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Markov Chain approach to Purchasing Power Convergence in the 15 European Union


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  • Alejandro Rodriguez Caro


  • Santiago Rodriguez Feijoó


  • Carlos Gonzalez Correa



In the present paper we study the degree of convergence in the European Union from the Purchasing Power Parity (PPP) point of view. The price of the shopping basket can be the cause of disparities in a global market in construction that, like the European Union, is formed by different countries with different consumption habits. In addition, in this construction process twelve out of fifteen countries of the EU have left its national currency to adopt the Euro like common currency. Therefore, it is necessary for the stability of the Union process in the long run that, among others, purchasing power of the different state members tends towards a same common value. Moreover, the question is whether that process of convergence within the European Union is taking place or not. In order to solve this question, the series of the Absolute Purchasing Power Parity (APPP) are estimated through the suggestion of Rodriguez et al (2004). These authors use the Harmonized Consumer Price Index in the European Union and the nominal exchange rates of the different currencies with euro. Monthly estimates of the APPP series for the 1995-2002 period are obtained for each of the fifteen countries. These figures show, for each country, their relative position to the average value of the European Union. Using these series we applied the Markov Chain methodology to study the time evolution of the distribution of APPP in the European Union. This methodology has been very used by its facility of calculation and interpretation of the results. Nevertheless, with the purpose of obtaining good estimations it is necessary to solve the discretization problem of a continuous variable. This is, to use a finite set, and relatively small number of states, for a variable with infinite values. In the present work different approaches are used to solve the problem. We test for structural change on the estimated probabilities using adapted test to Markov Chains. This allows us to study if an effect exists on the Purchasing Power Parity with the entrance of the Euro. Markov Chains are estimated by Maximum likelihood, and allow us to do different analyses. In the first place, we can study the mobility of the distribution, measured through the probabilities of permanence or not in the same state, and in the degree of diagonal structure of the resulting matrix. This objective can obtained by direct observation, calculating Mobility Index, or using expected time of first passage. Secondly, we can obtain the ergodic or long term distribution. This one shows the temporary evolution in the long run of the distribution, under the hypothesis of maintenance of the present conditions. This distribution would show the possible convergence or not of the whole distribution. We also estimate elasticities of ergodic probabilities, to analyze the effect of each probability in the Markov chain in the long run distribution. Results show differences with the Euro Entry, mobility towards convergence within the distribution is slow, with high elasticities of the ergodic distribution to changes in the transition probabilities.

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Paper provided by European Regional Science Association in its series ERSA conference papers with number ersa05p457.

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Date of creation: Aug 2005
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Handle: RePEc:wiw:wiwrsa:ersa05p457

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  1. Quah, Danny, 1996. "Regional Convergence Clusters Across Europe," CEPR Discussion Papers, C.E.P.R. Discussion Papers 1286, C.E.P.R. Discussion Papers.
  2. Enrique Alberola & José M. Marqués, 1999. "On the Relevance and Nature of Regional Inflation Differentials: the Case of Spain," Banco de Espa�a Working Papers, Banco de Espa�a 9913, Banco de Espa�a.
  3. Quah, Danny T., 1996. "Regional convergence clusters across Europe," European Economic Review, Elsevier, Elsevier, vol. 40(3-5), pages 951-958, April.
  4. Lucio Sarno & Mark P. Taylor, 2002. "Purchasing Power Parity and the Real Exchange Rate," IMF Staff Papers, Palgrave Macmillan, Palgrave Macmillan, vol. 49(1), pages 5.
  5. Quah, Danny, 1993. "Galton's Fallacy and Tests of the Convergence Hypothesis," CEPR Discussion Papers, C.E.P.R. Discussion Papers 820, C.E.P.R. Discussion Papers.
  6. Magrini, Stefano, 1999. "The evolution of income disparities among the regions of the European Union," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 29(2), pages 257-281, March.
  7. Bulli, Sandra, 2001. "Distribution Dynamics and Cross-Country Convergence: A New Approach," Scottish Journal of Political Economy, Scottish Economic Society, Scottish Economic Society, vol. 48(2), pages 226-43, May.
  8. Quah, Danny T., 1996. "Empirics for economic growth and convergence," European Economic Review, Elsevier, Elsevier, vol. 40(6), pages 1353-1375, June.
  9. Bode, Eckhardt & Bickenbach, Frank, 2002. "Markov or not Markov - this should be a question," ERSA conference papers, European Regional Science Association ersa02p024, European Regional Science Association.
  10. LE GALLO, Julie, 2001. "Space-time analysis of GDP disparities among European regions: A Markov chains approach," LATEC - Document de travail - Economie (1991-2003), LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne 2001-06, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
  11. Quah, Danny T, 1996. " Convergence Empirics across Economies with (Some) Capital Mobility," Journal of Economic Growth, Springer, Springer, vol. 1(1), pages 95-124, March.
  12. Enrique Lopez Bazo & Esther Vaya Valcarce & Antonio Jose Mora & Jordi Surinach Caralt, 1997. "Regional economic dynamics and convergence in the european union," Working Papers in Economics, Universitat de Barcelona. Espai de Recerca en Economia 12, Universitat de Barcelona. Espai de Recerca en Economia.
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