# A Remark on the Asymptotic Distribution of the OLS Estimator for a Purely Autoregressive Spatial Model

## Author Info

• Mynbaev, Kairat
• Ullah, Aman
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## Abstract

We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only low-level conditions are used. As the sample size increases, the spatial matrix is assumed to approach a square-integrable function on the square $(0,1)^2$. The asymptotic distribution is a ratio of two infinite linear combinations of $\chi$-square variables. The formula involves eigenvalues of an integral operator associated with the function approached by the spatial matrices. Under the conditions imposed identification conditions for the maximum likelihood method and methods of moments fail. A remedial iterative procedure using the OLS estimator is proposed. Additional Information: This paper has been delivered at North American Summer Meeting of the Econometric Society in June 2006, see http://gemini.econ.umd.edu/conference/NASM2006/program/NASM2006.html. A revised and extended version (with computer simulations) has been accepted for publication as Mynbaev, K.T. and A. Ullah (2007) Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model. Journal of Multivariate Analysis, doi: 10.1016/j.jmva.2007.04.002.

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File URL: https://mpra.ub.uni-muenchen.de/3318/1/MPRA_paper_3318.pdf
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## Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3318.

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 Length: Date of creation: 16 Jan 2006 Date of revision: Handle: RePEc:pra:mprapa:3318 Contact details of provider: Postal: Ludwigstraße 33, D-80539 Munich, GermanyPhone: +49-(0)89-2180-2459Fax: +49-(0)89-2180-992459Web page: https://mpra.ub.uni-muenchen.deMore information through EDIRC

## References

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1. 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.
2. 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.
3. Harry H. Kelejian & Ingmar R. Prucha, 1995. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," Electronic Working Papers 95-001, University of Maryland, Department of Economics, revised Mar 1997.
4. 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.
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