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I am trying to estimate an IV model where my dependent variable is on the 0-1 scale, which is why I want a Probit estimator. However, my independent variable is a continuous, endogenous variable. For this reason, I'm trying to use IV. However, my IV is a "treatment" that is binary, but which nevertheless predicts this continuous variable quite well. Would Stata's ivprobit command give me consistent results? Also, does the ivprobit routine return values that are essentially the Two-Stage Residual Inclusion ones suggested by Terza et al (2008)?

Thanks!

Reference: 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.

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ivprobit is a control function estimator, so in spirit it is very similar to the Terza et al. 2SRI approach.

The requirement for consistency is that the first stage model be correctly specified (so no omitted instruments, and strong distributional assumptions on the two errors, multivariate normality and homoskedasticity). I don't see Terza making use of the same assumptions directly, but then their set-up is a bit more general than yours.

Stata's formulas are at the end of the pdf manual for ivprobit.

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