Binary Y, endogenous X and continuous instrument Z

[Laxman Timilsina]

Hi all,

I have binary Y, endogenous X and continuous instrument Z plus controls. I am following Angrist and Pischke's, mostly harmless econometrics and using ivreg2. But I get the coefficient of 5 for X. Is that even possible, how do I interpret it? Should I be using other methods?

Thanks,
Laxman

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. It would help if we could replicate your problem. It would also be nice to know the range of X.

In theory with a binary dv, you would use logit or probit but some do use regression.

What happens when you look at the predicted values? The magnitude of the parameter depends on the scale of X so finding a coefficient of 5 is not necessarily a problem..

[Laxman Timilsina]

Hi Phil, My X is binary as well. Thanks!

[Dimitriy V. Masterov]

Try using -biprobit-, and use -margins- to get the marginal effects. This will help you avoid all the LPM nonsense with marginal effects that don't make sense:

 
 webuse school biprobit (private = i.vote) (vote = loginc logptax years) margins, dydx(vote) predict(pmarg1) force

These estimates imply that voting for increasing property taxes makes someone 18 percentage points more likely to send their children to private school.

[Laxman Timilsina]

Hi Dimitriy,

Thanks, I used that and the margins look about right. I read here https://www.stata.com/statalist/arch.../msg01347.html which points to this https://www.stata.com/meeting/chicag...11_nichols.pdf that, it is harder to establish the first stage and other instrument diagnostics with biprobit. Do you know a paper that uses biprobit? Also, my instrument is continuous, which should be fine, right?

Thanks,
Laxman

[Dimitriy V. Masterov]

It's true that this terrain is less developed than the linear case, but, for example, you can certainly look at the marginal effects from the first stage to get a sense of instrument relevance. That is usually the first things people will demand to see.

There is a good paper comparing biprobit and linear IV by Chuburis et al that contains many more references to the literature. Chiburis also wrote a Stata command -scoregof-, that performs a goodness of fit test that you may find useful.

Here's the BibTeX reference:

@article{40392,
title = {A practical comparison of the bivariate probit and linear IV estimators},
author = {Richard C. Chiburis and Jishnu Das and Michael Lokshin},
year = {2012},
URL = {http://dx.doi.org/10.1016/j.econlet.2012.08.037},
journal = {Economics Letters},
pages = {762--766},
volume = {117}
}

Continuous instruments are certainly OK.

[Laxman Timilsina]

Thanks a lot for this! very helpful. Although, -scoregof- rejects the null for joint normality! Not sure if I can still use biprobit. Linear IV gives estimated values more than 1 (both endogenous and dependent variables are binary). Any suggestions?

[Dimitriy V. Masterov]

This is a hard one, and I don't have too much advice to give. Maybe try something like etregress?