Estimation and inference for distribution and quantile functions in endogenous treatment effect models

Yu Chin Hsu, Tsung Chih Lai*, Robert P. Lieli

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract (may include machine translation)

    Given a standard endogenous treatment effect model, we propose nonparametric estimation and inference procedures for the distribution and quantile functions of the potential outcomes among compliers, as well as the local quantile treatment effect function. The preliminary distribution function estimator is a weighted average of indicator functions, but is not monotonically increasing in general. We therefore propose a simple monotonizing method for proper distribution function estimation, and obtain the quantile function estimator by inversion. Our monotonizing method is an alternative to Chernozhukov et al. (2010) and is arguably preferable when the outcome has unbounded support. We show that all the estimators converge weakly to Gaussian processes at the parametric rate, and propose a multiplier bootstrap for uniform inference. Our uniform results thus generalize the pointwise theory developed by Frölich and Melly (2013). Monte Carlo simulations and an application to the effect of fertility on family income distribution illustrate the use of the methods. All results extend to the subpopulation of treated compliers as well.

    Original languageEnglish
    Pages (from-to)22-50
    Number of pages29
    JournalEconometric Reviews
    Volume41
    Issue number1
    DOIs
    StatePublished - 2022

    Keywords

    • Distribution function
    • local quantile treatment effect
    • monotonicity
    • multiplier bootstrap
    • quantile function

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