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The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term

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Abstract

This paper considers the estimation of a linear regression involving the spatial autoregressive (SAR) error term, which is nearly nonstationary. The asymptotics properties of the ordinary least squares (OLS), true generalized least squares (GLS) and feasible generalized least squares (FGLS) estimators as well as the corresponding Wald test statistics are derived. Monte Carlo results are conducted to study the sampling behavior of the proposed estimators and test statistics. Key Words: Spatial Autocorrelation; Ordinary Least Squares; Generalized Least Squares; Two-stage Least Squares; Maximum Likelihood Estimation JEL No. C23, C33

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  • Badi H. Baltagi & Chihwa Kao & Long Liu, 2012. "The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term," Center for Policy Research Working Papers 151, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:151
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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Martellosio, Federico, 2010. "Power Properties Of Invariant Tests For Spatial Autocorrelation In Linear Regression," Econometric Theory, Cambridge University Press, vol. 26(1), pages 152-186, February.
    3. Federico Martellosio, 2012. "Testing for Spatial Autocorrelation: The Regressors that Make the Power Disappear," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 215-240.
    4. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    5. Kramer, Walter & Michels, Sonja, 1997. "Autocorrelation- and heteroskedasticity-consistent t-values with trending data," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 141-147.
    6. Kramer, W., 1989. "On the robustness of the F-test to autocorrelation among disturbances," Economics Letters, Elsevier, vol. 30(1), pages 37-40.
    7. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
    8. Flachaire, Emmanuel, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 361-376, April.
    9. Martellosio, Federico, 2011. "Efficiency of the OLS estimator in the vicinity of a spatial unit root," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1285-1291, August.
    10. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    11. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
    12. Jørgen Lauridsen & Reinhold Kosfeld, 2007. "Spatial cointegration and heteroscedasticity," Journal of Geographical Systems, Springer, vol. 9(3), pages 253-265, September.
    13. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    14. Badi H. Baltagi & Chihwa Kao & Long Liu, 2008. "Asymptotic properties of estimators for the linear panel regression model with random individual effects and serially correlated errors: the case of stationary and non-stationary regressors and residu," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 554-572, November.
    15. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    16. Jørgen Lauridsen & Reinhold Kosfeld, 2006. "A test strategy for spurious spatial regression, spatial nonstationarity, and spatial cointegration," Papers in Regional Science, Wiley Blackwell, vol. 85(3), pages 363-377, August.
    17. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
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    Cited by:

    1. Baltagi, Badi H. & Fingleton, Bernard & Pirotte, Alain, 2014. "Spatial lag models with nested random effects: An instrumental variable procedure with an application to English house prices," Journal of Urban Economics, Elsevier, vol. 80(C), pages 76-86.
    2. Diego Martínez-Navarro & Ignacio Amate-Fortes & Almudena Guarnido-Rueda, 2020. "Inequality and development: is the Kuznets curve in effect today?," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 37(3), pages 703-735, October.
    3. 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.
    4. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    5. Liu, Long, 2015. "A note on 2SLS estimation of the mixed regressive spatial autoregressive model," Economics Letters, Elsevier, vol. 134(C), pages 49-52.

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    More about this item

    Keywords

    spatial autocorrelation; ordinary least squares; generalized least squares; two-stage least squares; maximum likelihood estimation jel no. c23; c33;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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