*** 10.649*** 9.168***
(0.102) (0.100) (0.093)
Observations 211,977 201,714 186,250
R-Squared 0.565 0.527 0.529
Notes: Standard errors in parentheses;*** p<0.01, ** p<0.05, * p<0.1. This table presents the results of
hedonic price regressions that regress log rents on several proxies for housing quality and county ﬁxed
effects. Regressions are estimated at the block-group level and separately for each decade. To proxy
housing quality in each block group, we use data on the median construction year, the median number
of rooms and the mode of housing unit types. Number of rooms and housing type enter as categorical
variables with the omitted categories being "1 Room" and "Detached one-family home."
OA - 8
observe the state(s) and division to which it belongs. CZs can overlap state borders, so
we allow CZs to belong to up to three different states. CZs are classiﬁed as coastal if they
are part of census division 1 or 9 and as urban if they are part of a metropolitan statistical
area (MSA). Distances between the centroids of two CZs are calculated in ArcGIS using
shapeﬁles from the census TIGER ﬁles.
B.2 Summary Statistics
We provide population-weighted summary statistics of the key data moments in Table
OA.3 using data from 2006-2010.
Panel A shows wage rates for each skill level. We normalize total US wages to have a
population-weighted mean of one. Low-skill wages average 0.7 with a standard deviation
of 0.07. High-skill wages average 1.3 with a standard deviation of 0.2. The average skill
premium–deﬁned as the log ratio between low- and high-skill wages–is 57 percent with
a standard deviation of 8 percent.
Panel B shows county-level rental rates normalized to have a population-weighted mean
of one. The standard deviation of county rent is 0.3. Rent in the county at the 90th per-
centile is 47 percent above average. In the county at the 10th percentile, rent is only 64
percent of the average.
Annual per student school funding is on average $12,430 (Panel C) which varies from
$9,254 in the county at the 10th percentile to $17,608 in the county at the 90th percentile.
Counties receive on average 12 percent of their school funding from the federal govern-
ment, which has a standard deviation of 5 percent. State and local governments each
provide on average 44 percent of funds with a standard deviation of 13.5 percent for state
funding and 15.5 percent for local funding.
Panel D documents children’s college attendance rates and the causal effects of childhood
counties on children’s college attendance rates for families at the 25th and 75th percentile
of the national income distribution. We obtain these estimates from Chetty and Hendren
(2018b). Children’s average college attendance rate is 55.8 percent for low-income fami-
lies and 84.2 percent for high-income families with standard deviations of 9 percent for
low-income families and 4 percent for high-income families. Chetty and Hendren (2018b)
estimate causal effects of childhood counties on college attendance rates per year of expo-
sure and ﬁnd linear exposure effects for ages below 20 years. We therefore multiply the
authors’ annual estimates by 20 to measure the total causal effect of spending an entire
childhood in a given county. The causal effects are estimated relative to the average, so
that their level is not identiﬁed. Causal effects vary substantially across counties with a
OA - 9
standard deviation of 15 percentage points (p.p.) for children from low- and high-income
families. Children from low-income families who spend their entire childhood in a county
at the 10th (90th) percentile have a 14 p.p. lower (higher) probability of attending college
than the average child from the same income group. For children from high-income fam-
ilies, the probability is 8 p.p. lower (higher) in the county at the 10th (90th) percentile.
TABLE OA.3: S UMMARY S TATISTICS OF R EGIONAL D ATA
Obs. Mean Std. Dev. p10 p90
Panel A: Wages and Skill Premia across CZs
Wages for Low-Skill Workers 692 0.69 0.07 0.6 0.8
Wages for High-Skill Workers 692 1.27 0.19 1.01 1.49
Skill Premia (%) 692 57 7.9 47.4 67.3
Panel B: Housing Rents across Counties
Rental Rates 2,841 1 0.31 0.64 1.47
Panel C: School Funding across Counties
School Funding per Student ($) 2,841 12,430 3,704 9,254 17,608
Share of Local Funding from (%)
Federal Government 2,841 11.8 5.0 5.4 17.8
State Government 2,841 43.8 13.5 25.8 61.6
Local Government 2,841 44.4 15.5 23.8 65.9
Panel D: College Attendance Rates and Causal Effects across Counties
College Attendance Rates by County (%)
Low-Income Parents 2,840 55.8 9.1 44.7 68.4
High-Income Parents 2,840 84.2 4.2 79.0 88.8
Causal Effect of County on College Attendance Rate (p.p.)
