XploRe Help : heckman

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:	tobit powell select sssm andrews

Quantlet:		heckman
Description:		2-step estimation of a regression equation in the presence of self-selection. Selection rule is of the probit type (hence, this is a Type 2 Tobit Model in chapter 10 of Amemiya's Advanced Econometrics).

Reference(s):

G.S. Maddala (1983): Limited-Dependent and Qualitative Variables in Econometrics, Chapter 8

Usage:	`heckit = heckman(x,y,z,q)`
Input:
	`x`	n x d matrix , the observed explanatory variables of the regression equation
	`y`	n x 1 matrix , the observed response variable of the regression equation
	`z`	n x p matrix , the observed explanatory variables of the selection equation
	`q`	n x 1 matrix , the observed response variable of the regression equation;
Output:
	`heckit.b`	d x 1 vector, contains the estimated coefficients of the components of x result of the second step
	`heckit.s`	scalar, contains the estimated covariance of the error terms in the selection equation and regression equation result of the second step
	`heckit.g`	p x 1 vector, contains the estimated coefficients of the components of z, result of the first step

Example:

library("metrics") n = 500 s1 = 1 s2 = 1 s12 = 0.7 ss = #(s1,s12)~#(s12,s2) ev = eigsm(ss) va = ev.values ve = ev.vectors ll = diag(va) ll = sqrt(ll) sh = ve*ll*ve' u = normal(n,2)*sh' z = 2*normal(n,2) g = #(1,2) q = (z*g+u[,1].>=0) x = matrix(n)~aseq(1, n ,0.25) b = #(-9, 1) y = x*b+u[,2] y = y.*(q.>0) heckit = heckman(x,y,z,q) heckit.b heckit.s heckit.g

Result:

2-step estimates of b, s and g

Author: A. Werwartz, 19960605