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Estimating derivatives of function-valued parameters in a class of moment condition models

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  • Rothe, Christoph
  • Wied, Dominik

Abstract

We develop a general approach to estimating the derivative of a function-valued parameter θo(u) that is identified for every value of u as the solution to a moment condition. This setup in particular covers interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that θo(u) solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and then estimate the components of this expression by suitable sample analogues. The last step generally involves (local linear) smoothing of the empirical moment condition. Our estimators can then be used for a variety of purposes, including the estimation of conditional density functions, quantile partial effects, and the distribution of bidders’ valuations in structural auction models.

Suggested Citation

  • Rothe, Christoph & Wied, Dominik, 2020. "Estimating derivatives of function-valued parameters in a class of moment condition models," Journal of Econometrics, Elsevier, vol. 217(1), pages 1-19.
    • Handle: RePEc:eee:econom:v:217:y:2020:i:1:p:1-19
    DOI: 10.1016/j.jeconom.2019.11.004
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    Cited by:

    1. Rafael Weißbach & Dominik Wied, 2022. "Truncating the exponential with a uniform distribution," Statistical Papers, Springer, vol. 63(4), pages 1247-1270, August.
    2. Jonas Meier, 2020. "Multivariate Distribution Regression," Diskussionsschriften dp2023, Universitaet Bern, Departement Volkswirtschaft.

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    More about this item

    Keywords

    Quantile regression; Distribution regression; Local linear smoothing; Conditional density estimation; Quantile partial effects;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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