【正文】 ??? ? ? ?ε W ε ε W εε εWI1()( ) , ( 39。 )tr a c eE I w h e r enK?? ? ??MW M I X X X X39。 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 W1? ?? ( 39。 ) 39。????ε yX ββ X X X yLMError Test Statistic Pooled Model ? LM Test Statistic for Spatial Error 239。22239。? ?()?~ ( 1 ). ( 39。 )?? ? ? ?,/TWL M ErrorT t rac e W W W WNT??????? ????????? ? ?ε I εε yX β ε εLMError Test Statistic Fixed Effects Model ? LM Test Statistic for Spatial Error 239。22239。? ?()?~ ( 1 )( 1 ) . ( 39。 )? ? ? ??, / ( 1 )TWL M Err orT t r ac e W W W WNT??????? ?????????? ? ? ?ε I εε yX β ε εLMError Test Statistic Random Effects Model ? LM Test Statistic for Spatial Error ? See Baltagi, B. H., S. H. Song, W. Koh (2020). 2222121441? ?39。 ( ) ( )( 1 ) ( 39。 )vvvRL M ErrorBR Q W J WB T t rac e W W W W????????????? ? ? ???????? ? ? ?????ε εLMLag Test Statistic Pooled Model ? LM Test Statistic for Spatial Lag 239。22239。39。2??~ ( 1 )?? ? ? ?, / ,? ? ?( ) ( ) / . ( 39。 )TL M L a gBW N TB y y T t ra c e WW W W???????????????? ? ? ? ???? ? ???ε WyWI ε ε ε yX βW M WLMLag Test Statistic Fixed Effects Model ? LM Test Statistic for Spatial Lag 239。22239。39。2??~ ( 1 )? ? ? ??, / ( 1 ) ,? ? ?( ) ( ) / ( 1 ) . ( 39。 )TL M L agBW N TB y y T t ra c e WW W W???????????????? ? ? ? ? ???? ? ? ???ε WyWI ε ε ε yX βW M WLMLag Test Statistic Random Effects Model ? LM Test Statistic for Spatial Lag ? See Baltagi, B., Liu, L. (2020). 22122111221? 39。[ ( ) ( ) ] /. ( 39。 )? ?39。[ ( 39。 ) ( 39。 ) ]?[ 39。 ]?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 Economic