EconBase
← All papers

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

Keita Sunada

arXiv 23 Aug 2026 · Econometrics

arXiv:2608.22605 · PDF · Extracted main text

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.

Citation extraction

27
references
82
in-text mentions
27
distinct cited
0
self-citations
11,055
main-text words

appendix boundary found by appendix_command · 41% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Newey, Whitney K, Powell, James L, Vella, Francis (1999) Nonparametric estimation of triangular simultaneous equations models1.00054100%
2Chiappori, Pierre-André, Komunjer, Ivana, Kristensen, Dennis (2015) Nonparametric identification and estimation of transformation models0.9285380%
3Torgovitsky, Alexander (2015) Identification of nonseparable models using instruments with small support0.874102100%
4Chernozhukov, Victor, Chetverikov, Denis, Kato, Kengo (2014) Anti-concentration and honest, adaptive confidence bands0.7636267%
5Février, Philippe (2015) Identification of nonseparable triangular models with discrete instruments0.73732100%
6Horowitz, Joel L., Lee, Sokbae (2012) Uniform confidence bands for functions estimated nonparametrically with instrumental variables0.73732100%
7Imbens, Guido W, Newey, Whitney K (2009) Identification and estimation of triangular simultaneous equations models without additivity0.73732100%
8Chen, Xiaohong, Christensen, Timothy M (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression0.64422100%
9Chen, Xiaohong, Christensen, Timothy, Kankanala, Sid (2025) Adaptive estimation and uniform confidence bands for nonparametric structural functions and elasticities0.64422100%
10Torgovitsky, Alexander (2017) Minimum distance from independence estimation of nonseparable instrumental variables models0.64422100%

Showing the top 10 of 27 scored citations.