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SEMIPARAMETRIC IDENTIFICATION AND FISHER INFORMATION

Published online by Cambridge University Press:  08 April 2021

Juan Carlos Escanciano
Juan Carlos Escanciano*
Affiliation:
Universidad Carlos III de Madrid
*
Address correspondence to Juan Carlos Escanciano, Department of Economics, Universidad Carlos III de Madrid, Getafe, Spain; e-mail: jescanci@eco.uc3m.es.
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Abstract

This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its “quality.” Identification can be regular or irregular, depending on whether the Fisher information for the parameter is positive or zero, respectively. I first characterize these cases in models with densities linear in an infinite-dimensional parameter. I then introduce a novel “generalized Fisher information.” If positive, it implies (possibly irregular) identification when other conditions hold. If zero, it implies impossibility results on rates of estimation. Three examples illustrate the applicability of the general results. First, I consider the canonical example of average densities. Second, I show irregular identification of the median willingness to pay in contingent valuation studies. Finally, I study identification of the discount factor and average measures of risk aversion in a nonparametric Euler equation with nonparametric measurement error in consumption.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 2 , April 2022 , pp. 301 - 338
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

First version: September 20, 2016. Research was funded by the Spanish Programa de Generación de Conocimiento, reference number PGC2018-096732-B-I00. I would like to thank Michael Jansson, Ulrich Müller, Whitney Newey, P.C.B Phillips, Jack Porter, Pedro Sant’Anna, Ruli Xiao, two anonymous referees and seminar participants at BC, Indiana, MIT, Texas A&M, UBC, Vanderbilt, and participants of the 2018 Conference on Identification in Econometrics for useful comments. This paper is dedicated to the memory of Gary Chamberlain, whose research motivated this investigation.

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