【導(dǎo)讀】TheGeneralModel. Assumptions. FixedEffects. RandomEffects. =0. SpatialLagModel:B=Ior?=0. PanelDataModel:A=B=I. 21(|,)(')vTVarWBB????εXI. BB??????(|,)0EW?εX. PanelDataModel. ln(GSP)=b0+b1ln(Public)+b2ln(Private)+b3ln(Labor)+b4(Unemp)+e. e?i?u+v. SpatialLagModel. ln(GSP)=b0+b1ln(Public)+b2ln(Private)+b3ln(Labor)+b4(Unemp). e?i?u+v. SpatialErrorModel. ln(GSP)=b0+b1ln(Public)+b2ln(Private)+b3ln(Labor)+b4(Unemp)+e. e??We?e,e?i?u+v. SpatialMixedModel. ln(GSP)=b0+b1ln(Public)+b2ln(Private)+b3ln(Labor)+b4(Unemp)+. e??We?e,e?i?u+v. SpatialErrorModel. SpatialLagModel. SpatialMixedModel. ModelEstimation. TheModel:SPLAG(1). ''FixedEffects. vNTvVarVarVar??'/(1),1?(')'??ZHHHHZ. RandomEffects. uTvTNVar??11,(')'()(')Var. 1?(')'??ZHHHHZ. Estimate?v2and?11111????????(')',()(')Var???????δZΩZZΩyδZΩZ. '/(1),'/. NTN??δZZZyvyZδ。TheModel:SPAR(1). FixedEffects. RandomEffects. 11(,VarT?????????

　　

【正文】 。 w1=wd。 w2=denseSubmat(sparseOnes(spwpower(spw(w1),2),n,n),0,0)。 w3=denseSubmat(sparseOnes(spwpower(spw(w1),3),n,n),0,0)。 w4=denseSubmat(sparseOnes(spwpower(spw(w1),4),n,n),0,0)。 w5=denseSubmat(sparseOnes(spwpower(spw(w1),5),n,n),0,0)。 w6=denseSubmat(sparseOnes(spwpower(spw(w1),6),n,n),0,0)。 call spwplot(spw(w1))。 end。 include gpe\。 Spatial Contiguity Weights Matrix China, 30 Provinces and Cities: W1, W2, W3 DistanceBased Spatial Weights Ertur and Kosh (2020) ? Geographical Location (x,y) ? Longitude (x) ? Latitude (y) ? Great Circle Distance ? d=gcd(x,y) ? (x,y) is in degree decimal units ? DistanceBased Spatial Weights Matrix ? Using Kernel Weight Function proc gcd(xc,yc)。 local x,y,d。 x=pi*xc/180。 @ convert to radian @ y=pi*yc/180。 d=3963*arccos(sin(y39。).*sin(y)+cos(y39。).*cos(y).*cos(abs(x39。x)))。 @ 3963 miles or 6378 km = radius of the earth @ retp(real(d))。 endp。 DistanceBased Spatial Weights Ertur and Kosh (2020) ? Kernel Weight Function ? Parzen Kernel ? Bartlett Kernel (Tricubic Kernel) ? TurkeyHanning Kernel ? Guassian or Exponeial Kernel 00: [ 1 , 1 ]( ) 0 | || | ( ) 0 | |KRE it he r K z if z z for som e zO r z K z as z????? ? ?( ) 1 , ( ) 0 , | ( ) |()K z dz z K z dz K z dzz K z dz k w he r e k i s a c ons t ant? ? ? ??? ? ??Kernel Weights Spatial Matrix An Example ? Negative Exponential Distance ? Negative Gaussian Distance ? ?( / ) e x p 2 /ij ij ijk K d d d d? ? ?? ?2m a x m a x( / ) e x p ( / )ij ij ijk K d d d d? ? ?1iiijijkw W Kk i j??? ? ? ????IGaussian Distance Weights Matrix Ertur and Kosh (2020) Spatial HAC Estimator ? The Classical Model 11垐垐39。 ( 39。), 1 , 2 , .. .,? ?? ( ) ( 39。 ) 39。( 39。 )ij i jk Ei j nV a ree????? ? ? ? ? ? ????????XX εεβ X X X X X X1? ( 39。 ) 39。????yX βεβ X X X y( | ) 0( | )EV a r???εXεXSpatial HAC Estimator General Heteroscedasticity ? HuberWhite Estimator 239。111? ?39。? ?? ( ) ( 39。 ) 39。( 39。 )ni i iiVare????????X X x xβ X X X X X X垐 1垐39。, 1 , 2 , . . . , 0ij i jijk i jki j n i jee ?? ? ?? ? ? ? ??????? ? ?XXSpatial HAC Estimator General Heteroscedasticity and Autocorrelation ? First Law of Geography ? Kelejian and Prucha (2020) 39。1111? 垐39。? ?? ( ) ( 39。 ) 39。( 39。 )nni j i j i jij kVaree??????????X X x xβ X X X X X Xm a x( / ) ( / )ij ij ij ijk K d d or k K d d??ij ijdk? ? ?Time Series HAC Estimator General Heteroscedasticity and Autocorrelation ? NeweyWest Estimator 239。139。39。1111? ?39。垐1 ( )1? ?? ( ) ( 39。 ) 39。( 39。 )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。11 , 2 , .. .,ni j jj wWin?????????? xXW? ? ?yX β X γ ε2( | , ) 0( | , ) ( 39。)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。)EWVa r W E e????? ???εXIε X ε εReferences ? T. Conley, 1999 “GMM estimation with cross sectional dependence,” Journal of Econometrics 92, 1999, 1–45. ? H. Kelejian and . Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: 131154. ? W. Newey, and K. West, 1987, “A simple, positive semidefinite, heteroskedastic and autocorrelated consistent covariance matrix,” Econometrica, 55, 1987, 703–708. ? H. White, “Maximum Likelihood Estimation of Misspecified Models,” Econometrica, 50, 1982, 126.