micEcon (version 0.1-7)

heckit: 2-step Heckman (heckit) estimation

Description

heckit performs a 2-step Heckman (heckit) estimation that corrects for non-random sample selection.

Usage

heckit( formula, probitformula, data, inst = NULL, print.level = 0 )

Arguments

formula

formula to be estimated

probitformula

formula for the probit estimation (1st step)

data

a data frame containing the variables in the model

inst

one-sided formula specifying instrumental variables for a 2SLS/IV estimation on the second step.

print.level

this argument determines the level of printing which is done during the minimization process. The default value of '0' means that no printing occurs, a value of '1' means that heckit reports what is currently done.

Value

• heckit returns an object of class 'heckit' containing following elements:
• coef
  estimated coefficients, standard errors, t-values and p-values
• vcov
  variance covariance matrix of the estimated coefficients
• probit
  object of class 'glm' that contains the results of the 1st step (probit estimation).
• lm
  object of class 'lm' that contains the results of the 2nd step (linear estimation). Note: the standard errors of this estimation are biased, because they do not account for the estimation of $\gamma$ in the 1st step estimation (the correct standard errors are returned in coef
• .
• sigma
  the estimated $\sigma$, the standard error of the residuals.
• rho
  the estimated $\rho$, see Greene (2003, p. 784).
• probitLambda
  the $\lambda$s based on the results of the 1sr step probit estimation (also known as inverse Mills ratio).
• probitDelta
  the $\delta$s based on the results of the 1sr step probit estimation.

References

Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.

Johnston, J. and J. DiNardo (1997) Econometric Methods, Fourth Edition, McGraw-Hill.

Wooldridge, J. M. (2003) Introductory Econometrics: A Modern Approach, 2e, Thomson South-Western.

See Also

lm, glm, binomial

Examples

## Greene( 2003 ): example 22.8, page 786
data( Mroz87 )
Mroz87$kids  <- ( Mroz87$kids5 + Mroz87$kids618 > 0 )
greene <- heckit( wage ~ exper + I( exper^2 ) + educ + city,
   lfp ~ age + I( age^2 ) + faminc + kids + educ, Mroz87 )
summary( greene )        # print summary
summary( greene$probit ) # summary of the 1st step probit estimation
                         # this is Example 21.4, p. 681f
greene$sigma             # estimated sigma
greene$rho               # estimated rho

## Wooldridge( 2003 ): example 17.5, page 590
data( Mroz87 )
wooldridge <- heckit( log( wage ) ~ educ + exper + I( exper^2 ),
   lfp ~ nwifeinc + educ + exper + I( exper^2 ) + age + kids5 + kids618, Mroz87 )
summary( wooldridge )        # summary of the 1st step probit estimation
                             # (Example 17.1, p. 562f) and 2nd step OLS regression
wooldridge$sigma             # estimated sigma
wooldridge$rho               # estimated rho

## example using random numbers
nObs <- 1000
myData <- data.frame( no = c( 1:nObs ), x1 = rnorm( nObs ), x2 = rnorm( nObs ) )
myData$y <- 2 + myData$x1 + 0.9 * rnorm( nObs )
myData$s <- ( 2 * myData$x1 + myData$x2 + 4 * rnorm( nObs ) - 0.2 ) > 0
myData$y[ !myData$s ] <- NA
myHeckit <- heckit( y ~ x1, s ~ x1 + x2, myData, print.level = 1 )

## example using random numbers with IV/2SLS estimation
nObs <- 1000
myData <- data.frame( no = c( 1:nObs ), x1 = rnorm( nObs ), x2 = rnorm( nObs ),
   u = 0.5 * rnorm( nObs ) )
myData$w <- 1 + myData$x1 + 0.2 * myData$u + 0.1 * rnorm( nObs )
myData$y <- 2 + myData$w + myData$u
myData$s <- ( 2 * myData$x1 + myData$x2 + 4 * rnorm( nObs ) - 0.2 ) > 0
myData$y[ !myData$s ] <- NA
myHeckit <- heckit( y ~ w, s ~ x1 + x2, data = myData,
   inst = ~ x1, print.level = 1 )