Low-Income Parents 2,350 – 14.8 -13.7 14.0
High-Income Parents 2,350 – 15.3 -8.2 7.8
Notes: All summary statistics are population-weighted. Aggregate wages and rents are nor-
malized to have a population-weighted mean of 1.
OA - 10
C. E STIMATION D ETAILS
C.1 Calibrated Parameters
Housing Expenditure Shares. Housing expenditure shares αek are calibrated to expendi-
ture data from the 2011 Consumer Expenditure Survey (CEX) provided by the Bureau of
Labor Statistics (BLS). The CEX ﬁle fmli111x provides information on individuals’ educa-
tion, presence of children in the household, expenditure on housing (variable sheltcq) and
total expenditure (variable totexpcq). We restrict our sample to families with and with-
out children (fam_types 1-4) who earn a minimum weekly income of 150 USD. We use
these data to compute average housing expenditure shares for each education and family
type in our model. The average low-skill (high-skill) family with children spends 38 (36)
percent of its income on housing compared to 34 (33) percent for those without children.
Fertility Probability. We set fertility probabilities for each education group, Pr(k | e),
to the observed fraction of workers with education e where children are present in the
household. We obtain this fraction from US census data from IPUMS. We restrict the
sample to ages between 35 to 44 years. Low-skill workers have a fertility probability of
56 percent, whereas high-skill workers have a fertility probability of 63 percent.
Elasticity of Substitution between Worker Types in Production. We follow Ciccone and
Peri (2005) and set the elasticity of substitution across low- and high-skill workers to 1.5,
which implies that ρ = 1/3. Ciccone and Peri (2005) use changes in compulsory schooling
laws in US cities to isolate exogenous variation in skill supply at the city level. They use
microdata from the US census and deﬁne workers to be high-skill if they have education
beyond a high school diploma, as we do in our paper. Other studies ﬁnd similar results
such as Katz and Murphy (1992) (1.41) and Heckman et al. (1998) (1.44). Autor et al. (1998)
review the literature.
Tax Rates and Rent Reimbursement. Federal and state governments tax wages and local
governments tax rents. We denote the tax rates respectively by τgw ,τ w , τ r , where g denotes
s n
the federal government and s denotes state governments. We assume that all tax revenues
are used for school funding and that each level of government balances its budget. Each
state funds schools only within its borders. These assumptions allow us to identify tax
rates from the budget constraints. For states, budget constraints are equal to:
(OA.10) ∑ s
Fn = τsw ∑ ∑ wm
e e
Ln ,
n ∈Ns n ∈Ns e
OA - 11
where Fns is total school funding from state s to neighborhood n. Aggregating over neigh-
borhoods in each state (n ∈ Ns ) derives states’ total school expenditure. The federal
budget constraint is equal to:
∑ Fn ∑ ∑(1 − τsw )wm
g w e e
(OA.11) = τg Ln ,
n ∈N n ∈N e
g
where we allow for deductibility of state taxes. Fn is total federal school funding given
to neighborhood n. We can identify federal and state wage taxes using these budget con-
straints and local data on wages, workers by skill type, and school funding from federal
and state governments to each neighborhood.
Local governments tax rents at a rate τnr . Tenants pay a rental rate r = (1 + τ r )r ∗ , which
n n n
∗ r
consists of market rate rn and tax rate τn . For local governments, budget constraints are
equal to:
r
τn
n r ∗
(OA.12) Fn = τn rn Hn = r H ,
r n n
1 + τn
n is total local school funding (raised and spent) in neighborhood n. Total rental
where Fn
expenditure in each neighborhood n is given by:
(OA.13) rn Hn = ∑∑αek Yn
e ek
Ln ,
e k
which we can construct from calibrated housing expenditure shares α ˆ ek , data on local
population stocks Lek e
n and information on local disposable income Yn . Disposable income
is equal to:
e w
Yn = (1 − τg e
)(1 − τsw )wm e
+ Dwm ,
which we can construct from calibrated federal and state income tax rates and data on
local wages. The “dividend” D reimburses national rental income back to all workers in
proportion to their wage income. D is therefore equal to the ratio between national rent
income (after taxes) and national wage income:
∗H n
∑ rn n ∑ rn Hn − ∑ Fn
n ∈N n ∈N n ∈N
(OA.14) D= = .
∑ ∑ wm
e Le
m ∑ ∑ wm
e Le
m
m ∈M e m ∈M e
Substituting Equation OA.13 into OA.14 and rearranging allows us to solve for D as a
function of observables in the following way:
∑ ∑∑ Lek ek e w w n
n α wm (1 − τg )(1 − τs ) − ∑ Fn
n ∈N e k n ∈N
D= .
