【文章內(nèi)容簡介】 ) 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。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。(transpose) ? Useful Algrbra and Matrix Operations exp ln log abs sqrt pi sin cos inv invpd(inverse) det(determinant) ? Example ? Least Squares: b=y/x GAUSS Programming Useful GAUSS Functions ? System Functions: use, load, output ? Data Generating Functions: ones, zeros, eye, seqa, seqm, rndu, rndn ? Data Conversion Functions: reshape, selif, delif, vec, vech, xpnd, submat, diag, diagrv ? Basic Matrix Functions: ? Matrix Description: rows, cols, maxc, minc, meanc, median, stdc ? Matrix Operations: sumc,cumsumc,prodc,cumprodc,sortc,sorthc,sortind ? Matrix Computation: det,inv,invpd,solpd,vcx,corrx,cond,rank,eig,eigh ? Probability and Statistical Functions: pdfn, cdfn, cdftc, cdffc, cdfchic, dstat, ols ? Calculus Functions: gradp, hessp, intsimp, linsolve, eqsolve, sqpsolve GAUSS Programming Controlling Execution Flow ? If Statement if。 then。 else。 elseif。 endif。 ? For Loop for i (start,stop,step)。 ... endfor。 ? Do Loop do while ... endo。 do until ... endo。 GAUSS Programming Write Your Own Functions ? Single Line Function fn fn_name(args) = code_for_function。 ? Procedure proc [[(nrets)=]] proc_name(arg_list)。 local list of local variables。 ... statements in the body of procedure。 retp(ret_list)。 endp。 GAUSS Programming Example 1 ? Do you know the accuracy of your puter39。s numerical calculation? This example addresses this important problem. Suppose e is a known small positive number, and the 5x4 matrix X is defined as follows: Verify that the eigenvalues of X39。X are 4+e2, e2, e2, and e2. How small of the value of e your puter will allow so that X39。X can be inverted? 11110000 0 00 0 0000eeee????????????????one=ones(1,4)。 e=。 do until e 。 x=one|(e.*eye(4))。 print e