Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model

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Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model

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Mynbaev, Kairat

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Kairat T. Mynbaev

Abstract

We find the asymptotics of the OLS estimator of the parameters $\beta$ and $\rho$ in the spatial autoregressive model with exogenous regressors $Y_n = X_n\beta+\rho W_nY_n+V_n$. Only low-level conditions are imposed. Exogenous regressors may be bounded or growing, like polynomial trends. The assumption on the spatial matrix $W_n$ is appropriate for the situation when each economic agent is influenced by many others. The asymptotics contains both linear and quadratic forms in standard normal variables. The conditions and the format of the result are chosen in a way compatible with known results for the model without lags by Anderson (1971) and for the spatial model without exogenous regressors due to Mynbaev and Ullah (2006).

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4411.

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Date of creation: 01 Aug 2006
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Handle: RePEc:pra:mprapa:4411

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Find related papers by JEL classification:
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

This paper has been announced in the following NEP Reports:

NEP-ALL-2007-08-14 (All new papers)
NEP-ECM-2007-08-14 (Econometrics)

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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. [Downloadable!] (restricted)
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 509-33, May.
Mynbaev, Kairat, 2001. "The strengths and weaknesses of L2 approximable regressors," MPRA Paper 9056, University Library of Munich, Germany. [Downloadable!]
Benedikt Pötscher & Ingmar Prucha, 1991. "Basic structure of the asymptotic theory in dynamic nonlinear econometric models," Econometric Reviews, Taylor and Francis Journals, vol. 10(3), pages 253-325. [Downloadable!] (restricted)
Mynbaev, Kairat & Ullah, Aman, 2006. "A Remark on the Asymptotic Distribution of the OLS Estimator for a Purely Autoregressive Spatial Model," MPRA Paper 3318, University Library of Munich, Germany. [Downloadable!]
H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September. [Downloadable!] (restricted)

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