Cointegrated Periodically Collapsing Bubbles in the Exchange Rate of 'BRICS' Countries

This paper tests the occurrence of rational bubbles in the exchange rate of Brazil, Russia, India, China and South Africa (the ‘BRICS’ countries group) against the US dollar. We consider bubbles of the periodically recurring variety, and assume that the fundamental value follows a modified PPP relation which takes into account interest rate differentials, starting from a reference value which is endogenously determined. At each point in time the probability of collapse of the bubble to is a nonlinear logistic function of the absolute size of the bubble and is, therefore, also endogenous. The expected next period bubble size if the future regime is collapse is a linear function of the current bubble size whose parameters are also endogenously estimated. The estimation uses a maximum likelihood procedure, and the results support the model, which passes the specification tests. The hypothesis of rational expectations in the market for the forward exchange rate, which is used as a proxy of the expected exchange rate, is also tested and accepted for 3 of the 5 countries. The hypothesis of two linear regimes (rather than the non-linear regimes we use) is also tested and rejected for 3 of the 5 countries. We discuss the dynamics of the absolute bubble, and also compare the time series of the bubbles for the several countries, relative to the corresponding fundamental value. We test for unit roots in the relative bubbles and find that they are integrated, and that they pass Johansen’s the cointegration test. Finally we estimate an error correction model to discuss the long term relation between the relative bubbles and the speed of adjustment of each country’s relative bubble to shocks to the long term relation between them.