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Culling the Herd of Moments with Penalized Empirical Likelihood

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  • Jinyuan Chang
  • Zhentao Shi
  • Jia Zhang

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 article 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.

Suggested Citation

  • Jinyuan Chang & Zhentao Shi & Jia Zhang, 2023. "Culling the Herd of Moments with Penalized Empirical Likelihood," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(3), pages 791-805, July.
    • Handle: RePEc:taf:jnlbes:v:41:y:2023:i:3:p:791-805
    DOI: 10.1080/07350015.2022.2071903
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