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Calculating Confidence Intervals for Continuous and Discontinuous Functions of Estimated Parameters

Author

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  • Ham, John C.

    (New York University, Abu Dhabi)

  • Woutersen, Tiemen

    (Johns Hopkins University)

Abstract

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.

Suggested Citation

  • Ham, John C. & Woutersen, Tiemen, 2011. "Calculating Confidence Intervals for Continuous and Discontinuous Functions of Estimated Parameters," IZA Discussion Papers 5816, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp5816
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    References listed on IDEAS

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    1. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
    2. Gaure, Simen & Røed, Knut & Westlie, Lars, 2012. "Job search incentives and job match quality," Labour Economics, Elsevier, vol. 19(3), pages 438-450.
    3. 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.
    4. Antonio Merlo & Kenneth I. Wolpin, 2008. "The Transition from School to Jail: Youth Crime and High School Completion Among Black Males, Second Version," PIER Working Paper Archive 09-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 16 Jan 2009.
    5. Fitzenberger, Bernd & Osikominu, Aderonke & Paul, Marie, 2010. "The Heterogeneous Effects of Training Incidence and Duration on Labor Market Transitions," IZA Discussion Papers 5269, Institute of Labor Economics (IZA).
    6. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    7. 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.
    8. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    9. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    11. 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.
    12. John C. Ham & Xianghong Li & Lara D. Shore-Sheppard, 2016. "The Employment Dynamics of Disadvantaged Women: Evidence from the SIPP," Journal of Labor Economics, University of Chicago Press, vol. 34(4), pages 899-944.
    13. A. Colin Cameron & Pravin K. Trivedi, 2010. "Microeconometrics Using Stata, Revised Edition," Stata Press books, StataCorp LP, number musr, March.
    14. 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.
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    More about this item

    Keywords

    confidence intervals; simulation; structural models; policy effects;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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