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A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results

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  • Edward Vytlacil

Abstract

The standard binary choice model in econometrics has the choice determined by a latent index crossing a threshold. The latent index is almost always assumed to be additively separable in observable and unobservable regressors, and most commonly linear in all regressors. This note provides a class of non‐separable latent index functions which will have equivalent representations as additively separable or linear index functions. These results demonstrate that assuming a linear or additively separable latent index function is less restrictive than previously recognized.

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  • Edward Vytlacil, 2006. "A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, August.
  • Handle: RePEc:bla:obuest:v:68:y:2006:i:4:p:515-518
    DOI: 10.1111/j.1468-0084.2006.00175.x
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    1. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Stefan Boes, 2013. "Nonparametric analysis of treatment effects in ordered response models," Empirical Economics, Springer, vol. 44(1), pages 81-109, February.
    2. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    3. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    4. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
    5. Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.
    6. Chen, Heng & Fan, Yanqin, 2019. "Identification and wavelet estimation of weighted ATE under discontinuous and kink incentive assignment mechanisms," Journal of Econometrics, Elsevier, vol. 212(2), pages 476-502.
    7. Alyssa Carlson, 2020. "Relaxing Conditional Independence in an Endogenous Binary Response Model," Working Papers 2008, Department of Economics, University of Missouri.
    8. Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
    9. Yu-Chang Chen & Haitian Xie, 2020. "Global Representation of LATE Model: A Separability Result," Papers 2007.08106, arXiv.org.

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