∑ ∑∑ Lek ek e
n (1 − α ) w m
n ∈N e k
ˆn
ˆ at hand, we can construct disposable local income Y
With the calibrated value of D e and
OA - 12
total rental expenditure rn Hn in each neighborhood (Equation OA.13). Using these mea-
r (Equation OA.12).
sures, we can then solve for the local tax rate on rents τn
Adjustment of School Funding Revenues. Our model aims at replicating the observed
distribution of per student school funding across neighborhoods. In our model, the num-
ber of children in each neighborhood depends on the local share of parents. Parents have
1/ Pr(k |e) children to keep total population constant, so the total number of children per
neighborhood is given by: ∑e Le 1
n / Pr( k | e ). In the data, locations vary in the average num-
ber of children per family. The model therefore does not precisely replicate the observed
distribution of children across neighborhoods. To ensure that our model nevertheless
matches the observed distribution of per student school funding, we adjust funding levels
to account for differences in the total number of students. We use the adjusted school
funding data to calibrate tax rates.
C.2 Deriving an Expression for County-Utility
ek as a function of
In this section, we derive Equation 17, which expresses county-utility xn
county population stocks Lek ek
n and average CZ-utility um in the following way:
ek Lek
n ek
exp(xn )= ek
exp(um ).
Lm
To derive this expression, we start from our model’s prediction of moving ﬂows of young
adults from their childhood labor market m to a destination labor market m , which is
equal to:
ek − c ek
exp um
Lek
m = ∑ ∑ ˜ ek
Pr(n | m, e, k ) L m = ∑ ek
mm
ek
˜ ek
L m,
m ∈M n ∈Nm m ∈M ∑ m ∈M exp(um − cmm )
where L˜ ek
m are young adults with education e and family type k in their childhood location
m. This equation follows from individuals’ utility-maximizing moving choices (Equation
OA.4). Rearranging this equation gives:
˜ ek
ek + log( L
exp −cmm m)
(OA.15) ek
exp(um ) = Lek
m / ∑ ∑m ek − c ek
.
m ∈M ∈M exp um mm
In addition, we can express the population stock in a county n by summing moving
inﬂows across origins, so that:
ek − c ek
exp xn
Lek
n = ∑ ˜ ek
Pr(n |m, e, k ) L m = ∑ ∑n
mm
ek ek
− cmm
˜ ek
L m.
m ∈M m ∈M ∈N exp xn
OA - 13
ek out of the sum, dividing and multiplying by Lek
Pulling destinations’ county-utilities xn m
and rearranging the equation gives the desired expression that links county utility to
county population stocks and CZ-utilities as follows:
Lek ˜ ek
ek + log( L
exp −cmm m)
ek
exp(xn ) = n
Lek
Lek
m/ ∑ ∑n ek − c ek
m m ∈M ∈N exp xn mm
Lek
n ek
= exp(um ),
Lek
m
where we used Equation OA.15 in the last row.
C.3 Deriving an Expression for Child Opportunity Values
We show that child opportunity values, Ot (n, e), for children with parents of education e
in neighborhood n can be expressed as:
Ot (n, e) = Rt+1 (m, l ) − σE log(Pr t (l | n, e)),
where Prt (l | n, e) is the share of these children that remains low-skill and Rt+1 (m, l ) is
the continuation value of low-skill young adults before knowing their fertility shocks.
We suppress time subscripts in the rest of the derivation. We start from the standard
expressions for child opportunity values and education choices which follow from the
assumption that education taste shocks are Gumbel distribution and which are equal to:
1 1
(OA.16) O(n, e) = σE log ∑ exp σE
R ( m , e ) + 1e = h Q e
σE n ,
e
and
1 1 e 1 1 e
exp σE R ( m, e )+ σE 1e =h Qn exp σE R ( m, e )+ σE 1e =h Qn
Pr(e | n, e) = = ,
1 1 1
∑ exp σE R ( m, e )+ e
σE 1e =h Qn exp σE O ( n, e )
e
where we substitute Equation OA.16 into the denominator of the education choice equa-
tion. We evaluate education choices for the option of remaining low-skill at e = l which
gives:
1
exp σE R ( m, l )
Pr(l | n, e) = .
1
exp σE O ( n, e )
Rearranging this equation gives the desired expression for child opportunity values. The
derivation uses the fact that education is a binary choice. Education quality therefore
shifts the probability of becoming high-skill relative to remaining low-skill which is equiv-
alent to normalizing the (utility) cost of remaining low-skill to zero.
