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Improving Likelihood-Ratio-Based Confidence Intervals for Threshold Parameters in Finite Samples

  • Donayre, Luiggi
  • Eo, Yunjong
  • Morley, James

Within the context of threshold regressions, we show that asymptotically-valid likelihood-ratio-based confidence intervals for threshold parameters perform poorly in finite samples when the threshold effect is large. A large threshold effect leads to a poor approximation of the profile likelihood in finite samples such that the conventional approach to constructing confidence intervals excludes the true threshold parameter value too often, resulting in low coverage rates. We propose a modification to the standard likelihood-ratio-based confidence interval that has coverage rates at least as high as the nominal level, while still being informative in the sense of including relatively few observations of the threshold variable.

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Paper provided by University of Sydney, School of Economics in its series Working Papers with number 2014-04.

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Date of creation: Mar 2014
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Handle: RePEc:syd:wpaper:2014-04
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  1. Jesús Gonzalo & Jean-Yves Pitarakis, 2013. "Estimation and inference in threshold type regime switching models," Chapters, in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 8, pages 189-205 Edward Elgar Publishing.
  2. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
  3. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
  4. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, 07.
  5. Jesús Gonzalo & Michael Wolf, 2001. "Subsampling inference in threshold autoregressive models," Economics Working Papers 573, Department of Economics and Business, Universitat Pompeu Fabra.
  6. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  7. Alan J. Auerbach & Yuriy Gorodnichenko, 2012. "Measuring the Output Responses to Fiscal Policy," American Economic Journal: Economic Policy, American Economic Association, vol. 4(2), pages 1-27, May.
  8. Nathan S. Balke, 2000. "Credit and Economic Activity: Credit Regimes and Nonlinear Propagation of Shocks," The Review of Economics and Statistics, MIT Press, vol. 82(2), pages 344-349, May.
  9. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  10. Pesaran, H.M. & Potter, S.M., 1995. "A Floor and Ceiling Model of U.S. Output," Cambridge Working Papers in Economics 9407, Faculty of Economics, University of Cambridge.
  11. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
  12. Gary Koop & Simon M. Potter, 1998. "Dynamic asymmetries in US unemployment," ESE Discussion Papers 15, Edinburgh School of Economics, University of Edinburgh.
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