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Rethinking Detroit

WP 17-04

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

Rethinking Detroit∗†
Raymond Owens III
Federal Reserve Bank of Richmond

Esteban Rossi-Hansberg
Princeton University

Pierre-Daniel Sarte
Federal Reserve Bank of Richmond

February 2, 2017
Working Paper No. 17-04
Abstract
We study the urban structure of the City of Detroit. Following several decades of decline, the city’s
current urban structure is clearly not optimal for its size, with a business district immediately surrounded
by a ring of largely vacant neighborhoods. We propose a model with residential externalities that features
multiple equilibria at the neighborhood level. In particular, developing a residential area requires the
coordination of developers and residents, without which it may remain vacant even if its fundamentals
are sound. We embed this mechanism in a quantitative spatial economics model and use it to rationalize
current city allocations. We then use the model to evaluate existing strategic visions to revitalize Detroit,
and to design alternative plans that rely on ‘development guarantees’ to yield better outcomes. The
widespread effects of these policies underscore the importance of using a general equilibrium framework
to evaluate policy proposals.

1

Introduction

The City of Detroit, an iconic example of urban development associated with modern industrialization,
is in disarray. Large declines in population over several decades have resulted in a city structure that is
clearly inefficient and that severely inhibits economic outcomes in the city. A business area that contains the
headquarters of large automobile companies such as General Motors, Ford and Chrysler and that employs
hundreds of thousands of people, is surrounded by nearly deserted residential areas that have been mostly
abandoned or demolished. This structure violates the most basic economic principles of urban design where
∗

Owens: raymond.owens@rich.frb.org. Rossi-Hansberg: erossi@princeton.edu. Sarte: pierre.sarte@rich.frb.org.
The views expressed herein are those of the authors and do not necessarily represent the views of the Federal Reserve Bank
of Richmond or the Federal Reserve System. We thank Daniel Schwam and Daniel Ober-Reynolds for outstanding research
assistance and seminar participants for useful comments.
†

1

residents utilize areas close to their employers to minimize commuting costs. The incentives to revitalize
these vacant areas around Detroit’s central business district are not generating the needed investments and
changes in the city. In this paper, we propose a quantitative economic model of the city of Detroit that can
help us rationalize the current state of the city and evaluate a variety of plans and policies that have been
proposed to improve its structure.
The problems of Detroit are not unique. Many cities throughout the industrialized world have experienced similar problems. The decline in manufacturing employment, and the displacement of manufacturing
from urban centers, have resulted in the decline of many cities for long periods of time. As Glaeser and
Gyourko (2005) argue, these declines can be protracted owing to the durability of the housing stock. Negative shocks to the industries operating in a city, or to the regional economy, lead to immediate declines in
land rents but also to protracted declines in population that follow the slow depreciation of buildings and
structures. However, while Detroit has demolished well over one hundred thousand housing units since the
1980’s, the city has not experienced any substantial adjustment in its basic layout or structure. Thus, the
slow depreciation of housing initially built before the 1930’s cannot be the main culprit of its evolution.
This lack of adjustment has arguably led to an under-utilization of its urban infrastructure. The system of
streets and highways built for a city three times its current size is not serving new booming industries but,
as in many other rustbelt cities, is weighing on its recovery. In particular, the high cost of maintaining this
large infrastructure has led to fiscal problems, an under-provision of essential public services, and ultimately
to bankruptcy and default (Detroit filed for chapter 9 bankruptcy in 2013).
Sectoral and local shocks that have led to these salient changes in urban landscape are not exceptional.
As new production technologies and trading possibilities lead to declines in today’s booming industries,
changing the comparative advantage of countries and regions, similar secular changes are to be expected in
the future. Moreover, environmental changes such as climate change and coastal flooding are likely going
to change the productivity and residential amenities of today’s cities. Dealing effectively with declining
cities then is an important challenge that requires careful policy design and measurement. Developing the
appropriate policies to improve the structure of declining cities can generate not only gains for its residents,
but could also lead to a better, and more efficient, use of resources and spatial allocation of economic activity
in the U.S., and the world.
A stylized look at the structure of the city of Detroit reveals a surprising pattern: a downtown area
with healthy numbers of employees and employers surrounded by a ring of vacant neighborhoods. Most of
these neighborhoods have been abandoned or demolished over the years, and in some of these areas, the city
has stopped providing services. The main question that arises when confronted with this structure, vividly
captured in Figure 1, is: why do residential developers not move into these areas and develop residential
communities where downtown workers can live?
With residential areas close to downtown, workers would clearly save on commuting and downtown
Detroit would benefit from more foot-traffic and demand for retail and other services. The basis of our
argument is simple and intuitive: residents do not want to be isolated in a neighborhood. They desire

2

Figure 1: The neighborhood of Brush Park in the foreground, downtown Detroit in the background, as
capured by the New York Times, Oct. 14, 2014
other residents with whom to socialize and who require the services they wish to consume. Neighborhood
development then requires a large enough scale because of residential and housing externalities (as in RossiHansberg et al., 2010), one that individual residential developers are not able, or not willing, to provide
on their own. Hence, neighborhoods have two equilibria, one that features a residential area with enough
development and residents to make it sustainable, and one in which no investment is made and no residential
activity occurs.
The issue of coordination among developers, and between developers, residents, and local governments,
is explicitly recognized as a key challenge in previous studies of Detroit’s ailments. Among the most comprehensive of those studies is a set of reports and proposals provided by Detroit Future City (DFC), a civic
organization created in 2012 that includes planning experts, community leaders, and residents, and whose
mission is to guide and help implement the revitalization of Detroit. The DFC reports repeatedly cite references to challenges in coordinating different parties as a key impediment to revitalization and development.1
Thus, we place this coordination problem at the center of our analysis and embed it in a quantitative spatial
1

In particular, the DFC Strategic Framework (2012) stresses that “Detroit’s ability to address its problem property issues
is impeded by its severe fiscal and market constraints, but it is equally impeded by the absence of a systematic, coordinated
approach to the problem, in which all public and private stakeholders are fully engaged.”

3

economics framework that allows us to model the city of Detroit in detail. We then use the model to design
and quantify the effects of a variety of policy proposals, including different strategic visions proposed, but
not quantified, by DFC. The general equilibrium framework we develop for Detroit is close to the literature
on quantitative spatial economics recently reviewed in Redding and Rossi-Hansberg (2016). The key addition to this literature, aside from a careful quantification of an urban model for the city of Detroit, is the
existence of residential externalities that lead to the coordination problem and multiplicity of neighborhood
equilibria described above. This novel mechanism allows us to both rationalize current allocations in the
city of Detroit and quantify the effects of various policy proposals.
The policies that we assess all involve coordinating on vacant residential neighborhoods. In particular,
we consider ‘development guarantees’ to resolve coordination challenges where the city government, or some
other outside institution, guarantees a minimum investment in residential development in a neighborhood
targeted for development. We then use our quantitative framework to compute the magnitude of the required
guarantees that would allow a neighborhood to coordinate in the equilibrium with a positive number of
residents and residential investment. If the policy is successful, the guarantee is never called upon and the
policy is costless. We compute the overall effect of policies addressing different areas of Detroit on a variety
of outcomes in the treated and non-treated neighborhoods. In our analysis, these outcomes reflect in part
all general equilibrium linkages embedded in the spatial structure of Detroit. We show that carrying out the
analysis in a general equilibrium framework, where locations are linked by commuting, is essential for the
generated outcomes. We further use our quantitative set-up to design policies that maximize the net gains
for Detroit, and compare their effects with those stemming from various proposals that DFC has advocated,
but not quantified, as possible equilibria. Our newly designed policies can yield gains of hundreds of millions
of dollars in additional land rents per year, and perform substantially better than the DFC proposals.
We carry out our analysis at the census tract level, which is the smallest unit for which commuting data
can be accurately matched to other aspects of Detroit such as workplace wages, employment, residential
prices and land use.2 We collect data from a variety of sources that include bilateral census commuting
data, local development and price data from assessors, local Detroit organizations focused on measuring
urban blight, and Google Analytics data on actual commuting times and distances between census tracts.
The resulting dataset is quite rich and allows us to quantify the model at a high level of detail. The hope is
that such a quantitative framework will inform the decision making process in Detroit and other declining
cities, and transform them into cities that can host the industries of the future.
The rest of the paper is structured as follows. Section 2 provides a brief account of Detroit’s recent history.
Section 3 presents the model and Section 4 describes how it is given quantitative content. Section 5 discusses
the policy counterfactuals and designs of alternative policies. Section 6 concludes. Appendix A provides
2

In principle, commute data is available at the block level from the Longitudinal Employer-Household Dynamics, Origin
Destination Employment Statistics (LODES) data set. However, LODES indicates that uncertainties in block coding make
block analyses unreliable, see Abowd, Stephens, Vilhuber, Andersson, McKinney, Roemer, and Woodcock (2005). Moreover, as
pointed out in Couture and Handbury (2016), noise infusion to maintain confidentiality at the block level further encourages
aggregation to the tract level for accurate analysis.

4

additional derivations not included in the text, while an on-line appendix provides a detailed description
of the data used to inform our analysis, and considers a variety of additional policy counterfactuals and
alternative model assumptions.

2

City of Detroit

To get a sense of Detroit’s evolution from world famous city to hollow shell during the past hundred years,
it is useful to note that the city entered the twentieth century as mid-tier American city of about 286,000
residents. Connected to the Great Lakes through its location on the Detroit River, the city had access
to waterborne shipments of iron ore from Minnesota and coal and oil from areas south. Metal related
production, from smelting to machinery production arose there, among other types of production.
By 1900 automobile producers were active in Detroit, though vehicle production numbered only a few
hundred units per year rising to a few thousand by mid-decade. Two developments changed the city into
the center of automobile production, however. The first was Ford Motor Company’s design of a simple,
rugged automobile, the Model T. The second was Henry Ford’s adoption of the assembly line for automobile
production beginning in late 1913. In combination, these developments provided a viable product for
the rough roads of the U.S. and technology that lowered labor costs required to assemble the Model T,
making automobiles affordable to the masses. The assembly line was rapidly employed by other automobile
producers.
As demand for automobiles soared, Ford and other producers constructed factories that stretched a half
mile or more, in some instances. To man the vast factories, Ford and other companies in Detroit needed
far more labor than was available locally. To obtain enough workers, automobile producers raised wages
to attract labor from the American south, Europe, the Middle East and other regions around the world
(Sugrue, 2007; Sugrue, 2015). By 1930, automobile production at Detroit’s largest companies neared a peak
that would not be surpassed until after World War II.
To house the workers, residential developers constructed vast tracts of single-family homes in seemingly
endless blocks stretching out on the plain surrounding the existing city. Detroit’s population reached nearly
a half million by 1910, almost one million by 1920 and approached 1.5 million by 1930. Figures 2 shows
that housing constructed before 1930 (in red) mainly surrounded the existing city in a broad band. Census
records from 1910 and 1920 indicate that many workers living in this band worked in automobile-related
manufacturing jobs (Minnesota Population Center and Ancestry.com, 2013). Subsequent census data from
1920, 1930, 1940 and 1950 show that the density of blue collar manufacturing jobs remained higher in this
band than in other areas of Detroit (Bogue, 2000; Minnesota Population Center and Ancestry.com, 2013).
As of 1950, Detroit built one of every two cars produced in the world, and the city’s population topped
1.8 million. But two developments during the decade laid the foundation for a prolonged period of decline
for the city. The first was a decision by the automobile companies to locate production plants outside of the
Detroit area. Both labor unrest in Detroit and the desire to locate closer to customers have been cited as

5

reasons for diversifying plant locations. A second was the initiation of the interstate highway system, which
would bring express highways through the city beginning less than a decade later (Sugrue, 1996; Sugrue,
2007; Sugrue, 2015).
As the 1960s arrived, Detroit saw population declines and job losses related to automobile production
mount. Unemployed households increased rapidly in the band surrounding downtown that had been built
prior to 1930 (Bogue, 2000; Minnesota Population Center, 2016). Related to the ongoing job losses and
diminished economic prospects, residents of the area became increasingly on edge and racial tensions became
more pronounced. Tensions exploded in the summer of 1967 with five days of rioting and looting following
a police raid on an illegal club. Over 2500 stores were burned, looted or destroyed in the episode, nearly all
Figure 1A

of them businesses located within thePre-1930
band Residential
of housing
builtTracts
before
1930.
Census
in Detroit

