Fixed Effects and the "Leave-Out" Instrument *

52 Pages Posted: 16 Apr 2024 Last revised: 2 Jul 2024

See all articles by Cameron Ellis

Cameron Ellis

University of Iowa - Department of Finance

Johannes Gerd Jaspersen

Ludwig Maximilian University of Munich (LMU) - Faculty of Business Administration (Munich School of Management)

Date Written: April 09, 2024

Abstract

We explore a novel bias in "leave-out" instruments that is induced by overlapping fixed effects. These instruments estimate exogenous shocks by averaging other observations along one data dimension. However, the inclusion of fixed effects reintroduces the focal observation's bias through demeaning. We show generally that the size of the bias is determined by the number of observations used to estimate both the fixed effect and the instrument. Our findings imply that the standard instrument strength test is meaningless in this context. We illustrate the magnitude of the bias via simulation and with patent examiner data. Even when scrambling the patent examiners, thus removing any instrument validity, the bias leads to a first-stage F-statistic over 1,000. We provide multiple solutions through either adjustment of the fixed effects or the instrument. The combination of leave-out instruments and overlapping fixed effects occurs regularly in Industrial Organization, Finance, Criminology, Education, and several other topics. By detailing when this combination introduces bias and when it does not, we provide a guidebook for applied econometricians who want to use leave-out instruments in their analyses.

Keywords: Leave-Out Instruments, Judge Fixed Effects, Hausman Instruments, Jackknife IV

JEL Classification: C13, C36, D22, K00

Suggested Citation

Ellis, Cameron and Jaspersen, Johannes Gerd, Fixed Effects and the "Leave-Out" Instrument * (April 09, 2024). Available at SSRN: https://ssrn.com/abstract=4787799 or http://dx.doi.org/10.2139/ssrn.4787799

Cameron Ellis

University of Iowa - Department of Finance ( email )

Iowa City, IA 52242-1000
United States

Johannes Gerd Jaspersen (Contact Author)

Ludwig Maximilian University of Munich (LMU) - Faculty of Business Administration (Munich School of Management) ( email )

Schackstr. 4
Munich, DE 80539
Germany

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