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Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis

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  • Bunzel, Helle
  • Vogelsang, Timothy J.

Abstract

In this paper we propose tests for hypotheses regarding the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data and they are robust to strong serial correlation. The data can contain a unit root and the tests still have the correct size asymptotically. The tests we analyze are standard heteroskedasticity autocorrelation (HAC) robust tests based on nonparametric kernel variance estimators. We analyze these tests using the ï¾…xed-b asymptotic framework recently proposed by Kiefer and Vogelsang (2002). This analysis allows us to analyze the power properties of the tests with regards to bandwidth and kernel choices. Our analysis shows that among popular kernels, there are speciï¾…c kernel and bandwidth choices that deliver tests with maximal power within a speciï¾…c class of tests. Based on the theoretical results, we propose a data dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang (1998). We apply the recommended test to the logarithm of a net barter terms of trade series and we ï¾…nd that this series has a statistically signiï¾…cant negative slope. This ï¾…nding is consistent with the well known Prebisch-Singer hypothesis.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 23 (2005)
Issue (Month): (October)
Pages: 381-394

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Handle: RePEc:bes:jnlbes:v:23:y:2005:p:381-394

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  1. Ardeni, Pier Giorgio & Wright, Brian, 1992. "The Prebisch-Singer Hypothesis: A Reappraisal Independent of Stationarity Hypotheses," Economic Journal, Royal Economic Society, vol. 102(413), pages 803-12, July.
  2. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  3. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  4. Powell, A., 1989. "Commodity And Developing Country Terms Of Trade, What Does The Long Run Show?," Economics Series Working Papers 9980, University of Oxford, Department of Economics.
  5. Spraos, John, 1980. "The Statistical Debate on the Net Barter Terms of Trade between Primary Commodities and Manufactures," Economic Journal, Royal Economic Society, vol. 90(357), pages 107-28, March.
  6. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  7. Cuddington, John T & Urzua, Carlos M, 1989. "Trends and Cycles in the Net Barter Terms of Trade: A New Approach," Economic Journal, Royal Economic Society, vol. 99(396), pages 426-42, June.
  8. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  9. Sapsford, D, 1985. "The Statistical Debate on the Net Barter Terms of Trade between Primary Commodities and Manufactures: A Comment and Some Additional Evidence," Economic Journal, Royal Economic Society, vol. 95(379), pages 781-88, September.
  10. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  11. Lutz, Matthias G, 1999. "A General Test of the Prebisch-Singer Hypothesis," Review of Development Economics, Wiley Blackwell, vol. 3(1), pages 44-57, February.
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