ML versus IV estimates of spatial SUR models: evidence from the case of Airbnb in Madrid urban area

AbstractIn recent decades we have seen an increased interest in the use of seemingly unrelated regressions models (SUR) in a spatial context, with compelling case studies in different fields. This upsurge has favoured the development of new and more efficient inference techniques. At present, the user has a basic toolkit to deal with this kind of model, that is, however, in need of improvement. This paper focuses on the question of estimating, quickly and accurately, spatial SUR models. The most popular procedure is maximum likelihood (ML) which guarantees precision at the cost of a high computational burden. This is especially true in cases of large sample size and strong spatial structure. We explore simpler estimation algorithms such as instrumental variables (IV), which expedites calculation at the cost of a certain loss in quality of the estimates. We focus on the importance of sample size and the trade-off between accuracy and speed. To that end, we perform a comprehensive simulation experiment in which we compare ML and IV algorithms, looking for their strengths and weaknesses. The paper includes two applications to the case of Airbnb in the urban area of Madrid. First, we estimate a spatial SUR hedonic model of accommodation prices, using micro-data for three different cross sections à la Anselin, that is, considering temporal correlation plus spatial structure. Then, the data are aggregated by neighbourhoods. We specify a spatial SUR model with two equations (apartments and rooms) also using three cross sections. In both cases, the models are estimated by ML and IV using the spsur R package (Angulo et al. in spSUR: spatial seemingly unrelated regression models. R Package version 1.0.0.3, 2019), with the aim of illustrating its capabilities.

[1]  Harry H. Kelejian,et al.  Estimation of simultaneous systems of spatially interrelated cross sectional equations , 2004 .

[2]  Coro Chasco,et al.  Spatial analysis of urban growth in Spain, 1900–2001 , 2008 .

[3]  R. Berrens,et al.  Proximity to Natural Amenities: A Seemingly Unrelated Hedonic Regression Model with Spatial Durbin and Spatial Error Processes , 2016 .

[4]  Denzil G. Fiebig,et al.  Seemingly Unrelated Regression , 2007 .

[5]  H. Kelejian,et al.  A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances , 1998 .

[6]  J. MacKinnon,et al.  Estimation and inference in econometrics , 1994 .

[7]  J. Lundberg.  Spatial interaction model of spillovers from locally provided public services , 2006 .

[8]  J. Byers,et al.  The Rise of the Sharing Economy: Estimating the Impact of Airbnb on the Hotel Industry , 2017 .

[9]  Jeffrey M. Wooldridge,et al.  Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data , 2003 .

[10]  Ronald P. Barry,et al.  Monte Carlo estimates of the log determinant of large sparse matrices , 1999 .

[11]  Geoffrey J. D. Hewings,et al.  SPACE‐TIME EMPLOYMENT MODELING: SOME RESULTS USING SEEMINGLY UNRELATED REGRESSION ESTIMATORS* , 1982 .

[12]  Nicole Gurran,et al.  When Tourists Move In: How Should Urban Planners Respond to Airbnb? , 2017 .

[13]  Lung-fei Lee,et al.  Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models , 2004 .

[14]  B. Benítez‐Aurioles.  The role of distance in the peer-to-peer market for tourist accommodation , 2018 .

[15]  James Durbin,et al.  Errors in variables , 1954 .

[16]  J. P. Elhorst,et al.  Spatial econometrics: from cross-sectional data to spatial panels , 2014 .

[17]  Badi H. Baltagi,et al.  Seemingly unrelated regressions with spatial error components , 2011 .

[18]  Peter Nijkamp,et al.  Dynamic Models of Spatial Autocorrelation , 1977 .

[19]  Tony E. Smith,et al.  Estimation Bias in Spatial Models with Strongly Connected Weight Matrices , 2009 .

[20]  Rob Law,et al.  Effect of sharing economy on tourism industry employment. , 2016 .

[21]  Jesús Mur,et al.  Testing for Spatial Effects in Seemingly Unrelated Regressions , 2010 .

[22]  L. Anselin,et al.  Fast maximum likelihood estimation of very large spatial autoregression models: a characteristic polynomial approach , 2001 .

[23]  H. Theil.  Principles of econometrics , 1971 .

[24]  S. Arora,et al.  Alternative Approaches to Spatial Autocorrelation: An Improvement Over Current Practice , 1977 .

[25]  Bernard Fingleton,et al.  A multi-equation spatial econometric model, with application to EU manufacturing productivity growth , 2007, J. Geogr. Syst..

[26]  G. Cotteleer,et al.  Expert opinion versus actual transaction evidence in the valuation of non-market amenities , 2012 .

