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【正文】 KuanPin Lin Portland State University Spatial Panel Data Analysis ? The Model Representation ? Based on panel data models (pooled, fixed effects, random effects), we consider: ? Spatial Lag Model ? Spatial Error Model ? Spatial Error AR(1) ? Spatial Error MA(1) ? Spatial Error Components ? Spatial Mixed Model ? Tfirst representation is more convenient to incorporate parametric spatial panel data analysis Spatial Panel Data Models Pooled Fixed Effects Random Effects Spatial Lag Model Spatial error Model Spatial Mixed Model Spatial Panel Data Models ? Spatial Lag Model 1()( ) ( )()t t t t Ttt TTTNW WAw he re A W? ???? ? ? ? ? ? ?? ?????? ? ? ???? ? ? ? ? ???y y X βε y I y X βεε u v ε i u vy I X β i u vISpatial Panel Data Models ? Spatial Error Model: AR(1), KKP (2020) 1()( ) ( ) , ( )t t tt t t Tt t TT T NW WB w he re B W? ????? ??? ????? ? ? ??????? ? ? ? ???? ? ? ? ? ? ? ?yX βε yX βεε ε e ε I ε ee u v e i u vyX β I i u v ISpatial Panel Data Models ? Spatial Error Model: AR(1) Alternative Specification, Anselin (1988) 1()( ) , ( )t t tTttTt t tT T NWWB w he re B W?????? ??? ???? ? ?? ? ????? ? ? ??? ??? ? ? ? ? ? ? ?yX βε yX βεε i u eε u ee I e ve e vyX β i u I v ISpatial Panel Data Models ? Spatial Error Model: MA(1) ( ) ( )( ) ( ) , ( )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。39。,TI n o rm a l ii d E I V InW n NT????? ? ?ε W ε ε W εε εWI1()( ) , ( 39。 2 22( ) [ ( ) ] [ ( ) ]( ) ( )( ) ( 2 )tr a c e tr a c e tr a c eV I E In K n K????? ? ?M W M W M W M W??? ( 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。~ ( ( ) , ( ) )? ??39。 )tr a c eE I w h e r enK?? ? ??MW M I X X X X39。 ) 39。22239。 )?? ? ? ?,/TWL M ErrorT t rac e W W W WNT??????? ????????? ? ?ε I εε yX β ε εL
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