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Nonstationary Discrete Choice: A Corrigendum and Addendum

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Sainan Jin (Guanghua School of Management, Peking University)
Ling Hu (Dept. of Economics, Ohio State University)

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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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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1516.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1516.

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Length: 53 pages
Date of creation: Jun 2005
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Publication status: Published in Journal of Econometrics (2007), 141(2): 115-130
Handle: RePEc:cwl:cwldpp:1516

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Brownian motion; Brownian local time; Discrete choices; Integrated processes; Pile-up problem; Threshold parameters;

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Find related papers by JEL classification:
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data
C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models

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References listed on IDEAS
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  1. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation, Yale University. [Downloadable!]
  2. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May. [Downloadable!] (restricted)
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  3. 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. [Downloadable!]
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  4. Peter C.B. Phillips, 1999. "Descriptive Econometrics for Nonstationary Time Series with Empirical Illustrations," Cowles Foundation Discussion Papers 1219, Cowles Foundation, Yale University. [Downloadable!]
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  5. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
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  6. 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. [Downloadable!] (restricted)
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