Use of xtheckmanfe to correct for sample selection bias due to an independent variable

[Ayrton Da Silva]

Hi all,

I am looking to understand if my use case falls outside of the scope of a Heckman correction. Thank you in advance for reading this post and providing any guidance!

I am working on a study which considers how the overconfidence of a management team may affect firm performance. We use a proxy derived from voluntarily issued earnings forecasts by firm management:

Firm performance _i,t = overconfidence _{i, t-1} + [control variables]_{i, t-1}

We are using a fixed effects panel regression with robust standard errors. We control the necessary industry, year and firm effects, and run several robustness checks.

Reviewer feedback suggests that sample selection issues may be a problem for our estimation, as not all firms opt to issue forecasts - and thus we can only compute our overconfidence proxy for these firms. A suggestion was to estimate a two-stage Heckman model to correct for the sample selection bias. However, in theory and practise I only see use of the Heckman model to correct for sample selection bias due to the dependent variable. I only find one case which matches our own: an implementation of a Heckman model to correct for sample selection of an independent variable (Wang et al.; 2008).

I am worried that the Heckman model may be the wrong tool for our case, and am hoping for some feedback regarding this. Finally, I wonder how much I should be concerned about this sample selection issue if I do not wish to generalise my findings outside of those firms which opt provide forecasts?

Thank you for considering my questions, I am deeply appreciative of the thoughtful and considered feedback freely given on this forum. Your contributions are sincerely appreciated.

Ayrton

References:
Wang, H., Choi, J., & Li, J. (2008). Too little or too much? Untangling the relationship between corporate philanthropy and firm financial performance. Organization Science, 19(1), 143-159.

[Ayrton Da Silva]

I should also note that I did try to run xtheckmanfe, and found models which either did not converge, or resulted in errors. The same specification would run quickly if i removed my overconfidence variables from the second stage model.

Here is how i specified the model:

xtheckmanfe firm_performance overconfidence <control vars> , selection(issue_forecast = market_cap rnd tsr) id(uid) time(year)