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Estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

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  • Hsu, Shih-Hsun
  • Kuan, Chung-Ming

Abstract

A well-known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments. In this paper, we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability. These unconditional moments depend on the “instruments” generated from a “generically comprehensively revealing” function, and they are further projected along the exponential Fourier series. The objective function is based on the resulting Fourier coefficients, from which an estimator can be easily computed. A novel feature of our method is that the full continuum of unconditional moments is incorporated into each Fourier coefficient. We show that, when the number of Fourier coefficients in the objective function grows at a proper rate, the proposed estimator is consistent and asymptotically normally distributed. An efficient estimator is also readily obtained via the conventional two-step GMM method. Our simulations confirm that the proposed estimator compares favorably with that of Domínguez and Lobato (2004, Econometrica) in terms of bias, standard error, and mean squared error.

Suggested Citation

  • Hsu, Shih-Hsun & Kuan, Chung-Ming, 2011. "Estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments," Journal of Econometrics, Elsevier, vol. 165(1), pages 87-99.
    • Handle: RePEc:eee:econom:v:165:y:2011:i:1:p:87-99
    DOI: 10.1016/j.jeconom.2011.05.008
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    Cited by:

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    3. Carlos Velasco & Xuexin Wang, 2021. "Instrumental variable estimation via a continuum of instruments with an application to estimating the elasticity of intertemporal substitution in consumption," Working Papers 2024-09-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Laurent Davezies & Xavier D'Haultfœuille & Martin Mugnier, 2023. "Fixed‐effects binary choice models with three or more periods," Quantitative Economics, Econometric Society, vol. 14(3), pages 1105-1132, July.
    5. Han, Hyojin, 2020. "On the identification of models with conditional characteristic functions," Economics Letters, Elsevier, vol. 186(C).
    6. Sadat, Nafis, 2015. "Estimation of International Financial Integration: Evidence from European Countries," MPRA Paper 66283, University Library of Munich, Germany, revised 25 Aug 2015.

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    More about this item

    Keywords

    Conditional moment restrictions; Fourier coefficients; Generically comprehensive revealing function; Global identifiability; GMM;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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