Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM

Francis DiTraglia

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

Abstract: In finite samples, the use of a slightly endogenous but highly relevant instrument can reduce mean-squared error (MSE). Building on this observation, I propose a moment selection criterion for GMM in which moment conditions are chosen based on the MSE of their associated estimators rather than their validity: the focused moment selection criterion (FMSC). I then show how the framework used to derive the FMSC can address the problem of inference post-moment selection. Treating post-selection estimators as a special case of moment-averaging, in which estimators based on different moment sets are given data-dependent weights, I propose a simulation-based procedure to construct valid confidence intervals for a variety of formal and informal moment-selection procedures. Both the FMSC and confidence interval procedure perform well in simulations. I conclude with an empirical example examining the effect of instrument selection on the estimated relationship between malaria transmission and per-capita income.

Keywords: Moment selection; GMM estimation; Model averaging; Focused Information Criterion; Post-selection estimators (search for similar items in EconPapers)
JEL-codes: C21 C26 C52 (search for similar items in EconPapers)
Pages: 58 pages
Date: 2011-11-09, Revised 2014-08-04
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

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Journal Article: Using invalid instruments on purpose: Focused moment selection and averaging for GMM (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:pen:papers:14-037

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