ivprobit and firm FE?

[Mahtab Karimi]

Hello all,

I am estimating a probit model for a set of firms; I have a panel dataset of firms where they experience or do not experience a shock in each year. Technically, there is no estimator for a fixed effect model. So I do not include any firm FE in the model.

Now, I have an IV for an endogenous variable, and I am using ivprobit. Should I include a firm FE in my ivprobit? If I don't, does that cause problems for exclusion restriction? What if Z(the IV) can affect the probability of S==1 through the firm FE(unobserved time-invariant heterogeneity)?

This is the probit model:
P(S=1)=a+b_1A_(i,t)+X_it+year FE+Industry FE+e

This is the First stage:
A_(i,t)=a'+yZ_(i,t)+X_it+year FE+Industry FE+e'
Z is the IV for A.

Thank you,
Mahtab

[Maxence Morlet]

1. there is now sufficient statistic for probit model, you're right, but there is one in logit. You could however try the Chamberlain-Mundlak device in probit

2. linear probability model is also an option; the IPP does not apply there

3. if the exclusion restriction only holds conditional on firm FE, this may make reviewers question the overall exogeneity of your instrument...

[Mahtab Karimi]

Thank you. LPM is not a good choice because the number of ones is much smaller than the number of zeros...

[Maxence Morlet]

A good solution to that is the trimeed estimator of Horrace and Oaxaca (2006).

Also a bit of self-promotion regarding LPM: in the following paper, section 6.3.:
Gendered choices of labour market integration programmes: evidence from the United States | Emerald Insight