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Nonstationary discrete choice

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

Abstract

This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence (n^{3/4} and n^{1/4}) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for the sample proportions of the various choices. The new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters.
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Suggested Citation

  • Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
  • Handle: RePEc:eee:econom:v:120:y:2004:i:1:p:103-138
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    References listed on IDEAS

    as
    1. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, pages 1249-1280.
    2. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
    3. Graciela Kaminsky & Saul Lizondo & Carmen M. Reinhart, 1998. "Leading Indicators of Currency Crises," IMF Staff Papers, Palgrave Macmillan, vol. 45(1), pages 1-48, March.
    4. 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.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, pages 277-301.
    6. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, pages 277-301.
    8. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    9. 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.
    10. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation for Research in Economics, Yale University.
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    Citations

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    Cited by:

    1. Isela Elizabeth Téllez León & Francisco Venegas Martínez, 2013. "Principales determinantes en las decisiones de política monetaria de México: un análisis econométrico," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 28(1), pages 79-108.
    2. 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.
    3. Hyeongwoo Kim & Wen Shi, 2014. "The Determinants of the Benchmark Interest Rates in China: A Discrete Choice Model Approach," Auburn Economics Working Paper Series auwp2014-12, Department of Economics, Auburn University.
    4. Hyeongwoo Kim, 2014. "Estimating Interest Rate Setting Behavior in Korea: An Ordered Probit Model Approach," Auburn Economics Working Paper Series auwp2014-02, Department of Economics, Auburn University.
    5. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    6. Xu, Peng, 2015. "Testing for joint significance in nonstationary ordered choice model," Economics Letters, Elsevier, vol. 130(C), pages 5-8.
    7. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, pages 710-738.
    8. Hyeongwoo Kim & Wen Shi & Kwang-Myoung Hwang, 2016. "Estimating interest rate setting behaviour in Korea: a constrained ordered choices model approach," Applied Economics, Taylor & Francis Journals, vol. 48(23), pages 2199-2214, May.
    9. repec:eee:ecolet:v:159:y:2017:i:c:p:37-41 is not listed on IDEAS
    10. Phillips, Peter C.B. & Jin, Sainan & Hu, Ling, 2007. "Nonstationary discrete choice: A corrigendum and addendum," Journal of Econometrics, Elsevier, pages 1115-1130.
    11. David-Jan Jansen & Jakob de Haan, 2006. "Does ECB Communication Help in Predicting its Interest Rate Decisions?," CESifo Working Paper Series 1804, CESifo Group Munich.
    12. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    13. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, Elsevier.
    14. John B. Carlson & Ben R. Craig & William R. Melick, 2005. "Recovering market expectations of FOMC rate changes with options on federal funds futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(12), pages 1203-1242, December.
    15. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation for Research in Economics, Yale University.
    16. Dong He & Laurent L. Pauwels, 2008. "What Prompts the People's Bank of China to Change Its Monetary Policy Stance? Evidence from a Discrete Choice Model," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 16(6), pages 1-21.
    17. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, pages 103-138.
    18. 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.
    19. Hans G. P. Jansen & John Pender & Amy Damon & Willem Wielemaker & Rob Schipper, 2006. "Policies for sustainable development in the hillside areas of Honduras: a quantitative livelihoods approach," Agricultural Economics, International Association of Agricultural Economists, vol. 34(2), pages 141-153, March.
    20. Pauwels, Laurent L. & Vasnev, Andrey L., 2016. "A note on the estimation of optimal weights for density forecast combinations," International Journal of Forecasting, Elsevier, vol. 32(2), pages 391-397.
    21. 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.
    22. Chiara Scotti, 2006. "A bivariate model of Fed and ECB main policy rates," International Finance Discussion Papers 875, Board of Governors of the Federal Reserve System (U.S.).
    23. YABE, Ryota, 2014. "Empirical Likelihood Confidence Intervals for Nonparametric Nonlinear Nonstationary Regression Models," Discussion Papers 2014-20, Graduate School of Economics, Hitotsubashi University.
    24. 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.
    25. Jef Boeckx, 2011. "Estimating monetary policy reaction functions : A discrete choice approach," Working Paper Research 210, National Bank of Belgium.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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