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

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  • Francis J. DiTraglia

    (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.

Suggested Citation

  • Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM," PIER Working Paper Archive 14-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 04 Aug 2014.
    • Handle: RePEc:pen:papers:14-037
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    More about this item

    Keywords

    Moment selection; GMM estimation; Model averaging; Focused Information Criterion; Post-selection estimators;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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