Spatial Lag Models with Nested Random Effects: An Instrumental Variable Procedure with an Application to English House Prices

This paper sets up a nested random effects spatial autoregressive panel data model to explain annual house price variation for 2000–2007 across 353 local authority districts in England. The estimation problem posed is how to allow for the endogeneity of the spatial lag variable producing the simultaneous spatial spillover of prices across districts together with the nested random effects in a panel data setting. To achieve this, the paper proposes new estimators based on the instrumental variable approaches of Kelejian and Prucha (1998) and Lee (2003) for the cross-sectional spatial autoregressive model. Monte Carlo results show that our estimators perform well relative to alternative approaches and produces estimates based on real data that are consistent with the theoretical house price model underpinning the reduced form.

[1]  J. Paul Elhorst.  Spatial Panel Data Models , 2010 .

[2]  J. Hausman.  Specification tests in econometrics , 1978 .

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

[4]  H. Ahrens,et al.  On Two Measures of Unbalancedness in a One-Way Model and Their Relation to Efficiency , 1981 .

[5]  Bernard Fingleton,et al.  Housing Supply, Housing Demand, and Affordability , 2008 .

[6]  Gordon H. Hanson.  Scale Economies and the Geographic Concentration of Industry , 2000 .

[7]  Claude Montmarquette,et al.  Does school matter for educational achievement? a two-way nested-error components analysis , 1989 .

[8]  Sukesh K. Ghosh.  Estimating from a More General Time-Series Cum Cross-Section Data Structure , 1976 .

[9]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[10]  D. Kodlin.  A new response time distribution. , 1967, Biometrics.

[11]  Elhanan Helpman,et al.  The Size of Regions , 1995 .

[12]  Werner Antweiler,et al.  Nested random effects estimation in unbalanced panel data , 2001 .

[13]  Bernard Fingleton,et al.  Spurious Spatial Regression: Some Monte Carlo Results with a Spatial Unit Root and Spatial Cointegration , 1999 .

[14]  Bernard Fingleton,et al.  A cross-sectional analysis of residential property prices: the effects of income, commuting, schooling, the housing stock and spatial interaction in the english regions , 2006 .

[15]  Bernard Fingleton.  A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors , 2008 .

[16]  W. Fuller,et al.  Transformations for Estimation of Linear Models with Nested-Error Structure , 1973 .

[17]  M. Beenstock,et al.  Testing for Unit Roots and Cointegration in Spatial Cross-Section Data , 2012 .

[18]  Luisa Corrado,et al.  Multilevel Modelling with Spatial Effects , 2011 .

[19]  Badi H. Baltagi,et al.  SIMPLE LM TESTS FOR THE UNBALANCED NESTED ERROR COMPONENT REGRESSION MODEL , 2002 .

[20]  R. Barro.  Determinants of Economic Growth: A Cross-Country Empirical Study , 1996 .

[21]  J. Lauridsen,et al.  A wald Test for Spatial Nonstationarity , 2004 .

[22]  B. Baltagi,et al.  The unbalanced nested error component regression model , 2001 .

[23]  Gordon H. Hanson.  Market Potential, Increasing Returns, and Geographic Concentration , 1998 .

[24]  M. Partridge.  Does Income Distribution Affect U.S. State Economic Growth? , 2005 .

[25]  J. Paul Elhorst,et al.  Dynamic models in space and time , 2010 .

[26]  Daniel Levy,et al.  Growth and Convergence across the United States: Evidence from County-Level Data , 2006, The Review of Economics and Statistics.

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

[28]  Edward L. Glaeser,et al.  Cities, Agglomeration And Spatial Equilibrium , 2008 .

[29]  The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term , 2013 .

[30]  S. Brakman,et al.  The Spatial Distribution of Wages: Estimating the Helpman-Hanson Model for Germany , 2004 .

[31]  Kristian Behrens,et al.  Krugman'sPapers in Regional Science: The 100 dollar bill on the sidewalk is gone and the 2008 Nobel Prize well-deserved , 2009 .

[32]  Lung-fei Lee,et al.  Near Unit Root in the Spatial Autoregressive Model , 2013 .

[33]  C. Manski.  Identification of Endogenous Social Effects: The Reflection Problem , 1993 .

[34]  L. Anselin,et al.  Spatial Panel Econometrics , 2008 .

[35]  Jørgen Lauridsen,et al.  A test strategy for spurious spatial regression, spatial nonstationarity, and spatial cointegration , 2006 .

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

[37]  Bernard Fingleton,et al.  Estimating spatial models with endogenous variables, a spatial lag and spatially dependent disturbances : finite sample properties , 2008 .

[38]  J. Paul Elhorst,et al.  Specification and Estimation of Spatial Panel Data Models , 2003 .

[39]  J. Paul Elhorst,et al.  Applied Spatial Econometrics: Raising the Bar , 2010 .

[40]  Luc Anselin,et al.  Thirty years of spatial econometrics , 2010 .

[41]  B. Fingleton.  Simulating wages and house prices using the NEG , 2009 .

[42]  B. Fingleton,et al.  Where is the Economics in Spatial Econometrics? , 2012 .

[43]  A. Venables,et al.  The Spatial Economy: Cities, Regions, and International Trade , 1999 .

[44]  Jesús Mur,et al.  Unit Roots and Deterministic Trends in Spatial Econometric Models , 2003 .