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Nonlinear Trends and Co-trending in Canadian Money Demand

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  • Cushman David O.

    (Department of Economics, University of Saskatchewan)

Abstract

Several authors have suggested that, instead of being unit root processes, some macro variables may actually be stationary around nonlinear deterministic trends (Perron, 1989, 1990, Bierens, 1997). This paper investigates this for four variables in a standard money demand specification, using Canadian data. Evidence is first presented that the null of unit root with drift (constant, linear, or nonlinear) can be rejected in favor of nonlinear trend stationarity for the variables. Then, Bierens' (2000) nonlinear co-trending test finds two common nonlinear trends among the variables. The trends are consistent with a standard money demand relationship. All unit root and co-trending test conclusions are based on size and power results from Monte Carlo simulations as well as on asymptotic critical values. The paper concludes with a discussion of how the observed nonlinear trending and co-trending might arise in a theoretical model, and with implications for further empirical tests.

Suggested Citation

  • Cushman David O., 2002. "Nonlinear Trends and Co-trending in Canadian Money Demand," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-29, April.
  • Handle: RePEc:bpj:sndecm:v:6:y:2002:i:1:n:4
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    References listed on IDEAS

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    1. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    2. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
    3. 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.
    4. 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 819-840, September.
    5. Haug, Alfred A & Lucas, Robert F, 1996. "Long-Run Money Demand in Canada: In Search of Stability," The Review of Economics and Statistics, MIT Press, vol. 78(2), pages 345-348, May.
    6. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    7. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    8. Hoffman, Dennis L. & Rasche, Robert H. & Tieslau, Margie A., 1995. "The stability of long-run money demand in five industrial countries," Journal of Monetary Economics, Elsevier, vol. 35(2), pages 317-339, April.
    9. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
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    Cited by:

    1. Cushman, David O. & Michael, Nils, 2011. "Nonlinear trends in real exchange rates: A panel unit root test approach," Journal of International Money and Finance, Elsevier, vol. 30(8), pages 1619-1637.
    2. Roberto Ricciuti, 2008. "The quest for a fiscal rule: Italy, 1861–1998," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 2(3), pages 259-274, October.
    3. David O. Cushman, 2008. "Real exchange rates may have nonlinear trends," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(2), pages 158-173.
    4. Roberto Ricciuti, 2004. "Nonlinearity in testing for fiscal sustainability," Money Macro and Finance (MMF) Research Group Conference 2003 80, Money Macro and Finance Research Group.

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