Econometrics 2013, 1(1), 71-114; doi:10.3390/econometrics1010071
Article

Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments

1email and 2,* email
1 School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China 2 Department of Economics, The Ohio State University, Columbus, OH 43210, USA
* Author to whom correspondence should be addressed.
Received: 25 March 2013; in revised form: 25 April 2013 / Accepted: 25 April 2013 / Published: 27 May 2013
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Abstract: This paper studies the generalized spatial two stage least squares (GS2SLS) estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the case that the number of instruments K increases with, but at a rate slower than, the sample size, and derive the approximate mean square errors (MSE) that account for the trade-offs between the bias and variance, for both the GS2SLS estimator and a bias-corrected GS2SLS estimator. A criterion function for the optimal K selection can be based on the approximate MSEs. Monte Carlo experiments are provided to show the performance of our procedure of choosing K.
Keywords: spatial autoregressive; spatial error; 2SLS; endogenous regressor; instrumental variable selection

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MDPI and ACS Style

Jin, F.; Lee, L.-F. Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments. Econometrics 2013, 1, 71-114.

AMA Style

Jin F, Lee L-F. Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments. Econometrics. 2013; 1(1):71-114.

Chicago/Turabian Style

Jin, Fei; Lee, Lung-fei. 2013. "Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments." Econometrics 1, no. 1: 71-114.

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