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Optimal Power For Testing Potential Cointegrating Vectors with Known Parameters for Nonstationarity

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  • Graham Elliott
  • Michael Jansson
  • Elena Pesavento

Abstract

In situations where theory specifies a potential cointegrating vector amongst integrated variables, it is often required that one test for a unit root in the constructed cointegrating vector. Although it is common to simply employ a univariate test for a unit root for this test, it is known that this does not take into account all available information. We show here that in such testing situations a family of tests with optimality properties exists. We use this to characterize the extent of the loss in power from using popular methods, as well as to derive a test that works well in practice. We also characterize the extent of the losses of not imposing the cointegrating vector in the testing procedure. We apply various tests to the hypothesis that price forecasts from the Livingston data survey are cointegrated with prices, and find that although most tests fail to reject the presence of a unit root in forecast errors the tests presented here strongly reject this (implausible) hypothesis.

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Paper provided by Department of Economics, Emory University (Atlanta) in its series Emory Economics with number 0303.

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Date of creation: Feb 2003
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Handle: RePEc:emo:wp2003:0303

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  1. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1148-1171, October.
  2. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July.
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  4. Aggarwal, Raj & Mohanty, Sunil & Song, Frank, 1995. "Are Survey Forecasts of Macroeconomic Variables Rational?," The Journal of Business, University of Chicago Press, vol. 68(1), pages 99-119, January.
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  10. Pesavento, Elena, 2000. "Analytical Evaluation of the Power of Tests for the Absence of Cointegration," University of California at San Diego, Economics Working Paper Series qt4cq4773c, Department of Economics, UC San Diego.
  11. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  12. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  13. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October.
  14. Bernard, A.B. & Durlauf, S.N., 1993. "Convergence in International Output," Working papers 93-7, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  16. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  17. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  18. Horvath, Michael T.K. & Watson, Mark W., 1995. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified," Econometric Theory, Cambridge University Press, vol. 11(05), pages 984-1014, October.
  19. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  20. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-99, October.
  21. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
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Citations

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Cited by:
  1. Shahbaz, Muhammad & Farhani, Sahbi & Ozturk, Ilhan, 2013. "Coal Consumption, Industrial Production and CO2 Emissions in China and India," MPRA Paper 50618, University Library of Munich, Germany, revised 12 Oct 2013.
  2. Elena Pesavento, 2005. "Residuals Based Tests for the Null of No Cointegration: An Analytical Comparison," Emory Economics 0503, Department of Economics, Emory University (Atlanta).
  3. Fossati, Sebastian, 2012. "Covariate unit root tests with good size and power," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3070-3079.
  4. Elliott, Graham & Pesavento, Elena, 2006. "On the Failure of Purchasing Power Parity for Bilateral Exchange Rates after 1973," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1405-1430, September.
  5. Graham Elliott & Elena Pesavento, 2005. "Higher Power Tests for Bilateral Failure of PPP after 1973," Emory Economics 0502, Department of Economics, Emory University (Atlanta).
  6. Ladislava Grochova & Ludek Kouba, 2010. "Elite Political Instability and Economic Growth: An Empirical Evidence from the Baltic States," MENDELU Working Papers in Business and Economics 2010-01, Mendel University in Brno, Faculty of Business and Economics.
  7. Elliott, Graham & Jansson, Michael, 2002. "Testing for Unit Roots with Stationary Covariates," University of California at San Diego, Economics Working Paper Series qt4v35s2gv, Department of Economics, UC San Diego.
  8. Chandran Govindaraju, V.G.R. & Tang, Chor Foon, 2013. "The dynamic links between CO2 emissions, economic growth and coal consumption in China and India," Applied Energy, Elsevier, vol. 104(C), pages 310-318.
  9. Elena Pesavento, 2006. "Near-optimal Unit Root Test with Stationary Covariate with Better Finite Sample Size," Emory Economics 0606, Department of Economics, Emory University (Atlanta).
  10. Christian Bayer & Christoph Hanck, 2013. "Combining non-cointegration tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 83-95, 01.
  11. Pesavento, Elena & Rossi, Barbara, 2005. "Do Technology Shocks Drive Hours Up Or Down? A Little Evidence From An Agnostic Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 9(04), pages 478-488, September.
  12. Girardi, Riccardo & Paruolo, Paolo, 2013. "Wages and prices in Europe before and after the onset of the Monetary Union," Economic Modelling, Elsevier, vol. 35(C), pages 643-653.
  13. Barbara Rossi & Elena Pesavento, 2004. "Do Technology Shocks Drive Hours Up or Down?," Econometric Society 2004 North American Summer Meetings 96, Econometric Society.

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