【正文】 oints. How you extend the singleline version of time series conversion function to a multiline procedure so that it can handle the conversion of more than one time series? fn qtoa1(x) = meanc(reshape(x,rows(x)/4,4)39。 r=eigrs(x39。 GAUSS Programming Example 1 ? Do you know the accuracy of your puter39。 ? Do Loop do while ... endo。12 2 2 2( , , , , )1l n( 2 ) l n | | ( ) l n | | l n | |2 2 2( , )( ) , ( )( , , | , , ) ( ) ( ) ( )uvNT v u v uNNT T TLN T NI T A T Bw he re I JA I W B I WW I B I A I B? ? ? ??? ? ? ???????? ? ? ? ? ? ? ?? ? ? ? ?? ? ? ?? ? ? ? ? ?βeeee β y X y X βExample: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: QML (Spatial Lag) ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λW ln(GSP) + e , e = i?u + v Fixed Effects Random Effects b1 b2 * * b3 * * b4 * * b0 * λ * * Example: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: QML (Spatial Error) ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + e, e =ρW e + e , e = i?u + v Fixed Effects Random Effects b1 b2 * * b3 * * b4 * * b0 ρ * * Example: U. S. Productivity Baltagi (2020) [] ? Spatial Panel Data Model: QML (Spatial Mixed) ln(GSP) = b0 + b1 ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λW ln(GSP) + e , e =ρW e + e , e = i?u + v Fixed Effects Random Effects b1 b2 * * b3 * * b4 * * b0 * λ ρ * * References ? Elhorst, J. P. (2020). Specification and estimation of spatial panel data models, International Regional Science Review 26, 244268. ? Kapoor M., Kelejian, H. and I. R. Prucha, “Panel Data Models with Spatially Correlated Error Components,” Journal of Econometrics, 140, 2020: 97130. ? Lee, L. F., and J. Yu, “Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects,” Journal of Econometrics 154, 2020: 165185. Spatial Econometric Analysis Using GAUSS 2 KuanPin Lin Portland State Univerisity GAUSS Mathematical and Statistical System ? Windows Interface ? Windows ? Command, Error, Log, … ? Menu ? File, Edit, Run, …, Help ? Operation ? Interactive Mode ? Command (Input / Output) ? Batch Mode ? Writing Program ? Online Help GAUSS Basics ? Basic Operations on Matrices + ^ .* ./ % ! * / . .= .== .= . ./= = == = /= .not .and .or .xor not and or xor ~ | .*. *~ ? Special Operators [] {} : . 39。 ) / ( 39。 ) / ( 1 ) ( 39。 , ( ) ( 39。 ) 39。 )vTV a r W B B? ???ε X I2 2 1( | , )( ) ( 39。 , ( ) ( 39。 ) 39。 /? ?? ? ? ?( ) , ( )TF E F E i ittvuu T v T N u T v T Nv v TN T N??? ? ? ???? ? ?? ? ? ?? ? ?? ? ? ? ? ??δ Z Z Z y v y Z δv v v vΩ J I I Ω J I ISpatial Error Model Estimation ? The Model: SPAR(1) ? Fixed Effects ? Random Effects ()TTWi???? ? ?? ? ?yX βεε I ε ee u v2 2 2 2 211(,( ) ,v u vT T N T NV a r T? ? ? ? ?? ? ? ?? ? ? ? ?11e ) Q I J I Q J I2( ) ( ) v NTV a r V a r ???e v I11( ) ( ) ( ) ( ) 39。 ) /( 39。~ ( , ) ,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。 endif。 ... statements in the body of procedure。 do until e 。 print invx。 c = cols(x)。 endp。 load wd[n,n]=c:\course09\WISE\data\anselin\。 end。).*cos(y).*cos(abs(x39。( 39。 )ni i iiVare????????X X x xβ X X X X X X垐 1垐39。39。)EWVa r W E e????? ???εXIε X ε εReferences ? T. Conley, 1999 “GMM estimation with cross sectional dependence,” Journal of Econometrics 92, 1999, 1–45. ? H. Kelejian and . Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: 131154. ? W. Newey, and K. West, 1987, “A simple, positive semidefinite, heteroskedastic and autocorrelated consistent covariance matrix,” Econometrica, 55, 1987, 703–708. ? H. White, “Maximum Likelihood Estimation of Misspecified Models,” Econometrica, 50, 1982, 126. 。垐1 ( )1? ?? ( ) ( 39。1111? 垐39。 ) 39。 3963 miles or 6378 km = radius of the earth