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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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  • James H. Stock & Mark W. Watson, 1996. "Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model," NBER Technical Working Papers 0201, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0201
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    1. N. G. Shephard & A. C. Harvey, 1990. "On The Probability Of Estimating A Deterministic Component In The Local Level Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(4), pages 339-347, July.
    2. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(1), pages 72-87, February.
    3. 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.
    4. 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.
    5. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    6. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    7. 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.
    8. 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.
    9. 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.
    10. Alexander H. Sarris, 1973. "A Bayesian Approach To Estimation Of Time-Varying Regression Coefficients," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 2, number 4, pages 501-523, National Bureau of Economic Research, Inc.
    11. Davis, Richard A. & Dunsmuir, William T.M., 1996. "Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 12(1), pages 1-29, March.
    12. Cooley, Thomas F & Prescott, Edward C, 1976. "Estimation in the Presence of Stochastic Parameter Variation," Econometrica, Econometric Society, vol. 44(1), pages 167-184, January.
    13. Saikkonen, Pentti & Luukkonen, Ritva, 1993. "Point Optimal Tests for Testing the Order of Differencing in ARIMA Models," Econometric Theory, Cambridge University Press, vol. 9(3), pages 343-362, June.
    14. 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.
    15. Shephard, Neil, 1993. "Distribution of the ML Estimator of an MA(1) and a local level model," Econometric Theory, Cambridge University Press, vol. 9(3), pages 377-401, June.
    16. 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 248-256, May.
    17. Thomas S. Shively, 1988. "An Exact Test For A Stochastic Coefficient In A Time Series Regression Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(1), pages 81-88, January.
    18. 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.
    19. 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 364-371, June.
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    2. Ian Dew-Becker & Robert J. Gordon, 2005. "Where Did Productivity Growth Go? Inflation Dynamics and the Distribution of Income," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 36(2), pages 67-150.
    3. Schalck, Christophe & Chenavaz, Régis, 2015. "Oil commodity returns and macroeconomic factors: A time-varying approach," Research in International Business and Finance, Elsevier, vol. 33(C), pages 290-303.
    4. 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.
    5. 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.
    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. Alberto Ronchi Neto & Osvaldo Candido, 2020. "Measuring the neutral real interest rate in Brazil: a semi-structural open economy framework," Empirical Economics, Springer, vol. 58(2), pages 651-667, February.
    8. Primiceri, Giorgio E. & van Rens, Thijs, 2009. "Heterogeneous life-cycle profiles, income risk and consumption inequality," Journal of Monetary Economics, Elsevier, vol. 56(1), pages 20-39, January.
    9. Mr. Papa M N'Diaye & Mr. Douglas Laxton, 2002. "Monetary Policy Credibility and the Unemployment-Inflation Tradeoff: Some Evidence From 17 Industrial Countries," IMF Working Papers 2002/220, International Monetary Fund.
    10. 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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