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)?垐垐,/J Wy M Wy TnT t r ace WW W Wn??????????????yX β ε εLMBased Test Statistics ? Robust LM Test Statistic for Spatial Error ? Robust LM Test Statistic for Spatial Lag 239。 )tr a c e M WE I w h e r e MnK?? ? ?? I X X X X39。)EWV a r W E ?? ??? ? ? ?υXυ X υ υ ISpatial Error Components Model ? The Model W??ε ψ υ22( ) ( ) 0 , ( , )( 39。)EWVa r W 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) + ? OLS Parameter OLS . Robust b g bw gw a R2 Spatial Endogeneity Lagged Dependent Variable ? Spatial Lag Model W?? ? ?y y X βε11 , 2 , .. .,nij jj wyWin??????????y2( | , ) 0( | , ) ( 39。139。( 39。 ) 39。).*sin(y)+cos(y39。 call spwplot(spw(w1))。 n=49。 w4=denseSubmat(sparseOnes(spwpower(spw(w1),4),n,n),0,0)。 x=pi*xc/180。 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。111? ?39。 ) 39。( 39。( ) ]( , ) ( ) 0WWWVar W WC ov W W W?????? ? ???????? ? ? ?? ? ? ? ?? ? ?