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A likelihood ratio test for spatial model selection

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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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    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.
    4. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised Mar 2023.
    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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