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Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime STAR Model

  • Frédérique Bec
  • Mélika Ben Salem
  • Marine Carrasco

Recent studies on general equilibrium models with transaction costs show that the dynamics of the real exchange rate are necessarily nonlinear. Our contribution to the literature on nonlinear price adjustment mechanisms is treefold. First, we model the real exchange rate by a Multi-Regime Logistic Smooth Transition AutoRegression (MR-LSTAR), allowing for both ESTAR-type and SETAR-type dynmaics. This choice is motivated by the fact that even the theoretical models, which predict a smooth behavior for the real exchange rate, do not rule out the possibility of a discontinuous adjustment as a limit case. Second, we propose two classes of unit-root tests against this MR-LSTAR alternative, based respectively on the likelihood and on a auxiliary model. Their asymptotic distributions are derived analytically. Third, when applied to 28 bilateral real exchange rates, our tests reject the null hypothesis of a unit root for eleven series bringing evidence in favor of the purchasing power parity. Des études récentes sur les modèles d'équilibre général prenant en considération les coûts des transactions démontrent que la dynamique du taux de change réel est nécessairement non linéaire. Notre contribution à la littérature portant sur les mécanismes d'ajustement non linéaire des prix comporte trois volets. Premièrement, nous modélisons le taux de change réel en recourant à une autorégression de type MR-LSTAR (Multi-Regime Logistic Smooth Transition AutoRegression), qui permet d'observer la dynamique des modèles ESTAR (Exponential Smooth TAR) et SETAR (Self-Exciting Treshold Autoregressive). Notre choix est motivé par le fait que même les modèles théoriques, qui prédisent un comportement lisse du taux de change réel, n'excluent pas la possibilité d'un ajustement discontinu à la limite. Deuxièmement, nous proposons deux catégories de tests de racine unitaire, dans le cadre de l'option MR-LSTAR, fondées respectivement sur la vraisemblance et sur un modèle auxiliaire. Leurs distributions asymptotiques résultent d'un processus analytique. Troisièmement, lorsque nos tests sont appliqués à 28 taux de change réels bilatéraux, ils rejettent l'hypothèse nulle d'une racine unitaire dans le cas de onze séries, faisant ainsi la preuve de la parité du pouvoir d'achat.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2009s-18.

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Length: 38 pages
Date of creation: 01 May 2009
Date of revision:
Handle: RePEc:cir:cirwor:2009s-18
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