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A likelihood ratio test for spatial model selection

Author

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  • Liu, Tuo
  • Lee, Lung-fei
Abstract
This paper develops a nondegenerate likelihood-ratio test for model selection between two competitive spatial econometrics models. It generalizes the test of Vuong (1989) to models with spatial near-epoch dependent (NED) data. We do not make any structural assumption on the true model specification and allow for the cases where both or one of the two competing models are mis-specified. The test is valid whether two models are nested or non-nested. As a prerequisite of the test, we first show that quasi-maximum likelihood estimators (QMLE) of spatial econometrics models are consistent estimators of their pseudo-true values and are asymptotically normal under regularity conditions. In particular, we study spatial autoregressive models with spatial autoregressive errors (SARAR) and matrix exponential spatial specification (MESS) models. We derive the limiting null distribution of the test statistic. A spatial heteroskedastic and autoregressive consistent estimator of asymptotic variance of the test statistic under the null, which is necessary to implement the test, is constructed. Monte Carlo experiments are designed to investigate finite sample performance of QMLEs for SARAR and MESS models, as well as the size and power of the proposed test.

Suggested Citation

  • Liu, Tuo & Lee, Lung-fei, 2019. "A likelihood ratio test for spatial model selection," Journal of Econometrics, Elsevier, vol. 213(2), pages 434-458.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:2:p:434-458
    DOI: 10.1016/j.jeconom.2019.07.001
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    References listed on IDEAS

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    1. 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.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    3. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    4. Xu, Xingbai & Lee, Lung-fei, 2015. "A spatial autoregressive model with a nonlinear transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 186(1), pages 1-18.
    5. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    6. Chen, Xiaohong & Hong, Han & Shum, Matthew, 2007. "Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models," Journal of Econometrics, Elsevier, vol. 141(1), pages 109-140, November.
    7. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    9. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.
    10. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    11. Kim, Min Seong & Sun, Yixiao, 2011. "Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix," Journal of Econometrics, Elsevier, vol. 160(2), pages 349-371, February.
    12. Yu‐Chin Hsu & Xiaoxia Shi, 2017. "Model‐selection tests for conditional moment restriction models," Econometrics Journal, Royal Economic Society, vol. 20(1), pages 52-85, February.
    13. 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.
    14. Luc Anselin, 1984. "Specification Tests On The Structure Of Interaction In Spatial Econometric Models," Papers in Regional Science, Wiley Blackwell, vol. 54(1), pages 165-182, January.
    15. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    16. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    17. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    18. Xiaoxia Shi, 2015. "A nondegenerate Vuong test," Quantitative Economics, Econometric Society, vol. 6(1), pages 85-121, March.
    19. 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.
    20. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    21. 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.
    22. Shi, Xiaoxia, 2015. "Model selection tests for moment inequality models," Journal of Econometrics, Elsevier, vol. 187(1), pages 1-17.
    23. Xu, Xingbai & Lee, Lung-fei, 2015. "Maximum likelihood estimation of a spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 188(1), pages 264-280.
    24. Choi, Hwan-sik & Jeong, Minsoo & Park, Joon Y., 2014. "An asymptotic analysis of likelihood-based diffusion model selection using high frequency data," Journal of Econometrics, Elsevier, vol. 178(P3), pages 539-557.
    25. 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.
    26. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
    27. 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.
    28. Hwan-sik Choi & Nicholas M. Kiefer, 2010. "Improving robust model selection tests for dynamic models," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 177-204, July.
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    Cited by:

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    2. Liu, Tuo & Xu, Xingbai & Lee, Lung-fei, 2022. "Consistency without compactness of the parameter space in spatial econometrics," Economics Letters, Elsevier, vol. 210(C).
    3. Karunanayake, N. & Aimmanee, P. & Lohitvisate, W. & Makhanov, S.S., 2020. "Particle method for segmentation of breast tumors in ultrasound images," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 257-284.
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    5. Bing Su & Fukang Zhu & Ke Zhu, 2023. "Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables," Papers 2301.06658, arXiv.org.
    6. Ye Yang & Osman Dogan & Suleyman Taspinar & Fei Jin, 2023. "A Review of Cross-Sectional Matrix Exponential Spatial Models," Papers 2311.14813, arXiv.org.

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    More about this item

    Keywords

    Likelihood ratio; Near-epoch dependence; Spatial autoregressive model; Matrix exponential spatial specification; Model selection;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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