At least 75 percent of Residential Properties built prior to 1930

Figure 2: Pre-1930 residential census tracts in Detroit with at least 75 percent of residential properties built
prior to 1930
In the riots’ aftermath, existing households in the area found fewer businesses to serve them (600 grocery
stores were damaged or destroyed, for example) and were concerned about safety going forward. Business
owners who were not insured often could not reopen their operations. Those who were insured assessed the
changed environment of the area and many were not confident that their customers—both households and
other business–would remain. The prospect of fewer customers in the area led many to not reopen in the
city. With the interstate highway construction well underway by 1967, some businesses and residents chose
to relocate to suburbs outside of Detroit. In the end, the perception of increased danger, lower commute
costs, and a lack of coordination between residents’ location plans and those of neighborhood businesses,
contributed to an acceleration of the outflow of businesses and residents. Home values fell and new residents
entering the area had lower incomes on average.
In the decades following the riots, Detroit’s landscape continued to show the scars of the riots. Vacant
6

760

521
483
442
326
377 367
321 337 356 385 421454 475
292 302
280
293
496 464 433 398 359 328 329 308
266 276
319
354 386 426
282
281
357
396
239
250
445
330
304
294
537
246
463 425
232
262
597
725
376 338 314
498
290 312
217
648
241 263
323 355 387
197
200
324 295 275 260 235 226 209
225
481 427 392
269
195
586
518
706
343
368
300
191 216 234 255
169 171
182
247 221 204 192
383 332 299
459
514
162 166 180 194 218
572
149
148
155
175
695 656 624 603
252 274 303
236
447 399 361 315 283
506
561
352
201
160
715
133 128
228
309
430 371 325 296 267 231 210 183 157151 143
117
126
168 184
110
215 243
666 634 608 562 530 504 480 419
118
257
347
322
127
251
199
161
96
105
121
474
173
405 350 306 272 240 202 174 152 122 108
258
527
609
207
88
91
83
164 123
456 393 340 297 265 229
116138 188 176
570 526
242
288
79
638
99
62
78
68
490 448
135
373 327 284 254 220 181 144 113 98 93
206
64
522
82
104
61
159
60
52
167 186
259
394 362 307
622 577
120 107 86
72
525 482 428
76
48
112 140
270 227 190
137
212237
158
313
75
102
366
44
178
429
564
510
124
640
50
208 172
69
85
261
478
132
130 103
70 58 4139 36
51
224
409 353 298
30 33
67
193
81
145
37
619
25
253 205
54 42
348
153
89
566 524 473 431
18 28
49 66
94
170 131 100 80 65 43
26
249
214
291
32
345
416
468
40
141
605
13
23
189
29
56
14
156 101
223
47
341 286
15
141
411
31
95 73
599
8
35 1716
558 503 461 406
146
11 20
336
268 233
111 90
4
600
57 38 22 10 6
196
9
3
331 278
407
136 114 84
230
12
27
5
487
45
179154 109
1 2
653 594 543
74
397
264
21
7
150 106 77 59
245
333
287
641
19
584 542
46 34
450
248
97
642
71 55
185 142
87
578
119
289
519
63
434
134
501
620
546
379
125
277
592 545
198
420
644
360
491 439
165
279
549
611
219 203
675
Detroit City Boundary
187
369
661
547
256
316
453
301
639
238
569 511 467
213
285
441 400 372
244
652
517
579
351 320
271
305
Fully Developed
488 444
541
382 344
596
673
311
404 349
273
Partially Developed
485
273
560
616
678
414 370 339
374 342
507
403
437
Vacant
602
712
476
744

714

689

659

630

601 573
539

591

509

Legend

Tract Classification (Benchmark)

733

691

613

551

508 470 432 391 457

Figure 3: Empty and Partially Developed Census Tracts in Detroit Today
lots where businesses were not rebuilt were eventually joined by vacant lots where houses once stood. The
spreading vacancies resulted from a cycle in which lower wages and high unemployment in the band of the
city led to the inability, or unwillingness, of lower income residents to maintain some homes, lowering home
values and the corresponding city tax revenues. The reductions in tax revenues were not matched by lower
costs of providing city services to increasingly sparsely populated areas of Detroit, however (Scorsone, 2013).
Over time, houses were abandoned as the value of the housing services at locations in the pre-1930
band fell further. Crime rates rose and tax revenues declined to the point that the city curtailed services
to some areas of the city. Under Mayor Dave Bing, proposals to bulldoze tens of thousands of abandoned
homes began in an effort to reduce crime occurring in and around the vacant structures. Proposals from the
mayor also suggested clearing sparsely populated areas and relocating remaining residents to more densely
populated areas to concentrate the provision of city services to “viable” areas of the city (Bing, 2010). But
the relocations did not occur, and many blocks adjacent to downtown Detroit were dominated by empty
lots and high vacancy rates of the remaining housing stock. House prices fell to essentially zero in some of
these areas. As a result, the nation’s once fourth largest city became the poster child for urban decay.
The resulting city structure is presented in Figure 3. The figure classifies the census tracts in Detroit and

7

surrounding areas as featuring full residential development, partial residential development, or no residential
development (vacant).3 It also features the number code for the census tract and the boundary of Detroit
proper. The census tracts that are labeled vacant largely correspond to the neighborhoods constructed
before 1930 (see Figures 2 and 3), and form a rough half-ring outside the central business district.

3

The Model

We now describe a spatial framework that will allow us to describe the current state of Detroit quantitatively
along various dimensions such as employment, residential population, commuting, and land prices. With this
quantitative framework in hand, we will then be in a position to carry out various counterfactual exercises
aimed at assessing the effectiveness of different policy proposals.
Consider a city that consists of a set of J areas located on a two dimensional surface, indexed by j (or
i). Space in these locations can be used for either residential or business purposes, and the amount of space
designated for each use is determined by law according to the city zoning ordinance. We denote by T̄jb ≥ 0
the total area zoned for business land and T̄jr the total area of land zoned for residential purposes at location
j. Actual developed residential land, Tjr , is determined in equilibrium, but Tjr ≤ T̄jr . In the model, business
land is always developed so Tjb = T̄jb . Three types of agents live and do business in the city, namely residents,
firms, and residential developers. Individuals can move freely in and out of the city and can obtain a utility
ū elsewhere in the economy. If they choose to live in the city, they also decide where to live and work,
and how much consumption and housing services to acquire. Firms produce a single consumption good and
choose where and how much to produce of that good. Residential developers decide where to build housing
units that individuals rent to live.

3.1

Firms

Firms produce the single consumption good using land and labor and a constant returns to scale technology.
Productivity in a location j is determined by a local component, Aj , that determines how suitable the
location is for goods production, and an agglomeration component determined by the density of employment
in the area. This second component constitutes an externality that producers take as given. In particular, if
Lj denotes the total number of workers in location j, then lj ≡ Lj /Tjb denotes workers per unit of business
land in the area, and productivity is given by a (lj ; j) = Aj ljα for α > 0.
Production per unit of land in the business district of location j is then given by
Yj
≡ yj = a
Tjb
3

Lj
;j
Tjb

!

Lj
Tjb

!β


≡ Aj ljα ljβ .

The methodology underlying this classification is explained in Section 4 below.

8

(1)

Let wj denote the wage in location j. Then, the problem of firm k is given by
β
− wj lkj ,
max a (lj ; j) lkj

(2)

lkj

where lkj denotes firm k’s choice of workers per unit of land. We assume that firms are small and so do not
internalize the local externality. Hence, firms do not take into account the dependence of productivity on
equilibrium density, lj . The representative firm’s first order condition is given by
β−1
βa (lj ; j) lkj
= wj .

(3)

Since all producers at j are identical, in equilibrium lkj = lj for all k. Hence, using a (lj ; j) = Aj ljα ,

lj =

Aj β
wj



1
1−β−α

,

so that local labor demand at j is given by

Lj =

Aj β
wj



1
1−β−α

Tjb .

(4)

Throughout the paper, we assume that 1 − β > α to guarantee that local labor demand is downward
sloping. Namely, the congestion force, governed by the share of land in production, (1 − β), that determines
the decreasing returns to labor, is stronger than the agglomeration force, determined by the elasticity of
productivity with respect to employment density, α.
Firms compete for land and are willing to bid for business land at j until they make zero profits. Hence,
the commercial rent at j is
qjb

1
1−β−α

= (1 − β) Aj



β
wj



β+α
1−β−α

.

(5)

We assume that business land is owned by absentee landlords.

3.2

Individuals

Agents consume goods and housing at their residential location and commute to a business area where they
receive a wage. Agents experience their place of residence differently depending on local residential amenities.
Amenities depend on the characteristics of the neighborhood, for example its beauty or convenience, as well
as on the number of other residents living in the area, Rj . In addition, agents are allowed to have idiosyncratic
preferences for particular residence-work combinations as in Monte et al. (2016).
The preferences of an individual living in location j (with Rj residents) and working in i, who consumes
Cij goods, lives in a house that provides housing services given by Hij , and has idiosyncratic preference for

9

the residence-work pair ij parametrized by sij , is given by
sij B (Rj ; j)
κij



Cij
γ

γ 

Hij
1−γ

1−γ
.

Commuting costs are expressed in utility terms and given by κij ≥ 1, with κjj = 1. In particular, commuting
costs reduce utility except for agents that work where they live. Residential amenities at location j are given
by B (Rj ; j), and depend on the number of agents that decide to locate in the neighborhood: a housing
σ

externality (as in Rossi-Hansberg, et al., 2010)). We let Bj (Rj ; j) = Rj j , so that the elasticity of amenities
with respect to residents depends on the characteristics of the neighborhood.4 Some urban neighborhoods
might depend heavily on some of these externalities, while other more suburban neighborhoods might
appeal less to density as an amenity. Throughout, we assume that the congestion force embedded in rising
housing demand as the number of residents increases (governed by the parameter 1 − γ), with corresponding
increasing rents, is dominated by the externality in amenities governed by σj . That is, we assume that
σj > 1 − γ for all j. The implication is that neighborhood demand by residents is an increasing function of
its number of residents, as we show below.
Individuals have idiosyncratic preferences for residing in location j and working in location i. We assume
that s is drawn from a Fréchet distribution with scale parameter specific to the residence-work location pair,
λij > 0, and shape parameter θ > 0. Namely,
−θ

Pr(sij ≤ s) = e−λij s .

(6)

This random idiosyncratic component captures individual-specific reasons that make particular residencework locations appealing beyond those we model directly, such as wages in the place of work compared to
rents in the place of residence, or the commuting costs between the two locations. The scale parameter λij
in (6) determines the average idiosyncratic utility from working in i when commuting from j, and the shape
parameter θ governs the dispersion of the idiosyncratic component of utility.5
Conditional on living in j and working in i, the problem of a resident having drawn idiosyncratic utility
component s is given by
sB (Rj ; j)
Uij (s) = max
Cij ,Hij
κij



Cij (s)
γ

γ 

Hij (s)
1−γ

1−γ
(7)

subject to wi = qjr Hij (s) + Cij (s),
4

Amenities depend on the number of residents because individuals enjoy the ability to interact with neighbors and join community groups, or because the number of residents affects the cost of some community services or infrastructure, or discourages
crime. Examples abound but their relevance varies across neighborhoods. Here, σj captures, in reduced form, the heterogeneity
in the elasticity of amenities with respect to the number of residents across neighborhoods.
5
Note that λij and κij are, in general, not independently identified. In the application below, we use commuting cost data
to determine κij , and identify the λij needed to match commuting flows.

