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Culling the herd of moments with penalized empirical likelihood

Jinyuan Chang, Zhentao Shi and Jia Zhang

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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.

Date: 2021-08, Revised 2022-05
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-isf and nep-ore
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Published in Journal of Business & Economic Statistics 2023, Vol. 41, pp. 791-805

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