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Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong


Mathematical Citation Quotient (MCQ) 2018: 0.06

Online
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2156-6674
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Testing Spatial Dependence in Spatial Models with Endogenous Weights Matrices

Anil K. Bera / Osman Doğan / Süleyman Taşpınar
Published Online: 2018-10-09 | DOI: https://doi.org/10.1515/jem-2017-0015

Abstract

In this study, we propose simple test statistics for identifying the source of spatial dependence in spatial autoregressive models with endogenous weights matrices. Elements of the weights matrices are modelled in such a way that endogenity arises when the unobserved factors that affect elements of the weights matrices are correlated with the unobserved factors in the outcome equation. The proposed test statistics are robust to the presence of endogeneity in the weights and can be used to detect spatial dependence in the dependent variable and/or the disturbance terms. The robust test statistics are easy to calculate as computationally simple estimations are needed for their calculations. Our Monte Carlo results indicate that these tests have good size and power properties in finite samples. We also provide an empirical illustration to demonstrate the usefulness of the robust tests in identifying the source of spatial dependence.

Keywords: endogenous spatial weights matrix; inference; Lagrange multiplier test; LM test; parametric misspecification; Rao’s score test; robust LM test; SARAR model; specification testing

JEL Classification: C13; C21; C31

References

  • Anderson, J. E., and E. van Wincoop. 2003. “Gravity with Gravitas: A Solution to the Border Puzzle.” American Economic Review 93 (1): 170–192.CrossrefGoogle Scholar

  • Anselin, L. 1988. Spatial Econometrics: Methods and Models. New York: Springer.Google Scholar

  • Anselin, L., A. K. Bera, R. Florax, and M. J. Yoon. 1996. “Simple Diagnostic Tests for Spatial Dependence.” Regional Science and Urban Economics 26 (1): 77–104.CrossrefGoogle Scholar

  • Baltagi, B. H., and D. Li. 2001. “LM Tests for Functional Form and Spatial Error Correlation.” International Regional Science Review 24 (2): 194–225.CrossrefGoogle Scholar

  • Baltagi, B. H., and Z. Yang. 2013a. “Heteroskedasticity and Non-normality Robust LM Tests for Spatial Dependence.” Regional Science and Urban Economics 43 (5): 725–739.CrossrefGoogle Scholar

  • Baltagi, B. H., and Z. Yang. 2013b. “Standardized LM Tests for Spatial Error Dependence in Linear or Panel Regressions.” The Econometrics Journal 16 (1): 103–134.CrossrefGoogle Scholar

  • Behrens, K., C. Ertur, and W. Koch. 2012. “‘Dual’ Gravity: Using Spatial Econometrics to Control for Multilateral Resistance.” Journal of Applied Econometrics 27 (5): 773–794.CrossrefGoogle Scholar

  • Bera, A. K., Y. Bilias, M. Yoon, S. Taşpınar, and O. Doğan. 2017. “Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications,” Working Paper.Google Scholar

  • Bera, A. K., O. Doğan, and S. Taşpınar. 2018. “Simple Tests for Endogeneity of Spatial Weights Matrices.” Regional Science and Urban Economics 69: 130–142.CrossrefGoogle Scholar

  • Bera, A. K., and M. J. Yoon. 1993. “Specification Testing with Locally Misspecified Alternatives.” Econometric Theory 9(4): 649–658.CrossrefGoogle Scholar

  • Born, B., and J. Breitung. 2011. “Simple Regression-Based Tests for Spatial Dependence.” The Econometrics Journal 14 (2): 330–342.CrossrefGoogle Scholar

  • Brueckner, J. K. 1998. “Testing for Strategic Interaction Among Local Governments: The Case of Growth Controls.” Journal of Urban Economics 44 (3): 438–467.CrossrefGoogle Scholar

  • Brueckner, J. K., and L. A. Saavedra. 2001. “Do Local Governments Engage in Strategic Property-Tax Competition?” National Tax Journal 54 (2): 203–230.CrossrefGoogle Scholar

