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Inference on conditional moment restriction models with generated variables

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  • Kimoto, Ryo
  • Otsu, Taisuke

Abstract

A seminal work by Domínguez and Lobato (2004) proposed a consistent estimation method for conditional moment restrictions, which does not rely on additional identification assumptions as in the GMM estimator using unconditional moments and is free from any user-chosen number. Their methodology is further extended by Domínguez and Lobato (2015, 2020) for consistent specification testing of conditional moment restrictions, which may involve generated variables. We follow up this literature and derive the asymptotic distribution of Domínguez and Lobato’s (2004) estimator that involves generated variables. Our simulation result illustrates that ignoring proxy errors in the generated variables may cause severer distortions for the coverage or size properties of statistical inference on parameters.

Suggested Citation

  • Kimoto, Ryo & Otsu, Taisuke, 2022. "Inference on conditional moment restriction models with generated variables," Economics Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:ecolet:v:215:y:2022:i:c:s0165176522001008
    DOI: 10.1016/j.econlet.2022.110454
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    References listed on IDEAS

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    1. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, September.
    2. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    3. Manuel A. Domínguez & Ignacio N. Lobato, 2020. "Specification testing with estimated variables," Econometric Reviews, Taylor & Francis Journals, vol. 39(5), pages 476-494, May.
    4. Domínguez, Manuel A. & Lobato, Ignacio N., 2015. "A Simple Omnibus Overidentification Specification Test For Time Series Econometric Models," Econometric Theory, Cambridge University Press, vol. 31(4), pages 891-910, August.
    5. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Conditional moment restriction; Generated variable; GMM;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    Statistics

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