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Large T and small N : A three-step approach to the identification of cointegrating relationships in time series models with a small cross-sectional dimension

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  • Roger Hammersland

    ()
    (Norges Bank)

Abstract

This paper addresses cointegration in small cross-sectional panel data models. In addition to dealing with cointegrating relationships within the cross-sectional dimension, the paper explicitly addresses the issue of cointegration between cross-sections. The approach is based upon a well-known distributional result for the trace test when some of the cointegrating vectors are a priori known, and advocates a three-step procedure for the identification of the cointegrating space when dealing with two-dimensional data. The first step of this procedure utilizes traditional techniques to identify the long-run relationships within each cross-sectional unit separately. In the second step these first step relationships are then treated as known when searching for potential long run relationships between units in a joint analysis comprising the whole cross-sectional dimension. The third step of the procedure then finally reestimate all free parameters of the identified long-run structure to get rid of a potential simultaneity bias as a result of a non-diagonal covariance matrix. Identification of the long-run structures of Norwegian exports and international interest rate relationships are used as examples. Norwegian mainland exports have here been divided into two cross-sectional units; the traditional goods sector and the service sector. While in the study of international interest rate relationships the two sectors investigated are Germany and the US. The examples are used to address the more general issues of the degree of independence in capital markets and in goods markets of small open economies.

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Bibliographic Info

Paper provided by Norges Bank in its series Working Paper with number 2004/15.

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Length: 63 pages
Date of creation: 12 Nov 2004
Date of revision:
Handle: RePEc:bno:worpap:2004_15

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Keywords: Cointegration; Panel data; transmission mechanism; monopolistic competition; exports;

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  1. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  2. Roger Hammersland, 2004. "The degree of independence in European goods markets : An I(2) analysis of German and Norwegian trade data," Working Paper 2004/19, Norges Bank.
  3. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(01), pages 25-59, February.
  4. 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.
  5. Suzanne McCoskey & Chihwa Kao, 1998. "A residual-based test of the null of cointegration in panel data," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 57-84.
  6. Froot, Kenneth A & Thaler, Richard H, 1990. "Foreign Exchange," Journal of Economic Perspectives, American Economic Association, vol. 4(3), pages 179-92, Summer.
  7. Mark P. Taylor & Ronald MacDonald, 1991. "Exchange Rate Economics: A Survey," IMF Working Papers 91/62, International Monetary Fund.
  8. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356.
  9. Frankel, Jeffrey A. & Rose, Andrew K., 1996. "A panel project on purchasing power parity: Mean reversion within and between countries," Journal of International Economics, Elsevier, vol. 40(1-2), pages 209-224, February.
  10. Danny Quah, 1993. "Exploiting Cross Section Variation for Unit Root Inference in Dynamic Data," FMG Discussion Papers dp171, Financial Markets Group.
  11. Larsson, Rolf & Lyhagen, Johan & Löthgren, Mickael, 1998. "Likelihood-Based Cointegration Tests in Heterogeneous Panels," Working Paper Series in Economics and Finance 250, Stockholm School of Economics, revised 27 Aug 1998.
  12. Roger Hammersland, 2004. "Who was in the driving seat in Europe during the nineties, International financial markets or the BUBA?," Working Paper 2004/20, Norges Bank.
  13. Larsson, Rolf & Lyhagen, Johan, 1999. "Likelihood-Based Inference in Multivariate Panel Cointegration Models," Working Paper Series in Economics and Finance 331, Stockholm School of Economics.
  14. MacDonald, Ronald, 1996. "Panel unit root tests and real exchange rates," Economics Letters, Elsevier, vol. 50(1), pages 7-11, January.
  15. Paruolo Paolo, . "LR cointegration tests when some cointegrating relations are known," Economics and Quantitative Methods qf0106, Department of Economics, University of Insubria.
  16. 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.
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