  • Burridge, P. 1980. “On the Cliff-Ord Test for Spatial Correlation.” Journal of the Royal Statistical Society, Series B: Methodological 42: 107–108.Google Scholar

  • Case, A. C., H. S. Rosen, and J. R. Hines. 1993. “Budget Spillovers and Fiscal Policy Interdependence.” Journal of Public Economics 52 (3): 285–307.CrossrefGoogle Scholar

  • Cheng, W., and L.-F. Lee. 2017. “Testing Endogeneity of Spatial and Social Networks.” Regional Science and Urban Economics 64: 81–97.CrossrefGoogle Scholar

  • Cliff, A., and K. Ord. 1972. “Testing for Spatial Autocorrelation Among Regression Residuals.” Geographical Analysis 4 (3): 267–284.Google Scholar

  • Davidson, R., and J. G. MacKinnon. 1987. “Implicit Alternatives and the Local Power of Test Statistics.” Econometrica 55 (6): 1305–1329.CrossrefGoogle Scholar

  • Doğan, O., S. Taşpınar, and A. K. Bera. 2018. “Simple Tests for Social Interaction Models with Network Structures.” Spatial Economic Analysis 13 (2): 212–246.CrossrefGoogle Scholar

  • Elhorst, J. P. 2010. “Applied Spatial Econometrics: Raising the Bar.” Spatial Economic Analysis 5 (1): 9–28.CrossrefGoogle Scholar

  • Elhorst, J. P. 2014. Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer Briefs in Regional Science. New York: Springer Berlin Heidelberg.Google Scholar

  • Feenstra, R. C. 2004. Advanced International Trade. Princeton, NJ: Princeton University Press.Google Scholar

  • Fuller, W. A. 1996. Introduction to Statistical Time Series. Wiley Series in Probability and Statistics. New York: Wiley.Google Scholar

  • Goldsmith-Pinkham, P., and G. W. Imbens. 2013. “Social Networks and the Identification of Peer Effects.” Journal of Business & Economic Statistics 31 (3): 253–264.CrossrefGoogle Scholar

  • Hsieh, C.-S., and L. F. Lee. 2016. “A Social Interactions Model with Endogenous Friendship Formation and Selectivity.” Journal of Applied Econometrics 31 (2): 301–319.CrossrefGoogle Scholar

  • Jackson, M. 2010. Social and Economic Networks. Princeton University Press. Princeton University Press.Google Scholar

  • Jenish, N., and I. R. Prucha. 2009. “Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields.” Journal of Econometrics 150 (1): 86–98.CrossrefGoogle Scholar

  • Jenish, N., and I. R. Prucha. 2012. “On Spatial Processes and Asymptotic Inference Under Near-Epoch Dependence.” Journal of Econometrics 170 (1): 178–190.CrossrefGoogle Scholar

  • Kelejian, H. H., and I. R. Prucha. 2010. “Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances.” Journal of Econometrics 157: 53–67.CrossrefGoogle Scholar

  • Lee, L.-f. 2004. “Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models.” Econometrica 72 (6): 1899–1925.CrossrefGoogle Scholar

  • Lee, L.-f., and J. Yu. 2010. “A Spatial Dynamic Panel Data Model with both Time and Individual Fixed Effects.” Econometric Theory 26: 564–597.CrossrefGoogle Scholar

  • LeSage, J., and R. K. Pace. 2007. “A Matrix Exponential Spatial Specification.” Journal of Econometrics 140: 190–214.CrossrefGoogle Scholar

  • LeSage, J., and R. K. Pace. 2009. Introduction to Spatial Econometrics (Statistics: A Series of Textbooks and Monographs. London: Chapman and Hall/CRC.Google Scholar

  • McCallum, J. 1995. “National Borders Matter: Canada-U.S. Regional Trade Patterns.” The American Economic Review 85 (3): 615–623.Google Scholar

  • Moran, P. A. P. 1950. “A Test for the Serial Independence of Residuals.” Biometrika 37 (1/2): 178–181.CrossrefGoogle Scholar