OA - 14
C.4 Estimation of Regional Characteristics
C.4.1 Inferring Regional Characteristics as Structural Residuals
Production Technology. We use ﬁrms’ ﬁrst-order conditions (Equation OA.8) to identify
the productivity parameters of the CES production function in each location. Firms’ ﬁrst-
order conditions imply that:
ρ −1
h
Sm h
wm Ll
m
l
= l h
,
Sm wm Lm
where we can infer skill intensities Sme using the calibrated value of ρ = 1/3, data on
h + Sl = 1. We then use these
local wages and local labor stocks, and the property that Sm m
results together with ﬁrms’ ﬁrst-order conditions to infer local total factor productivity
Zm as follows:
wme
Zm = 1− ρ
.
e ( L e ) ρ −1 × S l L l
Sm
ρ h Lh
+ Sm
ρ ρ
m m m m
Housing Supply. We infer housing supply Hn to ensure that local rental markets clear in
each neighborhood. To do so, we use Equation OA.7 and local data on rent expenditure
and rental rates.
Exogenous Education Quality. We infer the exogenous component of local education
quality from data on local education probabilities, local school funding, and our estimates
of local returns to education R(m, e) in the following way:
e Pr(h | n, e)
Kn = R(m, h) − R(m, l ) + γe log( f n ) − σE log .
1 − Pr(h | n, e)
Amenities. We infer amenities for each education type from estimated county-utilities of
non-parents and from data on real disposable income in the following way:
e e0 1 e0
(OA.17) an = xn − I .
σN n
C.4.2 Identifying the Level of Amenities and Education Quality
Amenities for each education type are identiﬁed from residential choices of non-parents
which are static decisions. A change in amenity levels affects non-parents’ utility only
through an additive shifter of ﬂow utilities. Such an additive increase or decrease in
utility in all locations does not affect residential choices because the shifter simply cancels
from the numerator and denominator of residential choice probabilities. Amenities are
OA - 15
therefore identiﬁed only up to constant of normalization. In this section, we show that
we can normalize amenities for each skill type without loss of generality because the
dynamic residential choices of parents as well as children’s dynamic education choices
are also invariant to amenity levels.
First, we show that a normalization of amenity levels does not affect parents’ residential
choices conditional on children’s education choices. To do so, we write parents’ residential
choices as:
(OA.18)
exp an e + 1 I e1 − c e1 + β R ( m , l ) − βσE log (Pr( l | n , e ))
σN n mm σN σN
Pr(n | m, e, 1) = ,
e + 1 I e1 − c e1 + β R ( m , l ) − βσE log (Pr( l | n , e ))
∑n ∈N exp an σN n mm σN σN
where we express local child opportunity values o (n, e) as a function of local probabilities
of remaining low-skill Pr(l |n, e) and local continuation values for low-skill adults R(m, l ).
Amenity levels affect parents’ residential choices by shifting their ﬂow utility and con-
tinuation values R(m, l ). The additive shifter of ﬂow utilities directly cancels from the
residential choice. To show how a level shift of amenities affects continuation values, we
ﬁrst write local value functions as:
1 ek
v(m, e, k ) = log ∑ exp an e
+ ek
In − cmm + 1k=1 β ∑ Pr(k | l )v(m , l , k )
n ∈N
σN k
βσE
− 1k =1 log Pr(l | n , e) ,
σN
where we again express local child opportunity values o (n, e) as a function of local con-
tinuation values for low-skill adults and local probabilities of remaining low-skill. We
now guess and verify that shifting amenity levels by a factor be will shift value functions
additively by a factor Bek . In particular, we show that v ˜ (m, e, k) = Bek + v(m, e, k), where
we deﬁne v ˜ (m, e, k ) to be the value function that corresponds to the shifted amenity val-
e + be . For non-parents, this is trivial to show since amenities only affect ﬂow utility
ues an
so that:
1 e0
˜ (m, e, 0) = Be0 + v(m, e, 0) = log ∑ exp be + an
v e
+ e0
In − cmm ,
n ∈N
σN
where our guess holds if Be0 = be . For parents, amenity levels affect ﬂow utility and
OA - 16
continuation values so that we apply our guess on both sides of the equation:
1 e1
˜ (m, e, 1) = log
v ∑ e
exp be + an + e1
I − cmm
σN n
+ β ∑ Pr(k | l ) Blk + v(m , l , k )
n ∈N k
βσE
− log Pr(l | n , e)
σN
= be + β ∑ Pr(k | l ) Blk + v(m, e, 1).
