【正文】 )ni i iiLni i i i i iiLVareee?? ? ?? ? ???????? ? ???????????X X x xx x x xβ X X X X X XCrime Equation Anselin (1988) [] ? Basic Model (Crime Rate) = a + b (Family Ine) + g (Housing Value) + e ? Spatial HAC Estimator OLS Parameter OLS . Robust Robust b g a R2 GDP Output Production China 2020 [] ? CobbDouglass Production Function ln(GDP) = a + b ln(L) + g ln(K) + e ? Spatial HAC Estimator OLS Parameter OLS . Robust Robust b g a R2 Spatial Exogeneity Lagged Explanatory Variables ? Spatial Exogenous Model 39。( 39。? ?? ( ) ( 39。 ( 39。 convert to radian y=pi*yc/180。 w5=denseSubmat(sparseOnes(spwpower(spw(w1),5),n,n),0,0)。 do model prediction ? end。 i = i+1。 proc qtoa(x)。 print r39。X are 4+e2, e2, e2, and e2. How small of the value of e your puter will allow so that X39。 GAUSS Programming Write Your Own Functions ? Single Line Function fn fn_name(args) = code_for_function。 then。 ) / 0 , ( )TENE N trac e W W NE N whe re W????? ? ?e Q ee Q ee Q e e I eSpatial Error Model Estimation Random Effects ? The Model: SPAR(1) ? Estimate b and ? iteratively: GMM/GLS ? OLS ? GMM ? GLS **()TTTW??? ?? ???? ? ? ???? ? ???? ? ? ?yX βεyX βeε I ε ee i u ve i u v**?? ? ?( ) ( ) ( )?? ?( ) ( )T W????? ? ??? ? ? ???? ? ? ?yX β ε βε β I ε β eyX β e β**[ ( ) ] , [ ( ) ]T N T Nwhe re W W??? ? ? ? ? ?y I I y X I I XSpatial Mixed Model Estimation ? The Model: SARAR(1,1) ? ? ? ?1()()( ) ( )( ) , 39。 ) / ( 1 ) 0vvE N TE N T trac e W W NE N T????????vvvvvv****, ( )[ ( ) ] , [ ( ) ]TT N T Nw h e r e WWW??? ? ?? ? ? ? ? ?v y X β v I vy I I y X I I XSpatial Error Model Estimation Fixed Effects ? The Model: SPAR(1) ? Estimate b and ? iteratively: GMM/GLS ? OLS ? GMM ? GLS **()T W????? ? ??? ? ? ?yX βε yX βvε I ε v**?? ? ?( ) ( ) ( )?? ?( ) ( )T W????? ? ??? ? ? ???? ? ??yX β ε βε β I ε β vyX β v βSpatial Error Model Estimation Random Effects ? Moment Functions (Kapoor, Kelejian and Prucha, 2020) 22( 39。 ) 39。 ) 39。39。T W????? ? ?Z I y XδβyZ δεSpatial Lag Model Estimation ? Fixed Effects 2 2( ) ( ) ()Tv N T vV a r V a r V a r? ?? ? ? ? ?? ????????? ?? ?? ?yZ δ i u v yZ δvε v I vQ,()T T Nw h e r e? ? ?y = Q y Z = Q Z v = Q vQ I J ISpatial Lag Model Estimation Fixed Effects: IV or 2SLS ? Instrumental Variables ? TwoStage Least Squares 1 2 12? ? ?? ? ?( 39。? ?( ) ( 39。 , , /? ? ? ?? ?39。 ) / ( 1 )( 39。 39。 else。 ? Procedure proc [[(nrets)=]] proc_name(arg_list)。X can be inverted? 11110000 0 00 0 0000eeee????????????????one=ones(1,4)。 invx=invpd(x39。 local r,c,y,i。 endo。 important: don’t fet this GPE2 for GAUSS Examples ? More than 70 examples covering linear and nonlinear least squares, instrumental variables, system of simultaneous linear equations, time series analysis, panel data, limited dependent variables, maximum likelihood, generalized methods of moments, and … ? The latest extensions include spatial lag model estimation, hypothesis testing, and robust inference. ? Updates for spatial econometric analysis (, ). Software Demonstration ? Installation ? GAUSS Light ? GPE2 for GAUSS ? Example: China GDP Output ? CobbDouglas Production Function ln(GDP) = a + b ln(L) + g ln(K) + e ? Generalized CobbDouglas Production Function ln(GDP) + q GDP = a + b ln(L) + g ln(K) + e China GDP Output Production Using GPE2 for GAUSS: A Review ? CobbDouglas Production Function () ? OLS Estimator ? Hypothesis Testing ? Constant Returns to Scale? ? Homoscedasticity? ? Generalized Production Function (Zellner and Revanka, 1970) () ? Output Effects? ? Instrumental Variables References ? . Lin, Computational Econometrics: GAUSS Programming for Econometricians and Financial Analysts, ETEXT Publishing, Los Angeles, 2020. ? . Chung, Learning Econometrics with GAUSS, Institute of Economics, Academia Sinica, 2020. ? A. Zellner and N. Revankar, Generalized Production Functions, Review of Economic Studies, 1970, 241250. Spatial Econometric Analysis Using GAUSS 3 KuanPin Lin Portland State University Spa