[27]  Ronald P. Barry,et al.  Quick Computation of Spatial Autoregressive Estimators , 2010 .

[28]  Gustavo Romanillos,et al.  The eruption of Airbnb in tourist cities: Comparing spatial patterns of hotels and peer-to-peer accommodation in Barcelona , 2016, 1606.07138.

[29]  Peter E. Kennedy.  A Guide to Econometrics , 1979 .

[30]  J. Cegarra-Navarro,et al.  Spatial spillovers in public expenditure on a municipal level in Spain , 2017 .

[31]  J. Sargan.  THE ESTIMATION OF ECONOMIC RELATIONSHIPS USING INSTRUMENTAL VARIABLES , 1958 .

[32]  J. Nicolau,et al.  Price determinants of sharing economy based accommodation rental : a study of listings from 33 cities on Airbnb.com , 2017 .

[33]  Michael Luca,et al.  Digital Discrimination: The Case of Airbnb.com , 2014 .

[34]  Aris Spanos,et al.  Statistical Foundations of Econometric Modelling , 1986 .

[35]  Jun Li,et al.  Pros vs Joes: Agent Pricing Behavior in the Sharing Economy , 2016 .

[36]  Lung-fei Lee,et al.  GMM and 2SLS estimation of mixed regressive, spatial autoregressive models , 2007 .

[37]  Giuseppe Arbia,et al.  Spatial Data Configuration in Statistical Analysis of Regional Economic and Related Problems , 1989 .

[38]  Kara M. Kockelman,et al.  Specification and estimation of a spatially and temporally autocorrelated seemingly unrelated regression model: application to crash rates in China , 2007 .

[39]  Martin Knapp,et al.  Sur model with spatial effects: an application to mental health expenditure. , 2007, Health economics.

[40]  Florian Hawlitschek,et al.  Price Determinants on Airbnb: How Reputation Pays Off in the Sharing Economy , 2017 .

[41]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[42]  Venoo Kakar,et al.  The Visible Host: Does race guide Airbnb rental rates in San Francisco? , 2017, Journal of Housing Economics.

[43]  E. Malinvaud,et al.  Statistical Methods of Econometrics. by E. Malinvaud , 1972 .

[44]  Wolfgang Polasek,et al.  Production technology and agglomeration for Japanese prefectures during 1991–2000 , 2012 .

[45]  Mickael Bech,et al.  A spatiotemporal analysis of public pharmaceutical expenditure , 2010 .

[46]  S. Dall’erba,et al.  Evaluating the Temporal and Spatial Heterogeneity of the European Convergence Process, 1980-1999 , 2006 .

[47]  Zezhou Wu,et al.  Key Factors Affecting Informed Consumers’ Willingness to Pay for Green Housing: A Case Study of Jinan, China , 2018 .

[48]  Michael Pfaffermayr,et al.  Distance, Trade, and FDI: A Hausman-Taylor Sur Approach , 2001 .

[49]  Kara M. Kockelman,et al.  Predicting the Distribution of Households and Employment: Seemingly Unrelated Regression Model with Two Spatial Processes , 2009 .

[50]  Harry H. Kelejian,et al.  A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model , 1999 .

[51]  Georges Bresson,et al.  Maximum Likelihood Estimation and Lagrange Multiplier Tests for Panel Seemingly Unrelated Regressions with Spatial Lag and Spatial Errors: An Application to Hedonic Housing Prices in Paris , 2010, SSRN Electronic Journal.

[52]  Ulrich Gunter,et al.  What makes an Airbnb host a superhost? Empirical evidence from San Francisco and the Bay Area , 2018, Tourism Management.

[53]  Mudit Kapoor,et al.  Panel data models with spatially correlated error components , 2007 .

[54]  Lung-fei Lee,et al.  Best Spatial Two‐Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances , 2003 .

[55]  Wei-Ting Hung,et al.  Pricing determinants in the hotel industry: Quantile regression analysis , 2010 .

[56]  L. Anselin.  A test for spatial autocorrelation in seemingly unrelated regressions , 1988 .

[57]  F. López,et al.  Spatial model selection strategies in a SUR framework. The case of regional productivity in EU , 2014 .

[58]  Harry H. Kelejian,et al.  INSTRUMENTAL VARIABLE ESTIMATION OF A SPATIAL AUTOREGRESSIVE MODEL WITH AUTOREGRESSIVE DISTURBANCES: LARGE AND SMALL SAMPLE RESULTS , 2004 .

[59]  Beatriz Benítez-Aurioles,et al.  Why are flexible booking policies priced negatively? , 2018, Tourism Management.

[60]  Sergio J. Rey,et al.  US Regional Income Convergence: A Spatial Econometric Perspective , 1999 .