Culling the herd of moments with penalized empirical likelihood

TL;DR

This paper introduces a penalized empirical likelihood method for high-dimensional models with many moments, effectively identifying invalid moments and improving estimation accuracy.

Contribution

It proposes a novel penalized empirical likelihood estimator with oracle properties and bias correction, enhancing moment selection and inference in high-dimensional settings.

Findings

PEL estimator has oracle property and consistent invalid moment detection

Projected PEL reduces asymptotic bias and improves finite sample accuracy

Simulation results show strong performance in estimation and inference

Abstract

Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This paper investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approximation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference.