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Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances

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  • Jin, Fei
  • Lee, Lung-fei

Abstract

In this paper, we consider the Cox-type tests of non-nested hypotheses for spatial autoregressive (SAR) models with SAR disturbances. We formally derive the asymptotic distributions of the test statistics. In contrast to regression models, we show that the Cox-type and J-type tests for non-nested hypotheses in the framework of SAR models are not asymptotically equivalent under the null hypothesis. The Cox test in a non-spatial setting has been found often to have large size distortion, which can be removed by bootstrap. Cox-type tests for SAR models with SAR disturbances may also have a large size distortion. We show that the bootstrap is consistent for Cox-type tests in our framework. Performances of the Cox-type and J-type tests as well as their bootstrapped versions in finite samples are compared via a Monte Carlo study. These tests are of particular interest when there are competing models with different spatial weight matrices. Using bootstrapped p-values, the Cox tests have relatively high power in all experiments and can outperform J-type and several other related tests in some cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:regeco:v:43:y:2013:i:4:p:590-616
    DOI: 10.1016/j.regsciurbeco.2013.03.003
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    More about this item

    Keywords

    Specification; Spatial autoregressive model; Non-nested; Cox test; J test; QMLE;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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