【正文】 )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。139。? ?? ( ) ( 39。( 39。????yX βεβ X X X y( | ) 0( | )EV a r???εXεXSpatial HAC Estimator General Heteroscedasticity ? HuberWhite Estimator 239。 ) 39。 endp。).*sin(y)+cos(y39。 local x,y,d。 call spwplot(spw(w1))。 w3=denseSubmat(sparseOnes(spwpower(spw(w1),3),n,n),0,0)。 n=49。 initialize global variables ? /* ? ** Set input control variables for model estimation ? ** (. _names for variable names, see Appendix A) ? */ ? call estimate(y,x)。 retp(y)。 do until i c。 r = rows(x)。 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 points. How you extend the singleline version of time series conversion function to a multiline procedure so that it can handle the conversion of more than one time series? fn qtoa1(x) = meanc(reshape(x,rows(x)/4,4)39。x)。 r=eigrs(x39。 e=。 GAUSS Programming Example 1 ? Do you know the accuracy of your puter39。 local list of local variables。 ? Do Loop do while ... endo。 elseif。12 2 2 2( , , , , )1l n( 2 ) l n | | ( ) l n | | l n | |2 2 2( , )( ) , ( )( , , | , , ) ( ) ( ) ( )uvNT v u v uNNT T TLN T NI T A T Bw he re I JA I W B I WW I B I A I B? ? ? ??? ? ? ???????? ? ? ? ? ? ? ?? ? ? ? ?? ? ? ?? ? ? ? ? ?βeeee β y X y X βExample: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: QML (Spatial Lag) ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λW ln(GSP) + e , e = i?u + v Fixed Effects Random Effects b1 b2 * * b3 * * b4 * * b0 * λ * * Example: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: QML (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: QML (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 * * References ? Elhorst, J. P. (2020). Specification and estimation of spatial panel data models, International Regional Science Review 26, 244268. ? Kapoor M., Kelejian, H. and I. R. Prucha, “Panel Data Models with Spatially Correlated Error Components,” Journal of Econometrics, 140, 2020: 97130. ? Lee, L. F., and J. Yu, “Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects,” Journal of Econometrics 154, 2020: 165185. Spatial Econometric Analysis Using GAUSS 2 KuanPin Lin Portland State Univerisity GAUSS Mathematical and Statistical System ? Windows Interface ? Windows ? Command, Error, Log, … ? Menu ? File, Edit, Run, …, Help ? Operation ? Interactive Mode ? Command (Input / Output) ? Batch Mode ? Writing Program ? Online Help GAUSS Basics ? Basic Operations on Matrices + ^ .* ./ % ! * / . .= .== .= . ./= = == = /= .not .and .or .xor not and or xor ~ | .*. *~ ? Special Operators [] {} : . 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 ? T