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Testing for Unit Roots with Stationary Covariates

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  • Elliott, Graham
  • Jansson, Michael

Abstract

We derive the family of tests for a unit root with maximal power against a point alternative when an arbitrary number of stationary covariates are modeled with the potentially integrated series. We show that very large power gains are available when such covariates available. We then derive tests which are simple to construct (involving the running of vector autoregressions) and achieve at a point the power envelopes derived under very general conditions. These tests are excellent properties in small samples. We also show that these are obvious and internally consistent tests to run when identifying structural VAR's using long run restrictions.

Suggested Citation

  • Elliott, Graham & Jansson, Michael, 2002. "Testing for Unit Roots with Stationary Covariates," Department of Economics, Working Paper Series qt4v35s2gv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    • Handle: RePEc:cdl:econwp:qt4v35s2gv
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    References listed on IDEAS

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    1. Jordi Gali, 1999. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," American Economic Review, American Economic Association, vol. 89(1), pages 249-271, March.
    2. 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.
    3. 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.
    4. repec:bla:obuest:v:61:y:1999:i:4:p:583-95 is not listed on IDEAS
    5. Graham Elliott & Michael Jansson & Elena Pesavento, 2005. "Optimal Power for Testing Potential Cointegrating Vectors With Known Parameters for Nonstationarity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 34-48, January.
    6. Elliott, Graham & Jansson, Michael & Pesavento, Elena, 2004. "Optimal Power for Testing Potential Cointegrating Vectors with Known," University of California at San Diego, Economics Working Paper Series qt2bv7n071, Department of Economics, UC San Diego.
    7. 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.
    8. 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(5), pages 984-1014, October.
    9. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    10. Guglielmo Maria Caporale & Nikitas Pittis, 1999. "Unit Root Testing Using Covariates: Some Theory and Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 583-595, November.
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