GMM Gradient Tests for Spatial Dynamic Panel Data Models

Taspinar, Suleyman and Dogan, Osman and Bera, Anil K. (2017): GMM Gradient Tests for Spatial Dynamic Panel Data Models. Published in: Regional Science and Urban Economics No. 65 (2017): pp. 65-88.

Abstract

In this study, we formulate the adjusted gradient tests when the alternative model used to construct tests deviates from the true data generating process for a spatial dynamic panel data model (SDPD). Following Bera et. al. (2010), we introduce these adjusted gradient tests along with the standard ones within a GMM framework. These tests can be used to detect the presence of (i) the contemporaneous spatial lag terms, (ii) the time lag term, and (iii) the spatial time lag terms in an higher order SDPD model. These adjusted tests have two advantages: (i) their null asymptotic distribution is a central chi-squared distribution irrespective of the misspecified alternative model, and (ii) their test statistics are computationally simple and require only the ordinary least-squares (OLS) estimates from a non-spatial two-way panel data model. We investigate the finite sample size and power properties of these tests through Monte Carlo studies. Our results indicate that the adjusted gradient tests have good finite sample properties.

• Item Type: MPRA Paper
• Language: English
• Keywords: Spatial Dynamic Panel Data Model, SDPD, GMM, Robust LM Tests, GMM Gradient Tests, Inference
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C31 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models

References

Amemiya, Takeshi (1985). Advanced Econometrics. Cambridge: Harvard University Press.

Anderson, T.W. (2003). An Introduction to Multivariate Statistical Analysis. 3rd ed. Wiley Series in Probability and Statistics. Wiley-Interscience.

Anselin, Luc et al. (1996). Simple diagnostic tests for spatial dependence. In: Regional Science and Urban Economics 26.1, pp. 77-104.

Anselin, Luc, Julie Le Gallo, and Hubert Jayet (2008). Spatial Panel Econometrics. In: The Econometrics of Panel Data. Ed. by Laszlo Matyas et al. Vol. 46. Advanced Studies in Theoretical and Applied Econometrics. Springer Berlin Heidelberg.

Baltagi, Badi. (2008). Econometric Analysis of Panel Data. John Wiley & Sons.

Baltagi, Badi H. and Zhenlin Yang (2013). Standardized LM tests for spatial error dependence in linear or panel regressions. In: The Econometrics Journal 16.1, pp. 103-134.

Baltagi, Badi H., Seuck Heun Song, and Won Koh (2003). Testing panel data regression models with spatial error correlation. In: Journal of Econometrics 117.1, pp. 123-150.

Baltagi, Badi H. et al. (2007). Testing for serial correlation, spatial autocorrelation and random effects using panel data. In: Journal of Econometrics 140.1, pp. 5-51.

Bera, Anil K. and Yannis Bilias (2001). Rao's score, Neyman's C(alpha) and Silvey's LM tests: an essay on historical developments and some new results. In: Journal of Statistical Planning and Inference 97.1, pp. 9 - 44.

Bera, Anil K. and Mann J. Yoon (1993). Specification Testing with Locally Misspecified Alternatives. In: Econometric Theory 9.4, pp. 649 - 658.

Bera, Anil K., Gabriel Montes-Rojas, and Walter Sosa-Escudero (2010). General Specification Testing with Locally Misspecified Models. In: Econometric Theory 26.6, pp. 1838 - 1845.

Breusch, T. S. and A. R. Pagan (1980). The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics. In: The Review of Economic Studies 47.1, pp. 239 - 253.

Davidson, Russell and James G. MacKinnon (1987). Implicit Alternatives and the Local Power of Test Statistics. English. In: Econometrica 55.6, pp. 1305 - 1329.

Davidson, Russell and James G. MacKinnon (1998). Graphical Methods for Investigating the Size and Power of Hypothesis Tests. In: The Manchester School 66.1, pp. 1 - 26.

Debarsy, Nicolas and Cem Ertur (2010). Testing for spatial autocorrelation in a fixed effects panel data model. In: Regional Science and Urban Economics 40.6, pp. 453 - 470.

