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Multivariate Unit Root Tests and Testing for Convergence

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Author Info
Harvey, A.
Bates, D.

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Abstract

We examine the properties of a multivariate Dickey-Fuller t-statistic designed to test for a unit root in a panel while taking account of cross-sectional dependence. The asymptotic distribution is presented and critical values provided. When intercepts are present, a modification along the lines of Elliot, Rothenberg and Stock (1996) can be implemented. The tests have invariance properties and can be carried out even if the number of series exceeds the number of time periods. Non-zero initial conditions actually boost the power of the (unmodified) Dickey-Fuller tests confirming that they are useful for testing the hypothesis that the series are in the process of converging. Typical applications are for a moderate number of series observed over a reasonably long period of time. The example given is for the per capital incomes of six US regions observed annually from 1950 to 1999.

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Publisher Info
Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0301.

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Length: 43
Date of creation: Jan 2003
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Handle: RePEc:cam:camdae:0301

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Web page: http://www.econ.cam.ac.uk/index.htm

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Related research
Keywords: balanced growth; cross-sectional dependence; Dickey-Fuller test; initials conditions; power envelope; stationarity tests;

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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
O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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  1. Fischer, Christoph, 2007. "An assessment of the trends in international price competitiveness among EMU countries," Discussion Paper Series 1: Economic Studies 2007,08, Deutsche Bundesbank, Research Centre. [Downloadable!]
  2. Alina M. Spiru, 2008. "Inflation Convergence In Central And Eastern European Economies," Romanian Economic Business Review, Romanian-American University, vol. 3(4), pages 14-34, Winter. [Downloadable!]
  3. Jönsson, Kristian, 2003. "Cross-sectional dependency and size distortion in a small-sample homogeneous panel-data unit root test," Working Papers 2003:10, Lund University, Department of Economics.
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  4. Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006. "Convergences of prices and rates of inflation," Temi di discussione (Economic working papers) 575, Bank of Italy, Economic Research Department. [Downloadable!]
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  5. GRENADE, Kari & MOORE, Winston, 2008. "Co-Movements Between Foreign And Domestic Interest Rates In A Fixed Exchange Rate Regime: The Case Of The Eccu And The Us," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 8(1), pages 119-130. [Downloadable!] (restricted)
  6. Pesaran, M.H., 2003. "A Simple Panel Unit Root Test in the Presence of Cross Section Dependence," Cambridge Working Papers in Economics 0346, Faculty of Economics, University of Cambridge. [Downloadable!]
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  7. Fabio Busetti & Lorenzo Forni & Andrew Harvey & Fabrizio Venditti, 2006. "Inflation convergence and divergence within the European Monetary Union," Working Paper Series 574, European Central Bank. [Downloadable!]
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  8. Fischer, Christoph & Porath, Daniel, 2006. "A reappraisal of the evidence on PPP: a systematic investigation into MA roots in panel unit root tests and their implications," Discussion Paper Series 1: Economic Studies 2006,23, Deutsche Bundesbank, Research Centre. [Downloadable!]
  9. Alina Spiru, 2007. "Inflation convergence in the new EU member states," Working Papers 005221, Lancaster University Management School, Economics Department. [Downloadable!]
  10. David E.A. Giles & Hui Feng, 2003. "Testing For Convergence in Output and in 'Well-Being' in Industrialized Countries," Econometrics Working Papers 0302, Department of Economics, University of Victoria. [Downloadable!]
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