## Two-Step Estimator of Heckman

Heckman (1976a) proposed the two-step estimator of the reduced-form parameters (which we discussed in Section 10.8.1); but he also reestimated the labor supply model of Heckman (1974) using the structural equations version. Because (10.8.6) is a reduced-form as well as a structural equation, the estimation of fi2 is done in the same way as discussed in Section 10.8.1, namely, by applying least squares to the regression equation for E( W,Hf> 0) after estimating the argument of X (the hazard rate) by probit MLE. So we shall discuss only the estimation of (10.8.7), which we can rewrite as

Hi = y~lWt – г’,ау~1 ~ rlvt – (Ю.8.9)

By subtracting E(v,Hf > 0) from vt and adding the same, we can rewrite (10.8.9) further as

щ = ri Wi – Z’ay~‘ – olvo^rlK*uPJox)- Г’е„ (10.8.10)

where aX...

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