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I am mostly an R user. But since I have not found a way yet to reproduce generalised residuals in R (link), I am using Stata for my estimation of a CF/2SRI (references below). The jist is as follows: I run an oprobit on my ordinal EEV, I get the generalised residual (apparently that is just one residual per observation, instead of on per level?). I add the residual with the EEV in the second stage, which I estimate with fracreg. And finally I calculate the AME/APE.

Am I correctly implementing this?

ordinal_var is an ordinal variable with four levels

depvar is the dependent variable with values ranging between (and including) 0 and 1.

// ordinal probit regression
 oprobit ordinal_var instrumentalvar1 instrumentalvar2      

// to able to re-run the code
 drop residual                                 
         
 // Generalised Residual (Vella, 1993)
 predict residual, score
 
 // Because dep var is ration between and including 0 - 1                               
 fracreg logit depvar i.ordinal_var residual, vce(robust)

 // Because I am interested in the marginal effects.   
 margins, dy/dx(i.ordinal_var)                                       

Outcome:

----------------------------------------------------------------------------------
                 |            Delta-method
                 |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
ordinal_var      |
              1  |  -.0707792   .0093849    -7.54   0.000    -.0891732   -.0523851
              2  |  -.1159215   .0162036    -7.15   0.000    -.1476799   -.0841631
              3  |   -.175346   .0289114    -6.06   0.000    -.2320114   -.1186807
----------------------------------------------------------------------------------

References

Chiburis, R., & Lokshin, M. (2007). Maximum Likelihood and Two-Step Estimation of an Ordered-Probit Selection Model. The Stata Journal, 7(2), 167–182. https://doi.org/10.1177/1536867X0700700202

Terza J. V, Basu A., Rathouz, P.J. (2008) Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling. Journal of health economics 27 (3), 531-543, 2008

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

Wooldridge,JM. (2014) Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables. Journal of Econometrics Volume 182, Issue 1, September 2014, Pages 226-234

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