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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?" $\endgroup$ – Mike Hunter Nov 6 '17 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 Nov 6 '17 at 16:26
  • $\begingroup$ Will edit the question now to clarify. $\endgroup$ – financial theory Nov 6 '17 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? $\endgroup$ – Mike Hunter Nov 7 '17 at 1:03
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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 the 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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