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IDENTIFICATION OF JOINT DISTRIBUTIONS IN DEPENDENT FACTOR MODELS

Published online by Cambridge University Press:  21 February 2017

Dan Ben-Moshe
Dan Ben-Moshe*
Affiliation:
The Hebrew University of Jerusalem
*
*Address correspondence to Dan Ben-Moshe, Department of Economics, The Hebrew University of Jerusalem, Mt. Scopus, Jerusalem 91905, Israel; e-mail: danbm@huji.ac.il.
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Abstract

This paper studies linear factor models that have arbitrarily dependent factors. Assuming that the coefficients are known and that their matrix representation satisfies rank conditions, we identify the nonparametric joint distribution of the unobserved factors using first and then second-order partial derivatives of the log characteristic function of the observed variables. In conjunction with these identification strategies the mean and variance of the vector of factors are identified. The main result provides necessary and sufficient conditions for identification of the joint distribution of the factors. In an illustrative example, we show identification of an earnings dynamics model with a subset of arbitrarily dependent income shocks. Closed-form formulas lead to estimators that converge uniformly and despite being based on inverse Fourier transforms have tight confidence bands around their theoretical counterparts in Monte Carlo simulations.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 1 , February 2018 , pp. 134 - 165
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

This paper is based on the first chapter of my PhD Thesis and is a revised version of my job market paper. I am grateful to Rosa Matzkin and Jinyong Hahn for their generous support, advice, and guidance. I benefited greatly from the feedback of two anonymous referees and the editor Liangjun Su, comments at seminars at Haifa University, Hebrew University of Jerusalem, Tel Aviv University, UCL and UCLA and discussions with Stefan Hoderlein, Max Kasy, Arthur Lewbel, Áureo de Paula, Daniel Wilhelm and Martin Weidner. The support of a grant from the Maurice Falk Institute for Economic Research is gratefully acknowledged.

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