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GMM Efficiency and IPW Estimation for Nonsmooth Functions

Author

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  • Otávio Bartalotti

    (Department of Economics, Tulane University)

Abstract

In a GMM setting this paper analyzes the problem in which we have two sets of moment conditions, where two sets of parameters enter into one set of moment conditions, while only one set of parameters enters into the other, extending Prokhorov and Schmidt's (2009) redundancy results to nonsmooth objective functions, and obtains relatively efficient estimates of interesting parameters in the presence of nuisance parameters. One-step GMM estimation for both set of parameters is asymptotically more efficient than two-step procedures. These results are applied to Wooldridge's (2007) inverse probability weighted estimator (IPW), generalizing the framework to deal with missing data in this context. Two-step estimation of beta_0 is more efficient than using known probabilities of selection, but this is dominated by one-step joint estimation. Examples for missing data quantile regression and instrumental variable quantile regression are provided.

Suggested Citation

  • Otávio Bartalotti, 2013. "GMM Efficiency and IPW Estimation for Nonsmooth Functions," Working Papers 1301, Tulane University, Department of Economics.
    • Handle: RePEc:tul:wpaper:1301
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    File URL: http://repec.tulane.edu/RePEc/pdf/tul1301.pdf
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    References listed on IDEAS

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    Cited by:

    1. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    2. Timo Dimitriadis & Julie Schnaitmann, 2019. "Forecast Encompassing Tests for the Expected Shortfall," Papers 1908.04569, arXiv.org, revised Aug 2020.

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    More about this item

    Keywords

    generalized method of moments; nonsmooth objective functions; inverse probability weighting; missing data; quantile regression;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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