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Two-Step Method for Parameter Estimation of the Classical Heckman Model

Source: R/HCinitial.R
HCinitial.Rd

Estimates the parameters of the classical Heckman sample selection model using the two-step estimation method.

Usage

HCinitial(selection, outcome, data = sys.frame(sys.parent()))

Arguments

selection

A formula specifying the selection equation.

outcome

A formula specifying the outcome equation.

data

A data frame containing the variables in the model.

Value

A named numeric vector containing:

  • Coefficients from the selection equation (probit model),

  • Coefficients from the outcome equation (excluding the IMR),

  • Estimated sigma,

  • Estimated rho.

Details

This function implements the two-step approach proposed by Heckman (1979) to estimate the parameters of the classic sample selection model. It is particularly useful for obtaining initial values for maximum likelihood estimation (MLE).

In the first step, a probit model is fitted to the selection equation to estimate the probability of selection. The second step involves estimating a linear regression of the outcome equation for the observed (selected) data, incorporating the inverse Mills ratio (IMR) as an additional regressor to correct for sample selection bias.

The function also estimates:

  • sigma: The standard deviation of the outcome equation's error term.

  • rho: The correlation coefficient between the errors of the selection and outcome equations.

References

James J Heckman (1979). “Sample selection bias as a specification error.” Econometrica: Journal of the econometric society, 153–161.

Examples

data(MEPS2001)
attach(MEPS2001)
selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income
outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins
HCinitial(selectEq, outcomeEq, data = MEPS2001)
#> xs(Intercept)         xsage      xsfemale        xseduc      xsblhisp 
#>  -0.668643899   0.086814848   0.663505390   0.061883892  -0.365784312 
#>      xstotchr         xsins      xsincome xo(Intercept)         xoage 
#>   0.795747277   0.169106526   0.002677301   5.288927373   0.202466773 
#>      xofemale        xoeduc      xoblhisp      xototchr         xoins 
#>   0.292133967   0.012388871  -0.182865733   0.500633176  -0.046509658 
#>         sigma           rho 
#>   1.290541875  -0.359316986