Advice on how to compute generalized residuals for order probit with panel data

[Ian Bowen]

Hello,

I am using a control function approach to correct for an endogenous ordinal variable (with three categories) in a panel dataset. I am basing this approach on Wooldridge (2014) who recommends using generalized residuals from the first stage, which in my case is an ordered probit (xtoprobit). The generalized residuals are written as follows:

gr = y_i2λ(z_iβ) - (1 - y_i2)λ(-z_iβ)

where y_i2 is the endogenous variable and λ(.) is the inverse Mills ratio from the first stage.

However, for xtoproit, there does not appear to a post-estimation command for the inverse Mills ratio. Therefore, I am wondering if the following code would work:

 xtoprobit ...
predict probitxb, xb
gen pdfprobit = normalden(probitxb)
gen cdfprobit = normprob(probitxb)
gen lamda = pdfprobit/cdfprobit

Or is this incorrect given that my variable is ordinal?

If the code is correct, can we then simply do the following to compute λ(-z_iβ)?

gen pdfprobit_n = normalden(-probitxb)
gen cdfprobit_n = normprob(-probitxb)
gen lamda_n = pdfprobit_n/cdfprobit_n

And then do we simply generate a variable with these two IMRs?

gen gr = y2*lamda -  (1 - y2)*lamda_n

Once again, I particularly concerned about whether this is correct given that my endogenous variable is not binary.

Reference:

Wooldridge, J. 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables."
https://econpapers.repec.org/article..._3a226-234.htm


EDIT:

It seems that given that the variable is ordinal, the code I have written above will not work, as the formula for the generalized residuals in Chiburis and Lokshin (2007) for an ordinal probit is much more complex. However, they do not present their formula in a panel data context. So, it seems my general point about there not being a "canned" post-estimation code to estimate the generalized residuals for xtoprobit still stands. Would the right approach, then, be to create a code replicating their equation 5?

Reference:

Chiburis and Lokshin, 2007. "Maximum likelihood and two-step estimation of an ordered-probit selection model."
https://journals.sagepub.com/doi/pdf...867X0700700202

[Tom Kisters]

Ian Bowen

Dear Ian,

Did you make any progress with respect to this issue?

Is the formula that can be found in Vella (1993), formula (18), perhaps what you need (I don't believe it is specific to panel data though).

Vella, F. (1993). A Simple Estimator for Simultaneous Models with Censored Endogenous Regressors. International Economic Review, 34(2), 441-457. doi:10.2307/2526924

See also this question: https://www.statalist.org/forums/for...of-2sri-method

I would be really happy if you would be willing share your code if you manage (because I do not really think I am able to figure it out myself).

Kind Regards, Tom

[Tom Kisters]

Ian Bowen I am asking for a solution for a similar issue (but then in R) here: https://stats.stackexchange.com/ques...nt-for-observa

If I figure it out in R, perhaps you can use the code to simply calculate the residuals, and add them to your Stata dataset.

[Ian Bowen]

Ian Bowen

Dear Ian,

Did you make any progress with respect to this issue?

Is the formula that can be found in Vella (1993), formula (18), perhaps what you need (I don't believe it is specific to panel data though).

Vella, F. (1993). A Simple Estimator for Simultaneous Models with Censored Endogenous Regressors. International Economic Review, 34(2), 441-457. doi:10.2307/2526924

See also this question: https://www.statalist.org/forums/for...of-2sri-method

I would be really happy if you would be willing share your code if you manage (because I do not really think I am able to figure it out myself).

Kind Regards, Tom

Hello, Tom. Thank you for your response.

I have not found an answer to my question pertaining to the generalized residuals for panel ordered probit models; there does not seem to be any literature on this. However, with the oprobit command, they can be computed simply with

predict gr, score

As for computing them manually, I also had a question about how to determine the pi_ji term in Vella (1993). A few days ago, I asked Prof. Wooldridge in the post you linked if he knew what that indicated, but he has not responded as of yet. So, I will be curious to know if you find the answer.

Best,
Ian

[Tom Kisters]

Ian Bowen Thank you very much for pointing that out Ian. If I get an answer on the meaning of pi_ji on crossvalidated, I will be sure to post that here.

[Tom Kisters]

Ian Bowen https://www.statalist.org/forums/for...ordered-probit

[Himanshu Arha]

Hello, Tom. Thank you for your response.

I have not found an answer to my question pertaining to the generalized residuals for panel ordered probit models; there does not seem to be any literature on this. However, with the oprobit command, they can be computed simply with

predict gr, score

As for computing them manually, I also had a question about how to determine the pi_ji term in Vella (1993). A few days ago, I asked Prof. Wooldridge in the post you linked if he knew what that indicated, but he has not responded as of yet. So, I will be curious to know if you find the answer.

Best,
Ian

Dear Ian

I am struggling with a similar problem, where I am using 2 stage residual inclusion to correct for endogeneity in my model. However, for first stage, I am using Poisson Regression. Can we generate the generalized residuals in this case also? Can you also please guide me with STATA command for this?