Closed-form estimation and uniform inference in additively separable triangular models with a nonseparable first stage

Keita Sunada

Papers from arXiv.org

Abstract: 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.

Date: 2026-08
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