10

where qjr is the price of a unit of housing services at j. We normalize the price of goods in the city to
one. Since we assume that transport costs for goods within the city are negligible, the price of goods in all
neighborhoods is the same. Hence,
Cij = γwi and Hij =

(1 − γ) wi
.
qj r

(8)

Observe that, as the notation recognizes in (8), consumption and housing choices do not depend on the
realization of idiosyncratic preferences s. Thus the indirect utility function, Uij (·) , is simply given by

Uij (s) =
3.2.1

 γ−1
σ
sRj j wi qjr
κij

.

(9)

Commuting Patterns

Given that the idiosyncratic preferences of individuals are drawn from the distribution in (6), the indirect
utility derived in (9) implies that
 γ−1 θ
σj
r
R
w
 j i qj

−Φij u−θ
Pr (Uij < u) = e
, where Φij = λij 
 .
κij


Standard manipulations then yield an expression for the expected utility of living in j, Uj , as a function of
the weighted sum of the utilities gained from commuting to the different business areas (raised to the θ).
Namely,

Uj = Γ

θ−1
θ



σ



r γ−1

Rj j qj

J
X


λij

i=1

wi
κij

θ ! θ1
,

(10)

where Γ is the Gamma function.
Let πij represent the proportion of residents living in j that commute to i. Then, if Rij is the number
P
of residents in j commuting to the business area of location i, Rij = πij Rj and Ji=1 πij = 1 for j = 1, ..., J.
Since agents choose freely their optimal residence-work pair,


πij = Pr Uij > max {Unj }
n6=i

so that6
πij = PJ

λij (wi /κij )θ

θ
n=1 λnj (wn /κnj )

.

(11)

The proportion of those living in j who commute to i for work depends on wages earned in i, net of
6

See Monte et al. (2016), among others, for a derivation of this result.

11

commuting costs, relative to average net wages from commuting elsewhere (raised to the θ). Note that the
agglomeration effects on amenities by way of Rj do not affect commuting patterns from j to i since all
residents of j experience the same externality equally. The characteristics of j determine the number of
residents, but not where they work.
3.2.2

The Residential Market

Condition (8) determines housing consumption for those living in j and commuting to i, Hij . Thus, average
housing per resident in area j, Hj , is given by
Hj =

J
X

J

πij Hij =

(1 − γ) X
πij wi .
qjr
i=1

i=1

Since Tjr denotes the total number of units of “developed” residential land in location j, equilibrium in the
residential market j implies that
Rj Hj = Tjr .

(12)

Thus, residential land rents are such that
qjr

J
(1 − γ) Rj X
=
πij wi .
Tjr

(13)

i=1

Residential land rents increase with the number of residents, decrease with total land developed, and increase
P
with total expenditures by commuters living in the neighborhood, as expected. Observe that Ji=1 πij wi
can alternatively be interpreted as the average wage of location j residents (where the weights are given by
the proportion of residents commuting to each area i for work).
We model an open city where individuals can move in and out freely and obtain utility ū elsewhere in
the economy. Hence, if an area within the city has a positive number of residents, it must be the case that
Uj ≥ ū. Using (10), as well as our assumption that σj > 1 − γ for all j, we conclude that a neighborhood is
viable only if


Rj ≥ 

1−γ

nP
J

o1−γ



ū (1 − γ)
i=1 πij wi

 1−γ hP
i1 


J
θ θ
Γ θ−1
Tjr
i=1 λij (wi /κij )
θ

1
σj +γ−1

.

(14)

Conditional on the amount developed residential land, Tjr , commuting flows, πij , and wages, wi , the number
of residents needed to make a neighborhood viable increases with ū and with a uniform increase in commuting
costs κij . Conditional on commuting flows and wages, an increase in developed residential land, Tjr , lowers
residential rents, and thus makes the need for residential amenities provided by the number of residents
less stringent. Conditional on developed residential land and commuting flows, a uniform increase in wages
lowers the number of residents needed to make the neighborhood viable. We denote by J the number of
12

areas that are viable. These are able to attract the required number of residents and, for these areas, (14)
holds with equality. It follows that J − J areas have no residents in equilibrium. We discuss multiplicity in
the neighborhood equilibrium in detail below.

3.3

Residential Developers

There is a large number of small residential developers, none of whom is large enough to internalize residential
externalities. Let hj denote the number of units of land developed by residential developers active in
neighborhood j. Suppose further that the cost associated with developing hj units of land is given by a
convex variable cost, V (hj ), that we specify as V (hj ) = V hvj for v > 1, in addition to a location specific
fixed cost, Fj > 0. Residential developers then maximize
Πj = max hj qjr − V (hj ) − Fj = max hj qjr − V hvj − Fj ,
hj

hj

(15)

so that, if hj > 0,
qjr

= vV

hv−1
j


⇔ hj =

qjr
vV

1
 v−1

.

(16)

Developers enter as long as profits are non-negative, so that hj > 0 if Πj ≥ 0, or alternatively,
hj qjr ≥ V hvj + Fj .
Substituting for hj from the first-order-condition, and residential land rents in equation (13), Πj ≥ 0 implies
that
vV
Rj ≥

(1 −

 v−1



v
Fj
(v−1)V
Tjr .
P
γ) Ji=1 πij wi

(17)

Hence, an individual developer will only invest in developing residential land if the density of residents,
Rj /Tjr , which determines residential prices, is large enough relative to the local fixed costs, Fj . These costs
would typically include getting the land ready for residential development, the installation of utilities such
as water services and sanitary sewer systems, the building of access roads and sidewalks if needed, as well
the handling of permits and legal fees, the design of the development, etc. Condition (17) implies that
the number of residents required for developers to be willing to invest in a given location is increasing in
the amount of developed residential land, in equilibrium, and in the fixed costs of developing residential
properties in that location. This is intuitive since developers need high enough demand to cover the fixed
costs, given the increasing returns in their technology.
Equilibrium in the residential market implies that
r

nj hj = Rj Hj = Tjr ≤ T j ,

13

(18)

r

where nj is the number of active residential developers and T j is the upper bound on residential development
r

in j, assumed to be dictated by zoning ordinance. Since total developed land is given by Tjr = nj hj ≤ T j ,
substituting from (16), we obtain that the number of active developers is given by

nj = 

(1−γ)
vV Rj

Tjr



v
v−1

PJ

i=1 πij wi



1
v−1

(19)

if condition (17) is satisfied, and nj = 0 otherwise.

3.4

Neighborhood Residential Equilibrium

Having described the actions of agents in our economy, we are ready to discuss the determination of the
number of residents, Rj , and the amount of residential land, Tjr , in different neighborhoods j ∈ J, given
the characteristics of the city summarized by the model’s parameters, the utility level ū, wages {wi }J1 , and
commuting patterns, {πij }JJ
11 . The two key conditions in this respect are those that determine resident
entry, (14), and developer entry, (17).
In viable neighborhoods, where the number of residents is positive, a neighborhood equilibrium always
makes agents indifferent among their location choices, which implies that condition (14) holds with equality.
As discussed above, this condition implies a negative relationship between the number of residents, Rj , and
total developed land in the neighborhood. In Figure 4, we illustrate this relationship using the downward
sloping curve labeled “Resident Entry”.
Consider now developer entry. As explained above, developers enter if condition (17) is satisfied. In
a viable neighborhood, either condition (17) is satisfied with equality, or the residential zoning constraint
r

binds, so that Tjr = T j . Consider first the former case, which is depicted in Figure 4. The relationship in
(17) is a straight upward slopping line starting from the origin. The crossing between the two curves in
Figure 4 determines one of the neighborhood equilibria.7 In this case, the zoning restriction does not bind
and we refer to such a neighborhood equilibrium as an area that is partially developed or semi-developed.
This equilibrium is depicted by one of the red dots in Figure 4.
The crossing between these two curves could be such that the resulting amount of developed land
violates the zoning restriction. In that case, the number of residents is determined by the crossing between
the zoning constraint and the resident entry condition. The developer entry condition is then satisfied with
strict inequality and developers potentially make positive profits. Other developers might wish to enter the
neighborhood, given the number of residents, but the amount of residential land available for development
is exhausted. We refer to neighborhoods that are in this situation as fully developed areas. The equilibrium
7

The diagrams in Figure 4 above and Figure 5 below take as given wages and commuting patterns and so cannot be used
alone to make certain arguments. For example, neighborhood equilibrium stability arguments, where a new resident or developer
enters or leaves (as an out of equilibrium deviation), would change wages and commuting patterns and thereby shift the resident
and developer entry conditions themselves.

14

𝑅𝑗

Developer Entry

𝑇�𝑗𝑟

Resident Entry
𝑇𝑗𝑟

r

Figure 4: Determination of Rj and Tjr when Tjr < T j
is depicted as one of the red dots in Figure 5.

Independently of whether the zoning constraint is binding or not, conditional on wages and commuting
patterns, an equilibrium with developed land and positive numbers of residents always exists and is unique.
The reason is that the developer entry condition is continuous, upward slopping, linear, and starts from
the origin, while the resident entry condition is continuous, downward sloping, positive, and bounded away
from zero. The Intermediate Value Theorem then implies that the two curves cross, and the shape of the
curves imply that they cross only once, so that a neighborhood equilibrium with positive Rj and Tjr exists
and is unique.
In either case, however, there always exists an additional equilibrium that describes a non-viable neighborhood, specifically an equilibrium where Rj = Tjr = 0. The reason is that residential externalities are
such that if Rj = 0, the utility that agents derive from living in the neighborhood is also zero. That is,
Bj (0; j) = 0. At the same time, when Rj = 0 developers supply zero developed land. Therefore, the nonviable allocation is always an equilibrium. It follows that every neighborhood in the city, independent of
its fundamental characteristics, might be in an equilibrium where residents and developers coordinate and
make it viable, or one in which they fail to coordinate and the neighborhood is vacant. Put another way,
in order for an area to coordinate on the equilibrium with positive development, enough developers have to
expect that others will also invest, and that sufficiently many residents will populate the neighborhood. This
in turn requires that enough residents expect other residents to want to live in the developed neighborhood.

15

𝑅𝑗

Developer Entry

Resident Entry

𝑇𝑗𝑟

𝑇�𝑗𝑟

r

Figure 5: Determination of Rj and Tjr when Tjr = T j

In the coordinated equilibrium, the fundamental characteristics of a given neighborhood ultimately
determine the number of residents and amount of developed land required to remain viable. Neighborhoods
with relatively good fundamentals (e.g. a low Fj , or uniformly low κij ) require small numbers of residents and
developed land to become or remain viable. In contrast, neighborhoods with poor fundamentals need much
more coordination as the required magnitude of the external effect on amenities is larger to compensate for
the poor fundamentals. We now proceed to solve for the values of Rj and Tjr in the coordinated equilibrium
for the cases of fully and partially developed areas.
3.4.1

The Case of Fully Developed Areas
r

r

Consider first the case in which Tjr = T j . We let ΩF = {j|Tjr = T j } denote the set of all locations that end
up fully developed in equilibrium. This is the case depicted in Figure 5. Since residents can move freely
r

across different areas of the city, condition (14) evaluated at T j , has to hold with equality. Namely,


ū(1 −


Rj = 
Γ



θ−1
θ

γ)1−γ

nP
J

i=1 πij wi

h
r 
1−γ PJ

Tj

i=1 λij

16

o1−γ

(wi /κij )


θ


i1 
θ

1
σj +γ−1

.

(20)

From equation (13), we also know that for all j ∈ ΩF ,
qjr = (1 − γ)

J
Rj X
πij wi .
r
T j i=1

(21)

In these locations, since all available land for potential development is already built up, developers may
earn strictly positive rents, and so condition (17) will hold with strict inequality, as depicted in Figure
5. Furthermore, residential land rents in fully developed tracts are determined by demand for residential
properties rather than the cost of developing residential housing.
3.4.2

The Case of Partially Developed Areas
r

Consider now the case of neighborhoods in which the zoning constraint is not binding, so Tjr < T j . We
r

denote the set of these locations as ΩS = {j|Tjr < T j } and refer to them as semi-developed or partially
developed. This is the case depicted in Figure 4. As discussed above, in this case, both (14) and (17) hold
with equality. Furthermore, equations (13) and (17) may be combined to give a simple expression for (per
unit) residential prices,
qjr


= νV

Fj
(v − 1) V

 v−1
v

.

