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Marginal effects for probit and tobit with endogeneity

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  • Kirill Evdokimov
  • Ilze Kalnina
  • Andrei Zeleneev

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.

Suggested Citation

  • Kirill Evdokimov & Ilze Kalnina & Andrei Zeleneev, 2024. "Marginal effects for probit and tobit with endogeneity," CeMMAP working papers 04/24, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:04/24
    DOI: 10.47004/wp.cem.2024.0424
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    References listed on IDEAS

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    1. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
    2. Newey, Whitney K., 1987. "Efficient estimation of limited dependent variable models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 36(3), pages 231-250, November.
    3. Hahn, Jinyong & Ridder, Geert, 2017. "Instrumental variable estimation of nonlinear models with nonclassical measurement error using control variables," Journal of Econometrics, Elsevier, vol. 200(2), pages 238-250.
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