k
Our guess holds if:
Be1 = be + β Pr(k = 0 | l )bl + Pr(k = 1 | l ) Bl 1 ,
where we use our result that Be0 = be for non-parents. Rearranging this equation allows
us to solve for the additive shifters of value functions. For low-skill parents, the shifter is:
l1bl (1 + β Pr(k = 0 | l ))
B = ,
1 − β Pr(k = 1 | l )
and for high-skill parents:
βbl (1 + Pr(k = 0 | l ))
B h1 = b h + .
1−β
We have now shown that a shift in amenity levels also shifts value function levels ad-
ditively. These additive shifters therefore cancel from parents’ residential choice proba-
bilities (cf. Equation OA.18). Parents’ residential choices are therefore invariant to the
normalization of amenity levels conditional on education choices.
Last, we have to show that children’s education choices are also invariant to changes in
amenity levels. Local education choices are given by:
Pr(h | n, e) e
(OA.19) σE log = R ( m, h ) − R ( m, l ) + K n + γe log( f n ),
Pr(l | n, e)
where Kn e is exogenous education quality, f is school funding, and R ( m, h ) − R ( m, l ) are
n
returns to education. Returns to education are given by the difference in continuation
values for low- and high-skill adults, where R(m, e) is the expected continuation value
of young adults of education e before knowing their fertility shock which is deﬁned as:
R(m, e) ≡ ∑k Pr(k |e)V (m, e, k). Recall that we infer the exogenous education quality Kn e
as a structural residual from Equation OA.19 to ﬁt observed education choices.
We have shown above that a shift in amenity levels by be shifts value function levels by
Bek , which shifts education returns additively by: ∑k Pr(k |h) Bhk − ∑k Pr(k |l ) Blk . To ﬁt ob-
served education outcomes, our model offsets the shift in education returns by inversely
adjusting the level of exogenous local education quality Kn e (cf. Equation OA.19). The
level of skill-speciﬁc amenities ane and the level of exogenous education quality K e are
n
OA - 17
therefore jointly, but not separately, identiﬁed. We have shown that the normalization of
amenities for each skill type is without loss of generality because all model outcomes are
invariant to the normalization.
Identifying Amenity and Education Quality Levels. In the implementation of our esti-
mation strategy, we infer amenities an e as a structural residual from non-parents’ county-
utilities. We normalize these amenities to have mean zero across all neighborhoods within
each education type. We then use value function iteration to solve for the value functions
v(m, e, k) that are consistent with these amenity levels. Last, we use Equation OA.19 and
the value function estimates to infer the exogenous component of education quality Kn e
as a structural residual that ﬁts observed education choices.
C.5 Transitional Dynamics and Persistence in Regional Characteristics
We hold regional characteristics constant in our counterfactual analysis. To test this as-
sumption, we investigate how much characteristics are changing over the decades that
we observe in the data. We use the structure of the model to infer regional characteris-
tics for 1990, 2000, and 2010 and compute their correlations across decades. We restrict
the sample to workers who are older than 25 years, which is the only age restriction
we can implement in all three decades. Table OA.4 shows that total factor productivity
and skill intensities in CZs are very persistent, with correlations between 0.81 and 0.93
across decades and correlations above 0.89 for consecutive decades. Likewise, county-
level housing supply strongly correlates over time with correlations above 0.94 across all
three decades. County amenities for low-skill families have a correlation of 0.73 between
1990 and 2000 and 0.92 between 2000 and 2010. Amenities for high-skill families are more
persistent, with correlations of 0.92 and 0.94 for consecutive decades. Moving costs are
also very persistent, with correlations of 0.99 across decades for each education and fam-
ily type. We can infer the exogenous component of local education quality only for one
cross-section due to data constraints. As a result, we cannot test its persistence over time.
Our results indicate that regional characteristics are very persistent between 1990 and
2010, justifying our approach of holding them constant in our counterfactuals.
