My bibliography  Save this paper

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

## Author

Listed:
• Mynbaev, Kairat
• Ullah, Aman

## 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.

## Suggested Citation

• 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.
• Handle: RePEc:pra:mprapa:3318
as

File URL: https://mpra.ub.uni-muenchen.de/3318/1/MPRA_paper_3318.pdf
File Function: original version

## References listed on IDEAS

as
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. 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. 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. 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.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as

Cited by:

1. Mynbaev, Kairat, 2006. "Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model," MPRA Paper 4411, University Library of Munich, Germany.

### Keywords

spatial model; OLS estimator; asymptotic distribution; maximum likelihood; method of moments;

### JEL classification:

• C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:3318. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.