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.
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- Merlo, Antonio & Wolpin, Kenneth I., 2015.
"The transition from school to jail: Youth crime and high school completion among black males,"
European Economic Review,
Elsevier, vol. 79(C), pages 234-251.
- 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.
- Merlo, Antonio & Wolpin, Kenneth I., 2015. "The Transition from School to Jail: Youth Crime and High School Completion among Black Males," Working Papers 15-004, Rice University, Department of Economics.
- Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
- Inoue, Atsushi & Kilian, Lutz, 2011. "Inference on Impulse Response Functions in Structural VAR Models," CEPR Discussion Papers 8419, C.E.P.R. Discussion Papers.
- Atsushi Inoue & Lutz Kilian, 2013. "Inference on Impulse Response Functions in Structural VAR Models," DSSR Discussion Papers 11, Graduate School of Economics and Management, Tohoku University.
- 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.
- Gaure, Simen & Røed, Knut & Westlie, Lars, 2012. "Job search incentives and job match quality," Labour Economics, Elsevier, vol. 19(3), pages 438-450.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
- 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, 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 1465-1471, November.
- Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
- 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).
- 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.
- Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, 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.
- 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. Full references (including those not matched with items on IDEAS)
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