Nonparametric Identification of Two-Way Unobserved Heterogeneity

2026-08-27

AI Summary

该研究通过奇异值分解方法解决了面板数据中双向未观测异质性识别问题，利用左奇异函数作为代理变量实现参数的非参数识别。

Abstract

We study identification of two-way unobserved heterogeneity in the nonparametric panel regression $G_{it}=g(α_i,γ_t)+\varepsilon_{it}$, where identification of the latent types reduces to constructing identified, \emph{injective} proxies for them. To this end we consider the singular value decomposition (SVD) of the bivariate regression function $g(α,γ)$ on a product domain $Ω_α\timesΩ_γ$, whose left singular functions $\{u_r\}$ serve as proxies for the unobserved heterogeneity parameter $α$. The arguments are symmetric for $\{v_r\}$ vis-à-vis $γ$. We work under an \emph{observational-equivalence simplification}: two values of $α$ that induce the same conditional response $g(α,\cdot)$ are identified, so that the response map $α\mapsto g(α,\cdot)$ is injective by construction. We show two things. First, this reduction is \emph{equivalent} to injectivity of the full collection of left singular eigenfunctions, so no further condition is needed over the infinite collection $\{u_r\}_{r\ge1}$. Second, under a single additional \emph{local injectivity} condition, a finite collection of leading eigenfunctions $U_R=(u_1^{\top},\dots,u_R^{\top})^{\top}$ is injective for all sufficiently large $R$. The proof reduces a global univalence question to a local first-order condition plus a topological compactness argument, bypassing the global Jacobian conditions usually required.

Problem

• nonparametric identification
• unobserved heterogeneity
• panel regression

Innovation

• nonparametric identification
• singular value decomposition (SVD)
• two-way unobserved heterogeneity
• injective proxies
• local injectivity