  • Qu, X., L. fei Lee, and J. Yu. 2017. “QML Estimation of Spatial Dynamic Panel Data Models with Endogenous Time Varying Spatial Weights Matrices.” Journal of Econometrics 197 (2): 173–201.CrossrefGoogle Scholar

  • Qu, X., and L.-f. Lee. 2013. “Locally Most Powerful Tests for Spatial Interactions in the Simultaneous SAR Tobit Model.” Regional Science and Urban Economics 43 (2): 307–321.CrossrefGoogle Scholar

  • Qu, X., and L.-f. Lee. 2015. “Estimating a Spatial Autoregressive Model with an Endogenous Spatial Weight Matrix.” Journal of Econometrics 184 (2): 209–232.CrossrefGoogle Scholar

  • Qu, X., X. Wang, and L.-f. Lee. 2016. “Instrumental Variable Estimation of a Spatial Dynamic Panel Model with Endogenous Spatial Weights When T is Small.” The Econometrics Journal 19 (3): 261–290.CrossrefGoogle Scholar

  • Robinson, P. 2008. “Correlation Testing in Time Series, Spatial and Cross-sectional Data.” Journal of Econometrics 147 (1): 5–16.CrossrefGoogle Scholar

  • Robinson, P. M., and F. Rossi. 2014. “Improved Lagrange Multiplier Tests in Spatial Autoregressions.” The Econometrics Journal 17 (1): 139–164.CrossrefGoogle Scholar

  • Robinson, P. M., and F. Rossi. 2015a. “Refined Tests for Spatial Correlation.” Econometric Theory 31 (6): 1249–1280.CrossrefGoogle Scholar

  • Robinson, P. M., and F. Rossi. 2015b. “Refinements in Maximum Likelihood Inference on Spatial Autocorrelation in Panel Data.” Journal of Econometrics 189 (2): 447–456. Frontiers in Time Series and Financial Econometrics.CrossrefGoogle Scholar

  • Saikkonen, P. 1989. “Asymptotic Relative Efficiency of the Classical Test Statistics Under Misspecification.” Journal of Econometrics 42 (3): 351–369.CrossrefGoogle Scholar

  • Su, L., and Z. Yang. 2015. “QML estimation of dynamic panel data models with spatial errors.” Journal of Econometrics 185 (1): 230–258.CrossrefGoogle Scholar

  • Taşpınar, S., O. Doğan, and W. P. M. Vijverberg. 2016. . 2016. “GMM Inference in Spatial Autoregressive Models.“ Econometric Reviews 37(9): 931–954.Google Scholar

  • Taşpınar, S., O. Doğan, and A. K. Bera. 2017. “GMM Gradient Tests for Spatial Dynamic Panel Data Models.” Regional Science and Urban Economics 65: 65–88.CrossrefGoogle Scholar

  • Wasserman, S., and K. Faust. 1994. Social Network Analysis: Methods and Applications,,Structural Analysis in the Social Sciences. Cambridge UK: Cambridge University Press.Google Scholar

  • Weinberg, B. A. 2007. Social Interactions with Endogenous Associations. Working Paper 13038, National Bureau of Economic Research.Google Scholar

  • White, H. 1994. Estimation, Inference and Specification Analysis. Cambridge.Google Scholar

  • Yang, Z. 2015. “LM Tests of Spatial Dependence Based on Bootstrap Critical Values.” Journal of Econometrics 185 (1): 33–59.CrossrefGoogle Scholar

  • Yu, J., R. de Jong, and L. fei Lee. 2008. “Quasi-maximum Likelihood Estimators for Spatial Dynamic Panel Data with Fixed Effects when both n and T are Large.” Journal of Econometrics 146 (1): 118–134.CrossrefGoogle Scholar

About the article

Published Online: 2018-10-09


FundingThis research was supported, in part, by a grant of computer time from the City University of New York High Performance Computing Center under NSF Grants CNS-0855217 and CNS-0958379.


Citation Information: Journal of Econometric Methods, Volume 8, Issue 1, 20170015, ISSN (Online) 2156-6674, DOI: https://doi.org/10.1515/jem-2017-0015.

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