含不可分第一阶段的可加可分三角模型的闭式估计与一致推断
Closed-form estimation and uniform inference in additively separable triangular models with a nonseparable first stage
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中文总结 AI 辅助
本文针对含不可分第一阶段的可加可分三角模型，推导结果函数的闭式表达式，提出无需正则化的插件估计量，采用经验bootstrap构造一致置信带，完成非参数识别与估计并实现一致推断。
中文摘要 AI 辅助
本文研究含连续内生变量和工具变量且允许不可分第一阶段的可加可分三角模型的非参数识别与估计。在工具变量与不可观测变量独立的条件下，证明结果函数具有以条件累积分布函数为泛函的闭式表达式。所得插件估计量无需正则化，收敛速率为$n^{-m/(2m+1)}$（$m$为模型施加的光滑度阶数），且不存在收敛更快的结果函数估计量。采用经验bootstrap构造一致置信带，使其同时覆盖紧集上每一点的结果函数。
英文摘要
This paper studies the nonparametric identification and estimation of additively separable triangular models with continuous endogenous and instrumental variables, allowing for a nonseparable first-stage equation. Under the independence of instrumental variables and unobservables, we show that the outcome function possesses a closed-form expression as a functional of conditional cumulative distribution functions. The resulting plug-in estimators require no regularization and converge at the rate $n^{-m/(2m+1)}$, where $m$ is the order of smoothness the model imposes. Also, no estimator of the outcome function converges faster. We use the empirical bootstrap to construct a uniform confidence band that covers the outcome function at every point of a compact set simultaneously.
