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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

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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Bibliographic Info

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. 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.
  2. 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.
  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. 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.
  5. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(01), pages 72-87, February.
  12. 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.
  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. 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.
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Cited by:
  1. Primiceri, Giorgio E. & van Rens, Thijs, 2006. "Heterogenous Life-Cycle Profiles, Income Risk and Consumption Inequality," CEPR Discussion Papers 5881, C.E.P.R. Discussion Papers.
  2. Moussa, Zakaria, 2010. "The Japanese Quantitative Easing Policy under Scrutiny: A Time-Varying Parameter Factor-Augmented VAR Model," MPRA Paper 29429, University Library of Munich, Germany.
  3. Ian Dew-Becker & Robert J. Gordon, 2005. "Where Did the Productivity Growth Go? Inflation Dynamics and the Distribution of Income," NBER Working Papers 11842, National Bureau of Economic Research, Inc.
  4. Papa M'B. P. N'Diaye & Douglas Laxton, 2002. "Monetary Policy Credibility and the Unemployment-Inflation Tradeoff," IMF Working Papers 02/220, International Monetary Fund.
  5. 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.
  6. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
  7. 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.

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