Abstract
We define a moment-based estimator that maximizes the empirical saddlepoint (ESP) approximation of the distribution of solutions to empirical moment conditions. We call it the ESP estimator. We prove its existence, consistency and asymptotic normality, and we propose novel test statistics. We also show that the ESP estimator corresponds to the MM (method of moments) estimator shrunk toward parameter values with lower implied estimated variance, so it reduces the documented instability of existing moment-based estimators. In the case of just-identified moment conditions, which is the case we focus on, the ESP estimator is different from the MM estimator, unlike the more recent alternatives, such as the empirical-likelihood-type estimators.
Acknowledgments
Parts of the present paper have previously circulated under the title “The Empirical Saddlepoint Likelihood Estimator Applied to Two-Step GMM” [78]. Some proofs of the present paper also borrow technical results from [40]. Helpful comments were provided by Patrick Gagliardini (discussant), Philipp Ketz (discussant), Eric Renault, Enrique Sentana, Aman Ullah and seminar/conference participants at Carnegie Mellon University, CFE-CMStatistics 2017, Swiss Finance Institute (EPFL and the University of Lausanne), 10th French Econometrics Conference (Paris School of Economics), at the Econometric Society European Winter Meeting 2018 (University of Naples Federico II), the University of Luxembourg, and Collegio Carlo Alberto (University of Torino, 2nd LTI conference).
Citation
Benjamin Holcblat. Fallaw Sowell. "The empirical saddlepoint estimator." Electron. J. Statist. 16 (1) 3672 - 3694, 2022. https://doi.org/10.1214/21-EJS1976
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