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INFERENCE IN INSTRUMENTAL VARIABLE MODELS WITH HETEROSKEDASTICITY AND MANY INSTRUMENTS

Published online by Cambridge University Press:  26 March 2020

Federico Crudu ,
Giovanni Mellace  and
Zsolt Sándor
Federico Crudu
Affiliation:
Università di Siena and CRENoS
Giovanni Mellace*
Affiliation:
University of Southern Denmark
Zsolt Sándor
Affiliation:
Sapientia Hungarian University of Transylvania
*
Address correspondence to Giovanni Mellace, Department of Business and Economics, Campusvej 55, 5230Odense M, Denmark; e-mail: giome@sam.sdu.dk.
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Abstract

This paper proposes novel inference procedures for instrumental variable models in the presence of many, potentially weak instruments that are robust to the presence of heteroskedasticity. First, we provide an Anderson–Rubin-type test for the entire parameter vector that is valid under assumptions weaker than previously proposed Anderson–Rubin-type tests. Second, we consider the case of testing a subset of parameters under the assumption that a consistent estimator for the parameters not under test exists. We show that under the null, the proposed statistics have Gaussian limiting distributions and derive alternative chi-square approximations. An extensive simulation study shows the competitive finite sample properties in terms of size and power of our procedures. Finally, we provide an empirical application using college proximity instruments to estimate the returns to education.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 2 , April 2021 , pp. 281 - 310
Copyright
© Cambridge University Press 2020

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Footnotes

We thank two anonymous referees, the Co-Editor Patrik Guggenberger, and the Editor Peter Phillips for valuable comments and suggestions that greatly improved the paper. We are also grateful to Stanislav Anatolyev, Samuele Centorrino, and Neil Davies for valuable help. F.C. thanks financial support from the Chilean Government through CONICYT’s grant FONDECYT Iniciacion n. 11140433. Z.S. thanks financial support from grant PN-II-ID-PCE-2012-4-0066 of the Romanian Ministry of National Education, CNCS-UEFISCDI.

References

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