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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)

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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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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
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Handle: RePEc:bno:worpap:2004_15

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

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies
F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Chihwa Kao & Suzanne McCoskey, 1997. "A Residual-Based Test Of The Null Of Cointegration In Panel Data," Econometrics 9711002, EconWPA. [Downloadable!]
    Other versions:
  2. Froot, Kenneth A & Thaler, Richard H, 1990. "Foreign Exchange," Journal of Economic Perspectives, American Economic Association, vol. 4(3), pages 179-92, Summer. [Downloadable!] (restricted)
  3. Mark P. Taylor & Ronald MacDonald, 1991. "Exchange Rate Economics: A Survey," IMF Working Papers 91/62, International Monetary Fund.
  4. Danny Quah, 1993. "Exploiting Cross Section Variation for Unit Root Inference in Dynamic Data," FMG Discussion Papers dp171, Financial Markets Group. [Downloadable!] (restricted)
    Other versions:
  5. MacDonald, Ronald, 1996. "Panel unit root tests and real exchange rates," Economics Letters, Elsevier, vol. 50(1), pages 7-11, January. [Downloadable!] (restricted)
  6. Frankel, Jeffrey A & Rose, Andrew K, 1995. "A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries," CEPR Discussion Papers 1128, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  7. 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. [Downloadable!] (restricted)
  8. Johansen, S., 1991. "A Statistical Analsysis of Cointegration for I(2) Variables," Papers 77, Helsinki - Department of Economics.
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  9. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356. [Downloadable!] (restricted)
  10. 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. [Downloadable!]
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  11. 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. [Downloadable!]
  12. Andrew Levin & Chien-Fu Lin, 1992. "Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties," University of California at San Diego, Economics Working Paper Series 92-23, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  13. Andrew Levin & Chien-Fu Lin, 1993. "Unit Root Tests in Panel Data: New Results," University of California at San Diego, Economics Working Paper Series 93-56, Department of Economics, UC San Diego. [Downloadable!]
  14. Rolf Larsson & Johan Lyhagen & Mickael Lothgren, 2001. "Likelihood-based cointegration tests in heterogeneous panels," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 41.
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  15. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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