GMM and 2SLS estimation of mixed regressive, spatial autoregressive models

The GMM method and the classical 2SLS method are considered for the estimation of mixed regressive, spatial autoregressive models. These methods have computational advantage over the conventional maximum likelihood method. The proposed GMM estimators are shown to be consistent and asymptotically normal. Within certain classes of GMM estimators, best ones are derived. The proposed GMM estimators improve upon the 2SLS estimators and are applicable even if all regressors are irrelevant. A best GMM estimator may have the same limiting distribution as the ML estimator (with normal disturbances).

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[3]  Harry H. Kelejian,et al.  A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model , 1999 .

[4]  L. Anselin,et al.  Fast maximum likelihood estimation of very large spatial autoregression models: a characteristic polynomial approach , 2001 .

[5]  Luc Anselin,et al.  Some robust approaches to testing and estimation in spatial econometrics , 1990 .

[6]  H. Kelejian,et al.  A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances , 1998 .

[7]  L. Hansen.  LARGE SAMPLE PROPERTIES OF GENERALIZED METHOD OF , 1982 .

[8]  Harry H. Kelejian,et al.  A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model , 1993 .

[9]  T. Amemiya.  The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator , 1975 .

[10]  Lena Lee,et al.  Generalized Method of Moments Estimation of Spatial Autoregressive Processes , 2003 .

[11]  Harry H. Kelejian,et al.  On the asymptotic distribution of the Moran I test statistic with applications , 2001 .

[12]  Lung-fei Lee,et al.  Best Spatial Two‐Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances , 2003 .

[13]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[14]  Lung-fei Lee,et al.  Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models , 2004 .

[15]  Kenneth C. Land,et al.  On the Large-Sample Estimation of Regression Models with Spatial- Or Network-Effects Terms: A Two-Stage Least Squares Approach , 1992 .

[16]  Takeshi Amemiya,et al.  The nonlinear two-stage least-squares estimator , 1974 .

[17]  K. Ord.  Estimation Methods for Models of Spatial Interaction , 1975 .

[18]  A. Ullah,et al.  Handbook of Applied Economic Statistics , 2000 .

[19]  Michio Hatanaka,et al.  An efficient two-step estimator for the dynamic adjustment model with autoregressive errors , 1974 .

[20]  A. Case.  Spatial Patterns in Household Demand , 1991 .