# RECORD 05133875334147dc5ac7d37a0479720642327db6
# TITLE: Market Frictions, Arbitrage, and the Capitalization of Amenities
# YEAR: 2019.0  VENUE: nan  DOI: 10.3386/w25701
# AUTHORS: Amine Ouazad; Romain G. Ranciere
# PAGES: 58  CANDIDATE TABLE PAGES (1-based): [43, 44, 45]
# ABSTRACT: The price-amenity arbitrage is a cornerstone of spatial economics, as the response of land and house prices to shifts in the quality of local amenities and public goods is typically used to reveal households' willingness to pay for amenities. With informational, time, and cash constraints, households' ability to arbitrage across locations with different amenities (demographics, crime, education, housing) depends on their ability to compare locations and to finance the swap of houses. Arbitrageurs with deep pockets and better search and matching technology can take advantage of price dispersions and unexploited trade opportunities. We develop a disaggregated search and matching model of the housing market with endogenously bargained prices, identified on transaction-level data from the universe of deeds for 6,400+ neighborhoods of the Chicago metropolitan area, matched with school-level test scores and geocoded criminal offenses. Price-amenity gradients reflect preferences and the capitalization of trading opportunities, which are arbitraged away in the frictionless limit. Thus the time-variation in hedonic pricing coefficients partly reflects the time variation in search and credit frictions. Our model is able to explain that, between the peak of the housing boom and its trough, the sign of the price-amenity gradient flipped, due to the decline in trading opportunities in lower-amenity neighborhoods and due to the lower capitalization of trading opportunities in house prices.


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NBER WORKING PAPER SERIES
MARKET FRICTIONS, ARBITRAGE, AND THE CAPITALIZATION OF AMENITIES
Amine Ouazad
Romain Rancière
Working Paper 25701
http://www.nber.org/papers/w25701
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
March 2019
We would like to thank Joël David, Morris Davis, Mariacristina De Nardi, Anthony Heyes, 
Matthew E. Kahn,  Patrick Kehoe, Adam Lavecchia, Robert Lucas, Fabrizio Perri,  Hashem 
Pesaran for helpful comments, as well as the audience of the Federal Reserve of Minneapolis 
seminar series, the University of Southern California’s conference on housing and the 
macroeconomy, the meeting of the Canadian Economics Association, and seminar series at the 
University of Ottawa and Université Laval. The authors acknowledge financial support from 
HEC, INET, and USC. The views expressed herein are those of the authors and do not necessarily 
reflect the views of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been 
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies 
official NBER publications.
© 2019 by Amine Ouazad and Romain Rancière. All rights reserved. Short sections of text, not to 
exceed two paragraphs, may be quoted without explicit permission provided that full credit, 
including © notice, is given to the source.


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Table 1: Model Estimation – Preferences, Trading Opportunities, and Price-Amenity Gradients
When Accounting for Credit Opportunities
This table presents the estimation of preferences ⇠for amenities zjt and the intertemporal discount
factor β in columns (1) and (3). Columns (2) and (4) present the regression of the trading index
rijt, j = 1, 2, . . . , J, on amenities zjt. The trading index rijt is the difference between the owner’s
value V `
ijt of owning and occupying a unit and the value V v of owning a vacant or rented unit.
Columns (1) and (2) are estimated in the model with both credit and matching frictions (Section 2.3).
Columns (3) and (4) are estimated in the model with matching frictions only (Section 2.1).
(1)
(2)
(3)
(4)
Dependent variable:
Index of Trading
Index of Trading
Utility V `
ijt
Opportunities rijt
Utility V `
ijt
Opportunities rjt
Estimated with Matching and Credit Frictions
Estimated with Matching Frictions Only
log(Median Income)
0.048
(0.038)
0.026
(0.035)
−0.009
(0.006)
−0.006
(0.016)
Frac. Black
0.320
(0.343)
1.595⇤⇤⇤
(0.316)
0.036
(0.051)
−0.755⇤⇤⇤
(0.134)
Frac. Black ⇥Black
9.084⇤⇤⇤
(0.756)
11.373⇤⇤⇤
(0.697)
0.818
(1.961)
−8.267
(5.131)
Frac. Hispanic
−0.624⇤⇤
(0.269)
0.621⇤⇤
(0.247)
−0.169⇤⇤⇤
(0.042)
−1.316⇤⇤⇤
(0.110)
Frac. Hispanic ⇥Hispanic
8.582⇤⇤⇤
(0.573)
13.086⇤⇤⇤
(0.526)
0.219⇤⇤
(0.091)
4.727⇤⇤⇤
(0.236)
Frac. Asian
−1.281⇤⇤⇤
(0.417)
−1.538⇤⇤⇤
(0.384)
−0.049
(0.067)
0.104
(0.174)
Frac. Asian ⇥Asian
14.900⇤⇤⇤
(0.977)
23.259⇤⇤⇤
(0.900)
0.019
(0.139)
1.675⇤⇤⇤
(0.363)
log Offenses
−0.004
(0.009)
−0.043⇤⇤⇤
(0.008)
−0.002
(0.001)
0.003
(0.004)
Mean Test Score (IL)
−0.059⇤⇤⇤
(0.022)
−0.096⇤⇤⇤
(0.020)
0.006
(0.004)
−0.010
(0.009)
Median Test Score (WI)
−1.993
(5.837)
−3.382
(5.376)
−0.417
(0.915)
0.485
(2.394)
Year Structure Built
0.046⇤⇤⇤
(0.003)
0.041⇤⇤⇤
(0.003)
0.004⇤⇤⇤
(0.001)
0.009⇤⇤⇤
(0.001)
Median Nbr Rooms
0.809⇤⇤⇤
(0.045)
1.127⇤⇤⇤
(0.042)
0.102⇤⇤⇤
(0.007)
0.081⇤⇤⇤
(0.019)
E(V l(j0, t + 1)|j, t)
0.583⇤⇤⇤
(0.005)
-
0.518⇤⇤⇤
(0.001)
-
Observations
118,053†
118,053†
90,865†
90,865†
R2
0.842
0.845
0.997
0.993
⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01
†: These specifications have one observation by demographic group i, neighborhood j, and year t.
