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Nonparametric Estimation of Dynamic Discrete Choice Models for Time Series Data

Author

Listed:
  • Byeong U. Park

    (Department of Statistics, Seoul National University)

  • Leopold Simar

    (Inst. de Statistique, Biostatistique et Sciences Actuarielles, Universite Catholique de Louvain)

  • Valentin Zelenyuk

    (School of Economics, The University of Queensland)

Abstract

The non-parametric quasi-likelihood method is generalized to the context of discrete choice models for time series data where dynamics is modelled via lags of the discrete dependent variable appearing among regressors. Consistency and asymptotic normality of the estimator for such models in the general case is derived under the assumption of stationarity with strong mixing condition. Monte Carlo examples are used to illustrate performance of the proposed estimator relative to the fully parametric approach. Possible applications for the proposed estimator may include modelling and forecasting of probabilities of whether a subject would get a positive response to a treatment, whether in the next period an economy would enter a recession, or whether a stock market will go down or up, etc.

Suggested Citation

  • Byeong U. Park & Leopold Simar & Valentin Zelenyuk, 2016. "Nonparametric Estimation of Dynamic Discrete Choice Models for Time Series Data," CEPA Working Papers Series WP062016, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:116
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    File URL: https://economics.uq.edu.au/files/5043/WP062016.pdf
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    References listed on IDEAS

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    1. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    2. Harding, Don & Pagan, Adrian, 2011. "An Econometric Analysis of Some Models for Constructed Binary Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 86-95.
    3. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    4. Heikki Kauppi & Pentti Saikkonen, 2008. "Predicting U.S. Recessions with Dynamic Binary Response Models," The Review of Economics and Statistics, MIT Press, vol. 90(4), pages 777-791, November.
    5. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
    6. de Jong, Robert M. & Woutersen, Tiemen, 2011. "Dynamic Time Series Binary Choice," Econometric Theory, Cambridge University Press, vol. 27(4), pages 673-702, August.
    7. Russell, Jeffrey & Engle, Robert F, 1998. "Econometric Analysis of Discrete-Valued Irregularly-Spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model," University of California at San Diego, Economics Working Paper Series qt00m2c5hk, Department of Economics, UC San Diego.
    8. Li, Degui & Simar, Léopold & Zelenyuk, Valentin, 2016. "Generalized nonparametric smoothing with mixed discrete and continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 424-444.
    9. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    10. Arturo Estrella & Frederic S. Mishkin, 1998. "Predicting U.S. Recessions: Financial Variables As Leading Indicators," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 45-61, February.
    11. Marcelle Chauvet & Simon Potter, 2005. "Forecasting recessions using the yield curve," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(2), pages 77-103.
    12. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    13. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    14. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
    15. Michael Dueker, 2005. "Dynamic Forecasts of Qualitative Variables: A Qual VAR Model of U.S. Recessions," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 96-104, January.
    16. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    17. Dong, Yingying & Lewbel, Arthur, 2011. "Nonparametric identification of a binary random factor in cross section data," Journal of Econometrics, Elsevier, vol. 163(2), pages 163-171, August.
    18. Michael J. Dueker, 1997. "Strengthening the case for the yield curve as a predictor of U.S. recessions," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 41-51.
    19. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    20. Heikki Kauppi, 2012. "Predicting the Direction of the Fed's Target Rate," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 31(1), pages 47-67, January.
    21. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    22. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    23. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    24. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    25. Russell, Jeffrey & Engle, Robert F, 1998. "Econometric Analysis of Discrete-Valued Irregularly-Spaced Financial Transactions Data Using a New Autoregressive Conditional Multinomial Model," University of California at San Diego, Economics Working Paper Series qt00m2c5hk, Department of Economics, UC San Diego.
    26. Cosslett, Stephen R, 1987. "Efficiency Bounds for Distribution-free Estimators of the Binary," Econometrica, Econometric Society, vol. 55(3), pages 559-585, May.
    27. McFadden, Daniel, 1974. "The measurement of urban travel demand," Journal of Public Economics, Elsevier, vol. 3(4), pages 303-328, November.
    28. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    29. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    30. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
    31. Russell, Jeffrey R. & Engle, Robert F., 2005. "A Discrete-State Continuous-Time Model of Financial Transactions Prices and Times: The Autoregressive Conditional Multinomial-Autoregressive Conditional Duration Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 166-180, April.
    32. Estrella, Arturo, 1998. "A New Measure of Fit for Equations with Dichotomous Dependent Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 198-205, April.
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    Citations

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    Cited by:

    1. Camilla Mastromarco & Léopold Simar & Valentin Zelenyuk, 2021. "Predicting recessions with a frontier measure of output gap: an application to Italian economy," Empirical Economics, Springer, vol. 60(6), pages 2701-2740, June.
    2. Byeong U. Park & Léopold Simar & Valentin Zelenyuk, 2020. "Forecasting of recessions via dynamic probit for time series: replication and extension of Kauppi and Saikkonen (2008)," Empirical Economics, Springer, vol. 58(1), pages 379-392, January.
    3. Mastromarco, Camilla & Simar, Leopold & Wilson, Paul, 2019. "Predicting Recessions: A New Measure of Output Gap as Predictor," LIDAM Discussion Papers ISBA 2019023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Truquet, Lionel, 2023. "Strong mixing properties of discrete-valued time series with exogenous covariates," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 294-317.
    5. Qingyan Ning & Maosheng Li, 2022. "Modeling Pedestrian Detour Behavior By-Passing Conflict Areas," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    6. Byeong U. Park & Leopold Simar & Valentin Zelenyuk, 2017. "Revisiting Forecasting of Recessions via Dynamic Probit for Time Series by Kauppi and Saikkonen (2008)," CEPA Working Papers Series WP032017, School of Economics, University of Queensland, Australia.
    7. Toru Kitagawa & Weining Wang & Mengshan Xu, 2022. "Policy Choice in Time Series by Empirical Welfare Maximization," Papers 2205.03970, arXiv.org, revised Jun 2023.
    8. Tatiana Anopchenko & Olga Gorbaneva & Elena Lazareva & Anton Murzin & Gennady Ougolnitsky, 2019. "Modeling Public—Private Partnerships in Innovative Economy: A Regional Aspect," Sustainability, MDPI, vol. 11(20), pages 1-18, October.

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    More about this item

    Keywords

    Nonparametric; Dynamic Discrete Choice; Probit;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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