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Following my question Heckman sample selection vs. OLS about the meaning of Mills ratio I am wondering why some researchers estimate a generalization of Heckman instead of the actual Heckman's procedure. (based on Das et. al 2003 http://www.jstor.org/stable/3648610 (gated version).

Instead of using Mills ratio only, the generalized version also includes predicted probabilities, Mills ratio, their squares and interaction terms in the 2 step.

I do no understand the advantages / disadvantages of this approach compared to "basic" Heckman sample selection? Which model should I prefer for testing sample selection?

Ferdi
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Steven
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1 Answers1

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Heckman's selection correction procedure assumes that 1) the selection equation is a linear probit and 2) the outcome equation is a linear normal regression equation. So, this involves two assumptions of linearity and the assumption of joint normality of the errors in the two regressions. These are strong assumptions.

The paper you link introduces a method to relax all of these assumptions. You get the usual trade-offs when you do this. If the strong assumptions in Heckman's procedure are true in your application, then the Heckman procedure will be more efficient (i.e. narrower confidence intervals, lower standard error) than the Das method. If the strong assumptions in Heckman's procedure are false in your application, then the Heckman procedure will result in bias and inconsistency.

Bill
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