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

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James H. Stock
Mark W. Watson

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Abstract

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
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Handle: RePEc:nbr:nberte:0201

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  1. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. 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.
  4. Andrews, Donald W. K. & Lee, Inpyo & Ploberger, Werner, 1996. "Optimal changepoint tests for normal linear regression," Journal of Econometrics, Elsevier, vol. 70(1), pages 9-38, January. [Downloadable!] (restricted)
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  5. 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.
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  6. 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. [Downloadable!] (restricted)
  7. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
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  8. 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.
  9. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research Department. [Downloadable!]
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  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
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  1. Papa M'B. P. N'Diaye & Douglas Laxton, 2003. "Monetary Policy Credibility and the Unemployment-Inflation Tradeoff: Some Evidence from 17 Industrial Countries," IMF Working Papers 02/220, International Monetary Fund. [Downloadable!]
  2. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Giorgio E. Primiceri & Thijs van Rens, 2006. "Heterogeneous Life-Cycle Profiles, Income Risk and Consumption Inequality," Economics Working Papers 945, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2008. [Downloadable!]
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  4. Massimiliano De Santis, 2005. "Movements in the Equity Premium: Evidence from a Bayesian Time-Varying VAR," Money Macro and Finance (MMF) Research Group Conference 2005 62, Money Macro and Finance Research Group. [Downloadable!]
  5. Dew-Becker, Ian & Gordon, Robert J, 2005. "Where did the Productivity Growth Go? Inflation Dynamics and the Distribution of Income," CEPR Discussion Papers 5419, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  6. Laurence Boone & Michel Juillard & Doug Laxton & Papa N'Diaye, 2002. "How Well Do Alternative Time-Varying Parameter Models of the NAIRU Help Policymakers Forecast Unemployment and Inflation in the OECD Countries?," Computing in Economics and Finance 2002 359, Society for Computational Economics. [Downloadable!]
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