【正文】 t t tt t t t t N tttT T NWWC w here C W????? ??? ? ? ? ? ? ??????? ? ? ? ? ? ? ?yX βεε e e y X β I u ve u vyX β I i u v ISpatial Panel Data Models ? Spatial Error Components ()()t t t TNt t t TT N TW WW? ? ? ? ? ? ?? ?????? ? ? ???? ? ? ? ? ? ?yX β u e yX β i u ee ζξ eI ζξyX β i u I ζ ξSpatial Panel Data Models ? Spatial Seemingly Unrelated Regressions 1 , 2 , .. .,t t t t t tt t t t t tttWWWtT???? ? ?? ? ????y y X βεε ε e ee u vSpatial Panel Data Models ? Spatial Mixed Model: Anselin AR(1) 11()()( ) [ ( ) ]t t t tt t tTTTT T TWWWWAB??????? ? ? ? ???? ?? ? ? ? ? ??? ?? ? ??? ? ? ? ? ? ?y y X β uee e vy I y X β i u ee I e vy I X β i u I vSpatial Panel Data Models ? Spatial Mixed Model: KKP AR(1) 11()()( ) [ ( ) ( ) ]t t t tt t tTTTT T TWWWWAB??????? ? ? ??? ? ? ?? ? ? ??? ?? ? ? ? ??? ? ? ? ? ? ?y y X β εε ε uvy I y X β εε I ε i u vy I X β I i u vSpatial Model Specification Tests ? Based on panel data models (pooled, fixed effects, random effects), we consider: ? Moran Test ? LM Test and Robust LM Test ? Spatial Error Model ? Spatial Lag Model Spatial Model Specification Tests Pooled Fixed Effects Random Effects Moran’s I ? ? LMError ? ? ? LMLag ? ? ? Robust LMError ? ? Robust LMLag ? ? Moran’s I Test Statistic Pooled Model ? Moran’s I Index ? Can not distinguish between spatial lag or spatial error 2? ? ? ?39。???ε y X ββ X X X yMoran’s I Test Statistic Fixed Effects Model ? Moran’s I Index ? Can not distinguish between spatial lag or spatial error 2? ? ? ?39。22239。22239。[ ( ) ( ) ] /. ( 39。 )vTV a r W B B? ???ε X I2 2 1( | , )( ) ( 39。 ) 39。 , ( ) ( 39。 ) / ( 1 ) ( 39。 ) / ( 39。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.