Elhorst, J. Paul (2005). Unconditional Maximum Likelihood Estimation of Linear and Log-Linear Dynamic Models for Spatial Panels . In: Geographical Analysis 37.1. pp. 85 - 106.

Hall, Alastair R. (2004). Generalized Method of Moments. Advanced Texts in Econometrics. Oxford University Press.

Hsiao, Cgeng. (2014). Analysis of Panel Data. Analysis of Panel Data. Cambridge University Press.

Kapoor, Mudit, Harry H. Kelejian, and Ingmar R. Prucha (2007).Panel data models with spatially correlated error components. In: Journal of Econometrics 140.1, pp. 97 - 130.

Kelejian, Harry H. and Ingmar R. Prucha (2010).Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. In: Journal of Econometrics 157, pp. 53 - 67.

Lee, Lung-fei and Jihai Yu (2010a). A Spatial Dynamic Panel Data Model with both Time and Individual Fixed Effects. In: Econometric Theory 26.2, pp. 564 - 597.

Lee, Lung-fei and Jihai Yu (2010b). Some recent developments in spatial panel data models. In: Regional Science and Urban Economics 40.5. pp. 255 - 271.

Lee, Lung-fei and Jihai Yu (2011).A Unifed Transformation Approach for the Estimation of Spatial Dynamic Panel Data Models: Stability, Spatial Cointegration and Explosive Roots. In: Handbook of Empirical Economics and Finance (Statistics: A Series of Textbooks and Monographs). Ed. by Aman Ullah and David E.A. Giles. Statistics: Textbooks and Monographs. Chapman & Hall/CRC Taylor & Francis Group.

Lee, Lung-fei and Jihai Yu (2012a). QML Estimation of Spatial Dynamic Panel Data Models with Time Varying Spatial Weights Matrices. In: Spatial Economic Analysis 7.1, pp. 31 - 74.

Lee, Lung-fei and Jihai Yu (2012b). The C(alpha)-type gradient test for spatial dependence in spatial autoregressive models. In: Letters in Spatial and Resource Sciences 5.3, pp. 119 - 135.

Lee, Lung-fei and Jihai Yu (2014). Effcient GMM estimation of spatial dynamic panel data models with fixed effects. In: Journal of Econometrics 180.2, pp. 174 - 197.

Lee, Lung-fei and Jihai Yu (2015). Estimation of fixed effects panel regression models with separable and non-separable space-time filters. In: Journal of Econometrics 184.1, pp. 174 - 192.

Newey, Whitney K. and Kenneth D. West (1987). Hypothesis Testing with Effcient Method of Moments Estimation. In: International Economic Review 28.3, pp. 777 - 787.

Parent, Olivier and James P. LeSage (2011). A space-time filter for panel data models containing random effects". In: Computational Statistics & Data Analysis 55.1, pp. 475 - 490.

Saikkonen, Pentti (1989). Asymptotic relative effciency of the classical test statistics under misspecification. In: Journal of Econometrics 42.3, pp. 351 - 369.

Su, Liangjun and Zhenlin Yang (2015). QML estimation of dynamic panel data models with spatial errors. In: Journal of Econometrics 185.1, pp. 230 - 258.

White, Halbert (2001). Asymptotic Theory for Econometricians. Economic theory, econometrics, and mathematical economics. Academic Press.

Yang, Zhenlin (2015). Unified M-Estimation of Fixed-Effects Spatial Dynamic Models with Short Panels. Research Collection School of Economics 1783. Singapore Management University.

Yu, Jihai and Lung-fei Lee (2010). Estimation of Unit root Spatial Dynamic Panel Data Models. In: Econometric Theory 26.5, pp. 1332 - 1362.

Yu, Jihai, Robert de Jong, and Lung fei Lee (2008). Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large. In: Journal of Econometrics 146.1, pp. 118 - 134.

Yu, Jihai, Robert de Jong, and Lung fei Lee (2012). Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration. In: Journal of Econometrics 167.1, pp. 16 - 37.