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Table 2: The Reversal of the Correlation Between Prices and School Test Scores
This table presents the time varying coefficient of the regression of transaction prices (column (1)),
trading opportunities (column (2)), and expectations (column (3)) on standardized school test scores.
Dependent variable:
log(Transaction Pricejt)
Trading Opportunities rjt
E(V `
jt)
(1)
(2)
(3)
log(Median Household Income)
0.041⇤⇤
(0.019)
0.017
(0.036)
0.012⇤⇤⇤
(0.002)
Frac Black
−0.120
(0.080)
0.475⇤⇤⇤
(0.182)
−0.040⇤⇤⇤
(0.006)
Frac Hispanic
−0.166⇤⇤⇤
(0.057)
0.446⇤⇤⇤
(0.126)
−0.012⇤⇤⇤
(0.004)
Frac Asian
−0.069
(0.088)
0.174
(0.217)
0.109⇤⇤⇤
(0.008)
Average Test Score (IL) ⇥2005
−0.156⇤⇤⇤
(0.027)
−0.096⇤⇤⇤
(0.035)
−0.025⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2006
−0.175⇤⇤⇤
(0.027)
−0.096⇤⇤⇤
(0.035)
−0.024⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2007
−0.143⇤⇤⇤
(0.027)
−0.073⇤⇤
(0.035)
−0.023⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2008
0.025
(0.028)
−0.056
(0.034)
−0.018⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2009
0.128⇤⇤⇤
(0.027)
0.045
(0.034)
−0.015⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2010
0.114⇤⇤⇤
(0.027)
0.053
(0.035)
−0.008⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2011
0.081⇤⇤⇤
(0.026)
0.047
(0.035)
−0.015⇤⇤⇤
(0.001)
Average Test Score (IL) ⇥2012
0.077⇤⇤⇤
(0.027)
0.043
(0.038)
−0.0001
(0.002)
Share of Schools with B
0.018
(0.061)
−0.084
(0.131)
0.009⇤⇤
(0.004)
Share of Schools with C
−0.205⇤⇤⇤
(0.053)
0.026
(0.111)
0.019⇤⇤⇤
(0.003)
Share of Schools with D
−0.111⇤
(0.061)
0.107
(0.133)
−0.021⇤⇤⇤
(0.003)
Share of Schools with F
−0.104
(0.145)
0.291
(0.208)
−0.092⇤⇤⇤
(0.009)
Median Test Score (WI)
−0.045
(1.220)
0.195
(0.890)
0.158⇤⇤⇤
(0.054)
Median Year Structure Built
0.004⇤⇤⇤
(0.001)
0.007⇤⇤⇤
(0.002)
0.0001
(0.0001)
Median Number of Rooms
0.032⇤⇤⇤
(0.010)
0.176⇤⇤⇤
(0.023)
0.004⇤⇤⇤
(0.001)
log(Offenses Per Capita)
−0.376
(0.686)
−1.318
(0.986)
−0.228⇤⇤⇤
(0.045)
Observations
37,564
37,666
37,666
R2
0.793
0.822
0.99
Adjusted R2
0.754
0.789
0.99
Residual Std. Error
0.358 (df = 31574)
0.461 (df = 31673)
0.020 (df = 31673)
Note:
⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01
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Table 3: The Capitalization of Trading Opportunities Into House Prices
This regression tests the predictions of Section 3 (The Price-Amenity Gradient at Equilibrium). The second column
estimates the impact of trading opportunities on observed transaction prices. The third column estimates how credit
frictions affects such capitalization of trading opportunities into house prices.
