【導(dǎo)讀】SpatialLagModel. SpatialErrorModel. SpatialErrorAR(1). SpatialErrorMA(1). SpatialMixedModel. SpatialLagModel. 1,2,...,MoranTest. SpatialErrorModel. SpatialLagModel. Moran’sI??LM-Error???LM-Lag???Moran’sIIndex. '''(')'Moran’sIIndex. ''~((),())??'

　　

【正文】 ( ) ]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) + ?, ? =ρW ? + 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) + ? , ? =ρW ? + 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。~ ( , ) ,TNu T v T T T TN??? ? ? ? ? ?? ? ? ?e i u v 0 Ω Ω IJ I J i i22~ ( , ) , ~ ( , ) ,v N T u NN N t?? ?v 0 I u 0 IT??e i u + vMaximum Likelihood Estimation Fixed Effects ? LogLikelihood Function 222( , , , ) l n( 2 ) l n( )2239。l n | | l n | |2( ) , ( )( , , | , , ) ( ) ( ) ( )vvvNNT T TN T N TLT A T Bw here A I W B I WW I B I A I B? ? ? ? ??????? ? ?? ? ?? ? ? ?? ? ? ? ? ?βeeee β y X y X βMaximum Likelihood Estimation Fixed Effects ? LogLikelihood Function (Lee and Yu, 2020) ? Where z* is the transformation of z using the orthogonal eigenvector matrix of Q. 2239。* *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。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) + ? , ? = 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) + ?, ? =ρW ? + 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) + ? , ? =ρW ? + 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.