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Nonstationary Discrete Choice: A Corrigendum and Addendum




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.

Suggested Citation

  • 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.
  • Handle: RePEc:cwl:cwldpp:1516
    Note: CFP 1214.

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    References listed on IDEAS

    1. 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.
    2. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    3. Phillips, Peter C.B. & Jin, Sainan & Hu, Ling, 2007. "Nonstationary discrete choice: A corrigendum and addendum," Journal of Econometrics, Elsevier, vol. 141(2), pages 1115-1130, December.
    4. 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.
    5. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    6. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
    7. 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.
    8. 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.
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    Cited by:

    1. Helmut Herwartz & Konstantin A. Kholodilin, 2014. "In‐Sample and Out‐of‐Sample Prediction of stock Market Bubbles: Cross‐Sectional Evidence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(1), pages 15-31, January.
    2. Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
    3. Rebeca I. Muñoz Torres & David Shepherd, 2014. "Inflation Targeting and the Consistency of Monetary Policy Decisions in Mexico: an Empirical Analysis with Discrete Choice Models," Manchester School, University of Manchester, vol. 82, pages 21-46, December.
    4. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    5. Xu, Peng, 2015. "Testing for joint significance in nonstationary ordered choice model," Economics Letters, Elsevier, vol. 130(C), pages 5-8.
    6. Phillips, Peter C.B. & Jin, Sainan & Hu, Ling, 2007. "Nonstationary discrete choice: A corrigendum and addendum," Journal of Econometrics, Elsevier, vol. 141(2), pages 1115-1130, December.
    7. 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.
    8. 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.
    9. Nojković, Aleksandra & Petrović, Pavle, 2015. "Monetary policy rule in inflation targeting emerging European countries: A discrete choice approach," Journal of Policy Modeling, Elsevier, vol. 37(4), pages 577-595.
    10. Hyeongwoo Kim & John Jackson & Richard Saba, 2009. "Forecasting the FOMC's interest rate setting behavior: a further analysis," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 145-165.
    11. Jef Boeckx, 2011. "Estimating monetary policy reaction functions : A discrete choice approach," Working Paper Research 210, National Bank of Belgium.

    More about this item


    Brownian motion; Brownian local time; Discrete choices; Integrated processes; Pile-up problem; Threshold parameters;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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