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

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

We propose an improved method for constructing likelihood-ratio-based confidence intervals for threshold parameters in threshold regressions. Related methods have been extensively developed in the literature and are asymptotically valid. However, their performance in finite samples is not satisfactory. We suggest two modifications to the standard inverted likelihood ratio approach. First, we consider a middle point adjustment for the boundaries of confidence intervals. Second, we propose an interpolation approach for evaluating the likelihood ratio profile at non-observable threshold values. Our extensive Monte Carlo simulations suggest that our proposed confidence intervals outperform existing methods, including bootstrap approaches, by attaining very accurate coverage rates with relatively short lengths in finite samples.

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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
Contact details of provider: Postal: Sydney, NSW 2006
Phone: 61 +2 9351 5055
Fax: 61 +2 9351 4341
Web page: http://sydney.edu.au/arts/economics
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  1. 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.
  2. 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.
  3. Jesús Gonzalo & Michael Wolf, 2001. "Subsampling inference in threshold autoregressive models," Economics Working Papers 573, Department of Economics and Business, Universitat Pompeu Fabra.
  4. 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.
  5. Oliver Linton & Myunghwan Seo, 2005. "A smoothed least squares estimator for threshold regression models," LSE Research Online Documents on Economics 4434, London School of Economics and Political Science, LSE Library.
  6. Koop, Gary & Potter, Simon M, 1999. "Dynamic Asymmetries in U.S. Unemployment," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 298-312, July.
  7. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
  8. 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.
  9. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  10. 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.
  11. Eo, Yunjong & Morley, James, 2011. "Likelihood-Ratio-Based Confidence Sets for the Timing of Structural Breaks," Working Papers 2011-07, University of Sydney, School of Economics, revised Feb 2014.
  12. 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.
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