Control Function Approach with Two Endogenous Variables

[Antoaneta Momcheva]

Dear all,

I have a count dependent variable Y, endogenous variables X1 and X2 and control variables C. I am using a control function approach and I have identified two instrumental variables Z1 and Z2, the approach is as follows:

reg X1 Z1 Z2 C (equation 1)
predict resid1, residuals
reg X2 Z1 Z2 C (equation 2)
predict resid2, residuals
poisson Y X1 X2 C resid1 resid2 (equation 3)

However, the coefficient of Z2 in (2) is not significant. Could you please help me understand if it is a problem that one of the instruments is not a significant predictor of one of the endogenous variables?

Thank you very much in advance!

[George Ford]

This is a guess, but given the close relationships between 2SLS and CF, you could probably run ivreg2 and use the first-stage tests for weak instruments.

[Antoaneta Momcheva]

This is a guess, but given the close relationships between 2SLS and CF, you could probably run ivreg2 and use the first-stage tests for weak instruments.

Thank you very much George for the suggestion. I will try it.

[Jeff Wooldridge]

In fact, an ideal situation is when Z1 is "mainly" an IV for X1, and Z2 is "mainly" an IV for X2 (or vice versa). This is because then identification is clear cut. If Z2 doesn't appear in either first stage significantly (and strongly) then you'd be in trouble, of course. Studying the weak IV problem with more than one EEV is tricky, but George has a good suggestion to study it in the linear case.

If you show your output I could say a bit more. In particular, what do the first stages look like?

BTW, you'll want to bootstrap the standard errors for the two-step estimation, or adjust them analytically.

[Antoaneta Momcheva]

Thank you very much Prof. Wooldridge,

My situation is that I have two potentially endogenous variables (ie , two different characteristics of workers' schedules) which are driven by the same unobserved variable ("managerial preferences"), so I find it hard to argue why one instrument will be affecting only one and not the other endogenous variable.

I am also wondering if I actually need two different instruments given that the omitted variable is just one?

ps thank you for the reminder to bootstrap the errors.

thank you!

[Palla Chakraborty]

In fact, an ideal situation is when Z1 is "mainly" an IV for X1, and Z2 is "mainly" an IV for X2 (or vice versa). This is because then identification is clear cut. If Z2 doesn't appear in either first stage significantly (and strongly) then you'd be in trouble, of course. Studying the weak IV problem with more than one EEV is tricky, but George has a good suggestion to study it in the linear case.

If you show your output I could say a bit more. In particular, what do the first stages look like?

BTW, you'll want to bootstrap the standard errors for the two-step estimation, or adjust them analytically.

Hello Professor,

I am struggling with a situation where I have a binary endogenous regressor with a binary instrument for it to correct for endogeneity. The main issue is that I have a sample selection problem in my model such that the endogenous regressor appears in both the selection and the outcome model (Heckprobit). Given this complex set up, I could not find any option in Stata menu to compute all of these together. Is there any way by which I can calculate the generalized residuals manually to get at the control function, which I can include subsequently in both the outcome and selection models?

Thank you. Looking forward to your comments on this.

[Palla Chakraborty]

Hello Professor,

I am struggling with a situation where I have a binary endogenous regressor with a binary instrument for it to correct for endogeneity. The main issue is that I have a sample selection problem in my model such that the endogenous regressor appears in both the selection and the outcome model (Heckprobit). Given this complex set up, I could not find any option in Stata menu to compute all of these together. Is there any way by which I can calculate the generalized residuals manually to get at the control function, which I can include subsequently in both the outcome and selection models?

Thank you. Looking forward to your comments on this.

To add to my point, I have already fitted an Extended probit regression which takes care of any combinations of sample selection and endogeneity. This fits an MLE. But, I am trying to use the CF approach as an alternate method.