Optimal Estimation of Large-Dimensional Nonlinear Factor Models

TL;DR

This paper introduces a local principal component analysis method for estimating large-dimensional nonlinear factor models, effectively recovering latent structures without specifying functional forms.

Contribution

It develops a novel local PCA approach combining nearest neighbors and PCA, with proven large-sample properties and optimal convergence rates for nonlinear factor estimation.

Findings

Method achieves optimal uniform convergence rates.

Estimates are consistent and accurate in large samples.

Empirical application demonstrates practical effectiveness.

Abstract

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified. A local principal component analysis method is proposed to estimate the factor structure and recover information on latent variables and latent functions, which combines $K$-nearest neighbors matching and principal component analysis. Large-sample properties are established, including a sharp bound on the matching discrepancy of nearest neighbors, sup-norm error bounds for estimated local factors and factor loadings, and the uniform convergence rate of the factor structure estimator. Under mild conditions our estimator of the latent factor structure can achieve the optimal rate of uniform convergence for nonparametric regression. The method is illustrated with a Monte Carlo experiment and an empirical application studying the effect of tax cuts on economic growth.