XploRe Help : powell

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	metrics
See also:	heckman select andrews sssm gennorm dwade

Quantlet:		powell
Description:		powell calculates the semiparametric estimator proposed by Powell (1987) of the slope coefficients of the outcome equation in a sample selection model.

Usage:	`b = powell(x,y,id,h)`
Input:
	`x`	n x M regressor matrix. WARNING: x may not contain a vector of ones!
	`id`	n x 1 vector containing the estimated index of the first-step selection equation.
	`y`	n x 1 matrix containing n observ. of the dependent variable
	`h`	scalar, the bandwidth
Output:
	`b`	M x 1 vector of estimated slope coefficients

Example:

library("xplore") library("metrics") randomize(66666) n = 200 ; sample size ss1 = #(1,0.9)~#(0.9,1) ; covariance matrix of error terms g = #(1) ; true coefficient of decision equation b = #(-9, 1) ; true intercept and slope of outcome equation u = gennorm(n, #(0,0), ss1) ; generate realizations of joint distribution of error terms ss2 = #(1,0.4)~#(0.4,1) ; covariance matrix of regressors xz = gennorm(n, #(0,0), ss2) ; generate realizations of joint distribution of regressors z = xz[,2] ; regressor of decision equation q =(z*g+u[,1].>=0) ; generate binary dependent variable of decision equation hd = 0.1*(max(z) - min(z)) ; bandwidth for dwade procedure d = dwade(z,q,hd)*(2*sqrt(3)*pi) ; dwade estimate * scaling factor id = z*d ; estimated first-step index h = 0.2*(max(id) - min(id)) ; bandwidth for powell procedure x = matrix(n)~xz[,1] ; regressors for outcome equation y = x*b+u[,2] ; dependent variable for outcome equation zz = paf(y~x~id, q) ; impose censored sampling y = zz[,1] x = zz[,3:(cols(zz)-1)] id = zz[,cols(zz)] b = powell(x,y,id,h) b ; estimated slope coefficient

Result:

estimated slope of the outcome equation of a semiparametric
sample selection model according to Ahn and Powel (1993)

Author: A. Werwartz, 19961011