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Marginal Effects for Probit and Tobit with Endogeneity

Kirill S. Evdokimov, Ilze Kalnina, Andrei Zeleneev

arXiv 26 Jun 2023 · Econometrics · publishedEconometrics Journal (2025) · 2 citations (OpenAlex)

arXiv:2306.14862 · PDF · DOI · OpenAlex · Extracted main text

Abstract

When evaluating partial effects, it is important to distinguish between structural endogeneity and measurement errors. In contrast to linear models, these two sources of endogeneity affect partial effects differently in nonlinear models. We study this issue focusing on the Instrumental Variable (IV) Probit and Tobit models. We show that even when a valid IV is available, failing to differentiate between the two types of endogeneity can lead to either under- or over-estimation of the partial effects. We develop simple estimators of the bounds on the partial effects and provide easy to implement confidence intervals that correctly account for both types of endogeneity. We illustrate the methods in a Monte Carlo simulation and an empirical application.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Rivers, D. and Q. H. Vuong (1988) Limited Information Estimators And Exogeneity Tests For Simultaneous Probit Models1.00054100%
2Smith, R. J. and R. W. Blundell (1986) An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply1.00054100%
3Wooldridge, J. M (2010) Econometric Analysis of Cross Section and Panel Data, Second Edition1.00054100%
4Imbens, G. and W. Newey (2009) Identification and Estimation of Triangular Simultaneous Equations Models without Additivity0.73732100%
5Adusumilli, K. and T. Otsu (2018) Nonparametric Instrumental Regression with Errors in Variables0.40511100%
6Blundell, R. and J. L. Powell (2003) Endogeneity in Nonparametric and Semiparametric Regression Models, in0.40511100%
7Chesher, A (2003) Identification in Nonseparable Models0.40511100%
8Chesher, A., D. Kim, and A. M. Rosen (2023) IV methods for Tobit models0.40511100%
9Hahn, J. and G. Ridder (2017) Instrumental variable estimation of nonlinear models with nonclassical measurement error using control variables0.40511100%
10Kotlarski, I (1967) On Characterizing The Gamma And The Normal Distribution0.40511100%

Showing the top 10 of 22 scored citations.