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Is it possible to compare coefficients across an OLS model and a Heckman model that has the same covariates (plus the inverse Mills ratio)?

The coefficient of my main variable of interest changes when I run the Heckman model. This is to be expected as I indeed have a severe sample selection problem. What I wonder is if I could test for the statistical significance of this change. That is, can I compare the coefficients reported by the OLS and Heckman models?

I'm using Stata for my analysis.

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  • $\begingroup$ You're assuming too much and need to say more about the models, e.g., what is "its Heckman counterpart?" $\endgroup$
    – user78229
    Commented Nov 6, 2017 at 16:24
  • $\begingroup$ Heckman counterpart (estimated via maximum likelihood) has the same covariates as the OLS model plus the inverse Mills ratio. $\endgroup$
    – financial theory
    Commented Nov 6, 2017 at 16:26
  • $\begingroup$ Will edit the question now to clarify. $\endgroup$
    – financial theory
    Commented Nov 6, 2017 at 16:27
  • $\begingroup$ Have you run any diagnostics for collinearity on the OLS model? How does the sign of the pairwise correlations between the covariates and the target? Are they the same or not? What does the scatterplot between them tell you? $\endgroup$
    – user78229
    Commented Nov 7, 2017 at 1:03

2 Answers 2

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I think you're putting the cart before the horse. If you really have a sample selection problem, then your OLS results are meaningless anyways. But to verify the former, you need to test the significance of the Heckman lambda (or inverse Mills ratio). See this brief paper by Melino for further details.

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While I agree with Durden's answer, I think your original question also raises a common problem: How to compare results of two different estimation methods?

You could do what you ask in three ways:

  • use GMM for the full system,
  • use ML also to do the same,
  • make your life easier and suest all.

This last option is the simplest:

webuse womenwk
heckman wage educ age, select(married children educ age)
est sto m1
reg wage educ age
est sto m2
suest m1 m2

After obtaining the last outcome, you can compare the coefficients across models.

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