(22)

Thus, rents across partially developed neighborhoods vary only because of variation in the fixed costs of
developing residential land.
Solving for Tjr from equations (14) and (17) gives
1

σj +γ−1  σj
1−γ
J
 X
 u(1 − γ)


r
Tj = 
πij wi ,

o1

 nPJ


θ θ
θ−1
i=1
Γ θ
i=1 λij [wi /κij ]




(v−1)V
Fj

 v−1 
v

1−γ
vV

(23)

r

where Tjr < T j . Hence, Tjr is increases with ū, and decreases with Fj . Note also that a uniform increase in
wages, {wi }J1 , that leaves commuting patterns constants per equation (11), decreases Tjr if σj < 1, leaves it
unchanged if σj = 1, and increases developed residential land if σj > 1. In our quantitative application to
Detroit data below, we obtain that σj < 1 for virtually all neighborhoods, so that residential development,
Tjr , decreases with wages.8 This finding is natural; consider a city in which many neighborhoods are not
viable because coordination has failed. Since employment opportunities are still available, equilibrium wages
will tend to to be high throughout the city since residential rents in viable neighborhoods are relatively high.
The resulting lower Tjr then implies that the level of coordination needed to develop neighborhoods is then
lower, all else equal. This mechanism does not necessarily guarantee that coordination will be more pervasive;
8

In the quantitative application to Detroit that we present in the next section, the mean of σj is 0.570, with a standard
deviation of 0.046, a minimum of 0.446 and a maximum of 1.024. We only found one census tract for which σj > 1.

17

such an outcome would depend in part on the factors affecting equilibrium selection, including the policies
we discuss below. However, all else equal, any attempt to coordinate the relevant agents is likely to be less
costly in such a scenario. The response of the neighborhood equilibrium to a uniform increase in wages is
illustrated in Figure 6.

𝑅𝑗

𝑤𝑖 

𝑇�𝑗𝑟

𝑇𝑗𝑟

Figure 6: Neighborhood equilibrium and a uniform increase in wages
Another interesting comparative static relates to decreases in κij , particularly given the availability of a
vast set of limited access highways that reduce commuting costs between Detroit’s central business district
and its suburbs. A decline in some κij reduces Tjr . Hence, it is conceivable that these highways had the effect
of reducing coordination issues in the suburbs and, through general equilibrium effects on wages, increasing
the level of coordination needed in neighborhoods close to downtown areas. Figure 7 illustrates the change
in neighborhood equilibrium resulting from changes in commuting costs.

3.5

The City Equilibrium

The above discussion determines Rj and Tjr given ū, wages {wi }J1 , and commuting patterns, {πij }JJ
11 . We
now proceed to discuss the citywide equilibrium where wages and commuting patterns are endogenous. Since
transport costs of goods are assumed to be negligible, and we have normalized the price of goods throughout
the city to one, the goods market equilibrium is guaranteed by Walras’ law. The only remaining market to
clear is the labor market.
Equilibrium in the labor market is guaranteed when, for each business area i ∈ J, labor supply is equal
18

𝑅𝑗

𝜅𝑖𝑗 
𝑇�𝑗𝑟

𝑇𝑗𝑟

Figure 7: Neighborhood equilibrium and an increase in commuting costs
to labor demand. Labor supply in neighborhood i is the sum of the flows of workers commuting from all
PJ
neighborhoods, specifically j=1 πij Rj . Labor demand is in turn given by firms’ choices in each location i
derived in (4). Hence, equilibrium in the labor market is guaranteed by

Li =

J
X

πij Rj for all i ∈ J,

j=1

or


Ai β
wi



1
1−β−α

Tib =

J
X

πij Rj for all i ∈ J.

(24)

j=1

Labor demand on the left-hand side is decreasing in wi given our maintained assumption that 1 − β > α.
Labor supply on the right-hand side, in contrast, is more difficult to characterize since it depends on the
number of developed tracts, J, which itself depends on the distribution of wages in equilibrium. In general,
however, higher wages will increase labor supply by attracting more residents to the city and to nearby
residential neighborhoods, and by lowering the number of residents needed to make neighborhoods viable.
We can substitute (14) with equality for the J viable neighborhoods in (24), and set Rj = 0 for the
remaining neighborhoods, to obtain a system of equations in wi , i = 1, ..., J, given the amount of land in
business and residential uses as well as commuting patterns throughout the city. The amount of land devoted
to business use is exogenous, Tib , and residential land in viable neighborhoods, Tjr , is given by equation (23).
19

Finally, we can substitute equation (11), that determines commuting patterns as a function of wages, for πij
in equations (23) and (24). The result is a system of J equations in the J unknown wages. To the extent
some subset I ⊂ J of tracts does not contain any business activity, Tib = 0 and πij = 0 in those tracts, so
that (24) holds trivially for i ∈ I within this system of equations. The solution determines the citywide
equilibrium. Appendix A provides a description of the solution and algorithm we use to compute equilibria.
3.5.1

A Closed City

So far we have assumed that individuals can flow freely in and out of the city: an open city. In some
of the exercises we present below, we wish to consider the case of a closed city whereby total population,
P
R = Jj=1 Rj , remains constant. In such a case, instead of having a fixed utility level determined in the
wider economy, we let ū be determined endogenously so that total population is equal to the observed total
population in the city. We present several exercises with this constraint imposed in the on-line appendix.

4

Quantitative Application

We make use of current data on various aspects of Detroit to quantify the spatial urban framework described
above. The benchmark year in our analysis is 2014. Our analysis is carried out at the census tract level, since
this is the smallest spatial unit for which we can assemble an accurate and complete matching dataset. Thus
an area or neighborhood in the theory above is associated with a census tract in Detroit’s metropolitan area.
Our analysis covers the 297 census tracts in Detroit, as well as the surrounding adjacent metro area (Wayne
County, Oakland County, and Macomb County), which includes 866 additional tracts. We exclude 12 tracts
owing to missing or problematic data, and carry out the analysis on the remaining 1151 tracts. We aim to find
values of the underlying characteristics of neighborhoods (amenities, technology, fixed costs, externalities
and residential zoning) for each one of these tracts that rationalize, in our framework, the available data
on Detroit. Below, we give a brief description of the various data sources that provide information on the
variables of interest, and a detailed discussion of all data definitions and manipulations is provided in the
on-line appendix.
The data on the number of residents, Rj , workers, Lj , and pairwise commuting patterns, πij , is available
from the Longitudinal Employer-Household Dynamics (LEHD), Origin-Destination Employment Statistics
(LODES). This data is broken down into different classifications for job types including all private and
federal jobs. Wages, wj , are primarily determined using hourly wage bins provided by the LODES data
set, and are also complemented with data from the ZIP Business Patterns published by the United States
(US) Census Bureau. The complement, in particular, provides an additional bin at the upper end of the
distribution, with an upper bound set to 87560 dollars per year.
Information on developed residential land, Tjr , commercial land, Tjb , and residential prices, qjr , is available
at the parcel level from several different sources of microdata. The sources include Detroit’s Assessment

20

Office, Wayne County’s Office of Equalization and Assessment, Oakland County’s Office of Economic Affairs
and Community Development, and CoreLogic for Macomb county.
Our primary source for measuring commuting costs between census tracts, kij , is Google Analytics.
In particular, the Application Programming Interface (API) for Google Maps Distance allows the user to
specify one-among-many different possible travel methods between any two coordinates (or addresses), 11512
such pairs in our case. We consider the fastest driving route suggested by the API and do not impose any
restrictions, such as avoiding major highways or tolls. Data on both time and distance take into account
historical traffic patterns and geography by way of existing road networks.9
Finally, we make use of data on active building and demolition permits from Detroit’s Demolition
Program and Detroit’s Buildings, Safety, and Environment Department. This information helps us identify
the number of unique contractors in a given census tract, nj , with at least one currently active permit.
An active permit is any permit issued up until our benchmark year, 2014, and still active from that year
onward.

4.1

Vacant, Partially Developed, and Fully Developed Locations

An important step in matching our model to observed allocations in the city of Detroit is to designate
particular tracts as fully developed, partially developed, or empty or vacant. In particular, we need to
partition the complete set of tracks, Ω, into sets Ω = ΩF ∪ Ωs ∪ Ωv , where Ωv denotes the set of vacant
tracts. Note that this classification refers only to residential development in the different tracts. In Detroit,
all tracts (except for one) contain business areas with positive measured employment.
4.1.1

Vacant Tracts

We start by describing our methodology to select the tracts j ∈ Ωv . Our analysis relies on a key survey,
known as the Motor City Mapping project (MCM), involving a collaboration of private and public entities.
This project was developed in order to label blighted and abandoned properties in Detroit for removal or
revitalization. By collecting this data, the goal was to provide policy-makers and non-profit associations
with information that would guide urban policies aimed at attracting new residents to the city.
The Detroit Blight Removal Task Force and two other organizations, (Loveland Technologies and Data
Driven Detroit (D3)), led a physical survey of Detroit’s 380,000 parcels of land on behalf of MCM. This
physical survey was an expansion of the Residential Parcel Survey conducted in 2009 for 135,000 residential
properties in the city of Detroit and now covers commercial properties and parcels used for other purposes
(e.g. parks, parking, etc.)
Blighted areas identified by the MCM survey tend to be dominated by vacant lots and unoccupied
structures. Consistent with the MCM survey, we classify vacant census tracts in the context of our model
9

Interestingly, commute data between census tracts is not entirely symmetric in the sense that kij can differ significantly
from kji . For instance, one way streets and other asymmetries in the road network can lead to differences of ten minutes or
more for about 5800 commute pairs.

21

(i.e. associated with the no-development residential equilibrium) according to the following three criteria:
1. The percentage of parcels in a census tract classified as vacant (i.e. with no physical structure) is
greater than or equal to 50 percent AND
2. The percentage of residential properties in a census tract labeled empty or potentially empty is greater
than or equal to 30 percent OR
3. The percentage of commercial properties in a census tract labeled empty or potentially empty is greater
than or equal to 30 percent
Using these thresholds, we arrive at 17.5 percent of census tracts in Detroit being associated with the
residential no-development case, which closely matches the percentage of blighted parcels identified by the
MCM survey, (22 percent).10 The resulting Ωv set includes 52 tracts. These are the tracts that we identify
as currently being in the non-coordinated equilibrium, or vacant in terms of residents. The location of these
tracts is presented in Figure 3 in Section 2. As discussed there, these tracts are closely associated with the
expansion of the city of Detroit before 1930 and form a ring just outside the business district of the city.
4.1.2

Fully versus Partially Developed Tracts

Of the ncensus tracts
tracts
o not considered vacant, the model distinguishes between
n
o that are fully developed,
F
r
r
S
r
r
Ω = j|Tj = T̄j , and those that are partially developed, Ω = j|Tj < T̄j . Because the D3 survey,
which provides the percentage of empty parcels, is only available for the 297 census tracts within Detroit
proper, we have to impute this allotment for the remaining census tracts of Macomb, Oakland, and Wayne
Counties.
We do so by fitting a linear model of the determinants of the percentage of empty parcels in tracts within
Detroit proper, and then use it to estimate the percent of empty parcels in all tracts of the surrounding the
suburbs. The linear specification that we fit includes tract population, Rj , developed residential land, Tjr ,
average census tract wages, and commuting costs from downtown. The model’s adjusted R2 is 0.59. Using
data on these neighborhood characteristics, as well as the coefficient estimates, we estimate the fraction
of empty parcels in each tract in the suburbs.11 As a benchmark, we then designate a tract where more
than 2/3 of its parcels are occupied as being fully developed. Other tracts with less than 2/3 occupancy
are considered only partially developed. Figure 3 in Section 2 presents the resulting selection of tracts (for
10
11

DFC, in developing a strategic framework to revitalize Detroit, assessed that 17 percent of its parcels are vacant.
We estimate
ln %V acantj = ω1 + ω2 Rj + ω3 Tjr + ω4 wj + ω5 κ1j + εj

where %V acantj is the ratio of vacant parcels and parcels with unoccupied structures to the total number of parcels, and κ1j
denotes the distance from j to the CBD (labeled as tract 1 in our analysis). The resulting coefficients (with standard errors
in parenthesis) are ω1 = 6.26 (0.95), ω2 = −0.0012 (0.0002), ω3 = −0.38 (0.2), ω4 = −0.00015 (0.000024), and ω5 = −0.06
(0.0081). The regression has 242 observations and yields an adjusted R2 of 0.59.

