Cointegrated Periodically Collapsing Bubbles in the Exchange Rate of “BRICS”

ABSTRACT

We test the occurrence of periodically recurring rational bubbles in the exchange rate of each of the “BRICS” countries currency relative to the US dollar. The forward exchange rate is used as a proxy for the expected exchange rate, different Purchasing Parity Power (PPP)-based rules for the fundamental exchange rate are considered, and its initial value is endogenously determined. For the chosen model, the regime switching equation satisfactorily fits the data, confirming the presence of rational bubbles for all countries. The dynamics of the exchange rate series for each country is interpreted with the help of the estimated bubbles. The bubbles are compared across countries, found to be cointegrated, and this is interpreted as evidence of the international transmission of exchange rate shocks between these countries.

KEY WORDS:

• BRICS
• cointegration test
• error correction models
• exchange rate bubbles

JEL CLASSIFICATION:

• C30
• F31

Acknowledgments

Wilfredo L. Maldonado thanks the support of Aquiles de Farias with the data collection.

Funding

Wilfredo L. Maldonado was partially supported by CNPq (Brazil) (grant numbers 304844/2009-8 and 401461/2009-2). Octavio A. F. Tourinho received financial support from UERJ/FAPERJ through a PROCIENCIA/2012 grant.

Notes

1. The use of a periodically collapsing bubble approach to model exchange rate series was inspired by Jarrow and Protter (2010).

2. In Maldonado, Tourinho, and Valli (2012), a third specification for the fundamental value was tested for Brazil: the monetary model. It includes information about the monetary aggregates in the country and in the USA as well as industrial production. Since reliable data are not available for all the countries in the group for the period we considered, for the sake of preserving the comparability of the results of the estimation of the model for five countries, we opted not to include that specification in our analysis.

3. For China, the earlier period was excluded because the currency was pegged to the US dollar. After that, a basket of currencies was used to quote the Yuan to better capture of the monetary movements in the international market. For Russia, we excluded from the sample the period where the exchange rate was managed to fluctuate within a band (dirty float).

4. This estimate for the innovation in the exchange rate is predicated on the assumption that the agents in this market are risk neutral. If they were risk-averse, they would incorporate a risk premium in the forward contract price for exchange rate, and this component would have to be subtracted from the forward price to obtain a proxy for the innovation. Whether this effect is empirically relevant for the countries for which we implement the model remains to be established and is left for further refinement of the data for model estimation.

5. The EMBI+ is calculated by J.P. Morgan as the average over all major issues of the difference between in the interest rate paid by a given country on sovereign debt denominated in US dollars, and the T-Bill of similar maturity.

6. Since this is a nonlinear stochastic model, the exact distribution of the coefficient estimators is not known; so, the quasi-maximum likelihood method (Hamilton (1994, 1996)) was used to estimate the standard errors.

7. The values in Table 3 for Brazil are different from the ones for Model IIB in Maldonado, Tourinho, and Valli (2012) because the sample here includes 28 additional data points.

8. It is likely that the failure of the model to pass the specification tests for Brazil is related to the nature of the exchange rate dynamics reflected in the data between 2011:13 and 2013:16, because Markovian state independence was not rejected in Maldonado, Tourinho, and Valli (2012). This inversion of the result of that test may be due to the fact that the database here includes periods which were the repercussions of the 2009 subprime crisis struck the Brazilian economy more strongly, impacting the trajectory of the exchange rate in manners which may be unrelated to the model specification. For China, the failure is a consequence of the small sample size.

9. In February 2005, the Russian central bank changed the reference of the exchange rate from the US$ to a basket of currencies composed of 10% Euros and 50% US$. The basket is now composed 45% Euros and 55% US$.

10. According to Bhundia and Gottschalk (2003), these are the reasons indicated by Myburgh Commission of Inquire, created by the South African Government, to investigate the reasons for that sudden and significant rand devaluation in 2000–2001.

11. Recently, Chang, Ranjbar, Aye, and Gupta (2014) apply a new recursive test proposed by Phillips, Wu, and Yu (2011), Philips, Shi, and Yu (2015a, 2015b) which is not based on the estimation of a full fledged parametric approach, like the one here, to investigate whether there exist multiple bubbles in the BRICS stock markets, find multiple bubbles, and argue that they correspond to specific events in those markets.

12. Applegate (2003) describes the operation of China’s and India’s controls on capital flows.

Additional information

Funding

Wilfredo L. Maldonado was partially supported by CNPq (Brazil) (grant numbers 304844/2009-8 and 401461/2009-2). Octavio A. F. Tourinho received financial support from UERJ/FAPERJ through a PROCIENCIA/2012 grant.