LLef {JLLprod}R Documentation

Homothetic Production Function: Most Efficient Estimator

Description

This function implements the most efficient version of Lewbel & Linton's (2005) estimator. In general it estimates the model Y=r(x,z)+e, imposing the following structure r(x,z)=E[Y|X=x,Z=z]=h[g(x,z)], and g(bx,bz)=b*g(x,z). The unknown function g is assumed to be smooth and h is assumed to be a strictly monotonic smooth function.

Usage

LLef(xx, zz, yy, LLob, h0 = NULL, kernel0=NULL , kernel = NULL)

Arguments

xx Numerical: Nx1 vector.
zz Numerical: Nx1 vector.
yy Numerical: Nx1 vector.
LLob LL object
h0 Numerical: Bandwidth for smoothing. Default is the Silverman's rule of thumb.
kernel0 Kernel function for smoothing. Default is `gauss'.
kernel Kernel function for all steps. Default is `gauss'.

Details

User may choose a variety of kernel functions. For example `uniform', `triangular', `quartic', `epanech', `triweight' or `gauss', see Yatchew (2003), pp 33. Another choice may be `order34', `order56' or `order78', which are third, fifth and seventh (gauss based) order kernel functions, see Pagan and Ullah (1999), pp 55.

Value

gef N x 1 vector: Efficient Nonparametric component g (see above) evaluated at data points, i.e. g(xxi,zzi).
hef N x 1 vector: Efficient Nonparametric component h (see above) evaluated at data points, i.e. h[g(xxi,zzi)].
hdef N x 1 vector: Efficient Nonparametric first derivative of h (see above) evaluated at data points, i.e. h'[g(xxi,zzi)].

Author(s)

David Tomás Jacho-Chávez

References

Lewbel, A., and Linton, O.B. (2005) Nonparametric Matching and Efficient Estimation of Homothetically Separable Functions. Unpublished manuscript.

Yatchew, A. (2003) Semiparametric Regression for the Applied Econometrician. Cambridge University Press.

Pagan, A. and Ullah, A. (1999) Nonparametric Econometrics. Cambridge Universtiy Press.

See Also

JLL, LL , locpoly, Blocc

Examples


data(ecu)
##This part simply does some data sorting & trimming
xlnK <- ecu$lnk
xlnL <- ecu$lnl
xlnY <- ecu$lny
xqKL <- quantile(exp(xlnK)/exp(xlnL),  probs=c(2.5,97.5)/100)
yx <- cbind(xlnY,xlnK,xlnL)
tlnklnl <- yx[((exp(yx[,2])/exp(yx[,3]))>=xqKL[1]) 
              & ((exp(yx[,2])/exp(yx[,3]))<=xqKL[2]),]
Y<-tlnklnl[,1]
K<-exp(tlnklnl[,2])/median(exp(tlnklnl[,2]))
L<-exp(tlnklnl[,3])/median(exp(tlnklnl[,3]))

LLb<-LL(xx=K,zz=L,yy=Y,xxo=median(K),zzo=median(L),k=80,j=100)
LLbef <- LLef(xx=K,zz=L,yy=Y,h0=1,LLob=LLb)

#win.graph()
nf <- layout(matrix(c(1,2,1,2),2,2, byrow=TRUE),respect=TRUE)
plot(log(K)-log(L),log(LLbef$gef)-log(L),pch=3,xlab="ln(K/L)"
     ,ylab="ln(g(K/L,1))",main="Homogeneous Component g")
plot(log(LLbef$gef),LLbef$hef,xlab="ln(g)",pch=3,ylab="h(g)"
     ,main="Nonhomogeneous Component h",ylim=c(min(min(LLbef$hef)
     ,min(LLb$r)),max(max(LLbef$hef),max(LLb$r))))
points(log(LLbef$gef),LLb$r,type="p",pch=1,col="blue",lwd=2)
legend(-0.5,15.6,c("Nonparametric","Kernel Regression")
       ,merge=TRUE,lty=c(1,-1),pch=c(3,1),lwd=c(1,2)
       ,col=c("black","blue"),cex=0.95)

[Package JLLprod version 1.0.0 Index]