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【導(dǎo)讀】SPLAG(1). 垐垐??垐垐'/,1?(')'??ZHHHHZ. (|)0,(,)0ECov??垐垐??垐?Var??'垐'nn. ijijijijk????HHhh. (|)0(,)'0ECov????εHεHHε。'''minarg(). 垐'(')''(')'()'(')'Var. '垐'nn. ijijijijk????HHhh. 2~(0,)Wnormaliid???????yZδεyXβεI. '1'JacobianMatrix. 1lnlnln(1)'iiW????'W?12,,...,:neigenvaluesofW???垐??'''垐'垐垐(),SpatialLagModel. +?W(CrimeRate)+?OLSvs.IVEstimator. SpatialLagModel. +?W(CrimeRate)+?SpatialLagModel. +?W(CrimeRate)+?GMMEstimator. SpatialLagModel. +?W(CrimeRate)+?QMLvs.GMMEstima
【正文】 ????????? ? ???????? ?1139。 39。 39。 39。垐 垐 垐 垐( ) ( ) ( ) ( ) ( ( ) ) ( ) ( ) ( )V a r G G G V a r m G G G? ? ? ? ? ? ? ???? ? ? ?? ? ? ? ?? ? ? ?Spatial Error AR(1) Model Generalized Method of Moments ? Minimum Distance (MD) Estimator ? Efficient GMM Estimator 1? m in a r g ( )( ) ( ) 39。[ ( ( ) ) ] ( )Qw h e r e Q m V a r m m??? ? ? ????? m in a r g ( )( ) ( ) 39。 ( )Qw h e r e Q m m??? ? ???? ?1139。 39。 39。垐 垐 垐 垐( ) ( ) ( ) ( ) ( ( ) ) ( ) ( ) ( )V a r G G G V a r m G G G? ? ? ? ? ? ? ???? ? ? ?? ? ? ? ?? ? 1139。垐垐( ) ( ) ( ( ) ) ( )V a r G V a r m G? ? ? ? ????? ??Spatial Error AR(1) Model Generalized Method of Moments ? Estimation of the variancecovariance matrix of moment functions 39。2 1139。m a x( ( ) )1( ) ( )?( ) ( 。 , , , )( / ) ( / )( 1 , 0)nnij i jiji i iij ij ij ijij ij ii ijVar m c an be c onsi st e ntl y e st i m ate d byk m mnw he re m m y Wk K d d or k K d dd k k k??????????? ? ? ? ???x β( ( ) ) ( ( ) ( ) 39。)Var m E m m? ? ??Model Estimation Spatial Error Model ? Spatial AR(1) Model ? Estimate b and ? simultaneously: QML ? Estimate b and ? iteratively: GMM/GLS ? OLS ? GMM ? GLS W?????yX βεε ε υCrime Equation Anselin (1988) [] ? Spatial Error AR(1) Model (Crime Rate) = a + b (Family Ine) + g (Housing Value) + ? ? = ? W? + u ? GMM vs. QML Estimator GMM Parameter GMM QML Parameter QML ? b g a Q References ? H. Kelejian and I. R. Prucha,1998. A Generalized Spatial Twostage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbance. Journal of Real Estate Finance and Economics, 17, 99121. ? ， 2020. Best Spatial Twostage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances. Econometrics Reviews, 22, 307335. ? . Lee, 2020. GMM and 2SLS Estimation of Mixed Regressive Spatial Autoregressive Models. Journal of Econometrics, 137, 489514.
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