Calculating Confidence Intervals for Continuous and Discontinuous Functions of Estimated Parameters
The delta method is commonly used to calculate confidence intervals of functions of estimated parameters that are differentiable with non-zero, bounded derivatives. When the delta method is inappropriate, researchers usually first use a bootstrap procedure where they i) repeatedly take a draw from the asymptotic distribution of the parameter values and ii) calculate the function value for this draw. They then trim the bottom and top of the distribution of function values to obtain their confidence interval. This note first provides several examples where this procedure and/or delta method fail to provide an appropriate confidence interval. It next presents a method that is appropriate for constructing confidence intervals for functions that are discontinuous or are continuous but have zero or unbounded derivatives. In particular the coverage probabilities for our method converge uniformly to their nominal values, which is not necessarily true for the other methods discussed above.
|Date of creation:||Jun 2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +49 228 3894 223
Fax: +49 228 3894 180
Web page: http://www.iza.org
|Order Information:|| Postal: IZA, Margard Ody, P.O. Box 7240, D-53072 Bonn, Germany|
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.:
- Gunter J. Hitsch & Ali Horta�su & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-63, March.
- Fitzenberger, Bernd & Osikominu, Aderonke & Paul, Marie, 2010.
"The heterogeneous effects of training incidence and duration on labor market transitions,"
ZEW Discussion Papers
10-077, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
- Fitzenberger, Bernd & Osikominu, Aderonke & Paul, Marie, 2010. "The Heterogeneous Effects of Training Incidence and Duration on Labor Market Transitions," IZA Discussion Papers 5269, Institute for the Study of Labor (IZA).
- Inoue, Atsushi & Kilian, Lutz, 2013.
"Inference on impulse response functions in structural VAR models,"
Journal of Econometrics,
Elsevier, vol. 177(1), pages 1-13.
- Atsushi Inoue & Lutz Kilian, 2013. "Inference on Impulse Response Functions in Structural VAR Models," TERG Discussion Papers 307, Graduate School of Economics and Management, Tohoku University.
- Inoue, Atsushi & Kilian, Lutz, 2011. "Inference on Impulse Response Functions in Structural VAR Models," CEPR Discussion Papers 8419, C.E.P.R. Discussion Papers.
- Donald W.K. Andrews, 1988.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
- Andrews, Donald W K, 1987. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers [On Unification of the Asymptotic Theory of Nonlinear Econometric Models]," Econometrica, Econometric Society, vol. 55(6), pages 1465-71, November.
- Antonio Merlo & Kenneth I. Wolpin, 2008. "The Transition from School to Jail: Youth Crime and High School Completion Among Black Males," PIER Working Paper Archive 08-033, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Gaure, Simen & Røed, Knut & Westlie, Lars, 2012. "Job search incentives and job match quality," Labour Economics, Elsevier, vol. 19(3), pages 438-450.
- Eberwein, Curtis & Ham, John C. & LaLonde, Robert J., 2002. "Alternative methods of estimating program effects in event history models," Labour Economics, Elsevier, vol. 9(2), pages 249-278, April.
- Keisuke Hirano & Jack R. Porter, 2012.
"Impossibility Results for Nondifferentiable Functionals,"
Econometric Society, vol. 80(4), pages 1769-1790, 07.
- Hirano, Keisuke & Porter, Jack, 2009. "Impossibility Results for Nondifferentiable Functionals," MPRA Paper 15990, University Library of Munich, Germany.
When requesting a correction, please mention this item's handle: RePEc:iza:izadps:dp5816. 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: (Mark Fallak)
If references are entirely missing, you can add them using this form.