Models defined by moment conditions is at the center of empirical structural economic estimation. One of the challenges is the presence of invalid moments in a large pool of valid moments that may improve estimation efficiency. This paper studies empirical likelihood estimation of moment-defined models in general high-dimensional settings which accommodate invalid moments, where the number of moments and parameters are allowed to be much larger than the sample size. We show that penalized empirical likelihood (PEL) enjoy the oracle property which consistently estimates the invalid moments and the zero coefficients. Although the asymptotic normality of PEL is accompanied by an asymptotic bias term incurred by the herd of moments, PEL can serve as an initial estimator for the second-step projected PEL if the interest lies in the statistical inference of a low-dimensional parameter. Simulation exercises are carried out to demonstrate excellent finite sample performance of our methods in estimation and inference. We apply this method to stay the determinants of institution in development economics.

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