1# RECORD 05133875334147dc5ac7d37a0479720642327db62# TITLE: Market Frictions, Arbitrage, and the Capitalization of Amenities3# YEAR: 2019.0 VENUE: nan DOI: 10.3386/w257014# AUTHORS: Amine Ouazad; Romain G. Ranciere5# PAGES: 58 CANDIDATE TABLE PAGES (1-based): [43, 44, 45]6# 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.789===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1011NBER WORKING PAPER SERIES12MARKET FRICTIONS, ARBITRAGE, AND THE CAPITALIZATION OF AMENITIES13Amine Ouazad14Romain Rancière15Working Paper 2570116http://www.nber.org/papers/w2570117NATIONAL BUREAU OF ECONOMIC RESEARCH181050 Massachusetts Avenue19Cambridge, MA 0213820March 201921We would like to thank Joël David, Morris Davis, Mariacristina De Nardi, Anthony Heyes, 22Matthew E. Kahn, Patrick Kehoe, Adam Lavecchia, Robert Lucas, Fabrizio Perri, Hashem 23Pesaran for helpful comments, as well as the audience of the Federal Reserve of Minneapolis 24seminar series, the University of Southern California’s conference on housing and the 25macroeconomy, the meeting of the Canadian Economics Association, and seminar series at the 26University of Ottawa and Université Laval. The authors acknowledge financial support from 27HEC, INET, and USC. The views expressed herein are those of the authors and do not necessarily 28reflect the views of the National Bureau of Economic Research.29NBER working papers are circulated for discussion and comment purposes. They have not been 30peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies 31official NBER publications.32© 2019 by Amine Ouazad and Romain Rancière. All rights reserved. Short sections of text, not to 33exceed two paragraphs, may be quoted without explicit permission provided that full credit, 34including © notice, is given to the source.353637===== PAGE 43 (score 70, numeric-paren 50, table-words 6, var-words 8) =====3839Table 1: Model Estimation – Preferences, Trading Opportunities, and Price-Amenity Gradients40When Accounting for Credit Opportunities41This table presents the estimation of preferences ⇠for amenities zjt and the intertemporal discount42factor β in columns (1) and (3). Columns (2) and (4) present the regression of the trading index43rijt, j = 1, 2, . . . , J, on amenities zjt. The trading index rijt is the difference between the owner’s44value V `45ijt of owning and occupying a unit and the value V v of owning a vacant or rented unit.46Columns (1) and (2) are estimated in the model with both credit and matching frictions (Section 2.3).47Columns (3) and (4) are estimated in the model with matching frictions only (Section 2.1).48(1)49(2)50(3)51(4)52Dependent variable:53Index of Trading54Index of Trading55Utility V `56ijt57Opportunities rijt58Utility V `59ijt60Opportunities rjt61Estimated with Matching and Credit Frictions62Estimated with Matching Frictions Only63log(Median Income)640.04865(0.038)660.02667(0.035)68−0.00969(0.006)70−0.00671(0.016)72Frac. Black730.32074(0.343)751.595⇤⇤⇤76(0.316)770.03678(0.051)79−0.755⇤⇤⇤80(0.134)81Frac. Black ⇥Black829.084⇤⇤⇤83(0.756)8411.373⇤⇤⇤85(0.697)860.81887(1.961)88−8.26789(5.131)90Frac. Hispanic91−0.624⇤⇤92(0.269)930.621⇤⇤94(0.247)95−0.169⇤⇤⇤96(0.042)97−1.316⇤⇤⇤98(0.110)99Frac. Hispanic ⇥Hispanic1008.582⇤⇤⇤101(0.573)10213.086⇤⇤⇤103(0.526)1040.219⇤⇤105(0.091)1064.727⇤⇤⇤107(0.236)108Frac. Asian109−1.281⇤⇤⇤110(0.417)111−1.538⇤⇤⇤112(0.384)113−0.049114(0.067)1150.104116(0.174)117Frac. Asian ⇥Asian11814.900⇤⇤⇤119(0.977)12023.259⇤⇤⇤121(0.900)1220.019123(0.139)1241.675⇤⇤⇤125(0.363)126log Offenses127−0.004128(0.009)129−0.043⇤⇤⇤130(0.008)131−0.002132(0.001)1330.003134(0.004)135Mean Test Score (IL)136−0.059⇤⇤⇤137(0.022)138−0.096⇤⇤⇤139(0.020)1400.006141(0.004)142−0.010143(0.009)144Median Test Score (WI)145−1.993146(5.837)147−3.382148(5.376)149−0.417150(0.915)1510.485152(2.394)153Year Structure Built1540.046⇤⇤⇤155(0.003)1560.041⇤⇤⇤157(0.003)1580.004⇤⇤⇤159(0.001)1600.009⇤⇤⇤161(0.001)162Median Nbr Rooms1630.809⇤⇤⇤164(0.045)1651.127⇤⇤⇤166(0.042)1670.102⇤⇤⇤168(0.007)1690.081⇤⇤⇤170(0.019)171E(V l(j0, t + 1)|j, t)1720.583⇤⇤⇤173(0.005)174-1750.518⇤⇤⇤176(0.001)177-178Observations179118,053†180118,053†18190,865†18290,865†183R21840.8421850.8451860.9971870.993188⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01189†: These specifications have one observation by demographic group i, neighborhood j, and year t.19042191192193===== PAGE 44 (score 86, numeric-paren 60, table-words 9, var-words 8) =====194195Table 2: The Reversal of the Correlation Between Prices and School Test Scores196This table presents the time varying coefficient of the regression of transaction prices (column (1)),197trading opportunities (column (2)), and expectations (column (3)) on standardized school test scores.198Dependent variable:199log(Transaction Pricejt)200Trading Opportunities rjt201E(V `202jt)203(1)204(2)205(3)206log(Median Household Income)2070.041⇤⇤208(0.019)2090.017210(0.036)2110.012⇤⇤⇤212(0.002)213Frac Black214−0.120215(0.080)2160.475⇤⇤⇤217(0.182)218−0.040⇤⇤⇤219(0.006)220Frac Hispanic221−0.166⇤⇤⇤222(0.057)2230.446⇤⇤⇤224(0.126)225−0.012⇤⇤⇤226(0.004)227Frac Asian228−0.069229(0.088)2300.174231(0.217)2320.109⇤⇤⇤233(0.008)234Average Test Score (IL) ⇥2005235−0.156⇤⇤⇤236(0.027)237−0.096⇤⇤⇤238(0.035)239−0.025⇤⇤⇤240(0.001)241Average Test Score (IL) ⇥2006242−0.175⇤⇤⇤243(0.027)244−0.096⇤⇤⇤245(0.035)246−0.024⇤⇤⇤247(0.001)248Average Test Score (IL) ⇥2007249−0.143⇤⇤⇤250(0.027)251−0.073⇤⇤252(0.035)253−0.023⇤⇤⇤254(0.001)255Average Test Score (IL) ⇥20082560.025257(0.028)258−0.056259(0.034)260−0.018⇤⇤⇤261(0.001)262Average Test Score (IL) ⇥20092630.128⇤⇤⇤264(0.027)2650.045266(0.034)267−0.015⇤⇤⇤268(0.001)269Average Test Score (IL) ⇥20102700.114⇤⇤⇤271(0.027)2720.053273(0.035)274−0.008⇤⇤⇤275(0.001)276Average Test Score (IL) ⇥20112770.081⇤⇤⇤278(0.026)2790.047280(0.035)281−0.015⇤⇤⇤282(0.001)283Average Test Score (IL) ⇥20122840.077⇤⇤⇤285(0.027)2860.043287(0.038)288−0.0001289(0.002)290Share of Schools with B2910.018292(0.061)293−0.084294(0.131)2950.009⇤⇤296(0.004)297Share of Schools with C298−0.205⇤⇤⇤299(0.053)3000.026301(0.111)3020.019⇤⇤⇤303(0.003)304Share of Schools with D305−0.111⇤306(0.061)3070.107308(0.133)309−0.021⇤⇤⇤310(0.003)311Share of Schools with F312−0.104313(0.145)3140.291315(0.208)316−0.092⇤⇤⇤317(0.009)318Median Test Score (WI)319−0.045320(1.220)3210.195322(0.890)3230.158⇤⇤⇤324(0.054)325Median Year Structure Built3260.004⇤⇤⇤327(0.001)3280.007⇤⇤⇤329(0.002)3300.0001331(0.0001)332Median Number of Rooms3330.032⇤⇤⇤334(0.010)3350.176⇤⇤⇤336(0.023)3370.004⇤⇤⇤338(0.001)339log(Offenses Per Capita)340−0.376341(0.686)342−1.318343(0.986)344−0.228⇤⇤⇤345(0.045)346Observations34737,56434837,66634937,666350R23510.7933520.8223530.99354Adjusted R23550.7543560.7893570.99358Residual Std. Error3590.358 (df = 31574)3600.461 (df = 31673)3610.020 (df = 31673)362Note:363⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.0136443365366367===== PAGE 45 (score 76, numeric-paren 46, table-words 11, var-words 8) =====368369Table 3: The Capitalization of Trading Opportunities Into House Prices370This regression tests the predictions of Section 3 (The Price-Amenity Gradient at Equilibrium). The second column371estimates the impact of trading opportunities on observed transaction prices. The third column estimates how credit372frictions affects such capitalization of trading opportunities into house