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Efficient Minimum Distance Estimation with Multiple Rates of Convergence

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Abstract

This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations. Possible applications include econometric problems with two dimensions of asymptotics, due to trimming, tail estimation, infill asymptotic, social interactions, kernel smoothing or any kind of regularization.

Suggested Citation

  • Bertille Antoine & Eric Renault, 2012. "Efficient Minimum Distance Estimation with Multiple Rates of Convergence," Discussion Papers dp12-03, Department of Economics, Simon Fraser University.
  • Handle: RePEc:sfu:sfudps:dp12-03
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    Cited by:

    1. Zhentao Shi & Huanhuan Zheng, 2018. "Structural Estimation of Behavioral Heterogeneity," Papers 1802.03735, arXiv.org.
    2. Guerron-Quintana, Pablo & Inoue, Atsushi & Kilian, Lutz, 2017. "Impulse response matching estimators for DSGE models," Journal of Econometrics, Elsevier, vol. 196(1), pages 144-155.
    3. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    4. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    5. Simon Freyaldenhoven, 2017. "A Generalized Factor Model with Local Factors," 2017 Papers pfr361, Job Market Papers.
    6. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    7. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    8. Krogh, Tord S., 2015. "Macro frictions and theoretical identification of the New Keynesian Phillips curve," Journal of Macroeconomics, Elsevier, vol. 43(C), pages 191-204.
    9. David T. Frazierz & Éric Renault, 2016. "Efficient Two-Step Estimation via Targeting," CIRANO Working Papers 2016s-16, CIRANO.
    10. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    11. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    12. repec:eee:econom:v:201:y:2017:i:2:p:212-227 is not listed on IDEAS

    More about this item

    Keywords

    GMM; Mixed-rates asymptotics; Kernel estimation; Rotation in the coordinate system;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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