Dependent variable:
log(Transaction Pricejt)
(1)
(2)
(3)
log(Median Household Income)
0.044⇤⇤
(0.022)
0.001
(0.019)
0.005
(0.015)
Frac. Black
−0.160⇤
(0.090)
−0.118
(0.085)
−0.106⇤
(0.057)
Frac. Hispanic
−0.201⇤⇤⇤
(0.060)
−0.230⇤⇤⇤
(0.058)
−0.081⇤
(0.042)
Frac. Asian
0.032
(0.090)
−0.363⇤⇤⇤
(0.095)
−0.180⇤⇤⇤
(0.066)
Mean Test Score (IL)
−0.030⇤⇤⇤
(0.006)
0.016⇤⇤⇤
(0.006)
0.004
(0.005)
Share of Schools with B (IN)
0.015
(0.060)
0.004
(0.063)
0.006
(0.051)
Share of Schools with C (IN)
−0.201⇤⇤⇤
(0.053)
−0.265⇤⇤⇤
(0.058)
−0.161⇤⇤⇤
(0.045)
Share of Schools with D (IN)
−0.108⇤
(0.061)
−0.061
(0.067)
−0.056
(0.055)
Share of Schools with F (IN)
−0.093
(0.144)
0.141
(0.133)
−0.039
(0.124)
Median Test Score (WI)
−0.027
(1.219)
−0.557
(1.239)
−0.175
(1.047)
Median Year Structure Built
0.004⇤⇤⇤
(0.001)
0.002⇤⇤⇤
(0.001)
0.001
(0.001)
Median Number of Rooms
0.050⇤⇤⇤
(0.012)
0.002
(0.011)
0.011
(0.008)
Trading Opportunities r
0.169⇤⇤⇤
(0.008)
0.032⇤⇤⇤
(0.005)
⇥log Balance
−0.003⇤⇤⇤
(0.001)
⇥Approval Rates
0.352⇤⇤⇤
(0.042)
⇥log(Interest Cost)
0.005
(0.003)
E(V `)
3.090⇤⇤⇤
(0.132)
1.281⇤⇤⇤
(0.106)
log(Offenses per Capita)
−5.474⇤⇤⇤
(0.695)
−3.338⇤⇤⇤
(0.664)
−2.329⇤⇤⇤
(0.549)
Other Controls
log(Balance), Approval Rate, log(Interest Cost)
Observations
37,564
37,564
37,564
R2
0.772
0.788
0.844
Adjusted R2
0.728
0.747
0.814
Residual Std. Error
0.376 (df = 31581)
0.363 (df = 31579)
0.311 (df = 31573)
Note:
⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01
The index r of trading opportunities is standardized, s.d.(r) = 1 across neighborhoods.
44


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A
City Dynamics with Credit Constraints
This section of the Appendix presents the equations describing the city’s dynamics with credit fric-
tions. The city’s equilibrium is characterized by a vector of neighborhood-level trading opportunities
r, a vector of listings `, and a vector of mortgage balances B. The dynamics of trading opportu-
nities with credit frictions are affected by the probability of approval '(j, Z) in each neighborhood
j for a given distribution of city-wide amenities; these approval probabilities lower the probability
of a successful transaction. The dynamics are also affected by the mortgage balance in buyers’
neighborhoods B and the interest cost at destination. Overall, the Bellman equation for trading
opportunities r is:
r(j, Z) = zj(⇠−⇣) + βEr(j, Z0)
+ βE

J
X
j0=1
+
(1 −γ)δλ(j0, Z0)'(j0, Z0)Φ(r(j0, Z0) −(j0, Z0) −r(j, Z0) −B(j, Z0))
+ γδvµ(j, Z0)'(j, Z)Φ(r(j, Z0) −(j, Z0) −r(j0, Z0) −B(j0, Z0))
 &
+ ".
(29)
The dynamic of listings is affected as well by the presence of credit frictions.
Approval rates,
mortgage balances, and interest payments lower both flows into and out of a neighborhood.
∆`(j, Z) =
⇢
δn(j, Z)
J
X
j0=1
λ(j0, Z)'(j, Z)F
⇥
r(j, Z) −(j, Z) −r(j0, Z) −B(j0, Z)
⇤
−δv`(j, Z)
J
X
j0=1
µ(j0, Z)'(j0, Z)F
⇥
r(j0, Z) −(j0, Z) −r(j, Z) −B(j, Z)
⇤0
,
(30)
The third dynamics is the dynamics of mortgage balances, presented in equation (13) in the main
body of the paper.
B
Data Appendix
The paper combines five data sets to estimate the structural parameters. This section describes
how these data sets are built to estimate price-amenity gradients and households’ preferences for
45