Extended Regression Models for Sample Selection Bias

[Nitin Jain]

Hi,

I need guidance on using extended regression models (ERMs) for doing sample selection bias check in a panel data. I am using Mundlak model and then correcting for endogeneity using the control function approach. Can someone please suggest how to using the ERM for my case? This is the link I found but I am unable to find if it can be used with mundlak models also. Thanks.

https://www.stata.com/features/overv...ession-models/

[Jeff Wooldridge]

Is this sample selection or self-selection? That is, is it missing data or do you have an endogenous treatment with panel data?

[Nitin Jain]

Is this sample selection or self-selection? That is, is it missing data or do you have an endogenous treatment with panel data?

Hi, Jeff, Thanks. I think this is a case of self-selection. For example, the selection of suppliers or partners firms by a firm is not random but strategic.

Also, suppose it was a sample selection case. For example, the dependent variable for a firm is having missing values for some reason. Would the ERM approach be applicable.

Kindly advise how to deal with both these cases using ERM.

[Jeff Wooldridge]

I don't think you wan't to use ERM. It actually imposes more restrictions than you'd like (such as not allowing the coefficient on the generalized residual to differ across the two regimes). Instead, implement "by hand" and adjust the standard errors using the panel bootstrap. The procedure is spelled out in Murtazashvili and Wooldridge (2016, Journal of Econometrics), Procedure 3.1. If you don't have additional endogenous variables (besides the binary switching variable) then you just use pooled OLS, not pooled 2SLS, in the second stage.