Heckman Two-Step Model

[Mansoor Afzali]

Hi,
I am trying to estimate the effect of having a female director on board on earnings management. I have a continuous variable for earnings management as the dependent variable. I want to first predict the probability of having a female board member versus having an all-male board. I am doing this to mitigate the sample selection bias. Can I use Heckman's two step procedure for this?

I tried using the Heckman procedure as:

heckman em fem_dummy $Controls, select (fem_dummy = $Predictors) twostep

Where em is the earnings management variable, Controls is a set of other firm characteristics influencing em, fem_dummy is an indicator variable equal to 1 when there is a female on board and 0 otherwise, and Predictors is a set of variables predicting the probability of having a female on board. When I estimate this the fem_dummy variable gets dropped from the second step. However, if I estimate the two procedures separately, I get what I want. In other words, if I first estimate a probit and then include the inverse Mill's ratio in the second step, the dummy doesn't get dropped.

I want to know how a female on board can influence em but the automatic Heckman procedure won't tell me that. How can calculate the Heckman model without dropping the fem_dummy in the second step.

Thanks.

[David Benson]

You're going to use the treatreg command (which I just found out has been renamed etregress). (help etregress).

It's been a while since I've looked at this, but as I recall, the heckman command is used when you only observe outcomes for the treated (i.e. you only observe wages for women in the workforce, in Heckman's original example). You use the treatment effects version of the model (treatreg / etregress) when some outcome is observed for all units (i.e. you have an earnings_management measurement for all firms in your sample. You're trying to account for the endogeneity of having women on their boards).

If you try to do the calculation manually (i.e. 1st estimate the probit, then include the inverse mills in the 2nd stage) your standard errors will be wrong (some of the better statisticians / econometricians here can come along and explain why).

etregress em fem_dummy $Controls, treat(fem_dummy = $Predictors) twostep

[FernandoRios]

Hi Mansoor
In addition to David Benson helpful advice, i may add the following.
If you are still trying to do this by hand, keep in mind that the inverse mills ratio needs to be estimated in a slightly different way for each outcome (for when management is a man and when its a woman).
I havent check if you can obtain the IMR from etregress using predict, but you can certainly do that after the probit using the commands "predict imr, score"

As David already mentioned, doing this by hand needs you to correct for the standard errors because you are including in your model a variable that is coming from a previous estimation (IMR). My default option in cases like that its bootstrapping, but there are a few alternatives for doing it using asymptotic corrections.
Hope it helps
Fernando

[Mansoor Afzali]

Thank you so much David and Fernando. I think -etregress- does exactly what I want.

The paper I am following claims that they use Heckman's model but there is no way they can retain the same indicator variable in the second step. But they also state that the t-stats are "Heckman adjusted". I don't know what that means. Can we do some sort of Heckman adjustment to the standard errors in the second step when we are doing things by hand?

[FernandoRios]

Yes, It is possible, etregress does that adjustment automatically
Alternatively, you can almost always use bootstrap.

[Mansoor Afzali]

Thank you.

If the dependent variable is binary in the second step, does etregress still work?

[Alejandro Torres]

Dear Mansoor,
May I ask you please the variables that you are using for predicting the probability of having a female on board? I am doing something similar (heckman) but in CSR and I am struggling with those predictors without affecting my main regression.
Thank you for any help.

Alejandro