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Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models

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Abstract

This paper is concerned with the estimation of first-order autoregressive/unit root models with independent identically distributed normal errors. The models considered include those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive (AR) parameter alpha is allowed to lie in the interval (-1,1], which includes the case of a unit root. Exactly median-unbiased estimators of the AR parameter alpha are proposed. Exact confidence intervals for this parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function and the cumulative impulse response. An unbiased model selection procedure is discussed. The procedures that are introduced are applied to several data series including real exchange rates, the velocity of money, and industrial production.

Suggested Citation

  • Donald W.K. Andrews, 1991. "Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models," Cowles Foundation Discussion Papers 975, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:975 Note: CFP 832.
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    References listed on IDEAS

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    1. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
    2. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    3. Sims, Christopher A & Uhlig, Harald, 1991. "Understanding Unit Rooters: A Helicopter Tour," Econometrica, Econometric Society, vol. 59(6), pages 1591-1599, November.
    4. Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-680, August.
    5. Andrews, Donald W K, 1989. "Power in Econometric Applications," Econometrica, Econometric Society, vol. 57(5), pages 1059-1090, September.
    6. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, pages 435-459.
    7. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
    8. Donald W.K. Andrews & Peter C.B. Phillips, 1986. "Best Median Unbiased Estimation in Linear Regression with Bounded Asymmetric Loss Functions," Cowles Foundation Discussion Papers 786, Cowles Foundation for Research in Economics, Yale University.
    9. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
    10. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    11. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
    12. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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    Cited by:

    1. Klaus Neusser, 1993. "Dynamics of Total Factor Productivities," Revue Économique, Programme National Persée, vol. 44(2), pages 389-418.
    2. Ray C. Fair, 1992. "Estimates of the Bias of Lagged Dependent Variable Coefficient Estimates in Macroeconomic Equations," Cowles Foundation Discussion Papers 1005, Cowles Foundation for Research in Economics, Yale University.
    3. Donald W.K. Andrews & Hong-Yuan Chen, 1992. "Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series," Cowles Foundation Discussion Papers 1026, Cowles Foundation for Research in Economics, Yale University.
    4. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    5. Peter C.B.Phillips & Donggyu Sul, 2002. "Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence," Cowles Foundation Discussion Papers 1362, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

    Autoregressive process; confidence interval; time trend; model selection; unit roots;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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