Residuals for ordered probit model to include in the second stage of 2SRI method

[Maryam Bidgoli]

Dear statisticians,

I am using two stage residuals inclusion method to study the relationship between health status and employment status. I am using a longitudinal dataset. My first stage is an ordered probit and second stage is a probit regression. I want to calculate the residuals of the first stage of estimation to include in the second stage as a regressor. Stata does not provide residuals after xtoprobit. I GREATLY appreciate if anyone would help me with it. I searched a lot but no solution

Thanks,
Maryam

[Jeff Wooldridge]

Maryam: There's really no "right" answer here because 2SRI, also called a "control function" approach, is necessarily an approximation. Having said that, it seems to work fairly well for modest amounts of endogeneity.

In my 2014 Journal of Econometrics paper, available here, I suggest using the generalized residuals from the first stage estimation. When the first stage is linear, the GR are just the usual residuals. The expressions are known for probit, logit, Tobit, and so on. I haven't worked these out for the ordered probit model, but that should be out there somewhere.

Alternative, use the user-written -cmp- command and perform joint MLE. Doing both can be at least somewhat of a robustness check.

JW

[Jeff Wooldridge]

The GRs seem to be in the 1993 IER paper by Vella See equation (18).

[Ian Bowen]

The GRs seem to be in the 1993 IER paper by Vella See equation (18).

Professor Wooldridge, I have a similar question to Maryam. I was wondering if you could clarify two things about the paper that you cite.

1) When Vella says that the GRs in equation 18 require π_ji, is he referring to the density of each observation? I am a bit confused about why he is using the j subscript if this is the case.
2) Do you think that this equation would be appropriate to correct for endogeneity in a panel data model? If so, could the resulting generalized residual variable then be used in the flexible specification you recommend in your 2014 paper (i.e., equation 69)?

Thank you for the help.