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Specification Test for Spatial Autoregressive Models

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  • Liangjun Su
  • Xi Qu

Abstract

This article considers a simple test for the correct specification of linear spatial autoregressive models, assuming that the choice of the weight matrix Wn is true. We derive the limiting distributions of the test under the null hypothesis of correct specification and a sequence of local alternatives. We show that the test is free of nuisance parameters asymptotically under the null and prove the consistency of our test. To improve the finite sample performance of our test, we also propose a residual-based wild bootstrap and justify its asymptotic validity. We conduct a small set of Monte Carlo simulations to investigate the finite sample properties of our tests. Finally, we apply the test to two empirical datasets: the vote cast and the economic growth rate. We reject the linear spatial autoregressive model in the vote cast example but fail to reject it in the economic growth rate example. Supplementary materials for this article are available online.

Suggested Citation

  • Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
  • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:4:p:572-584
    DOI: 10.1080/07350015.2015.1102734
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    2. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2021.
    3. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    4. Liu, Li & Bu, Ruijun & Pan, Zhiyuan & Xu, Yuhua, 2019. "Are financial returns really predictable out-of-sample?: Evidence from a new bootstrap test," Economic Modelling, Elsevier, vol. 81(C), pages 124-135.
    5. Lu, Xun & Su, Liangjun, 2020. "Determining individual or time effects in panel data models," Journal of Econometrics, Elsevier, vol. 215(1), pages 60-83.

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