【正文】 9。 ) 39。TTNV a r B V a r Bw h e r e B W???? ? ???ε I e IISpatial Error Model Estimation Fixed Effects ? Moment Functions 22( 39。 ) / ( 1 ) 0vvE N TE N T trac e W W NE N T????????vvvvvv****, ( )[ ( ) ] , [ ( ) ]TT N T Nw h e r e WWW??? ? ?? ? ? ? ? ?v y X β v I vy I I y X I I XSpatial Error Model Estimation Fixed Effects ? The Model: SPAR(1) ? Estimate b and ? iteratively: GMM/GLS ? OLS ? GMM ? GLS **()T W????? ? ??? ? ? ?yX βε yX βvε I ε v**?? ? ?( ) ( ) ( )?? ?( ) ( )T W????? ? ??? ? ? ???? ? ??yX β ε βε β I ε β vyX β v βSpatial Error Model Estimation Random Effects ? Moment Functions (Kapoor, Kelejian and Prucha, 2020) 22( 39。 ) / ( 1 ) 0vvE N TE N T trac e W W NE N T????????e Qee Q ee Qe2112111( 39。 ) / 0 , ( )TENE N trac e W W NE N whe re W????? ? ?e Q ee Q ee Q e e I eSpatial Error Model Estimation Random Effects ? The Model: SPAR(1) ? Estimate b and ? iteratively: GMM/GLS ? OLS ? GMM ? GLS **()TTTW??? ?? ???? ? ? ???? ? ???? ? ? ?yX βεyX βeε I ε ee i u ve i u v**?? ? ?( ) ( ) ( )?? ?( ) ( )T W????? ? ??? ? ? ???? ? ? ?yX β ε βε β I ε β eyX β e β**[ ( ) ] , [ ( ) ]T N T Nwhe re W W??? ? ? ? ? ?y I I y X I I XSpatial Mixed Model Estimation ? The Model: SARAR(1,1) ? ? ? ?1()()( ) ( )( ) , 39。l n | | l n | |2( ) , ( )( , , | , , ) ( ) ( ) ( )vvvNNT T TN T N TLT A T Bw here A I W B I WW I B I A I B? ? ? ? ??????? ? ?? ? ?? ? ? ?? ? ? ? ? ?βeeee β y X y X βMaximum Likelihood Estimation Fixed Effects ? LogLikelihood Function (Lee and Yu, 2020) ? Where z* is the transformation of z using the orthogonal eigenvector matrix of Q. 2239。 then。 ? For Loop for i (start,stop,step)。 GAUSS Programming Write Your Own Functions ? Single Line Function fn fn_name(args) = code_for_function。 retp(ret_list)。X are 4+e2, e2, e2, and e2. How small of the value of e your puter will allow so that X39。 x=one|(e.*eye(4))。 print r39。 e=e/10。 proc qtoa(x)。 y = qtoa1(x[.,1])。 i = i+1。 GPE2 for GAUSS ? GPE2 is a package of econometric procedures written in GAUSS. There are four main functions, driven by a set of global control variables: ? Reset Set up global control (input and output) variables. ? Estimate Estimation of a linear or generalized linear model. ? Forecast Forecasting based on a linear or generalized linear model. ? Optimize Estimation of a nonlinear model. ? Gpehelp Online help of using GPE2. GPE2 for GAUSS Selected Global Control Variables ? Input Control Variables _names, _begin, _end, _rstat, _rtest, _rplot, _rlist,_const, _restr, _vcov, _hacv, _weight, _ivar, _dlags, _pdl, _eq, _id, _ar, _ma, _arma, _garch, _acf, _acf2, _nlopt, _method, _iter, _tol, _step, _conv, _fbrgin, _fend, _fstat, _fplot, _splag, _spw, _spwd ? Output Control Variables __y, __x, __e, __b, __vb, __v, __rss, __r2, __f, __vf, __t, __a, __va GPE2 for GAUSS A Typical Program Using GPE2 ? /* ? ** Comments on program title, purposes, and the usage of the program ? */ ? use gpe2。 do model prediction ? end。 w1=wd。 w5=denseSubmat(sparseOnes(spwpower(spw(w1),5),n,n),0,0)。 include gpe\。 convert to radian y=pi*yc/180。x)))。 ( 39。 )ij i jk Ei j nV a ree????? ? ? ? ? ? ????????XX εεβ X X X X X X1? ( 39。? ?? ( ) ( 39。, 1 , 2 , . . . , 0ij i jijk i jki j n i jee ?? ? ?? ? ? ? ??????? ? ?XXSpatial HAC Estimator General Heteroscedasticity and Autocorrelation ? First Law of Geography ? Kelejian and Prucha (2020) 39。( 39。1111? ?39。 )ni i iiLni i i i i iiLVareee?? ? ?? ? ???????? ? ???????????X X x xx x x xβ X X X X X XCrime Equation Anselin (1988) [] ? Basic Model (Crime Rate) = a + b (Family Ine) + g (Housing Value) + e ? Spatial HAC Estimator OLS Parameter OLS . Robust Robust b g a R2 GDP Output Production China 2020 [] ? CobbDouglass Production Function ln(GDP) = a + b ln(L) + g ln(K) + e ? Spatial HAC Estimator OLS Parameter OLS . Robust Robust b g a R2 Spatial Exogeneity Lagged Explanatory Variables ? Spatial Exogenous Model