C.6 Relationship between Amenity Estimates and Observable Charac-
teristics
We test the extent to which our model-implied amenity estimates correlate with observ-
able proxies of local amenities. We obtain data on local amenities from Diamond (2016)
OA - 18
TABLE OA.4: P ERSISTENCE OF R EGIONAL C HARACTERISTICS OVER T IME
Correlation Between Estimates From
Regional Characteristic 1990 & 2000 2000 & 2010 1990 & 2010
Productivity (Z ˆm) 0.97 0.95 0.87
Skill Intensity (Sˆm
e) 0.89 0.93 0.81
Housing Supply (H ˆ n) 0.97 0.96 0.94
Low-Skill Amenity (a
ˆnl) 0.73 0.92 0.81
High-Skill Amenity (a
ˆnh) 0.92 0.95 0.81
Notes: This table shows the correlation between regional characteristics estimated
from data in 1990, 2000, and 2010.
and Lee and Lin (2018) and extend their data sets over time and to the county level when
possible. Table OA.5 shows the results from regressing our model-inferred amenities on
these measures of observable amenities at the county level. For 2010, we ﬁnd that the re-
gressions have strong explanatory power with R-squared values of 0.8 for low- and high-
skill families. For 1990 and 2000, we ﬁnd somewhat lower R-squared values, ranging
from 0.52 to 0.77 across different education samples. We infer amenities from residential
choices and do not target any observable regional characteristics. The strong relationship
between our model-implied amenities and observed proxies is therefore reassuring.
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TABLE OA.5: C ORRELATION BETWEEN M ODEL A MENITY E STIMATES AND O BSERVABLE
C HARACTERISTICS
Amenity Estimates by Year and Skill Group
1990 2000 2010
Variable Low High Low High Low High
Moderate Temperature 0.562*** 0.188** 0.144* 0.133* -0.0458 -0.171**
(0.121) (0.0912) (0.0805) (0.0730) (0.0605) (0.0745)
Distance City D2 -0.445*** -0.448*** -0.467*** -0.480*** -0.477*** -0.653***
(0.118) (0.0888) (0.0835) (0.0758) (0.0604) (0.0744)
Distance City D3 -0.583*** -0.559*** -0.807*** -0.735*** -0.742*** -0.982***
(0.141) (0.106) (0.101) (0.0920) (0.0792) (0.0975)
Distance Lake D2 -0.00926 -0.00360 -0.0807 -0.0896 -0.0968* -0.129*
(0.101) (0.0758) (0.0698) (0.0633) (0.0554) (0.0682)
Distance Lake D3 0.00532 0.0244 -0.0680 -0.0678 -0.0968 -0.0995
(0.121) (0.0910) (0.0839) (0.0762) (0.0666) (0.0821)
Distance Shore D2 0.0807 -0.0251 0.115 0.0611 -0.0189 -0.0496
(0.105) (0.0786) (0.0746) (0.0677) (0.0618) (0.0762)
Distance Shore D3 -0.0743 0.0865 0.153* 0.140* -0.0151 0.0536
(0.136) (0.102) (0.0915) (0.0830) (0.0745) (0.0918)
Establishments 0.526*** 0.816*** 0.651*** 0.721*** 0.681*** 0.818***
(0.0705) (0.0529) (0.0540) (0.0490) (0.0241) (0.0297)
Property Crime Rate 0.308*** 0.252*** 0.162*** 0.110*** 1.012*** 0.968***
(0.0684) (0.0514) (0.0221) (0.0201) (0.105) (0.129)
Violent Crime Rate -0.116*** -0.196*** -0.0613*** -0.140*** -0.147** -0.328***
(0.0416) (0.0313) (0.0178) (0.0162) (0.0711) (0.0875)
Park Expenditure 0.138*** 0.0701* -0.0192 0.139*** -0.0313** -0.0125
(0.0514) (0.0386) (0.0371) (0.0337) (0.0154) (0.0190)
Observations 723 723 801 801 571 571
R-Squared 0.520 0.748 0.599 0.772 0.794 0.800
Notes: We use our model to infer county amenities by skill group for 1990, 2000, and 2010. We restrict the data
to population above 25 years. Moderate temperature is a dummy that is equal to 1 if the minimum temperature
during January lies between -5 and 15 degrees and the maximum temperature during July lies between 15 and
32 degrees. Distances from the city center, lakes, or shores enter each as three dummy variables indicating
whether a distance lies in the bottom quartile (D1), the second or third quartile (D2), or the top quartile (D3)
of distances observed in the sample. The omitted category is the shortest distance dummy (D1). Temperature
and distance variables are obtained from Lee and Lin (2018) and mapped to the county level. Total number of
establishments is constructed at the county level from the County Business Patterns. Government expenditure
for parks and recreational activities is obtained from the county-area ﬁles of the Census of Governments.
Property and violent crime rates are obtained from Diamond (2016) at the MSA level and expressed per 100,000
inhabitants.
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