Data sisaltaa 2 muuttujaa:
RealGDP: Quarterly values of Real GDP for the United States in Billions of Chained (2000) Dollars Seasonally Adjusted, Annual Rate.
TBillRate: Quarterly values of the rate on 3-month Treasury Bills. Quaterterly averages of daily rates in percentage points at an annual rate.
file<-"http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.csv" data<-read.table(file,skip=1,sep=",")
FILENAME myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.txt'; DATA USmacro; INFILE myurl firstobs=2; INPUT time $ gdpq tbill; RUN;
Olkoon Y(t) = log(RealGDP(t)) - log(RealGDP(t-1)) ja X(t) = TbillRate(t) - TbillRate(t-1)
Lasketaan Newey-West estimaatti virheiden kovarianssimatriisille.
# Luetaan data ja muokataan se file<-"http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.csv" data<-read.table(file,skip=1,sep=",") gdp<-data[,2] r<-data[,3] n<-length(r) y0<-log(gdp[2:n])-log(gdp[1:(n-1)]) plot(y0,type="l") x0<-r[2:n]-r[1:(n-1)] plot(x0,type="l") T1<-length(x0) y<-y0[2:T1] x<-x0[1:(T1-1)] plot(x,y) ##################### K<-2 T<-length(y) Y<-matrix(y,length(y),1) X<-matrix(0,length(x),K) X[,1]<-1 X[,2]<-x xtx<-t(X)%*%X inv.xtx<-solve(xtx,diag(K)) bls<-inv.xtx%*%t(X)%*%Y e<-Y-X%*%bls L<-6 w<-pmax(1-seq(0,(T-1))/(L+1),0) #w<-pmax(1-(seq(0,(T-1))/(L+1))^2,0) Omega<-matrix(0,T,T) for (i in 1:T){ for (j in 1:T){ Omega[i,j]<-w[abs(i-j)+1]*e[i]*e[j] } } Q<-t(X)%*%X/T invQ<-solve(Q,diag(K)) P<-t(X)%*%Omega%*%X/T HAC<-invQ%*%P%*%invQ/T HAC [,1] [,2] [1,] 6.683422e-07 1.141122e-08 [2,] 1.141122e-08 8.072963e-07 ############################## library(sandwich) model<-lm(y ~ x) bwNeweyWest(model) #[1] 6.092293 NeweyWest(model) (Intercept) x (Intercept) 7.571355e-07 2.400810e-08 x 2.400810e-08 7.921764e-07 NeweyWest(model,prewhite=FALSE) (Intercept) x (Intercept) 6.904282e-07 -2.529516e-10 x -2.529516e-10 7.668061e-07 vcovHAC(model) (Intercept) x (Intercept) 5.219359e-07 1.698986e-08 x 1.698986e-08 7.550875e-07 ################################ library(car) hccm() vcov()
Kokeillaan SAS:ia.
FILENAME myurl URL 'http://cc.oulu.fi/~jklemela/econometrics/USMacro_Quarterly.txt'; DATA USmacro; INFILE myurl firstobs=2; INPUT time $ gdpq tbill; loggdpq = log(gdpq); y = loggdpq - lag1(loggdpq); x0 = tbill - lag1(tbill); x = lag1(x0); RUN; PROC MODEL; parms b0 b1; y = b0 + b1*x; fit y / GMM kernel=(bart,0,); run; The SAS System 11:32 Thursday, February 20, 2014 3 The MODEL Procedure Nonlinear GMM Summary of Residual Errors DF DF Adj Equation Model Error SSE MSE Root MSE R-Square R-Sq y 2 228 0.0224 0.000098 0.00992 0.0166 0.0123 Nonlinear GMM Parameter Estimates Approx Approx Parameter Estimate Std Err t Value Pr > |t| b0 0.008457 0.000654 12.93 <.0001 b1 0.001782 0.000887 2.01 0.0457 Number of Observations Statistics for System Used 230 Objective 1.289E-32 Missing 2 Objective*N 2.966E-30