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A Note on Bias in First-Differenced AR(1) Models

Author

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  • Kazuhiko Hayakawa

    (Hitotsubashi University)

Abstract

In this note, we derive the finite sample bias of the modified ordinary least squares (MOLS) estimator, which was suggested by Wansbeek and Knaap (1999) and reconsidered by Hayakawa (2006a,b). From the formula for the finite sample bias, we find that the bias of the MOLS estimator becomes small as $\rho$, the autoregressive parameter, approaches unity. Simulation results indicate that the MOLS estimator has very small bias and that its empirical size is close to the nominal one.

Suggested Citation

  • Kazuhiko Hayakawa, 2006. "A Note on Bias in First-Differenced AR(1) Models," Economics Bulletin, AccessEcon, vol. 3(27), pages 1-10.
    • Handle: RePEc:ebl:ecbull:eb-06c20015
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    References listed on IDEAS

    as
    1. Kazuhiko Hayakawa, 2007. "Dynamic Panel Data Models with Cross Section Dependence and Heteroscedasticity," Hi-Stat Discussion Paper Series d07-212, Institute of Economic Research, Hitotsubashi University.
    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. Kazuhiko Hayakawa, 2007. "Consistent OLS estimation of AR(1) dynamic panel data models with short time series," Applied Economics Letters, Taylor & Francis Journals, vol. 14(15), pages 1141-1145.
    4. Tanaka, Katsuto, 1983. "Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean," Econometrica, Econometric Society, vol. 51(4), pages 1221-1231, July.
    5. Phillips, Peter C.B. & Han, Chirok, 2008. "Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root," Econometric Theory, Cambridge University Press, vol. 24(3), pages 631-650, June.
    6. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291, Decembrie.
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    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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