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The Power Of Single Equation Tests For Cointegration When The Cointegrating Vector Is Prespecified

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  • Zivot, Eric
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    Abstract

    In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson, and Dolado s (1992, Oxford Bulletin of Economics and Statistics 54, 325 348) conditional error correction model (ECM) based t-test for cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen s (1995, Econometric Theory 11, 1148 1171) covariate augmented t-test for a unit root, is valid for weakly exogenous regressors and depends on a consistently estimable nuisance parameter that takes on values in the unit interval. I show analytically, using asymptotic power functions based on near-cointegrated alternatives, that the ECM t-test with a prespecified cointegrating vector can have much higher power than single equation tests for cointegration based on estimating the cointegrating vector. I also characterize situations in which the ECM t-test computed with a misspecified cointegrating vector will have high power.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 16 (2000)
    Issue (Month): 03 (June)
    Pages: 407-439

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    Handle: RePEc:cup:etheor:v:16:y:2000:i:03:p:407-439_16

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    1. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    2. Engle, R. & Hendry, D., 1990. "Testing Super Exogeneity And Invariance In Regression Models," Economics Series Working Papers 99100, University of Oxford, Department of Economics.
    3. 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.
    4. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
    5. Bardsen, Gunnar, 1992. "Dynamic modeling of the demand for narrow money in Norway," Journal of Policy Modeling, Elsevier, vol. 14(3), pages 363-393, June.
    6. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
    7. 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.
    8. Fischer, Andreas M. & Nicoletti, Giuseppe, 1993. "Regression direction and weak exogeneity: Determining the conditioning properties of US money demand functions," Journal of Monetary Economics, Elsevier, vol. 32(2), pages 213-235, November.
    9. Peter Boswijk, H., 1994. "Testing for an unstable root in conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 37-60, July.
    10. Inder, Brett, 1993. "Estimating long-run relationships in economics : A comparison of different approaches," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 53-68.
    11. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
    12. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
    13. Ahumada, Hildegart, 1992. "A dynamic model of the demand for currency: Argentina 1977-1988," Journal of Policy Modeling, Elsevier, vol. 14(3), pages 335-361, June.
    14. Johansen, Soren, 1992. "Cointegration in partial systems and the efficiency of single-equation analysis," Journal of Econometrics, Elsevier, vol. 52(3), pages 389-402, June.
    15. Norrbin, Stefan C. & Reffett, Kevin L., 1996. "Exogeneity and forward rate unbiasedness," Journal of International Money and Finance, Elsevier, vol. 15(2), pages 267-274, April.
    16. Fischer, Andreas M, 1993. "Is Money Really Exogenous? Testing for Weak Exogeneity in Swiss Money Demand," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(2), pages 248-58, May.
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    Cited by:
    1. Yan, Bingcheng & Zivot, Eric, 2010. "A structural analysis of price discovery measures," Journal of Financial Markets, Elsevier, vol. 13(1), pages 1-19, February.
    2. Allan W. Gregory & Alfred A. Haug & Nicoletta Lomuto, 2004. "Mixed signals among tests for cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(1), pages 89-98.
    3. Bingcheng Yan & Eric Zivot, 2007. "A Structural Analysis of Price Discovery Measures," Working Papers UWEC-2006-08-FC, University of Washington, Department of Economics, revised Apr 2007.
    4. Fisher, Lance A. & Otto, Glenn & Voss, Graham M., 2010. "The response of Australian consumption to housing wealth," Journal of Macroeconomics, Elsevier, vol. 32(1), pages 284-299, March.
    5. Enders, Walter & Im, Kyung So & Lee, Junsoo & Strazicich, Mark C., 2010. "IV threshold cointegration tests and the Taylor rule," Economic Modelling, Elsevier, vol. 27(6), pages 1463-1472, November.
    6. Jansson, Michael, 2004. "Stationarity Testing With Covariates," Econometric Theory, Cambridge University Press, vol. 20(01), pages 56-94, February.
    7. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2007. "A Sieve Bootstrap Test for Cointegration in a Conditional Error Correction Model," Research Memorandum 054, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    9. Zivot, Eric, 2000. "Cointegration and forward and spot exchange rate regressions," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 785-812, December.
    10. Pierre Perron & Gabriel Rodriguez, 2012. "Residual test for cointegration with GLS detrended data," Documentos de Trabajo 2012-327, Departamento de Economía - Pontificia Universidad Católica del Perú.

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