【正文】 ? DistanceBased Spatial Weights Matrix ? Using Kernel Weight Function proc gcd(xc,yc)。 w6=denseSubmat(sparseOnes(spwpower(spw(w1),6),n,n),0,0)。 w2=denseSubmat(sparseOnes(spwpower(spw(w1),2),n,n),0,0)。 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 Spatial Weights Matrix ? Anselin (1988) [] ? China 30 Provinces [, ] ? Ertur and Kosh (2020) [] ? Homework ? . 48 Lower States [] ? . 3109 Counties [] [] Spatial Contiguity Weights Matrix Anselin (1988): W1, W2, W3 use gpe2。 using GPE package (version 2) ? // this must be the first executable statement ? /* ? ** Writing output to file or sending it to printer: ? ** specify file name for output ? */ ? // Loading data: read data series from data files. ? /* ? ** Generating or transforming data series: ? ** create and generate variables with data scaling or transformation ? ** (. y and x are generated here and will be used below) ? */ ? call reset。 endo。 i = 2。 local r,c,y,i。 endo。 invx=invpd(x39。 print e = e。X can be inverted? 11110000 0 00 0 0000eeee????????????????one=ones(1,4)。 endp。 ? Procedure proc [[(nrets)=]] proc_name(arg_list)。 ... endfor。 else。* *2* * * *( 1 ) ( 1 )( , , , ) l n( 2 ) l n( )22( 1 ) l n | | ( 1 ) l n | |2( ) , ( )( , , | , , ) ( ) ( ) ( )vvvNNT T TN T N TLT A T Bw he re A I W B I WW I B I A I B? ? ? ? ????????? ? ?? ? ? ? ?? ? ? ?? ? ? ? ? ?βeeee β y X y X βMaximum Likelihood Estimation Random Effects ? LogLikelihood Function 2239。 39。 ) /( 39。 ) / ( 1 )( 39。 ) / ( 1 )( 39。 , , /? ? ? ?? ?39。 ) 39。? ?( ) ( 39。 / ( 1 ) ,vvVarNT??????? ? ? ?δ Z Z Z y δ ZZv v v y Z δ1? ( 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。Spatial Econometric Analysis Using GAUSS 10 KuanPin Lin Portland State University Spatial Panel Data Models ? The General Model 11()()( ) [ ( ) ( ) ]( ) , ( )TTTT T TNNWWABw he re A W B W??????? ? ? ?? ? ? ? ?? ? ? ? ? ? ?? ? ? ?y I y X βεε I ε i u vy I X β I i u vIISpatial Panel Data Models ? Assumptions ? Fixed Effects ? Random Effects ? Spatial Error Model: A=I or ?=0 ? Spatial Lag Model: B=I or ?=0 ? Panel Data Model: A=B=I 21( | , ) ( 39。39。 )? ? ? ?? 39。 ) 39。??Z H H H H Z2( | ) 0 , ( , ) 0, TE C o vw h e r e W????? ? ???ε H Z HH X W X W X W ISpatial Lag Model Estimation Random Effects: IV/GLS ? Feasible Generalized Least Squares ? Estimate ?v2 and ?u2 from the fixed effects model: ? FGLS for random effects model: 1 1 1 1 1? ? ? ? ?? ? ?( 3