Testing Four Types of Bubbles in BRICS Exchange Rates

ABSTRACT

We test for the presence of four types of rational bubbles in the BRICS exchange rates against the US dollar. For the fundamental value of the exchange rate we use two structural specifications: the pure PPP rule, and a modified PPP rule where PPP is adjusted for the interest rate differential between the country and the US. For the bubble dynamics we consider four models: explosive bubbles, multiple bubbles, periodically collapsing bubbles of the Evans type, and intrinsic bubbles. We find evidence of the presence of at least one of these bubbles for Brazil, Russia, India, and South Africa, but none for China, confirming the results of other periodically recurring bubble tests for this dataset.

KEY WORDS:

• BRICS
• exchange rates
• explosive bubbles
• intrinsic bubbles
• multiple bubbles
• periodically recurring bubbles

JEL:

• F31
• C32

Acknowledgments

The authors would like to thank the remarks and suggestions of two anonymous referees which led to very significant improvements to the paper.

Notes

1. Examples are the Latin American sovereign debt crisis of 1992 (Brazil, Mexico, and Argentina), the Asian economies crisis of 1998, the Russian financial crisis of 1998, and the global financial crisis of 2008.

2. Diba and Grossman (1987, 1988b) study the inception of explosive rational bubbles, and show that they cannot be negative, and that once they emerge they must burst and eventually disappear, and cannot reappear if they ever collapse.

3. This testing approach has been used in the context of exchange rates by, for example, Jirasakuldech, Emekter, and Went (2006).

4. Chang, Ranjbar, and Gupta (2016) have also applied GSADF to test for the presence of bubbles in the stock markets of the BRICS countries, and found that those they identify correspond to specific events in those markets.

5. Evans (1991) argues that the unit-root ADF test is unable to detect periodically recurring bubbles. This limitation also applies to processes that have a stochastic explosive root, as shown by Charemza and Deadman (1995). However, Phillips, S-P., and Yu (2015b) claim that the GSADF test, which is a generalization of the ADF test, is able to detect both types of bubbles, even if they are of the mildly explosive variety.

6. The proofs of these propositions can be found in Appendix 1 of MT&V.

7. The PP test can be viewed as an ADF test that has been made robust to serial correlation by using the Newey and West (1987) heteroscedasticity and autocorrelation consistent covariance matrix estimator. However, Davidson and Mackinnon (2004) report that the PP test performs worse than the ADF test in finite samples. The KPSS test differs from the ADF and PP tests by assuming that the series is trend-stationary under the null hypothesis. The presence of a unit root is the alternative, and the absence of a unit root is not a proof that the series is stationary but rather, that it is trend-stationary.

8. More precisely, the alternative is that the process is a mildlyexplosive process, since the random walk process for the price is allowed to have an asymptotically negligible deterministic drift of the form $\tilde{\alpha }t{T}^{-\eta }$, where $\eta \ge 0$ under the null, i.e. $H_0:y_t=\tilde{\alpha }t/T^{-\eta }+y_{t-1}+{\epsilon }_t$. The Phillips, Wu, and Yu (2011) and the Diba and Grossman (1988a) models correspond to the cases $\eta \to \mathrm{\infty }$ and $\eta \to 0$, respectively. For the intermediate case $(0<\eta <\mathrm{\infty }$) the specification yields a localized drift process where the drift is present but is not the dominating component.

9. The $\mathrm{B}\mathrm{S}\mathrm{D}\mathrm{A}\mathrm{F}\left(r\right)$ statistic is the supremum of the $RT\mathrm{D}\mathrm{A}\mathrm{F}$ statistics for windows of all sizes that have their endpoint at the normalized “time” $r$, where $rϵ\left[r_0,1\right]$ and the extremes correspond, respectively, the minimum and the maximum calendar time. It is related to the $\mathrm{G}\mathrm{S}\mathrm{D}\mathrm{A}\mathrm{F}$ statistic as follows: $\mathrm{G}\mathrm{S}\mathrm{D}\mathrm{A}\mathrm{F}=\underset{r}{\mathrm{S}\mathrm{u}\mathrm{p}}\left\{\mathrm{B}\mathrm{S}\mathrm{D}\mathrm{A}\mathrm{F}\left(r\right)\right\}$.

10. Phillips and Shi (2017) point out that bubble expansion may be modeled using a mildly explosive process, and that bubble implosion may take several different forms, depending on the nature of the collapse, and that it is desirable that the model be flexible enough to capture it. They modify the Phillips, Shi and Yu (2015a) test to be capable of capturing various paths of return to normalcy.

11. Calculated by J.P. Morgan.

12. The results of the tests are available in the Supplementary Material – Appendix A, available online.

13. We use the Mackinnon (2010) critical values.

14. The test was performed allowing for a constant, but no time trend.

15. The tests were performed allowing for a constant, but no time trend.

16. However, Pavlidis, Paya, and Peel (2017) have recently proposed two novel methods to detect speculative bubbles using spot and forward prices which alleviate this misspecification problem, and allow the identification of start and end dates of the bubbles. They apply their method in the foreign exchange market.

17. For example, Van Norden and Vigfusson (1998) use simulation methods to examine the size and power of regime-switching tests for bubbles, and find that even with several 100 observations, the tests sometimes show considerable size distortion.

Additional information

Funding

Wilfredo L. Maldonado‘s work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil, through grants 311614/2015-9 and 470923/2012-1, Jussara Ribeiro work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior (CAPES), Brazil, (Brazil) through a graduate studies scholarship 88887.201797/2018-00, and Octavio A. F. Tourinho‘s work was supported in part by Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Brazil, through a PROCIENCIA grant, and by Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq (Brazil), through grant 459893/2014-9;