Spatial SUR models: Specification, Testing and Selection.

Our paper focuses on the case of SUR models with spatial effects. Specifically, the problem that we pose is testing for the presence of spatial effects in these multivariate models, considering that one of our main interests is to deal with the question of selecting the most adequate specification for the data. In order to do this, we obtain several tests that check for the fundamental hypothesis of the model, including the assumption of time stability of the spatial dependence mechanisms. We solve the discussion in a maximum-likelihood framework because this facilitates the obtaining of appropriate tests. The second part of the paper contains a Monte Carlo experiment in order to study the behaviour of the two most popular model selection strategies, Specific-toGeneral or General-to-Specific, using the collection of tests that have been proposed.

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

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

[3]  Leen Hordijk,et al.  Problems in estimating econometric relations in space , 1979 .

[4]  Valter Di Giacinto,et al.  A Generalized Space-Time ARMA Model with an Application to Regional Unemployment Analysis in Italy , 2006 .

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

[6]  David F. Hendry,et al.  Econometrics-Alchemy or Science? , 1980 .

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

[8]  Timothy G. Conley.  GMM estimation with cross sectional dependence , 1999 .

[9]  Gerald A. Carlino,et al.  The Differential Regional Effects of Monetary Policy: Evidence from the U.S. States , 1999 .

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

[11]  H. Badinger,et al.  Regional Convergence in the European Union, 1985- 1999: A Spatial Dynamic Panel Analysis , 2004 .

[12]  Anil K. Bera,et al.  Simple diagnostic tests for spatial dependence , 1996 .

[13]  Christian Dreger,et al.  Thresholds for employment and unemployment: A spatial analysis of German regional labour markets, 1992–2000* , 2006 .

[14]  Anil K. Bera,et al.  Specification Testing with Locally Misspecified Alternatives , 1993, Econometric Theory.

[15]  J. Paul Elhorst,et al.  New Evidence on the Wage Curve , 2007 .

[16]  H. Folmer,et al.  A comment on specification searches in spatial econometrics: The relevance of Hendry's methodology: A reply , 2006 .

[17]  Helmut Lütkepohl,et al.  General-to-Specific or Specific-to-General Modelling? An Opinion on Current Econometric Terminology , 2007 .

[18]  Bernard Fingleton.  Theoretical economic geography and spatial econometrics: dynamic perspectives , 2001 .

[19]  M. Beenstock,et al.  Regional Heterogeneity, Conditional Convergence and Regional Inequality , 2008 .

[20]  Valter Di Giacinto,et al.  Differential Regional Effects of Monetary Policy: A Geographical SVAR Approach: , 2003 .

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

[22]  Jean-Marie Dufour,et al.  Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions * , 2022 .

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

[24]  Timothy G. Conley,et al.  A new semiparametric spatial model for panel time series , 2001 .

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

[26]  L. Anselin.  SPATIAL DEPENDENCE AND SPATIAL STRUCTURAL INSTABILITY IN APPLIED REGRESSION ANALYSIS , 1990 .

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

[28]  Gerald A. Carlino,et al.  The Differential Regional Effects of Monetary Policy , 1998, Review of Economics and Statistics.

[29]  Adrian Pagan,et al.  The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics , 1980 .

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

[31]  J. Paul Elhorst.  Serial and spatial error correlation , 2008 .

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

[33]  M. Pesaran,et al.  Estimation and Inference in Large Heterogenous Panels with Cross Section Dependence , 2003, SSRN Electronic Journal.

[34]  Jesús Mur,et al.  The Spatial Durbin Model and the Common Factor Tests , 2006 .

[35]  J. Driscoll,et al.  Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data , 1998, Review of Economics and Statistics.

[36]  Daniel Felsenstein,et al.  Spatial Vector Autoregressions , 2007 .

[37]  David F. Hendry,et al.  A comment on “Specification searches in spatial econometrics: The relevance of Hendry's methodology” , 2006 .

[38]  J. Elhorst.  Unconditional Maximum Likelihood Estimation of Linear and Log‐Linear Dynamic Models for Spatial Panels , 2005 .

[39]  J. P. Elhorst.  Serial and spatial error dependence in space-time models , 2004 .

[40]  B. Baltagi,et al.  Econometric Analysis of Panel Data , 2020, Springer Texts in Business and Economics.

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

[42]  David F. Hendry,et al.  General-to-Specific Modeling: An Overview and Selected Bibliography , 2005 .

[43]  Patrick Sevestre,et al.  The Econometrics of Panel Data , 1993 .

[44]  Jesús Mur,et al.  Model selection strategies in a spatial setting: Some additional results , 2009 .

[45]  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 .

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

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

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

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

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

[51]  P. Burridge,et al.  Testing for a Common Factor in a Spatial Autoregression Model , 1981 .

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

[53]  Wojciech W. Charemza,et al.  New Directions in Econometric Practice: General to Specific Modelling, Cointegration and Vector Autoregression , 1991 .

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

[55]  Ronald Smith,et al.  A Principal Components Approach to Cross-Section Dependence in Panels , 2002 .

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

[57]  Timothy G. Conley,et al.  Technical Appendix for: Spatial Correlation Robust Inference with Errors in Location or Distance , 2005 .

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

[59]  Sergio J. Rey,et al.  Specification Searches in Spatial Econometrics: The Relevance of Hendry's Methodology , 2003 .

[60]  William E. Griffiths,et al.  Principles of Econometrics , 2008 .

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