【正文】 Estimation ? Generalized Least Squares (IV/GLS) ? Generalized Method of Moments (GMM/GLS) ? Maximum Likelihood Estimation Spatial Lag Model Estimation ? The Model: SPLAG(1) ? OLS is biased and inconsistent. ()( ( ) , ) 0TTTWCov W?? ? ? ?? ? ???y I y X βεε i u vIy ε? ?? ?()39。 ) 39。 )V a r? ? ?????δ Z Ω ZZ Ω yδ Z Ω Z1? ( 39。 / ( 1 ) , 39。 ) / ( 1 ) ( 39。TTTTTTNWWiBwhe re Wan d B W?????? ? ? ?? ? ? ? ?? ? ? ? ? ?? ? ???y I y X βεε I ε u vyZ δ I i u vZ I y X δβISpatial Mixed Model Estimation ? TwoStage Estimation ? Sample moment functions are the same as in the spatial error AR(1) model. The efficient GMM estimator follows exactly the same as the spatial error AR(1) model. ? The transformed model which removes spatial error AR(1) correlation is estimated the same way as the spatial lag model using IV and GLS. Spatial Mixed Model Estimation Fixed Effects ? The Model: SPARAR(1,1) * * *()()()()()TTTTTTWWWWW?????? ? ? ? ?? ? ? ? ??? ? ? ???? ? ???? ? ? ?? ? ? ? ?y I y X βεy I y X βεε I ε eε I ε ve i u vy I y X βv**, . . . , ( )[ ( ) ] , [ ( ) ]TNT N T Nw h e r eWW??? ? ? ?? ? ? ? ? ?y Q y Q I J Iy I I y X I I XSpatial Mixed Model Estimation Fixed Effects ? Estimate b and ? iteratively: GMM/GLS ? IV/2SLS ? GMM ? GLS * * *? ?( ) ,? ? ? ? ?( , ) ( ) ( , )? ?? ? ?( ) ( ) ( ) ( ) ,TTTWWW??? ? ? ?? ? ? ? ?? ? ? ? ??? ? ? ???? ? ? ? ??y I y X β ε βε β I ε β vy I y X β v β**( ) [ ( ) ] , ( ) [ ( ) ]T N T Nwhe re W W? ? ? ?? ? ? ? ? ?y I I y X I I XSpatial Mixed Model Estimation Random Effects ? The Model: SPARAR(1,1) * * *()()()TTTTTWWW???? ? ? ?? ? ?? ? ?? ? ? ? ?? ?? ? ??y I y X βεε I ε ee i u vy I y X βee i u v**[ ( ) ] , [ ( ) ]T N T Nwhe re W W??? ? ? ? ? ?y I I y X I I XSpatial Mixed Model Estimation Random Effects ? Estimate b,? and ? iteratively: GMM/GLS ? IV/2SLS ? GMM ? GLS 22* * *22? ?( ) ,? ? ? ? ? ? ?( , ) ( ) ( , ) , ,? ?? ? ?( ) ( ) ( ) ( ) ,? ? ?( , )TT v uTvuWWWw i t h??? ? ? ? ? ?? ? ? ? ???? ? ? ? ??? ? ? ??? ? ? ? ? ???? ? ??y I y X β ε βε β I ε β ey I y X β e β**( ) [ ( ) ] , ( ) [ ( ) ]T N T Nwhe re W W? ? ? ?? ? ? ? ? ?y I I y X I I XExample: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: GMM/GLS (Spatial Error) ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + e, e =ρW e + e, e = i?u + v Fixed Effects Random Effects b1 b2 * * b3 * * b4 * * b0 * ρ * * Example: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: GMM/GLS (Spatial Mixed) ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λW ln(GSP) + e , e =ρW e + e , e = i?u + v Fixed Effects Random Effects b1 b2 * * b3 * * b4 * * b0 * λ * * ρ * * Maximum Likelihood Estimation ? Error Components ? Assumptions ? Fixed Effects: ? Random Effects: 2~ ( , )v N TN ?v 0 I2 2 39。 elseif。 local list of local variables。 e=。x)。 r = rows(x)。 retp(y)。 n=49。 call spwplot(spw(w1))。).*sin(y)+cos(y39。 ) 39。( 39。139。)EWVa r W E e????? ???εXIε X ε ε GDP Output Production China 2020 [] ? CobbDouglass Production Function ln(GDP) = a + b ln(L) + g ln(K) + bw W ln(L) + gw W ln(K) + e OLS Parameter OLS . Robust b g bw gw a R2 Spatial Endogeneity Lagged Dependent Variable ? Spatial Lag Model W?? ? ?y y X βε11 , 2 , .. .,ni j jj wyWin??????????y2( | , ) 0( | , ) ( 39。 ) 39。? ?? ( ) ( 39。????yX βεβ X X X y( | ) 0( | )EV a r???εXεXSpatial HAC Estimator General Heteroscedasticity ? HuberWhite Estimator 239。 endp。 local x,y,d。 w3=denseSubmat(sparseOnes(spwpower(spw(w1),3),n,n),0,0)。 initialize global variables ? /* ? ** Set input control variables for model estimation ? ** (. _names for variable names, see Appendix A) ? */ ? call estimate(y,x)。 do until i c。 GAUSS Programming Example 2 ? Write a singleline GAUSS function to convert a quarterly time series into the annual series by taking the average of every four data p