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Testing for spatial dependence in a spatial autoregressive (SAR) model in the presence of endogenous regressors

Author

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  • Malabika Koley

    (University of Illinois at Urbana Champaign)

  • Anil K. Bera

    (University of Illinois at Urbana Champaign)

Abstract

Spatial modeling is one of the growing areas of research in economics in recent years. However, these models are not tested enough. Even if tests are performed, they are done in a piece-wise fashion. Another age-long problem in economic modeling is endogeneity of one or more variables. Endgeneity is caused due to a number of reasons one of which is simultaneous modeling of economic variables. This paper considers specification testing in the context of a spatial autoregresive (SAR) model with an endogenous regressor. First, we construct standard Rao’s Score (RS) tests for null hypothesis of the absence of spatial autocorrelation and endogeneity. These standard RS tests are invalid in the presence of local misspecification of the models under the alternative hypotheses. Therefore, in our next step, we develop adjusted tests using the technique of Bera and Yoon (Econom Theor 9:649–658, 1993), that are robust to local misspecification. These adjusted (or robustified) tests are simple to calculate and easy to implement. With a Monte Carlo study we investigate the finite sample performance of all the proposed tests, and the results confirm that the robust tests perform better compared to their non-robust counterparts both in terms of size and power.

Suggested Citation

  • Malabika Koley & Anil K. Bera, 2022. "Testing for spatial dependence in a spatial autoregressive (SAR) model in the presence of endogenous regressors," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-46, December.
    • Handle: RePEc:spr:jospat:v:3:y:2022:i:1:d:10.1007_s43071-022-00026-7
    DOI: 10.1007/s43071-022-00026-7
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    References listed on IDEAS

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    1. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    2. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-1329, November.
    3. Kelley Pace, R. & Barry, Ronald, 1997. "Sparse spatial autoregressions," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 291-297, May.
    4. 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.
    5. Liu, Xiaodong & Saraiva, Paulo, 2015. "GMM estimation of SAR models with endogenous regressors," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 68-79.
    6. Fang, Ying & Park, Sung Y. & Zhang, Jinfeng, 2014. "A simple spatial dependence test robust to local and distributional misspecifications," Economics Letters, Elsevier, vol. 124(2), pages 203-206.
    7. Saikkonen, Pentti, 1989. "Asymptotic relative efficiency of the classical test statistics under misspecification," Journal of Econometrics, Elsevier, vol. 42(3), pages 351-369, November.
    8. Bera, Anil K. & Montes-Rojas, Gabriel & Sosa-Escudero, Walter, 2009. "Testing under local misspecification and artificial regressions," Economics Letters, Elsevier, vol. 104(2), pages 66-68, August.
    9. Liu, Xiaodong, 2012. "On the consistency of the LIML estimator of a spatial autoregressive model with many instruments," Economics Letters, Elsevier, vol. 116(3), pages 472-475.
    10. Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
    11. Stanislav Stakhovych & Tammo H.A. Bijmolt, 2009. "Specification of spatial models: A simulation study on weights matrices," Papers in Regional Science, Wiley Blackwell, vol. 88(2), pages 389-408, June.
    12. Lung-Fei Lee & Jihai Yu, 2009. "Spatial Nonstationarity and Spurious Regression: the Case with a Row-normalized Spatial Weights Matrix," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(3), pages 301-327.
    13. Bera, Anil K. & Yoon, Mann J., 1993. "Specification Testing with Locally Misspecified Alternatives," Econometric Theory, Cambridge University Press, vol. 9(4), pages 649-658, August.
    14. Xiaodong Liu & Lung-Fei Lee, 2013. "Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 734-753, August.
    15. Xiuhua Wang & Jian Guan, 2017. "Financial inclusion: measurement, spatial effects and influencing factors," Applied Economics, Taylor & Francis Journals, vol. 49(18), pages 1751-1762, April.
    16. Cheng, Wei & Lee, Lung-fei, 2017. "Testing endogeneity of spatial and social networks," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 81-97.
    17. 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.
    18. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 252-277, April.
    19. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    20. David M. Drukker & Peter Egger & Ingmar R. Prucha, 2013. "On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 686-733, August.
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    1. Anil K. Bera & Yannis Bilias, 2024. "Three Scores and 15 Years (1948-2023) of Rao's Score Test: A Brief History," Papers 2406.19956, arXiv.org, revised Oct 2024.

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    More about this item

    Keywords

    SAR; Endogeneity; Specification testing; Rao’s Score (RS) tests; Parametric misspecification; Robust RS tests;
    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
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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