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Trend-stationary GNP: evidence from a new exact pointwise most powerful invariant unit root test

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  • Philip A. Shively

    (Department of Economics and Business, Lafayette College, Easton, PA 18042 USA)

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    Abstract

    There has been a substantial debate whether GNP has a unit root. However, statistical tests have had little success in distinguishing between unit-root and trend-reverting specifications because of poor statistical properties. This paper develops a new exact small-sample, pointwise most powerful unit root test that is invariant to the unknown mean and scale of the time series tested, that generates exact small-sample critical values, powers and p-values, that has power which approximates the maximum possible power, and that is highly robust to conditional heteroscedasticity. This test decisively rejects the unit root null hypothesis when applied to annual US real GNP and US real per capita GNP series. This paper also develops a modified version of the test to address whether a time series contains a permanent, unit root process in addition to a temporary, stationary process. It shows that if these GNP series contain a unit root process in addition to the stationary process, then it is most likely very small. Copyright © 2001 John Wiley & Sons, Ltd.

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    Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

    Volume (Year): 16 (2001)
    Issue (Month): 4 ()
    Pages: 537-551

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    Handle: RePEc:jae:japmet:v:16:y:2001:i:4:p:537-551

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    1. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    2. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    3. Campbell, John & Mankiw, Gregory, 1987. "Are Output Fluctuations Transitory?," Scholarly Articles 3122545, Harvard University Department of Economics.
    4. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
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    6. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    8. Julio J. Rotemberg & Michael Woodford, 1994. "Is the Business Cycles a Necessary Consequence of Stochastic Growth?," NBER Working Papers 4650, National Bureau of Economic Research, Inc.
    9. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
    10. Matthew Shapiro & Mark Watson, 1988. "Sources of Business Cycles Fluctuations," NBER Chapters, in: NBER Macroeconomics Annual 1988, Volume 3, pages 111-156 National Bureau of Economic Research, Inc.
    11. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
    12. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbance," Working papers 497, Massachusetts Institute of Technology (MIT), Department of Economics.
    13. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
    14. King, Maxwell L., 1985. "A point optimal test for autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 27(1), pages 21-37, January.
    15. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
    16. Shively, Thomas S., 1988. "An analysis of tests for regression coefficient stability," Journal of Econometrics, Elsevier, vol. 39(3), pages 367-386, November.
    17. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
    18. King, Maxwell L., 1983. "Testing for autoregressive against moving average errors in the linear regression model," Journal of Econometrics, Elsevier, vol. 21(1), pages 35-51, January.
    19. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    20. Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept.
    21. Cochrane, John H, 1994. "Permanent and Transitory Components of GNP and Stock Prices," The Quarterly Journal of Economics, MIT Press, vol. 109(1), pages 241-65, February.
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    Cited by:
    1. Berg, Nathan, 2004. "No-decision classification: an alternative to testing for statistical significance," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 33(5), pages 631-650, November.
    2. Brzoza-Brzezina, Michał & Chmielewski, Tomasz & Niedźwiedzińska, Joanna, 2010. "Substitution between domestic and foreign currency loans in Central Europe. Do central banks matter?," Working Paper Series 1187, European Central Bank.
    3. Broda, Simon & Paolella, Marc S. & Carstensen, Kai, 2007. "Bias-adjusted estimation in the ARX(1) model," Munich Reprints in Economics 19992, University of Munich, Department of Economics.

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