Efficient Minimum Distance Estimation with Multiple Rates of Convergence
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.
|Date of creation:||Mar 2012|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.sfu.ca/economics.html
More information through EDIRC
|Order Information:|| Postal: Working Paper Coordinator, Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada|
Web: http://www.sfu.ca/economics/research/publications.html Email:
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Phillips, Peter C B & Park, Joon Y, 1988.
"On the Formulation of Wald Tests of Nonlinear Restrictions,"
Econometric Society, vol. 56(5), pages 1065-83, September.
- Peter C.B. Phillips & Joon Y. Park, 1986. "On the Formulation of Wald Tests of Nonlinear Restrictions," Cowles Foundation Discussion Papers 801, Cowles Foundation for Research in Economics, Yale University.
- James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
- Yacine Aït-Sahalia & Jean Jacod, 2008. "Fisher's Information for Discretely Sampled Lévy Processes," Econometrica, Econometric Society, vol. 76(4), pages 727-761, 07.
- Caner, Mehmet, 2008.
"Nearly-singular design in GMM and generalized empirical likelihood estimators,"
Journal of Econometrics,
Elsevier, vol. 144(2), pages 511-523, June.
- Mehmet Caner, 2005. "Nearly Singular Design In Gmm And Generalized Empirical Likelihood Estimators," Econometrics 0509019, EconWPA.
- Mehmet Caner, 2005. "Nearly Singular design in gmm and generalized empirical likelihood estimators," Working Papers 211, University of Pittsburgh, Department of Economics, revised Jan 2005.
- Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
- Phillips, P.C.B., 1989.
"Partially Identified Econometric Models,"
Cambridge University Press, vol. 5(02), pages 181-240, August.
- Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
- Yuichi Kitamura & Peter C.B. Phillips, 1994.
"Fully Modified IV, GIVE and GMM Estimation with Possibly Non-Stationary Regressions and Instruments,"
Cowles Foundation Discussion Papers
1082, Cowles Foundation for Research in Economics, Yale University.
- Kitamura, Yuichi & Phillips, Peter C. B., 1997. "Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments," Journal of Econometrics, Elsevier, vol. 80(1), pages 85-123, September.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Douglas Staiger & James H. Stock, 1997.
"Instrumental Variables Regression with Weak Instruments,"
Econometric Society, vol. 65(3), pages 557-586, May.
- Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
- Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
- Federico M. Bandi & Peter C.B. Phillips, 2005.
"A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions,"
Cowles Foundation Discussion Papers
1522, Cowles Foundation for Research in Economics, Yale University.
- Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, vol. 137(2), pages 354-395, April.
- repec:dgr:uvatin:20010067 is not listed on IDEAS
- Kotlyarova, Yulia & Zinde-Walsh, Victoria, 2006.
"Non- and semi-parametric estimation in models with unknown smoothness,"
Elsevier, vol. 93(3), pages 379-386, December.
- Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Non And Semi-Parametric Estimation In Models With Unknown Smoothness," Departmental Working Papers 2006-15, McGill University, Department of Economics.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- P. Gagliardini & C. Gourieroux & E. Renault, 2011.
"Efficient Derivative Pricing by the Extended Method of Moments,"
Econometric Society, vol. 79(4), pages 1181-1232, 07.
- Patrick GAGLIARDINI & Christian GOURIEROUX & Eric RENAULT, 2004. "Efficient Derivative Pricing By The Extended Method of Moments," Swiss Finance Institute Research Paper Series 10-07, Swiss Finance Institute, revised Oct 2009.
- Lee, Lung-fei, 2010. "Pooling Estimates With Different Rates Of Convergence: A Minimum Χ2 Approach With Emphasis On A Social Interactions Model," Econometric Theory, Cambridge University Press, vol. 26(01), pages 260-299, February.
- Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
- Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
- Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
- Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S135-S171, 01.
- Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
When requesting a correction, please mention this item's handle: RePEc:sfu:sfudps:dp12-03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Working Paper Coordinator)
If references are entirely missing, you can add them using this form.