【正文】 )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. 。11 , 2 , .. .,ni j jj wWin?????????? xXW? ? ?yX β X γ ε2( | , ) 0( | , ) ( 39。( 39。垐1 ( )1? ?? ( ) ( 39。39。 )nni j i j i jij kVaree??????????X X x xβ X X X X X Xm a x( / ) ( / )ij ij ij ijk K d d or k K d d??ij ijdk? ? ?Time Series HAC Estimator General Heteroscedasticity and Autocorrelation ? NeweyWest Estimator 239。 ) 39。1111? 垐39。 )ni i iiVare????????X X x xβ X X X X X X垐 1垐39。 ) 39。111? ?39。 ) 39。( 39。), 1 , 2 , .. .,? ?? ( ) ( 39。 DistanceBased Spatial Weights Ertur and Kosh (2020) ? Kernel Weight Function ? Parzen Kernel ? Bartlett Kernel (Tricubic Kernel) ? TurkeyHanning Kernel ? Guassian or Exponeial Kernel 00: [ 1 , 1 ]( ) 0 | || | ( ) 0 | |KRE it he r K z if z z for som e zO r z K z as z????? ? ?( ) 1 , ( ) 0 , | ( ) |()K z dz z K z dz K z dzz K z dz k w he r e k i s a c ons t ant? ? ? ??? ? ??Kernel Weights Spatial Matrix An Example ? Negative Exponential Distance ? Negative Gaussian Distance ? ?( / ) e x p 2 /ij ij ijk K d d d d? ? ?? ?2m a x m a x( / ) e x p ( / )ij ij ijk K d d d d? ? ?1iiijijkw W Kk i j??? ? ? ????IGaussian Distance Weights Matrix Ertur and Kosh (2020) Spatial HAC Estimator ? The Classical Model 11垐垐39。 3963 miles or 6378 km = radius of the earth retp(real(d))。).*cos(y).*cos(abs(x39。 d=3963*arccos(sin(y39。 x=pi*xc/180。 Spatial Contiguity Weights Matrix China, 30 Provinces and Cities: W1, W2, W3 DistanceBased Spatial Weights Ertur and Kosh (2020) ? Geographical Location (x,y) ? Longitude (x) ? Latitude (y) ? Great Circle Distance ? d=gcd(x,y) ? (x,y) is in degree decimal units ? DistanceBased Spatial Weights Matrix ? Using Kernel Weight Function proc gcd(xc,yc)。 end。 w6=denseSubmat(sparseOnes(spwpower(spw(w1),6),n,n),0,0)。 w4=denseSubmat(sparseOnes(spwpower(spw(w1),4),n,n),0,0)。 w2=denseSubmat(sparseOnes(spwpower(spw(w1),2),n,n),0,0)。 load wd[n,n]=c:\course09\WISE\data\anselin\。 important: don’t fet this GPE2 for GAUSS Examples ? More than 70 examples covering linear and nonlinear least squares, instrumental variables, system of simultaneous linear equations, time series analysis, panel data, limited dependent variables, maximum likelihood, generalized methods of moments, and … ? The latest extensions include spatial lag model estimation, hypothesis testing, and robust inference. ? Updates for spatial econometric analysis (, ). Software Demonstration ? Installation ? GAUSS Light ? GPE2 for GAUSS ? Example: China GDP Output ? CobbDouglas Production Function ln(GDP) = a + b ln(L) + g ln(K) + e ? Generalized CobbDouglas Production Function ln(GDP) + q GDP = a + b ln(L) + g ln(K) + e China GDP Output Production Using GPE2 for GAUSS: A Review ? CobbDouglas Production Function () ? OLS Estimator ? Hypothesis Testing ? Constant Returns to Scale? ? Homoscedasticity? ? Generalized Production Function (Zellner and Revanka, 1970) () ? Output Effects? ? Instrumental Variables References ? . Lin, Computational Econometrics: GAUSS Programming for Econometricians and Financial Analysts, ETEXT Publishing, Los Angeles, 2020. ? . Chung, Learning Econometrics with GAUSS, Institute of Economics, Academia Sinica, 2020. ? A. Zellner and N. Revankar, Generalized Production Functions, Review of Economic Studies, 1970, 241250. Spatial Econometric Analysis Using GAUSS 3 KuanPin Lin Portland State University Spatial Weights Matrix ? Anselin (1988) [] ? China 30 Provinces [, ] ? Ertur and Kosh (2020) [] ? Homework ? . 48 Lower States [] ? . 3109 Counties [] [] Spatial Contiguity Weights Matrix Anselin (1988): W1, W2, W3 use gpe2。 do model estimation ? // variables y, x are generated earlier ? /* ? ** Retrieve output control variables for model evaluation and anal