Instrumental variable with binary endogenous regressor and binary D

[Matt Roberts]

Hi Statalist,

I want to run a model with a binary dependent variable and a binary endogenous regressor and I'm not sure what the best option is. Reading Angrist and Prischke it seemed that I could do this using 2SLS but every so often I come across a comment that this is an example of a "forbidden regression" which I thought was only the case if you have a binary dependent variable and continuous endogenous regressor.

The collective wisdom the forum would be really helpful to me here.

Thanks

[Jeff Wooldridge]

There are a couple of different issues. First, the Angrist and Pischke suggestion is to use a linear model even though the response is binary. In other words, estimate a linear probability model by 2SLS. There's nothing wrong with that provided you understand the LPM is at best an approximation, and is only supposed to approximate the average marginal effect.

The "forbidden regression" comes in if you try to use a probit in two stages. So, if y1 is the LHS variable and y2 is the RHS variable, the typical forbidden regression is

1. Probit of y2 on z1 z2 and obtain fitted probabilities, p2hat
2. Probit of y1 on p2hat, z1.

The second step is the forbidden regression. It is not consistent for either the parameters or the average marginal effects.

If you want to take the binary nature of y1 and y2 seriously, you should use the biprobit model (with the Stata command being the same).

JW

[Matt Roberts]

Thanks, Jeff. That makes things very clear

[Nikos Korompos]

Hi, I have a similar problem. The model has a 5-scale dependent variable and a 6-scale endogenous regressor. I was thinking to use 2SLS, assuming LPM.

Is there any method, with which I can consider the ordinal nature of both variables? I was thinking cmp command, specifying ind($cmp_oprobit $cmp_oprobit) at the end. I would really appreciate if I had your opinion on this.

Thank you.

Nikos

[NJ JAIN]

There are a couple of different issues. First, the Angrist and Pischke suggestion is to use a linear model even though the response is binary. In other words, estimate a linear probability model by 2SLS. There's nothing wrong with that provided you understand the LPM is at best an approximation, and is only supposed to approximate the average marginal effect.

The "forbidden regression" comes in if you try to use a probit in two stages. So, if y1 is the LHS variable and y2 is the RHS variable, the typical forbidden regression is

1. Probit of y2 on z1 z2 and obtain fitted probabilities, p2hat
2. Probit of y1 on p2hat, z1.

The second step is the forbidden regression. It is not consistent for either the parameters or the average marginal effects.

If you want to take the binary nature of y1 and y2 seriously, you should use the bi-probit model (with the Stata command being the same).

JW

Dear Jeoff and other members,

My outcome variable is binary, endogenous variable is also binary and three instruments are binary as well.
Can I use IV 2SLS here. If the marginals from Biprobit are different (-0.15) from that of IV-2SLS (-0.18). Kindly advice.

Thanks,
Nitin