22

ease of presentation we leave out some of the suburban tracts).12 As can be easily appreciated in the figure,
most of Detroit proper is designated as partially developed, while most of the suburbs as fully developed.

4.2

Parameters Values

The model features three different sets of parameters that differ in their dimensionality: citywide, neighborhood specific, and bilateral across neighborhoods. The city-wide parameters (α, β, γ, v) are matched to
estimates in the literature, except for θ and V , that we set to match respectively the slope of the gravity
equation, as in Monte et al. (2016), and the distribution of active contractors across neighborhoods. We
r

b

normalize u to 1. The neighborhood parameters (Aj, Fj , σj , T j , T j ) are determined so as to match four


neighborhood characteristics, wj , qjr , Rj , Tjb . Since tracts in equilibrium are either partially or fully develr

oped, with different residential pricing implications, Fj and T j cannot both be inferred from the data for
r

the same tract. Specifically, as explained below, Fj and T j

j

may be inferred for j ∈ ΩS and j ∈ ΩF respec-

tively. Therefore, conditional on tract classification and citywide parameters, characteristics of the city are
exactly matched as equilibrium benchmark allocations, and exactly identify the neighborhood parameters.
Finally, we choose the bilateral amenity matrix, λij to match bilateral commuting patterns in the data, πij ,
conditional on observed commuting costs, κij .
We set the values of the city-wide parameters using standard sources in the literature. Table 1 presents
the values of the five citywide parameters and the relevant source. We estimate two parameters either
because the literature does not offer a clear counterpart or because the context of Detroit is somewhat
unique. The first of these involve the parameter V , which governs the level of the variable cost of residential
construction. Combining equations (19) and (13), we know that the number of residential developers in
viable neighborhoods is
1

nj = (νV ) ν−1 qjr




ν
1−ν

(1 − γ)Rj

J
X

πij wi .

i=1

Given our data, for this purpose (qjr , Rj , wi, πij ), and the parameters in Table 1, we determine V to match
the mean of the distribution describing the number of contractors with active permits in the benchmark
year, 2014, across partially developed census tracts. These data are available from the Detroit Demolition
Program and Buildings, Safety Engineering and Environmental Department. The resulting mean of nj in
the data and model is 9.25 contractors with active permits per census tract. We can also compare the
standard deviation of nj in the data and model. The standard deviation of nj in the data is 4.52 and that
implied by the model is 4.51, a remarkable similarity given that we do not target this moment.
The second parameter that we estimate within the model is θ, which governs the elasticity of commuting
flows with respect to commuting costs. In particular, from equation (11), we can express commuting patterns
12

We choose a 2/3 threshold to define fully developed census tracts in our benchmark. While this threshold is somewhat
arbitrary, it acknowledges that desirable development also requires some empty and recreational areas. To the extent that
obtaining development rights, permits, and residents approval, becomes more difficult as fewer tracts remain unoccupied or
empty, increases in housing demand will start driving up rents in existing housing services.

23

Parameter
α
β
γ
θ
ν
V

Value
0.06
0.80
0.76
8.34
2.50
174, 941, 657

Source
Ciccone and Hall (1996)
Ahlfeldt, et. al (2015)
Davis and Ortalo-Magné (2011)
Gravity equation for commuting
Ahlfeldt and McMillen, (2015)
Equation for mean number of contractors

Table 1: Citywide parameter values and sources
in terms of the Head and Ries (2001) index as
λij (wi /κij )θ
πij
=
.
πjj
λjj (wj /κjj )θ
Similarly to Monte et al. (2016), we estimate the following equation,

log

πij
πjj




= −θ log

κij
κjj


+ µi + µj + λij ,

(25)

which, given commute costs data (distance or time), and fixed origin and destination effects, µi and µj ,
allows us to estimate θ. We invoke standard mean independence assumptions on the error term λij , which
in this case governs the mean of the idiosyncratic bilateral amenity. Here, κij ∈ [1, ∞). Thus, if πij = 0,
then either λij = 0 or κij → ∞.
The resulting estimates of θ using different measures of commuting costs are shown in Table 2. We
present results using κij measured by the straight-line distance between the centroid of i and j. This yields
an estimate of θ of 6.57. If we rely instead on distance estimates obtained from Google Analytics, we obtain
a lower estimate of θ given by 4.62. This measure of distance is arguably more accurate since it takes into
account the road infrastructure and geography in the city of Detroit. Our estimate for θ using this distance
measure is very similar to that obtained by Monte, et al. (2016) using commuting patterns across counties,
4.43. We also compiled data on an alternative measure of commuting costs based on all pairwise commute
times between census tracts. Such estimates are arguably more pertinent within a city since they take into
account road speed and average traffic.13 Using this alternative measure of commuting costs, we estimate a
larger elasticity for θ at 8.34. This is the value that we use in our benchmark calibration.
b

Given θ, we may immediately obtain λij as the residual in equation 25. We further set Tjb = T j for all
r

j ∈ Ω. Hence, the neighborhood specific parameters left to determine are (Aj, Fj , σj , T j ). Given data on
residential prices, qjr , residential population, Rj , wages, wi , and commute flows, πij , we recover either the
13
These issues are likely less relevant across counties than within cities, which explains why Monte et al. (2016)’s estimate
using distance is closer to our estimate using distance rather than time.

24

θ
S.E.
Work F.E.
Home F.E.
Observations
R2

Straight-Line Distance
6.57
(0.017)
yes
yes
1,187,423
0.39

Google Distance
4.62
(0.013)
yes
yes
1,187,423
0.37

Google Time
8.34
(0.022)
yes
yes
1,187,423
0.38

Table 2: Gravity equation estimation using different measures of commuting
development fixed costs Fj , for partially developed neighborhoods, or the upper bound on land development,
r

T j , for fully developed tracts. The observed allocations are informative in different ways depending on
whether a tract is partially or fully developed, which allows us to recover one parameter or the other but
not both, depending on the tract’s current classification. In particular,
we canuse equation (20), in the case

r

of fully developed tracts, to solve for T j using information on wj , qjr , Rj , πij
citywide parameters and

qjr

and γ. Alternatively, we use

to obtain Fj using equation (22) for partially developed tracts. The resulting

values of Fj are presented in Figure 8 and show a wide range of values. Naturally, we find the highest fixed
costs in downtown Detroit.
To compute σj , observe that equation (14) implies that

n
o1−γ
1−γ PJ
ū
(1
−
γ)
π
w
ij
i
i=1


ln 
 1−γ hP
i 1  − γ + 1,


J
θ θ
Γ θ−1
Tjr
i=1 λij (wi /κij )
θ



σj =

1
ln (Rj )



r

where Tjr = T j when j ∈ ΩF and Tjr is given by equation (23) when j ∈ ΩS . The resulting values for σj
are presented in Figure 9. These average to 0.57 across neighborhoods and do not exhibit large variations.
The minimum value is 0.446 which guarantees that σj > 1 − γ = 0.24; that is, this restriction is naturally
satisfied in our model, given observed Detroit allocations, without being explicitly imposed.
The final step is to choose neighborhood productivity parameters, Aj , to match the observed distribution
of wages across census tracts in the benchmark equilibrium. We use the labor market clearing condition in
(24) to set

1−β−α
J
wi  1 X
πij Rj 
,
Ai =
β
Tib j=1
given the data and parameters discussed above in addition to Tib for all j. Figure 9 presents the computed
values of Aj . The results are very intuitive. Productivity is high in downtown Detroit, but it declines
dramatically in some of the surrounding areas. It increases again in some of the suburbs where automobile
industry plants are located, such as in Dearborn, MI.
25

Legend
Vacant
Detroit City Outline

Res. Dev. Fixed Cost (Dollars)
0 to 70,000

70,000 to 190,000
190,000 to 260,000
260,000 to 1,250,000
1,250,000 to 6,500,000
6,500,000 to 15,162,887
Fully Occupied

Figure 8: Residential development fixed cost, Fj , in the baseline quantification

5

Coordinating Vacant Residential Tracts

The quantification of our theoretical model above allows us to exactly match the current configuration
of Detroit, and its surrounding counties, given the tract level data we use. Thus, we now make use of
our framework to quantify the effects of alternative, counterfactual, urban configurations of the city. We
identified 52 census tracts as being vacant, in the sense of being empty of residents, although we also saw
that all tracts (but one) contain some measure of business activity. The model rationalizes the existence
of these vacant neighborhoods as those that have failed to achieve coordination and that find themselves,
therefore, in the neighborhood equilibrium with no residents and no residential development. In this section,
we compute the value of a change to the alternative equilibrium for these neighborhoods, whereby these
areas coordinate into the equilibrium with positive amounts of residential development and residents.
Most of the policies that have been advocated to revitalize the city of Detroit involve a re-configuration
of sorts, including a degree of coordination and government involvement to revitalize specific parts of the
city. Our framework can help quantify the effects and gains from these policies, and can aid in determining
the set of census tracts where these policies might be most successful and valuable. There are a variety of
policies that could change equilibrium selection in a neighborhood. Our model, as with many models that
feature multiple equilibria, is not explicit about equilibrium selection. As with these other applications,
26

Legend

Legend

Vacant

Detroit City Outline

Productivity, Aj

Detroit City Outline

Residential Externality

0 to 110000

0 to 0.5

110000 to 140000

0.5 to 0.55

140000 to 175000

0.55 to 0.6

175000 to 215000

0.6 to 0.65

215000 to 260000

0.65 to 0.7

260000 to 310000

> 0.7 (max: 1.024)

310000 to 500825.5 (max)

Missing Data

Missing Data

Figure 9: Residential externality, σj , and productivity Aj, in the baseline quantification
however, we can think about policies that can eliminate the degenerate equilibrium, in our case the zero
residential development neighborhood allocation.14 An example of such a policy are development guarantees
by the government or an outside third party.
A development guarantee would credibly commit the issuer to invest a minimum amount of resources
in the treated area. Such investment guarantees would imply that Tjr > 0 and, therefore, can help select
the neighborhood into an equilibrium that involves coordination among both residents and developers.
If the guarantee is not large enough, residential developers and residents would fail to coordinate in the
neighborhood and the guarantee ends up being used (in which case the guarantor is nevertheless committed
to invest in the neighborhood, a likely undesirable outcome). However, if the guarantee is large enough, so
that Tjr is at least as large as it would be in the equilibrium with coordination, and fully credible, developers
would be willing to build and residents would be willing to live in the neighborhood. In such a case, the
guarantee would not end up being used and thus the policy would be ultimately costless. In fact, development
guarantees if credible need only be high enough to induce the marginal entrant tobuild in the
 neighborhood.

Put another way, in real terms, the guarantee needs to be greater than (nj − 1) V hvj + Fj , where nj and
14

In banking, for instance, the seminal work of Diamond and Dybvig (1983) features both a bank run and a no-run equilibrium
that also hinge on a coordination problem among agents, and deposit insurance has been advocated as an effective way to avoid
the bank run equilibirum.

27

hj are the values that obtain in the neighborhood equilibrium with coordination. By determining the value
of Tjr in the non-degenerate equilibrium (which itself depends on the configuration of the whole city and
any guarantees in place in other vacant neighborhoods), our analysis allows us to quantify the magnitude
of the required guarantees for the policy to be successful, and the potential set of resources that have to be
promised (and could be at risk if something fails).
In the analysis below, we present a series of counterfactuals that consider three approaches: i) we allow
all 52 vacant neighborhoods to move into a coordinated equilibrium at the same time, ii) we allow each
vacant neighborhood to move into a coordinated equilibrium one at a time, and iii) we allow particular
tract groups to move into a coordinated equilibrium in a way that resembles the desired outcome for plans
advocated by non-profit and other agencies to improve the city. In particular, for the latter scenarios, we
make use of the various proposals that DFC, an organization of planning experts, citizens, and civic leaders,
has put forward as perhaps the most well-known strategic vision for the future of Detroit. To our knowledge,
our analysis is the first to quantify the potential benefits and effects on allocations of these policies.

