What does the ivprobit command actually do?

Dear statalisters,
I've read dozens of times the ivprobit manual 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 =y_2iβ + x_1iγ + u_i
y_2i =x_1iΠ₁ + x_2iΠ₂ + v_i
where i = 1, . . . , N, y_2i is a 1×p vector of endogenous variables, x_1i is a 1×k1 vector of exogenous variables, x₂i is a 1 × k2 vector of additional instruments, and the equation for y_2i is written in reduced form. By assumption, (u_i , v_i) ∼ 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: y_2i appears in the equation for y*_1i , but y*_1i does not appear in the equation for y_2i . We do not observe y*_1i; instead, we observe y_1i= 0 if y*_1i< 0 and y_1i=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 u_i and v_i

In brief, three "schools of thought" seem to exist:
1. The second stage model includes in its u_i errors also the v_i errors calculated by the first stage model
2. The second stage model includes, instead of the actual values of the variable y_2i , 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

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