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Nonstationary discrete choice: A corrigendum and addendum

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  • Phillips, Peter C.B.
  • Jin, Sainan
  • Hu, Ling

Abstract

We correct the limit theory presented in an earlier paper by Hu and Phillips (Journal of Econometrics, 2004) for nonstationary time series discrete choice models with multiple choices and thresholds. The new limit theory shows that, in contrast to the binary choice model with nonstationary regressors and a zero threshold where there are dual rates of convergence (n^{1/4} and n^{3/4}), all parameters including the thresholds converge at the rate n^{3/4}. The presence of non-zero thresholds therefore materially affects rates of convergence. Dual rates of convergence reappear when stationary variables are present in the system. Some simulation evidence is provided, showing how the magnitude of the thresholds affects finite sample performance. A new finding is that predicted probabilities and marginal effect estimates have finite sample distributions that manifest a pile-up, or increasing density, towards the limits of the domain of definition.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 141 (2007)
Issue (Month): 2 (December)
Pages: 1115-1130

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Handle: RePEc:eee:econom:v:141:y:2007:i:2:p:1115-1130

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonstationary Binary Choice," Working Paper Series no5, Institute of Economic Research, Seoul National University.
  2. Wooldridge, Jeffrey M., 1986. "Estimation and inference for dependent processes," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 45, pages 2639-2738 Elsevier.
  3. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
  4. Peter C.B. Phillips & Sainan Jin & Ling Hu, 2005. "Nonstationary Discrete Choice: A Corrigendum and Addendum," Cowles Foundation Discussion Papers 1516, Cowles Foundation for Research in Economics, Yale University.
  5. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
  6. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  7. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  8. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Helmut Herwartz & Konstantin A. Kholodilin, 2011. "In-Sample and Out-of-Sample Prediction of Stock Market Bubbles: Cross-Sectional Evidence," Discussion Papers of DIW Berlin 1173, DIW Berlin, German Institute for Economic Research.
  2. Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, EconWPA, revised 15 Dec 2005.
  3. Peter C.B. Phillips & Sainan Jin & Ling Hu, 2005. "Nonstationary Discrete Choice: A Corrigendum and Addendum," Cowles Foundation Discussion Papers 1516, Cowles Foundation for Research in Economics, Yale University.
  4. de Jong, Robert & Hu, Ling, 2011. "A note on nonlinear models with integrated regressors and convergence order results," Economics Letters, Elsevier, vol. 111(1), pages 23-25, April.
  5. Ioannis Kasparis & Peter C.B. Phillips & Tassos Magdalinos, 2012. "Non-linearity Induced Weak Instrumentation," Cowles Foundation Discussion Papers 1872, Cowles Foundation for Research in Economics, Yale University.
  6. Jin, Sainan, 2009. "Discrete choice modeling with nonstationary panels applied to exchange rate regime choice," Journal of Econometrics, Elsevier, vol. 150(2), pages 312-321, June.

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