An extension of Kelejian's J-test for non-nested spatial models

In 2008 Kelejian extended the J-test procedure to a spatial framework. In that paper he considered a null model which could, but need not, contain spatial lags in both the dependent variable and disturbance term. Under the alternative, he considered one or more non-nested spatial models which could, but need not, also contain spatial lags. Although his suggested test was computationally simple and intuitive, it did not use the available information in an efficient manner. In this paper we suggest a modification of Kelejian's J-test which uses the available information in a more efficient way. We give large sample, as well as small sample Monte Carlo results. Perhaps counter to intuition, we also demonstrate that the "J-test procedure" cannot be used to establish a test for the structure of the error term.

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

[2]  Naorayex K. Dastoor,et al.  Some aspects of testing non-nested hypotheses , 1983 .

[3]  M. H. Pesaran,et al.  On the general problem of model selection , 1974 .

[4]  Harry H. Kelejian,et al.  A spatial J-test for model specification against a single or a set of non-nested alternatives , 2008 .

[5]  Harry H. Kelejian,et al.  The relative efficiencies of various predictors in spatial econometric models containing spatial lags , 2007 .

[6]  Y. Zenou,et al.  Peer Effects in Education, Sport, and Screen Activities: Local Aggregate or Local Average? , 2011 .

[7]  M. Pesaran,et al.  TESTING NON-NESTED NONLINEAR REGRESSION MODELS , 1978 .

[8]  H. Kelejian,et al.  A Spatial Cliff-Ord-Type Model with Heteroskedastic Innovations: Small and Large Sample Results , 2008, SSRN Electronic Journal.

[9]  Badi H. Baltagi,et al.  A companion to theoretical econometrics , 2003 .

[10]  Luc Anselin,et al.  New Directions in Spatial Econometrics , 2011 .

[11]  Thanasis Stengos,et al.  Semiparametric Specification Testing of Non-nested Econometric Models , 1994 .

[12]  Leslie Godfrey,et al.  Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence , 1983 .

[13]  Badi H. Baltagi,et al.  Testing Panel Data Regression Models with Spatial Error Correlation , 2002 .

[14]  Luc Anselin,et al.  Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results , 1995 .

[15]  L. Godfrey,et al.  TESTING NON-NESTED MODELS AFTER ESTIMATION BY INSTRUMENTAL VARIABLES OR LEAST SQUARES , 1983 .

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

[17]  James G. MacKinnon,et al.  TESTS FOR MODEL SPECIFICATION IN THE PRESENCE OF ALTERNATIVE HYPOTHESES Some Further Results , 1983 .

[18]  Gianfranco Piras,et al.  Spatial J-test: some Monte Carlo evidence , 2012, Stat. Comput..

[19]  Jan Kmenta,et al.  Elements of Econometrics: Second Edition , 1997 .

[20]  Peter Burridge.  A research agenda on general-to-specific spatial model search , 2011 .

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

[22]  M. Hashem Pesaran,et al.  Non-nested Hypothesis Testing: An Overview , 1999 .

[23]  M. Pesaran,et al.  Comparison of Local Power of Alternative Tests of Non-Nested Regression Models , 1982 .

[24]  Geoffrey H. Donovan,et al.  Wildfire Risk and Housing Prices: A Case Study from Colorado Springs , 2007, Land Economics.

[25]  Badi H. Baltagi,et al.  Testing for Serial Correlation, Spatial Autocorrelation and Random Effects , 2004 .

[26]  J. MacKinnon,et al.  Several Tests for Model Specication in the Pres-ence of Alternative Hypotheses , 1981 .