【正文】 ? See Baltagi, B., Liu, L. (2020). 22122111221? 39。 ) ( 39。 ) ( ) ]vvvL M L a g Q W J W bb T t ra c e WW W WQ W W J W WQ W W J W??????????????? ? ? ? ???? ? ? ???? ? ? ?ε yyyA X X AA X yHypothesis Testing Example ? U. S. Productivity () ? ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + ? (numbers in parentheses are pvalues of the tests) MoranI LMerr LMlag ln(GSP) () () () ln(Public) () () () ln(Private) () () () Unemp () () () Hypothesis Testing Example ? U. S. Productivity () ? Pooled Model ? Fixed Effects Model MoranI LMerr LMlag Robust LMerr Robust LMlag Hetero. () () () () () () MoranI LMerr LMlag Robust LMerr Robust LMlag Hetero. () () () () () () References ? Anselin L., J. Le Gallo, and H. Jayet. 2020. Spatial Panel Econometrics. In The Econometrics of Panel Data, Fundamentals and Recent Developments in Theory and Practice (3rd Edition), eds. L. Matyas and P. Sevestre, 627662. SpringerVerlag. ? Baltagi, B. H., S. H. Song, W. Koh, “Test Panel Data Regression Models with Spatial Error Correlation,” Journal of Econometrics 117, 2020: 123150. ? Baltagi, B. H., S. H. Song, B. C. Jung, W. Koh, “Test for Serial Correlation, Spatial Autocorrelation and Random Effects Using Panel Data,” Journal of Econometrics 140, 2020: 551. ? Baltagi, B., Liu, L. (2020) Testing for Random Effects and Spatial Lag Dependence in Panel Data Models. Statistics and Probability Letters, 78, 33043306. ? Lee, L. F., and J. Yu, “Some Recent Developments in Spatial Panel Data Models,” Regional Science and Urban Economics, Spatial Econometric Analysis Using GAUSS 10 KuanPin Lin Portland State University Spatial Panel Data Models ? The General Model 11()()( ) [ ( ) ( ) ]( ) , ( )TTTT T TNNWWABw he re A W B W??????? ? ? ?? ? ? ? ?? ? ? ? ? ? ?? ? ? ?y I y X βεε I ε i u vy I X β I i u vIISpatial Panel Data Models ? Assumptions ? Fixed Effects ? Random Effects ? Spatial Error Model: A=I or ?=0 ? Spatial Lag Model: B=I or ?=0 ? Panel Data Model: A=B=I 21( | , ) ( 39。T W????? ? ?Z I y XδβyZ δεSpatial Lag Model Estimation ? Fixed Effects 2 2( ) ( ) ()Tv N T vV a r V a r V a r? ?? ? ? ? ?? ????????? ?? ?? ?yZ δ i u v yZ δvε v I vQ,()T T Nw h e r e? ? ?y = Q y Z = Q Z v = Q vQ I J ISpatial Lag Model Estimation Fixed Effects: IV or 2SLS ? Instrumental Variables ? TwoStage Least Squares 1 2 12? ? ?? ? ?( 39。 / ( 1 ) ,vvVarNT??????? ? ? ?δ Z Z Z y δ ZZv v v y Z δ1? ( 39。? ?( ) ( 39。 ) 39。 , , /? ? ? ?? ?39。 ) / ( 1 )( 39。 ) / ( 1 )( 39。 ) /( 39。 39。* *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。~ ( , ) ,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。 ) /( 39。 ) /( 39。 ) /( 39。 /? ?? ? ? ?( ) , ( )TF E F E i ittvuu T v T N u T v T Nv v T