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Model selection using J-test for the spatial autoregressive model vs. the matrix exponential spatial model

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  • Han, Xiaoyi
  • Lee, Lung-fei

Abstract

We consider using the J-test procedure for the non-nested model selection problem between the spatial autoregressive (SAR) model and the matrix exponential spatial specification (MESS) model. The 2SLS and GMM methods are used to implement the J-test procedure and derive several test statistics under the GMM framework. We investigate the behavior of those J-test statistics in terms of pseudo true values. We extend the J-test procedure into the setting when error terms in the model are with unknown heteroskedasticity. Monte Carlo results suggest with strong spatial dependence the J-test statistics can have good power to distinguish the SAR and MESS models.

Suggested Citation

  • Han, Xiaoyi & Lee, Lung-fei, 2013. "Model selection using J-test for the spatial autoregressive model vs. the matrix exponential spatial model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 250-271.
    • Handle: RePEc:eee:regeco:v:43:y:2013:i:2:p:250-271
    DOI: 10.1016/j.regsciurbeco.2012.07.005
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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Zenou, Yves & Patacchini, Eleonora & Liu, Xiaodong, 2011. "Peer Effects in Education, Sport, and Screen Activities: Local Aggregate or Local Average?," CEPR Discussion Papers 8477, C.E.P.R. Discussion Papers.
    3. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    4. M. H. Pesaran, 1974. "On the General Problem of Model Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(2), pages 153-171.
    5. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    6. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    7. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    8. Russell Davidson & James G. Mackinnon, 1982. "Some Non-Nested Hypothesis Tests and the Relations Among Them," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(4), pages 551-565.
    9. Irani Arraiz & David M. Drukker & Harry H. Kelejian & Ingmar R. Prucha, 2010. "A Spatial Cliff‐Ord‐Type Model With Heteroskedastic Innovations: Small And Large Sample Results," Journal of Regional Science, Wiley Blackwell, vol. 50(2), pages 592-614, May.
    10. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    11. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    12. Olivier Parent & James Lesage, 2005. "Bayesian Model Averaging for Spatial Econometric Models," Post-Print hal-00375489, HAL.
    13. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-365, March.
    14. L W Hepple, 1995. "Bayesian Techniques in Spatial and Network Econometrics: 1. Model Comparison and Posterior Odds," Environment and Planning A, , vol. 27(3), pages 447-469, March.
    15. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    16. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    17. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
    18. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 419-429.
    19. Peter Burridge, 2012. "Improving the J Test in the SARAR Model by Likelihood-based Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 75-107, March.
    20. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    21. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 16(1), pages 103-119, May.
    22. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    23. L W Hepple, 1995. "Bayesian Techniques in Spatial and Network Econometrics: 2. Computational Methods and Algorithms," Environment and Planning A, , vol. 27(4), pages 615-644, April.
    24. Kelejian, Harry H. & Piras, Gianfranco, 2011. "An extension of Kelejian's J-test for non-nested spatial models," Regional Science and Urban Economics, Elsevier, vol. 41(3), pages 281-292, May.
    25. Dastoor, Naorayex K., 1983. "Some aspects of testing non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 21(2), pages 213-228, February.
    26. Davidson, Russell & MacKinnon, James G., 2002. "Bootstrap J tests of nonnested linear regression models," Journal of Econometrics, Elsevier, vol. 109(1), pages 167-193, July.
    27. Peter Burridge & Bernard Fingleton, 2010. "Bootstrap Inference in Spatial Econometrics: the J-test," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 93-119.
    28. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
    29. Davidson, Russell & MacKinnon, James G., 1983. "Testing the specification of multivariate models in the presence of alternative hypotheses," Journal of Econometrics, Elsevier, vol. 23(3), pages 301-313, December.
    30. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    31. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    32. Harry Kelejian, 2008. "A spatial J-test for model specification against a single or a set of non-nested alternatives," Letters in Spatial and Resource Sciences, Springer, vol. 1(1), pages 3-11, April.
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    Cited by:

    1. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    2. Debarsy, Nicolas & Jin, Fei & Lee, Lung-fei, 2015. "Large sample properties of the matrix exponential spatial specification with an application to FDI," Journal of Econometrics, Elsevier, vol. 188(1), pages 1-21.
    3. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    4. Han, Xiaoyi & Lee, Lung-fei, 2013. "Bayesian estimation and model selection for spatial Durbin error model with finite distributed lags," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 816-837.
    5. Ye Yang & Osman Dogan & Suleyman Taspinar & Fei Jin, 2023. "A Review of Cross-Sectional Matrix Exponential Spatial Models," Papers 2311.14813, arXiv.org.
    6. repec:cep:stiecm:/2013/568 is not listed on IDEAS
    7. Chengjun Liu & Fuqiang Nie & Dong Ren, 2021. "Temporal and Spatial Evolution of China's Human Development Index and Its Determinants: An Extended Study Based on Five New Development Concepts," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(1), pages 247-282, August.
    8. Liu, Tuo & Lee, Lung-fei, 2019. "A likelihood ratio test for spatial model selection," Journal of Econometrics, Elsevier, vol. 213(2), pages 434-458.
    9. Zhang, Xinyu & Yu, Jihai, 2018. "Spatial weights matrix selection and model averaging for spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 203(1), pages 1-18.

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    More about this item

    Keywords

    Spatial autoregressive model; Matrix exponential spatial model; J-test; Pseudo true value; GMM;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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