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Understanding Unit Rooters: A Helicopter Tour

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  • Sims, Christopher A
  • Uhlig, Harald

Abstract

For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient conditional on the estimate coexists with an asymmetric distribution for the estimate conditional on the coefficient. Prior densities implicit in treating classical significance levels as if they were Bayesian posterior probabilities are calculated. They are shown to depend sensitively on the estimated coefficient and to put substantial probability on values of the coefficient above one. Copyright 1991 by The Econometric Society.

Suggested Citation

  • Sims, Christopher A & Uhlig, Harald, 1991. "Understanding Unit Rooters: A Helicopter Tour," Econometrica, Econometric Society, vol. 59(6), pages 1591-1599, November.
  • Handle: RePEc:ecm:emetrp:v:59:y:1991:i:6:p:1591-99
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    References listed on IDEAS

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    1. Levine, David, 1983. "A remark on serial correlation in maximum likelihood," Journal of Econometrics, Elsevier, vol. 23(3), pages 337-342, December.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Davidson, Russell & MacKinnon, James G., 1981. "Efficient estimation of tail-area probabilities in sampling experiments," Economics Letters, Elsevier, vol. 8(1), pages 73-77.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 125-132.
    6. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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