5.1

Computing Counterfactuals

To compute counterfactual scenarios, where we allow some previously vacant residential tracts to move
into a coordinated equilibrium, requires that we first make a few choices. In particular, we need to assign
neighborhood-specific parameters to the vacant tracts. Since all tracts contain some business activity, we
b

already have values for productivity, Aj , and the amount of business land, T j . We are then missing Fj , σj ,
r

and T j . To determine Fj , and σj for a given tract j ∈ Ωv , we adopt the corresponding values in its nearest
partially developed census tract, obtained in Section 4. Straight-line distances are used to determine the
r

nearest tract to a given vacant tract. To determine T j , we make use of data on total available residential
land in the tract under consideration, less business and public land as reported by the city assessor’s data.
In addition to assigning values to the local parameters for vacant residential neighborhoods, we need to
assign values of Fj for all fully developed tracts. Indeed, in computing a counterfactual exercise, we need
to account for the possibility that some previously fully-developed tracts might revert to being partially
developed as a consequence of the policy.15 Throughout the analysis, we assign the median level of Fj to
fully developed tracts in the city since, in the suburbs of Detroit where most tracts are fully developed
(see Figure 3), the nearest tract can be very far. Observe also that in a counterfactual exercise, partially
r

developed tracts might conceivably become fully developed. Thus, an upper bound T j is needed for those
tracts as well, which we obtain in exactly the same way as for the vacant tracts as described in the data
appendix.
15
As described in Section 2, between 1910 and 1930, many if not all of the presently vacant tracts in Detroit contained
large contiguous neighborhoods composed of single-family structures. In practice, having allowed for this possibility in our
quantitative simulations, no fully developed tract reverts to a semi-developed state.

28

5.2

The Value of Coordination in One Tract

In an open city were individuals can move in and out of the city at a given utility level ū, changes to the
structure of the city have by construction no effect on the welfare of workers. The gains or losses that
result from a change in the organization of the city can, however, be measured by other criteria. One such
criterion relates to the corresponding increase or decrease in total residential rents. This change would
reflect any additional aggregate residential investment that the city generates following the change in policy,
in addition to any change in rents in tracts where developers earn positive profits. Evidently, a change in
policy would also affect the number of agents in the city, as well as the rents generated by business land. We
can, therefore, also measure its effects based on corresponding changes in population size or changes in total
business rents. In fact, given that we postulate the presence of absentee landlords who own commercial land,
and that these landlords are the only agents who gain from the policy (recall that workers all get ū, while
final goods firms and developers make zero profits, except in fully developed areas for the latter), increases
in business land rents constitute a pure economic gain from the policy. Thus, perhaps the clearest way to
measure the economic gains resulting from a given policy change is to sum the change in profits earned
by residential developers and the change in business rents. Below, we consider different policy proposals
according to these three alternative criteria.
Figure 10 presents the increase in total city-wide residential rents as a result of solving the coordination
problem in each of the 52 vacant tracts one at a time. The color associated with each tract in the Figure
represents the total increase in city-wide rents from a move to the coordinated equilibrium in that tract only.
The heterogeneity in the increase in total rents across tracts (and corresponding residential investments) is
quite pronounced. The vacant tract which generates the largest increase in citywide rents, were it to be in
the equilibrium with coordination, is tract 52, a small tract at the boundary with the city of Hamtramck
(which is surrounded by the city of Detroit). With a move to the equilibrium with positive population and
residential development, that tract alone generates an increase in citywide residential land rents of about 7.5
million dollars. This result reflects in part the fact that its closest neighboring tract, tract 48 in Hamtramck,
is itself a relatively prosperous and dense neighborhood with high residential prices for Detroit. In contrast,
other tracts generate less than one tenth of that amount in additional city-wide residential rents. This
heterogeneity points to the importance of track selection when implementing “development guarantees”.
Choosing the correct neighborhoods, and the corresponding required investment guarantees, can change the
policy outcomes dramatically.
Figure 11 presents the total city-wide increases in population and business rents resulting from moving
each of the 52 vacant tracts to a coordinated equilibrium one at a time. As with residential rents, both
maps point to a wide heterogeneity of outcomes from moving a single tract to an equilibrium with residential
development and population. Population in the city can increase from less than 80 residents to more than
800, while business rents would rise to between half a million and more than two and a half million. One
conclusion that emerges from these figures, however, is that the ranking of tracts in terms of the overall
effects of development guarantees, put into effect in each tract individually, is quite similar across all three
29

221
157

522
525
510

168

108
52

72
39 36
43

26

56
73
35 17
90
6
57 38
10
84
27
45
74
59

198

125

63

25

68

88
82

60

44

30 33
18
13
14

32

76
67
49 66

112 140
124
132
94

20

Legend
Detroit City Boundary

Change in Residential Rent
Previously Fully or Partially Developed
0 to 750,000
750,000 to 1,500,000
1,500,000 to 2,000,000
2,000,000 to 3,000,000
3,000,000 to 5,000,000
5,000,000 to 7,511,513

Figure 10: Total Citywide Residential Rent Increase from Coordinating Residential Development in One
Tract
measures. The tracts that generate the largest effects on residential rents also tend to generate the largest
effects on population and business rents. This finding suggests that policy proposals, all else equal, might
more easily achieve some degree of consensus among concerned stakeholders, since different stakeholders
might weight these effects in different ways.

5.3

Detroit Future City

Detroit Future City is a civic organization created in 2012 with the mission of providing guidance in laying
out a vision for the future of Detroit. The Detroit Future City (DFC) Strategic Framework lays out perhaps
the best known desired image of what the city of Detroit should look like, 10, 20, and 50 years into the future.
This framework points to both the strengths and weaknesses of Detroit’s current urban configuration. In
highlighting the significant amount of vacancies near the city center that contribute to blight and declining
property values, the DFC Strategic Framework in part focuses on key zones for residential development that
align with a subset of the vacant census tracts in our study. In particular, DFC proposes several distinct
plans for development that emphasize different criteria. In this paper, we focus on residential development
30

221

221
157

522
525
510

168

108
52

72
39 36
26
43
56
73
35 17
90
6
57 38
10
84
27
45
74
59

198

125

63

68

157

88
82

60

44

30 33
25
18
13
14

32

76
67
49 66

522
525
510

112 140
124
132

168

108
52

72
39 36

94

26
43
56
73
35 17
90
6
57 38
10
84
27
45
74
59

20

Legend

198

Detroit City Boundary

Change in Population

125

63

68

88
82

60

44

30 33
25
18
13
14

32

76
67
49 66

112 140
124
132
94

20

Legend
Detroit City Boundary

Change in Business Rent

Previously Fully or Partially Developed

Previously Fully or Partially Developed

1 to 80

0 to 500,000

81 to 160

500,000 to 750,000

161 to 240

750,001 to 1,000,000

241 to 400

1,000,000 to 1,500,000

401 to 560

1,500,000 to 2,000,000

561 to 823

2,000,000 to 2,736,965

Figure 11: Total Citywide Change in Population and Business Rents from Coordinating Residential Development in One Tract
and quantify the effects of several of the DFC proposals for its vision of Detroit 50 years into the future. The
most ambitious proposal, which we refer to the Detroit Future City (DFC) counterfactual, involves 22 tracts.
This DFC proposal considers different residential land use typologies. Examples of such typologies include
‘green residential’, that emphasizes landscape-based neighborhoods, ‘traditional low density,’ characterized
by detached single family houses on large parcels, or ‘live plus make,’ where housing is located near artisanal
and small fabrication facilities or workshops. These various residential land use typologies include different
combinations of a smaller number of residential tracts, and are individually evaluated and compared as
counterfactuals in the on-line appendix.
We carry out the DFC counterfactual by exploring an equilibrium where the 22 tracts matched to the
DFC’s strategic framework have switched from a no-development equilibrium to one with positive residential
population. We then explore other potential configurations of 22 tracts that can potentially yield larger
gains.
The first step in the analysis requires that we identify the tracts in the DFC proposal on a map of
Detroit, and compare them with the individual tracts identified in the previous sections as yielding the
largest gains with respect to land rents and investment. Figure 12 reproduces Figure 10 but adds an outline
of the tracts in the DFC proposal (left). It also shows an outline of an alternative plan where we select the
22 tracts that provide the highest increases in residential rents as each tract switches to an equilibrium with
residential population individually (right). We refer to the latter plan as the ‘Best 22 Residential’ plan. It is
evident from the maps that the two proposals overlap only in part, sharing only 11 out of 22 tracts. One of
the qualitative differences is that the DFC proposal focuses on developing the areas closest to the downtown
31

core, while the Best 22 Residential plan covers some of the same areas but also areas in a wider outer ring.

221

221
157

522
525
510

168

108
52

72
39 36
26
43
56
73
35 17
90
6
57 38
10
84
27
45
74
59

198

125

63

68

157

88
82

60

44

30 33
25
18
13
14

32

76
67
49 66

522
525
510

112 140
124
132

168

108
52

72
39 36

94

26
43
56
73
35 17
90
6
57 38
10
84
27
45
74
59

20

Legend
Detroit Future City

198

Detroit City Boundary

125

63

68

88
82

60

44

30 33
25
18
13
14

32

76
67
49 66

112 140
124
132
94

20

Legend
22 Highest Impact--Total Residential Rent
Detroit City Boundary

Change in Residential Rent

Change in Residential Rent

Previously Fully or Partially Developed

Previously Fully or Partially Developed

0 to 750,000

0 to 750,000

750,000 to 1,500,000

750,000 to 1,500,000

1,500,000 to 2,000,000

1,500,000 to 2,000,000

2,000,000 to 3,000,000

2,000,000 to 3,000,000

3,000,000 to 5,000,000

3,000,000 to 5,000,000

5,000,000 to 7,511,513

5,000,000 to 7,511,513

Figure 12: DFC Strategic and Best 22 Residential Plans Compared to Gains in Total Rents from Coordinating Individual Tracts
One might argue that the comparison above is not entirely complete since it does not take into account
the complementarities that could result from coordinating several tracts jointly rather than one at a time.
Below, we compare the implications of these proposals when the combined effects from coordinating groups
of tracts jointly are taken into account. However, it is important to note that the proposal we refer to as
the ‘Best 22’ grouping does not select the best 22 tract combination, out of all possible tract combinations,
taking any complementarity effect into account. Rather, we simply rank the citywide effects resulting from
moving each tract individually to an equilibrium with coordination as the main criterion, and then choose
the 22 tracts with the largest gains. A direct implication is that the true optimal policy might differ slightly
from our ‘Best 22’ calculation. Finding the best combination of tracts, out of all possible combinations of
vacant tracks, constitutes a prohibitively large computational task, and we cannot guarantee that such a
policy would be identical to our ‘Best 22’ proposal.16 However, given that the effects on residential rents of
switching a vacant neighborhood to an equilibrium with positive residential population are fairly local, the
difference in tract sets is unlikely to be large. In any case, we more precisely consider the ‘Best 22’ proposal
as a lower bound on what an optimal policy could potentially achieve.
We also carry out similar exercises with alternative criteria to determine the best 22 tracts. In particular,
we consider the tracts that yield the largest increases in population or aggregate business rents in a coordinated equilibrium with positive residential development and population. The resulting track selection using
these alternative criteria ends up looking quite similar. Using citywide changes in population, 21 tracts end
16

Taking into account all possible 22 tract combinations, out of 52 vacant tracts, amounts to

32

52!
30!×22!

counterfactual scenarios.

up being selected in common with those selected according to the largest increases in residential land rents,
implying that only one track differs. Using changes in citywide business rents, 18 tracts are common to the
selection according to citywide residential land rents, while only four tracks differ. Figure 13 outlines the 22
tracts that, when individually switched to an equilibrium with coordination among residents and developers,
yield the largest gains in citywide population and business rents. One notable qualitative difference is that
the selection of ‘Best 22’ tracts based on implied changes in business rents focuses on coordinating only the
tracts located in a relatively tight ring across the business area, leaving out those farther away from the
central business district.

