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

Christoph Rothe and Dominik Wied

Journal of Econometrics, 2020, vol. 217, issue 1, 1-19

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.

Keywords: Quantile regression; Distribution regression; Local linear smoothing; Conditional density estimation; Quantile partial effects (search for similar items in EconPapers)
JEL-codes: C13 C21 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:217:y:2020:i:1:p:1-19

DOI: 10.1016/j.jeconom.2019.11.004

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