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Bounds Testing Approaches to the Analysis of Long Run Relationships

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  • M Pesaran
  • Yongcheol Shin

    ()

  • Richard J Smith

Abstract

This paper develops a new approach to the problem of testing the existence of a long-run level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend- or first-difference stationary. The proposed tests are based on standard F- and t- statistics used to test the significance of the lagged levels of the variables on a first-difference regression. The asymptotic distributions of these statistics are non-standard under the null hypothesis that there exists no level relationship between the dependent variable and the included regressors, irrespective of whether the regressors are I(0) or I(1). Two sets of asymptotic critical values are provided: One set assuming that all the regressors are I(1), and another set assuming that they are all I(0). These two sets of critical values provide a band covering all possible classifications of the regressors into I(0), I(1) or mutually cointegrated. Accordingly, various bounds testing procedures are proposed. It is shown that the proposed tests are consistent, and their asymptotic distribution under the null and suitably defined local alternatives are derived. The empirical relevance of the bounds procedures are demonstrated by a re-examination of the earnings equation included in the UK Treasury macroeconometric model. This is a particularly relevant application as there is considerable doubt concerning the order of integration of the variables such as the unemployment rate, the union strength and the wedge between the "real produce wage" and the "real consumption wage" that enter the earnings equation.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 46.

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Length: 41
Date of creation: Apr 2004
Date of revision:
Handle: RePEc:edn:esedps:46

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Keywords: Long run Relationships; Unrestricted Error Correction Model; Cointegration; Unit Roots; Bounds Tests; Critical Value Bounds; Asymptotic Local Power; Earning Equation;

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References

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  1. Olivier J. Blanchard & Lawrence H. Summers, 1986. "Hysteresis and the European Unemployment Problem," NBER Working Papers 1950, National Bureau of Economic Research, Inc.
  2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  3. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100 Elsevier.
  4. Julia Darby & Simon Wren-Lewis, 1993. "Is There a Cointegrating Vector for UK Wages?," Journal of Economic Studies, Emerald Group Publishing, vol. 20(1/2), pages 87-115, January.
  5. 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.
  6. Clive, W.J. & Lin, Jin-Lung, 1995. "Causality in the Long Run," Econometric Theory, Cambridge University Press, vol. 11(03), pages 530-536, June.
  7. 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.
  8. Alan Manning, 1992. "Wage Bargaining and the Phillips Curve: The Identification and Specification of Aggregate Wage Equations," CEP Discussion Papers dp0062, Centre for Economic Performance, LSE.
  9. Layard, Richard & Nickell, Stephen & Jackman, Richard, 2005. "Unemployment: Macroeconomic Performance and the Labour Market," OUP Catalogue, Oxford University Press, number 9780199279173, September.
  10. Pesaran, M. H. & Shin, Y. & Smith, R. J., 1997. "Structural Analysis of Vector Error Correction Models with Exogenous I(1) Variables," Cambridge Working Papers in Economics 9706, Faculty of Economics, University of Cambridge.
  11. Urbain, J-P., 1991. "On Weak Exogeneity in Error Correction Models," Papers 9103, Liege - Centre de Recherches Economiques et Demographiques.
  12. 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.
  13. Boswijk, H. Peter, 1995. "Efficient inference on cointegration parameters in structural error correction models," Journal of Econometrics, Elsevier, vol. 69(1), pages 133-158, September.
  14. 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.
  15. Pesaran, M.H. & Shin, Y., 1995. "An Autoregressive Distributed Lag Modelling Approach to Cointegration Analysis," Cambridge Working Papers in Economics 9514, Faculty of Economics, University of Cambridge.
  16. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  17. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  18. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  19. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, September.
  20. repec:cup:etheor:v:11:y:1995:i:3:p:530-36 is not listed on IDEAS
  21. Layard, Richard & Nickell, Stephen, 1986. "Unemployment in Britain," Economica, London School of Economics and Political Science, vol. 53(210(S)), pages S121-69, Supplemen.
  22. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
  23. repec:cup:etheor:v:10:y:1994:i:1:p:95-115 is not listed on IDEAS
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