Estimating Derivatives of Function-Valued Parameters in a Class of\n Moment Condition Models

2016/10/28 by Rothe, Christoph, Dominik Wied, Wied, Dominik
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Economic Policies and Impacts #FOS: Computer and information sciences #Methodology (stat.ME) #Monetary Policy and Economic Impact

paper · pdf · doi:10.48550/arxiv.1610.09363

openalex publication_date 2016/10/28 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

We develop a general approach to estimating the derivative of a\nfunction-valued parameter \θ_o(u) that is identified for every value of\nu as the solution to a moment condition. This setup in particular covers many\ninteresting models for conditional distributions, such as quantile regression\nor distribution regression. Exploiting that \θ_o(u) solves a moment\ncondition, we obtain an explicit expression for its derivative from the\nImplicit Function Theorem, and estimate the components of this expression by\nsuitable sample analogues, which requires the use of (local linear) smoothing.\nOur estimator can then be used for a variety of purposes, including the\nestimation of conditional density functions, quantile partial effects, and\nstructural auction models in economics.\n

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