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Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model

  • James H. Stock
  • Mark W. Watson

This paper considers the estimation of the variance of coefficients in time varying parameter models with stationary regressors. The maximum likelihood estimator has large point mass at zero. We therefore develop asymptotically median unbiased estimators and confidence intervals by inverting median functions of regression-based parameter stability test statistics, computed under the constant-parameter null. These estimators have good asymptotic relative efficiencies for small to moderate amounts of parameter variability. We apply these results to an unobserved components model of trend growth in postwar U.S. GDP: the MLE implies that there has been no change in the trend rate, while the upper range of the median-unbiased point estimates imply that the annual trend growth rate has fallen by 0.7 percentage points over the postwar period.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0201.

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Date of creation: Aug 1996
Date of revision:
Handle: RePEc:nbr:nberte:0201
Note: ME
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  1. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
  2. Hansen, Bruce E, 1992. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 321-35, July.
  3. Cooley, Thomas F & Prescott, Edward C, 1973. "An Adaptive Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 364-71, June.
  4. Cooley, Thomas F & Prescott, Edward C, 1973. "Tests of an Adaptive Regression Model," The Review of Economics and Statistics, MIT Press, vol. 55(2), pages 248-56, May.
  5. Shephard, Neil, 1993. "Distribution of the ML Estimator of an MA(1) and a local level model," Econometric Theory, Cambridge University Press, vol. 9(03), pages 377-401, June.
  6. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(01), pages 72-87, February.
  7. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  8. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
  9. Pantula, Sastry G, 1991. "Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 63-71, January.
  10. Donald W.K. Andrews & Inpyo Lee & Werner Ploberger, 1992. "Optimal Changepoint Tests for Normal Linear Regression," Cowles Foundation Discussion Papers 1016, Cowles Foundation for Research in Economics, Yale University.
  11. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  12. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
  13. Chow, Gregory C., 1984. "Random and changing coefficient models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 21, pages 1213-1245 Elsevier.
  14. Saikkonen, Pentti & Luukkonen, Ritva, 1993. "Point Optimal Tests for Testing the Order of Differencing in ARIMA Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 343-362, June.
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