LPM and Probit IV comparison and Lasso IV

[oliver wei]

This is a general question regarding the application of ivreghdfe and ivprobit.

My question is that if LPM delivers a significant results, does it necessarily be significant in ivprobit?

The background of my question is that, I am testing different kinds of IV in LPM first. After I find out the combination of good IV, then I will apply to probit model. Probit with additional fixed effects just take forever to run.

Again, I much appreciate your kind reply.

OW

[oliver wei]

Any input will be sincerely appreciated!

[Jeff Wooldridge]

Oliver: Statistically (as well as computationally), it is not a good idea to include unit specific effects in nonlinear models when you have few observations per unit. From your other post, it appears you have maybe a million units? How many time periods per unit, roughly?

Fernando Rios-Avila suggested a correlated random effects approach in your case, and I second that. I the linear case, the CRE approach is the same as including the unit-specific dummies as in ivreghdfe. But CRE can be used for nonlinear models when using fixed effects can't be justified.

In my 2019 Journal of Econometrics paper, I show how to handle the unbalanced case. You should average all exogenous variables by unit only over the complete cases for each i. Then, including indicators for how many time periods per unit. You need to generate a complete cases indicator, "complete," which is one if and only if you have a full set of observations. Below, the z's are all exogenous variables (in the model and excluded). First K1 variables are in the model, K1p1 to K are intruments. I've assumed annual panel data.

egen sum_complete = sum(complete), by(id)
egen z_1bar = mean(z1) if complete, by(id)
...
egen z_Kbar = mean(zK) if complete, by(id)
ivprobit y1 z_1 ... z_K1 z_1bar ... z_Kbar i.year (y2 = z_K1p1 ... z_K), vce(cluster id)

An alternative is to use probit in a control function approach. Here's a link to a paper with a former student of mine. We show how to do the fractional probit case, which includes ivprobit as a special case.

https://www.google.com/books/edition...sec=frontcover