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Testing for spatial lag and spatial error dependence using double length artificial regressions

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Abstract

This paper obtains the joint and conditional Lagrange multiplier (LM) tests for a spatial lag regression model with spatial auto-regressive error derived in Anselin (Reg Sci Urban Ecom 26:77–104, 1996) using artificial double length regressions (DLR). These DLR tests and their corresponding LM tests are compared using an illustrative example and a Monte Carlo simulation.

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Notes

  1. In spatial models, the functional form changes with the sample size, i.e., the functions \(F\) and \(K\) should have a sample size subscript. As a result, Slutsky’s Lemma no longer applies and replacing the true parameter values \( \varphi \) with consistent estimates in (1) above does not necessarily lead to a consistent estimate of the information matrix. When \(F\) and \(K\) have the same functional form in different sample sizes, their continuity would guarantee this. Here, we need some stronger assumptions on the functions or require that the estimates are converging in a stronger sense (e.g. almost surely). We would like to thank an anonymous referee for pointing these caveats.

  2. It is important to point out that the asymptotic distribution of our test statistics were not explicitly derived in the paper. There is no proof in the literature that the LM tests are asymptotically \(\chi ^{2}\) under the null. Given the simulations below, they most likely are but we cannot say under what assumptions this holds. These are likely to hold under a similar set of primitive assumptions developed by Kelejian and Prucha (2001) for the Moran-I test.

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Acknowledgments

We would like to thank the anonymous referee and the editor Werner G. Müller for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Economics and Center for Policy Research, Syracuse University, 426 Eggers Hall, Syracuse, NY, 13244-1020, USA

    Badi H. Baltagi

  2. Department of Economics, College of Business, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249-0633, USA

    Long Liu

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  1. Badi H. Baltagi
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  2. Long Liu
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Correspondence to Badi H. Baltagi.

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Baltagi, B.H., Liu, L. Testing for spatial lag and spatial error dependence using double length artificial regressions. Stat Papers 55, 477–486 (2014). https://doi.org/10.1007/s00362-012-0492-8

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  • DOI: https://doi.org/10.1007/s00362-012-0492-8

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