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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.

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File URL: http://www.sfu.ca/econ-research/RePEc/sfu/sfudps/dp12-03.pdf
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Bibliographic Info

Paper provided by Department of Economics, Simon Fraser University in its series Discussion Papers with number dp12-03.

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Length: 47
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:sfu:sfudps:dp12-03

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Postal: Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada
Phone: (778)782-3508
Fax: (778)782-5944
Web page: http://www.sfu.ca/economics.html
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Postal: Working Paper Coordinator, Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada
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Keywords: GMM; Mixed-rates asymptotics; Kernel estimation; Rotation in the coordinate system;

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References

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Citations

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Cited by:
  1. Atsushi Inoue & Lutz Kilian, 2014. "Joint Confidence Sets for Structural Impulse Responses," Departmental Working Papers, Southern Methodist University, Department of Economics 1401, Southern Methodist University, Department of Economics.
  2. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, Elsevier, vol. 173(1), pages 57-82.
  3. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, Elsevier, vol. 172(2), pages 255-274.

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