Instrumental Variable using Panel Data with Binary Endogenous Variable

[Helen Liang]

Dear all,

Can someone let me know how to implement a procedure similar to XTIVREG but with a binary endogenous variable? Here is the model I want to estimate:

xtivreg DV controls (x1 = z1 z2), fe

where controls are exogenous variables, z1 & z2 are instruments;
x1 is a binary endogenous variable (0 or 1) and the first stage is a logit model so this doesn't fit the xtivreg specification.

Is there an existing procedures to implement this? Or do I have to do the two stages manually?

If I do the two stages manually, how do I adjust the standard errors in the second stage for significance tests?

Thank you very much!

[Jeff Wooldridge]

Helen: A couple of things. First, there is no need to use a logit first stage for x1 even though it is binary. If you are assuming the standard model with a constant coefficient on x1 then ysing the above command, but with the addition of vce(cluster id) is sufficient.

Nevertheless, you may get more efficiency by using a first-stage logit estimation. You haven't shown exactly how you're doing that. Is it a correlated random effects logit? Just a standard pooled logit? In any case, assuming the model is correctly specified, you don't need to adjust the standard errors in the second stage if you are using the fitted logit probabilities as instruments (not regressors). So something like this should do it:

logit x1 controls z1 z2
predict p1hat
xtivreg DV controls (x1 = p1hat), fe vce(cluster id)

Incidentally, I strongly recommend time effects in both models if this is a true panel data.

JW

[Helen Liang]

Thanks a lot, Jeff!

The first-stage is a random effects logit (but not a correlated random effects logit), because we assume x1, the endogenous variable (manager's investment choice), is determined by unobserved firm level variables, some of which are random. We also did a standard pooled logit just as a reference. The code used for the first stage is:

xtlogit x1 controls z1 z2, vce(robust)
predict p1hat, pr


I suppose we should go ahead using the xtivreg, and include the separate two stage manual estimation as a reference, in case significance levels vary between the two methods.
Thank you so much for the help!

[Nitin Jain]

D

Helen: A couple of things. First, there is no need to use a logit first stage for x1 even though it is binary. If you are assuming the standard model with a constant coefficient on x1 then ysing the above command, but with the addition of vce(cluster id) is sufficient.

Nevertheless, you may get more efficiency by using a first-stage logit estimation. You haven't shown exactly how you're doing that. Is it a correlated random effects logit? Just a standard pooled logit? In any case, assuming the model is correctly specified, you don't need to adjust the standard errors in the second stage if you are using the fitted logit probabilities as instruments (not regressors). So something like this should do it:

logit x1 controls z1 z2
predict p1hat
xtivreg DV controls (x1 = p1hat), fe vce(cluster id)

Incidentally, I strongly recommend time effects in both models if this is a true panel data.

JW

Dear Prof. Wooldridge, Could you please share a reference for this? Thanks.