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

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

Abstract

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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Bibliographic Info

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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Keywords: Threshold regression; Finite-sample inference; Inverted likelihood ratio;

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  1. Eo, Yunjong & Morley, James, 2011. "Likelihood-Ratio-Based Confidence Sets for the Timing of Structural Breaks," Working Papers, University of Sydney, School of Economics 2011-07, University of Sydney, School of Economics, revised Feb 2014.
  2. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, Elsevier, vol. 127(2), pages 201-224, August.
  3. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 274-294.
  4. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  5. Koop, Gary & Potter, Simon M, 1999. "Dynamic Asymmetries in U.S. Unemployment," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 17(3), pages 298-312, July.
  6. Alan J. Auerbach & Yuriy Gorodnichenko, 2010. "Measuring the Output Responses to Fiscal Policy," NBER Working Papers 16311, National Bureau of Economic Research, Inc.
  7. Pesaran, H.M. & Potter, S.M., 1995. "A Floor and Ceiling Model of U.S. Output," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9407, Faculty of Economics, University of Cambridge.
  8. Jesús Gonzalo & Jean-Yves Pitarakis, 2012. "Estimation and inference in threshold type regime switching models," Economics Working Papers we1204, Universidad Carlos III, Departamento de Economía.
  9. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
  10. Oliver Linton & Myunghwan Seo, 2005. "A smoothed least squares estimator for threshold regression models," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 4434, London School of Economics and Political Science, LSE Library.
  11. 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.
  12. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics, Boston College Department of Economics 319., Boston College Department of Economics, revised 12 May 1998.
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