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On the consistency of the LIML estimator of a spatial autoregressive model with many instruments

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  • Liu, Xiaodong

Abstract

This paper derives the LIML estimator for a spatial autoregressive model with endogenous regressors in the presence of many instruments. The LIML estimator is consistent when the number of instruments increases at a slower rate relative to the sample size. Due to spatial correlation, the LIML estimator in general is inconsistent when the number of instruments increases at the same rate as the sample size.

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File URL: http://www.sciencedirect.com/science/article/pii/S0165176512001863
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Bibliographic Info

Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 116 (2012)
Issue (Month): 3 ()
Pages: 472-475

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Handle: RePEc:eee:ecolet:v:116:y:2012:i:3:p:472-475

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Web page: http://www.elsevier.com/locate/ecolet

Related research

Keywords: Limited-information maximum likelihood; Spatial autoregressive models; Many instruments;

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  1. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
  2. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, 09.
  3. Manski, C.F., 1991. "Identification of Endogenous Social Effects: the Reflection Problem," Working papers 9127, Wisconsin Madison - Social Systems.
  4. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
  5. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, October.
  6. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
  7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  9. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  10. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
  11. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
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