【正文】 and Robust LM Test ? Spatial Error Model ? Spatial Lag Model Hypothesis Testing ? The Basic Model W o rW????????yX βεε ε υε υ υ2( | , ) 0( | , )EV a r ????υ X Wυ X W I010: 0 0: ( )H o rH n o t H????2~ ( 0 , )normal iid ??υIMoranBased Test Statistics ? Moran’s I Index ? Can not distinguish between spatial lag or spatial error 2垐垐39。222垐?~ ( 1 )WL M E rr or n In?? c??????? ? ?εεLMBased Test Statistics ? LM Test Statistic for Spatial Lag 239。22*2垐 ?垐~ ( 1 )WWL M L a gn J T???? c??????????ε y ε εHypothesis Testing Example ? China Output 2020 () ? ln(GDP) = a + b ln(L) + g ln(K) + ? (numbers in parentheses are pvalues of the tests) MoranI LMerr LMlag Robust LMerr Robust LMlag Hetero. ln(GDP) () () () ln(L) () () () ln(K) () () () ? () () () () () () Hypothesis Testing Example ? Crime Equation () ? (Crime Rate) = a + b (Family Ine) + g (Housing Value) + ? (numbers in parentheses are pvalues of the tests) MoranI LMerr LMlag Robust LMerr Robust LMlag Hetero. () () () () () () References ? L. Anselin, and A. K. Bera, R. . Florax, and M. Yoon (1996), “Simple Diagnostic Tests for Spatial Dependence,” Regional Science and Urban Economics, 26, 77104. ? L. Anselin, and H. Kelejian (1997), “Testing for Spatial Autocorrelation in the Presence of Endogenous Regressors,” International Regional Science Review, 20, 153–182. ? L. Anselin, and S. Rey (1991), “Properties of Tests for Spatial Dependence in Linear Regression Models,” Geographical Analysis, 23, 112131. ? H. Kelejian, and . Prucha (2020)., “On the Asymptotic Distribution of Moran I Test Statistic with Applications,” Journal Econometrics, 104, 219257.