221

221
157

522
525
510

168

108
52

72
39 36
26
43
56
73
35 17
90
6
57 38
10
84
27
45
74
59

198

125

63

68

157

88
82

60

44

30 33
25
18
13
14

32

76
67
49 66

522
525
510

112 140
124
132

168

108
52

72
39 36

94

26
43
56
73
35 17
90
6
57 38
10
84
27
45
74
59

20

Legend
22 Highest Impact--Change in Total Population

198

Detroit City Boundary

125

63

Change in Population

68

88
82

60

44

30 33
25
18
13
14

32

76
67
49 66

112 140
124
132
94

20

Legend
22 Highest Impact--Total Business Rent
Detroit City Boundary

Change in Business Rent

Previously Fully or Partially Developed

Previously Fully or Partially Developed

1 to 80

0 to 500,000

81 to 160

500,000 to 750,000

161 to 240

750,001 to 1,000,000

241 to 400

1,000,000 to 1,500,000

401 to 560

1,500,000 to 2,000,000

561 to 823

2,000,000 to 2,736,965

Figure 13: Best 22 Tracts Based on Population and Business Rents
Table 3 presents some citywide statistics corresponding to the alternative policy counterfactuals. The
first column in Table 3 presents the outcomes for the benchmark equilibrium, which matches by construction
the data used to identify the model parameters in Section 4.2. The second column presents findings from the
policy counterfactual that considers development guarantees for the 22 tracts selected in the DFC strategic
plan. The next three columns present findings for alternative ‘Best 22’ tracts according to citywide business
rents, residential rents, and population criteria. The final column presents the outcome of an exercise where
all vacant tracts are allowed to switch into an equilibrium with coordination. In these exercises, apart from
that in the last column, 22 tracts are always simultaneously allowed to switch from a no-development to
a development equilibrium, so that the findings reported in Table 3 reflect any complementarities between
those tracks.
In all policy counterfactuals, switching tracks into an equilibrium with coordination increases residential
development which attracts more residents to the city. Naturally, the proposal where tracts are selected
according to the implied increases in population yields the largest increase in residents among the policies
33

Detroit
Residents
Mean Wages, $
S.D. Wages, $
Mean Res. Rents, $/Sq. Ft.
S.D. Res. Rents, $/Sq. Ft.
Total Res. Rents, Mill. $
Total Bus. Rents, Mill. $

Benchmark
126,430
31,996
10,136
1.47
0.05
1,223
2,181

DFC
131,466
31,922
10,098
1.43
0.05
1,270
2,205

Best 22 Bus.
134,784
31,869
10,110
1.43
0.05
1,301
2,217

Best 22 Res.
135,286
31,875
10,130
1.43
0.05
1,304
2,216

Best 22. Pop.
135,312
31,875
10,132
1.43
0.05
1,303
2,215

All 52
139,455
31,801
10,081
1.37
0.05
1,343
2,235

Table 3: Detroit Proper Outcomes for Alternative Policies
considering 22 tracts. This proposal increases the number of residents in Detroit proper by 8882 residents
or about 7 percent. Allowing all 52 tracts to coordinate in the equilibrium with development yields an
increase of 10 percent in the number of residents. Given that the supply of new residents to the city is
perfectly elastic at ū, none of these scenarios changes residential mean rents per square foot significantly;
they decrease slightly within Detroit proper because rents in the newly developed tracts tend to be lower
than the existing tract average and the city has relatively few fully developed tracts. Only in the case where
we coordinate all 52 tract do residential rents per square foot fall slightly. The influx of workers into the
city lowers wages, although the changes are small in all cases.
Table 3 also presents total yearly residential and business rents in millions of dollars. Total residential
rents amount to about 1.2 billion dollars while total business rents amount to about 2.2 billion dollars
per year. Allowing for a coordination equilibrium in the best 22 tracts according to largest residential
rent gains increases residential rents by 81 million dollars per year or 6.6 percent. In contrast the DFC
strategic proposal increases rents by 47 million per year or 3.8 percent. Therefore, selecting the ‘Best 22’
tracts according to where residential investment is largest in a counterfactual yields 72 percent additional
investment relative to the DFC proposal.
The findings are somewhat less pronounced when examining business rents. Consider the ‘Best 22’ plan
according to the tracts that generate the largest individual increases in business rents. This policy raises
business rents by about 35 million per year or 1.6 percent. The DFC proposal increases business rents by
24 million per year. Therefore, in terms of business rents, the model-selected policy yields an increase in
gains of 46 percent relative to the DFC strategic plan. Note that, as mentioned above, all of the ‘Best 22’
policies in Table 3 yield very similar outcomes given that the set of selected tracts overlap significantly. If
all 52 tracts are allowed to switch to an equilibrium with coordination, gains can amount up to 54 million
per year or 2.5 percent relative to the benchmark equilibrium.
Table 4 presents the whole set of changes in residential and business rents, as well as changes in population, resulting from these different policy counterfactuals. The table further separates the outcomes into
those that are experienced directly in the treated tracts versus those that are experienced in the remaining

34

tracts of Detroit proper. Table 4 also shows the effect of these policies for the whole sample of tracts in
greater Detroit, which includes the counties of Wayne, Macomb, and Oakland. Finally, the first row of the
table gives the required development guarantee needed to induce a switch to the equilibrium with coordinaP
tion, calculated as Ωp (F j + V hνj )(nj − 1), where Ωp corresponds to the set of tracts in which the policies
are implemented.

Dev. Guarantee, Mill. $
Detroit Proper:
∆ in Res. Rent, Mill. $
Total
Treated Tracts
Other Tracts
∆ in Bis. Rent, Mill. $
Total
Treated Tracts
Other Tracts
∆ in Population
Total
Treated Tracts
Other Tracts
Greater Detroit:
∆ in Res. Rent, Mill. $
∆ in Bis. Rent, Mill. $
∆ in Population

DFC
41.156

Best 22 Bus.
70.581

Best 22 Res.
73.440

Best 22. Pop.
73.001

All 52
106.281

47.452
45.797
1.656

77.829
75.159
2.670

80.758
77.443
3.315

80.502
77.064
3.438

120.347
115.894
4.453

23.502
9.857
13.645

35.922
8.657
27.265

34.525
4.469
30.056

33.792
4.505
29.287

54.254
22.370
31.884

5,036
4,746
290

8,354
7,893
461

8,856
8,347
510

8,882
8,369
514

13,025
12,296
730

58.676
61.112
7,043

96.350
100.356
11,663

102.751
107.024
12,540

103.142
107.431
12,617

150.847
157.124
18,301

Table 4: Development Guarantees and Policy Outcomes in Detroit Proper and Greater Detroit
Table 4 underscores some key implications shared by all of the policy proposals. First, in all cases,
the plans are worth pursuing; that is all plans yield increases in aggregate residential and business rents
combined that exceed the needed development guarantees. Therefore, even if the development guarantees
were implemented in a way that ultimately required the guarantors to develop the targeted areas themselves,
the policies result in a gain for the city, particularly given the implied increase in business rents (the gains in
residential rents in non-treated tracts are generally small). It is important to keep in mind that the hope is
for the development guarantees not to be used in equilibrium since, if fully credible, they would be provided
only to coordinate private investors and residents. Table 4 shows that the benefits from this policy, once we
sum all of their implications for greater Detroit, can be quite large. Second, most of the gains in residential
land rents accrue to the treated tracts while most of the gains in business land rents accrue outside of the
treated tracts. In fact, about two thirds of increases in business land rents emerge outside of Detroit proper,
where all of the treated tracts are located. In contrast, only about a fifth of the increases in residential land
35

rents appear outside of the Detroit proper area. Increases in commercial land rents stem primarily from
commuting links and general equilibrium effects, because wages change everywhere in the broader city, so
that these findings highlight the perils of using partial equilibrium logic to carry out this type of policy
assessment. Third, increases in population are quite concentrated in treated tracts, which imply that the
newly developed areas provide workers not only to downtown firms but also to the suburbs. In that sense,
the policy revitalizes the core of the city as a residential center.
Comparing the different policies presented in the columns of Table 4 again emphasizes that the particular
criterion according to which ‘Best 22’ policy is selected is somewhat immaterial. Out of the set of policies
that move 22 tracts into an equilibrium with residential development, the best policy for Detroit as a whole is
one where tract selection is guided by the largest effects on population. Making Detroit proper an attractive
place to live with enough residential amenities is the key objective of the policy. The DFC strategic proposal
emerges as least effective in generating increases in rents, of either type, or population. Specifically, the
‘Best 22’ plans we consider all generate about 40 percent larger increases along all three dimensions. That
said, the needed development guarantees would then also have to be larger.
Net gains to the greater Detroit area become much larger when treating all 52 vacant tracts, which then
emerges as the best option. This more ambitious policy generates 157 million dollars a year in additional
business rents, and 150 million dollars a year in additional residential land rents. The corresponding development guarantees that would be required totals 106 million dollars. The rate of return for greater Detroit
on such a policy, even if one takes the guarantees in their entirety as a pure resource cost (and one should
not), is substantial: at least a 50 percent return on investment with an extra 18,301 residents. Put another
way, the returns to a well designed policy are potentially quite large. Observe also that the ‘Best 22’ plans
capture about two thirds of these gains while coordinating fewer than half of the tracts. As a consequence,
to the degree that development guarantees might conservatively be available only for a more limited set
of policies, then targeting the treated tracts judiciously is of the essence. In particular, not all of DFC’s
strategic framework focuses on residential development and, in fact, suggests developing ecological zones in
some of the currently vacant tracts, in particular those surrounding downtown. Our study makes clear that
this strategy, while undoubtedly carrying non-pecuniary benefits, also entails a substantial cost.

5.4

In Detail: Coordination in all 52 Tracts

The aggregate city statistics presented above do not illustrate, by design, the heterogenous responses of
particular neighborhoods to the different policies considered in the analysis thus far. In this section, we
make use of the plan that treats all 52 vacant neighborhoods to illustrate and discuss some of these effects
across tracts.
In Figure 14, we present the fraction of residential land that is developed in each tract after the policy
is implemented.17 The figure shows that, even after implementation, most of Detroit proper is still only
partially developed, that is Tjr < T̄jr . In many of the areas now in a new equilibrium with coordination,
17

Tracts marked in black represent tracts for which data is not available or includes obvious errors.