prices.373Dependent variable:374log(Transaction Pricejt)375(1)376(2)377(3)378log(Median Household Income)3790.044⇤⇤380(0.022)3810.001382(0.019)3830.005384(0.015)385Frac. Black386−0.160⇤387(0.090)388−0.118389(0.085)390−0.106⇤391(0.057)392Frac. Hispanic393−0.201⇤⇤⇤394(0.060)395−0.230⇤⇤⇤396(0.058)397−0.081⇤398(0.042)399Frac. Asian4000.032401(0.090)402−0.363⇤⇤⇤403(0.095)404−0.180⇤⇤⇤405(0.066)406Mean Test Score (IL)407−0.030⇤⇤⇤408(0.006)4090.016⇤⇤⇤410(0.006)4110.004412(0.005)413Share of Schools with B (IN)4140.015415(0.060)4160.004417(0.063)4180.006419(0.051)420Share of Schools with C (IN)421−0.201⇤⇤⇤422(0.053)423−0.265⇤⇤⇤424(0.058)425−0.161⇤⇤⇤426(0.045)427Share of Schools with D (IN)428−0.108⇤429(0.061)430−0.061431(0.067)432−0.056433(0.055)434Share of Schools with F (IN)435−0.093436(0.144)4370.141438(0.133)439−0.039440(0.124)441Median Test Score (WI)442−0.027443(1.219)444−0.557445(1.239)446−0.175447(1.047)448Median Year Structure Built4490.004⇤⇤⇤450(0.001)4510.002⇤⇤⇤452(0.001)4530.001454(0.001)455Median Number of Rooms4560.050⇤⇤⇤457(0.012)4580.002459(0.011)4600.011461(0.008)462Trading Opportunities r4630.169⇤⇤⇤464(0.008)4650.032⇤⇤⇤466(0.005)467⇥log Balance468−0.003⇤⇤⇤469(0.001)470⇥Approval Rates4710.352⇤⇤⇤472(0.042)473⇥log(Interest Cost)4740.005475(0.003)476E(V `)4773.090⇤⇤⇤478(0.132)4791.281⇤⇤⇤480(0.106)481log(Offenses per Capita)482−5.474⇤⇤⇤483(0.695)484−3.338⇤⇤⇤485(0.664)486−2.329⇤⇤⇤487(0.549)488Other Controls489log(Balance), Approval Rate, log(Interest Cost)490Observations49137,56449237,56449337,564494R24950.7724960.7884970.844498Adjusted R24990.7285000.7475010.814502Residual Std. Error5030.376 (df = 31581)5040.363 (df = 31579)5050.311 (df = 31573)506Note:507⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01508The index r of trading opportunities is standardized, s.d.(r) = 1 across neighborhoods.50944510511512===== PAGE 46 (score 3, numeric-paren 0, table-words 0, var-words 3) =====513514A515City Dynamics with Credit Constraints516This section of the Appendix presents the equations describing the city’s dynamics with credit fric-517tions. The city’s equilibrium is characterized by a vector of neighborhood-level trading opportunities518r, a vector of listings `, and a vector of mortgage balances B. The dynamics of trading opportu-519nities with credit frictions are affected by the probability of approval '(j, Z) in each neighborhood520j for a given distribution of city-wide amenities; these approval probabilities lower the probability521of a successful transaction. The dynamics are also affected by the mortgage balance in buyers’522neighborhoods B and the interest cost at destination. Overall, the Bellman equation for trading523opportunities r is:524r(j, Z) = zj(⇠−⇣) + βEr(j, Z0)525+ βE526527J528X529j0=1530+531(1 −γ)δλ(j0, Z0)'(j0, Z0)Φ(r(j0, Z0) −(j0, Z0) −r(j, Z0) −B(j, Z0))532+ γδvµ(j, Z0)'(j, Z)Φ(r(j, Z0) −(j, Z0) −r(j0, Z0) −B(j0, Z0))533 &534+ ".535(29)536The dynamic of listings is affected as well by the presence of credit frictions.537Approval rates,538mortgage balances, and interest payments lower both flows into and out of a neighborhood.539∆`(j, Z) =540⇢541δn(j, Z)542J543X544j0=1545λ(j0, Z)'(j, Z)F546⇥547r(j, Z) −(j, Z) −r(j0, Z) −B(j0, Z)548⇤549−δv`(j, Z)550J551X552j0=1553µ(j0, Z)'(j0, Z)F554⇥555r(j0, Z) −(j0, Z) −r(j, Z) −B(j, Z)556⇤0557,558(30)559The third dynamics is the dynamics of mortgage balances, presented in equation (13) in the main560body of the paper.561B562Data Appendix563The paper combines five data sets to estimate the structural parameters. This section describes564how these data sets are built to estimate price-amenity gradients and households’ preferences for56545566