Hello, I've read dozens of times the ivprobit manual ( https://www.stata.com/manuals13/rivprobit.pdf ) and searched for papers published on top journals that used the STATA ivprobit command with MLE estimation.

Based on the manual, the formal model is:

y*1i =y2iβ + x1iγ + ui y2i =x1iΠ1 + x2iΠ2 + vi where i = 1, . . . , N, y2i is a 1×p vector of endogenous variables, x1i is a 1×k1 vector of exogenous variables, x2i is a 1 × k2 vector of additional instruments, and the equation for y2i is written in reduced form. By assumption, (ui , vi) ∼ N(0, Σ), where σ11 is normalized to one to identify the model. β and γ are vectors of structural parameters, and Π1 and Π2 are matrices of reduced-form parameters. This is a recursive model: y2i appears in the equation for y*1i , but y*1i does not appear in the equation for y2i . We do not observe y*1i; instead, we observe y1i= 0 if y*1i< 0 and y1i=1 if y*1i≥ 0 The order condition for identification of the structural parameters requires that k2 ≥ p. Presumably, Σ is not block diagonal between ui and vi

In brief, three "schools of thought" seem to exist: 1. The second stage model includes in its ui errors also the vi errors calculated by the first stage model 2. The second stage model includes, instead of the actual values of the variable y2i , an estimation of it from the first stage regression 3. The β coefficient in the second stage model is calculated taking into account the results of the first stage regression

Where is the truth?

Thank you very much