36

residential development uses less than 15 percent of the potentially available residential land. In no sense,

therefore, does this policy
lead to a booming residential
that becomes
congested. Only in a few of the
Coordination
in All area
Census
Tracts,
ion in All
Census
Tracts,
new tracts with residential development
does residential Wages
land usage exceed 50 percent of the available land,
Workplace
Space and
as none
a Percent
ofbecome
the Constraint
of these
tracts
fully developed.
Workplace Wages
Change in Workplace Wages

Outline

eveloped

a

Legend

Legend

Vacant

Detroit City Outline

Legend
Detroit City Outline

Change in workplace wages

Percent
Fully
Detroit
CityDeveloped
Outline

< -250

0 to 15
Workplace
wages (Dollars)

-250 to -100

to 30
0 15
to 12,500

-100 to -50

30 to 50
12,500
to 25,000

-50 to -25

50 to 80
25,000
to 35,000

-25 to -10

80 to 99.9
35,000
to 45,000

-10 to 0

>Full
45,000

>0

MissingData
Data
Missing

Missing Data

Data
Coordination
in All Census Tracts

Coordination in All Census Tracts

Figure 14: Coordinating All 52 Vacant Tracts, Percent of Developed Residential Land and Change in
Workplace Wages
Figure 14 also illustrates the change in workplace wages in each tract. Virtually all tracts experience
declines in workplace wages. As agents migrate to the city following a policy aimed at revitalizing Detroit,
labor supply naturally increases which tends to depress wages. We discussed this effect earlier in the context
of the description of the model and its main mechanisms. As expected, the fall in wages is somewhat more
pronounced close to the affected areas, but the general decline in wages is fairly uniform across the city.
This general equilibrium effect, which extends well outside Detroit proper, is primarily responsible for the
increase in business land rents, through equation (5), described in the previous section.
Figure 15 shows the resulting change in the number of workers and residents at the census tract level.
Clearly, a development-guarantee policy that is provided in each of the 52 vacant tracts raises the number
of residents in essentially all tracts, although increases are naturally larger in the treated neighborhoods.
The areas immediately surrounding the treated tracts sees the smallest gains in residents, while gains in the
suburbs are more substantial. This localized pattern makes sense. The newly developed residential areas
now house downtown workers who substitute away from housing in other areas of Detroit proper. The change
37

in workers and their locations also show some clear patterns. Employment in downtown Detroit increases
substantially, but so does employment in many of the suburbs, including Dearborn. The newly developed

residential
tracts increase
labor supply nearby, in
which
depresses
wages and
encourages firms to employ more
ion in All
Census
Tracts,
Coordination
All
Census
Tracts,
workers. Furthermore, workers are not worse
off since they enjoy additional residential amenities and the
Workers
Residents
shorter commutes
to work.
Residents
Change
in Workers

Change in Residents

Legend

Legend

Vacant

Detroit City Outline

Detroit City Outline

Legend
Change in Workers

Change in Residents

<0
Vacant

<0

0 to 3City Outline
Detroit

0 to 1

0 to
10350
to 20

3 to 5

350
20toto700
35

5 to 10

0

700
35toto1,200
70

10 to 150

00

1,200
70 toto180
2,000

150 to 475

> 2,000
> 180

> 600

Missing
Missing
Data
Data

Missing Data

utline

3 to 10
Residents

1 to 3

Data
Coordination
in All Census Tracts

Coordination in All Census Tracts

Figure 15: Coordinating All 52 Vacant Tracts, Change in Workers and Residents
The final maps, presented in Figure 16, show the changes in business and residential rents by tract.
The results follow closely those discussed in Figure 15. Tracts that gain the most workers are those where
business rents increase most, and tracts that gain the most residents are those where residential rents increase
most. These findings are natural given our specification of technology and preferences with Cobb-Douglas
functions that feature constant factor and consumption shares respectively. Perhaps more interesting in this
case are the heterogeneity in the magnitudes of the implied changes. While some of the tracts in downtown
Detroit, Dearborn, and other suburbs, can see increases of more than a million dollars in yearly business
rents, other tracts near the boarder of Detroit see business rents increase by less than 25,000 dollars. Most
tracts experience modest increases in residential land rents, between 15,000 and 60,000 dollars. Only the
residential tracts that have switched from being vacant to an equilibrium with residential development show
increases in residential rents of more than one hundred thousand dollars. Areas where rents tend to increase
the least, either business or residential, are located in the outer ring of the city close to the boundary of
38

ion in All Census Tracts,
Coordination in All Census Tracts,
Business Rent
Residential Rent
Detroit proper.
Change
Residential
in Business
Rent Rent

Change in Residential Rent

Legend
Legend
Vacant

utline

Legend
Vacant

Detroit
City
Outline
Detroit
City
Outline

s, millions)

Detroit City Outline

Res.
Change
Rent in
(Dollars,
Biz. Rent
millions)
(Dollars)

Change in Res. Rent (Dollars)

0 to
0 to
3 25,000

<0

3 to
25,000
6
to 50,000

0 to 1,500

6 to
50,000
9
to 100,000

1,500 to 15,000

9 to
100,000
12
to 200,000

15,000 to 30,000

12200,000
to 15 to 500,000

30,000 to 60,000

15500,000
to 18 to 1,000,000

60,000 to 100,000

>18
> 1,000,000
(49 max)

> 100,000

Missing
Missing
Data
Data

Missing Data

Benchmark
All 52

All 52

Figure 16: Coordinating All 52 Vacant Tracts, Change in Workers and Residents

6

Conclusion

Declining cities have become and likely will continue be a pervasive phenomenon. The fact that cities tend
to specialize in certain industries, and that the importance of particular industries and the characteristics
of factors they employ vary over time, make this inevitable. Learning how to cope with urban downturns
can lead to improved utilization of past investments, and less dissatisfaction by local residents with respect
to technological progress and globalization. Cities or regions specialized in declining industries should be
able to reinvent themselves to host new thriving industries, albeit perhaps on a smaller scale. So far, this
process of urban reinvention has failed.
In this paper, we have argued that inefficiencies associated with urban decline can be related to specific
areas of a city, that potentially retain sound underlying fundamentals, but are nevertheless trapped in local
neighborhood equilibria in which developers and residents are unable to coordinate their actions. No resident
wants to be first to move into, and no developer wants to be first to invest in, a vacant neighborhood. In
the case of Detroit, we identified 52 census tracts that can be mapped into such an equilibrium. These
tracts were originally developed before the 1930’s to accommodate a rapidly growing demand for workers in
39

the automobile industry. However, as employment fell in that industry, and some plants moved elsewhere,
residential demand and income collapsed leading to riots in 1967 that eventually drove them into a nodevelopment equilibrium. The end result is a distorted, impractical, and inefficient city.
It is no surprise that thriving industries do not necessarily wish to locate in such a city. The high-skilled
workers required by the high-tech industry would likely not want to start their lives in vacant neighborhoods
near Detroit’s downtown, even if such locations are cheap relative to the available urban infrastructure. The
necessary density is simply not there, so new workers and firms do not enter.
Our analysis quantifies the forces that sustain this outcome as an equilibrium of the city, and uses the
resulting quantitative framework to assess policies that can help vacant neighborhoods switch back to an
equilibrium where developers and residents coordinate into building and living in these neighborhoods. In
particular, we consider development guarantees, provided by the government or outside parties, that commit
to a minimum amount of investment in a targeted vacant area. If fully credible, these guarantees would
resolve the coordination problem among private developers and residents, leading to a new equilibrium with
positive numbers of active developers and residents. Our framework allows us to quantify the magnitude
of the required guarantees in each vacant tract, and to identify the tracts in which the policy would be
most effective. In addition, we are able to compare our findings with those of alternative plans that have
been advocated by experts and local residents, such as those laid out by the Detroit Future City strategic
framework, and to quantify their implications. In all cases, we find that these guarantees can be quite
effective. Policies that utilize guarantees in the 22 tracts yielding the largest gains from a switch to an
equilibrium with development generate increases in residential and business rents in the hundreds of millions
of dollars a year. These can also attract thousands of new residents to the city.
We estimate that a large fraction of the gains stemming from any policy that develops the currently
vacant residential areas would accrue to business rents outside Detroit’s city boundary by way of general
equilibrium effects. Therefore, incorporating the appropriate stakeholders in policy design and initial investments appears to be important. In particular, our analysis underscores the existence and magnitude of
mutual gains to different parties, including developers, landowners, and new residents.
In any quantitative analysis, one inevitably confronts the need to abstract from some aspects of reality
that might be pertinent. One such dimension is the presence of citywide or region-wide agglomeration
effects. In our analysis, we consider local agglomeration effects in production and amenities that are at the
heart of the coordination problem we study, but these effects operate only within and not across census
tracts. To the degree that agglomeration effects across tracts also matter quantitatively, adding this feature
to our analysis would only serve to increase the gains from the advocated policies. In such a case, the gains
we measure then become a conservative lower bound.

40

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D.,

(2010),

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42

Appendix A: Solving the Model
The Basic Set of Equations and Unknowns
We solve the model given a set of parameters, P, and any set of vacant tracts, Ωv = Ω\(ΩF ∪ ΩS ), as follows:
From equation (11), we have
λij (wi /κij )θ
πij = PJ
.
θ
i=1 λij (wi /κij )

(26)

Then, from equation (23), we have

Tjr

=



(1−γ)Rj

r
T
PjJ
qjr



if j ∈ ΩF

i=1

πij wi

, if j ∈ ΩS

,

(27)

and from equation (17), in equilibrium,


Rj = 

γ)1−γ

o1−γ

nP
J



ū(1 −
i=1 πij wi

1 


h
i
1−γ

 r
PJ
θ θ
Γ θ−1
Tj
i=1 λij (wi /κij )
θ

1
σj +γ−1

.

(28)

Residential prices are given by

R PJ

 (1 − γ) T rj i=1 πij wi if j ∈ ΩF
j
 v−1

.
qjr =
v
Fj

S

vV
if
j
∈
Ω
(v−1)V

(29)

Finally from equation (24), reproduced below, wages solve


Ai β
wi



1
1−β−α

Tib =

J
X

πij Rj .

(30)

j=1

In general, equations (26) through (30) make up a system of J 2 + 4J equations in the same number of
unknowns, given by πij (P), Tjr (P), Rj (P), qjr (P) and wi (P), where J = 1151 census tracts in our application.
In solving this system, we must be cognizant that the sets of fully developed locations, ΩF , and partially
developed locations, ΩS , are themselves endogenous and determined as part of the equilibrium. Specifically,
given that
Tjr (Rj , wj , πij , qjr ; P)

P
(1 − γ)Rj Ji=1 πij wi
=
,
qjr

in the lower portion of equation (27) represents an unconstrained level of development for census tract j, it

43

must be the case that

(
j∈

r

ΩF

if Tjr (Rj , wj , πij , qjr ; P) ≥ T j

ΩS

if Tjr (Rj , wj , πij , qjr ; P) < T j

r

.

(31)

A direct implication is that the sets of fully developed and semi-developed locations, ΩF and ΩS , potentially
change in counterfactual scenarios relative to a given benchmark. All other equilibrium allocations follow
in a straightforward manner given the vector of equilibrium wages, wj .
Solution Algorithm
This section describes the algorithm used to implement the model solution described above.
1. Guess a vector of wages, w0 = (w10 , ..., wJ0 )0 .
2. Given this guess, calculate the matrix of commuting patterns,
λij (wi /κij )θ
.
πij (wi = wi0 ) = PJ
θ
i=1 λij (wi /κij )
3. Given our guess w0 and πij (wi = wi0 ) from step 2, from equation (23) in the text, we compute
1

σj +γ−1  σj
(v−1)V
1−γ
1−γ
J
 u(1 − γ)
 X
Fj
vV


r
0
Tj (wi = wi ) = 
πij (wi = wi0 )wi ,

nP
o1




J
θ θ
i=1
Γ θ−1
i=1 λij [wi /κij ]
θ


 v−1 



v

which also corresponds to the lower portion of equation (27).
(a) Ensure that Tjr (wi = wi0 ) above satisfies its upper bound constraint,
r

(
Tjr (wi

=

wi0 )

=

r

Tj

if Tjr (wi = wi0 ) ≥ T j

Tjr (wi = wi0 )

otherwise

4. At w0 , and given πij (wi = wi0 ) and Tjr (wi = wi0 ) from steps 2 and 3 respectively, compute residential
population,


Rj (wi = wi0 ) = 

γ)1−γ

nP
J

wi0 )wi

o1−γ



ū(1 −
i=1 πij (wi =


1−γ hP
i1 


J
θ θ
Γ θ−1
Tjr (wi = wi0 )
i=1 λij (wi /κij )
θ

44

1
σj +γ−1

.

(32)

5. At w0 and in each census tract, compute labor supply,
J
X

πij (wi = wi0 )Rj (wi = wi0 ),

j=1

and labor demand,
Li (wi =

wi0 )


=

Ai β
wi



1
1−β−α

Tib .

6. Compute excess labor demand at w0 , Xi (wi = wi0 ), in each census tract,


J


X
πij (wi = wi0 )Rj (wi = wi0 ) .
Xi (wi = wi0 ) = Li (wi = wi0 ) −


j=1

7. At our initial guess, w0 , any given census tract may have an excess supply of or demand for labor,
P
Xi (wi = wi0 ) ≶ 0. Then, if Ji=1 |Xi (wi = wi0 )| ≥ ε for some small ε, we update wages in each census
tract according the state of its labor market. In particular, our new guess, w1 , satisfies
w1 = w0 + δX,
for some small positive δ where X = (X1 , ..., XJ )0 .
8. Iterate on steps 1 through 7 until

PJ

i=1 |Xi (wi

= wi0 )| < ε.

45