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

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  • Mynbaev, Kairat

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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Keywords: mixed regressive spatial autoregressive model; OLS estimator; asymptotic distribution;

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  1. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
  2. 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.
  3. Mynbaev, Kairat, 2000. "$L_p$-Approximable sequences of vectors and limit distribution of quadratic forms of random variables," MPRA Paper 18447, University Library of Munich, Germany, revised 2001.
  4. 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.
  5. Mynbaev, Kairat, 2001. "The strengths and weaknesses of L2 approximable regressors," MPRA Paper 9056, University Library of Munich, Germany.
  6. 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.
  7. 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.
  8. Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005.
  9. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
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