The real exchange rate, regime changes and volatility shifts

Abstract

We make use of a data-set with both long span and high frequency to test for purchasing power parity (PPP) while allowing for a structural shift in the volatility of the Mexico–US bilateral real exchange rate (RER). The Kim, Leybourne and Newbold (2002) unit root test, robust to changes in the innovation variance, indicates mean stationarity of the monthly RER, and hence evidence of PPP, for the full sample, 1930–2012, and various subsamples. The persistence of deviations of the real rate from its PPP level as measured by half-lives ranges from 1.37 to 2.41 years.

Keywords:

• PPP
• variance shifts
• Mexico

JEL Classification:

• F31
• C22

Notes

¹ See Kim, Leybourne, and Newbold (2002, p. 366).

² Papell and Prodan (2006) classify stationary RERs displaying structural breaks by type of break in order to distinguish the behavior of such series from strict PPP: qualified PPP (stationary around a changing mean); trend PPP (trend stationary); trend–qualified PPP (trend stationary with changes in the intercept).

³ The KLN test uses a modified GLS-transformed regression related to Perron’s (1990) broken-mean DF test. The Perron test regression allows for a change in level, which implies that the test is robust to such shift. Furthermore, Ventosa-Santaulària and Gómez-Zaldívar (2009) have shown that DF-type tests are asymptotically robust to level shifts. Finally, Monte Carlo simulations described in Appendix indicate that the power of the KLN test increases with sample size. For samples of 500 and 1000 observations, the ADF, Perron and KLN tests almost always reject a false null. The shortest series in this study contains more than 800 observations, suggesting that the KLN test is robust in our application.

⁴ Gómez-Zaldívar et al. (2013) have already studied the RER stationarity using level and trend breaks (Kapetanios test) for a similar, albeit shorter series (monthly data from 1969 to 2010). They find that the RER reverts to a changing mean; most of the shifts occur in the late 1970s and the 1980s. Their results imply QPPP and TQPPP.

⁵ The only available Mexican price index for the period 1930–1960 is the WPI for Mexico City. To maintain consistency in the series, we used the Mexico City WPI for 1961–2000 rather than a PPI for the country available beginning 1969.

⁶ Cardenas identifies his source as the Bank of Mexico. These data are not reported on the Bank’s website. The data in Cardenas are, however, very close to the values reported for these series in the Bank’s annual reports for 1930–1960.

⁷ The conditional volatility is calculated using a GARCH(1,1) process for the $\mathrm{\Delta }{q}_t$ series.

⁸ The exact form of the flexible rate regime has varied since 1976. See Bank of Mexico (2009) for further discussion of these changes.

⁹ The testing procedure does not allow the break date to be ‘too’ close to the extremes of the sample.

¹⁰ Critical values can be found in Perron (1990).

¹¹ Results are available from the authors.

¹² The KLN test was developed to correct for size distortions, but the power of the test was not analysed in the original work. Monte Carlo simulations show that the power of the KLN test is similar to those of the ADF and Perron (1990) tests for larger sample sizes such as our RER series. See Appendix for details.

¹³ Edwards (2007) and Berganza and Broto (2012) have found that countries with inflation targeting (IT) regimes have higher exchange rate instability. The positive relationship between IT and volatility in Latin American countries uncovered by Berganza and Broto is identified only for the post-crisis period, 2008:Q3–2010:Q1, and can be attenuated with intervention in the foreign exchange markets or by accumulating foreign reserves. It is possible that our procedure did not identify a break in volatility during the IT period because Mexico’s central bank actively intervened in the market and sought to accumulate reserves during this period. It should also be noted that it is difficult for any test to uncover evidence of a break at either the beginning or the end of the sample period.

¹⁴ See note 2.

¹⁵ Analysing the three series with Perron’s (1990) unit root test and imposing an exogenous break in the mean in July 1976, it is possible to reject the stationarity null. These results imply QPPP, a less stringent version of PPP. To appraise whether strict PPP or QPPP is a more accurate representation of the data, we first compute the mean and the variance of RER3 before and after the estimated break date. The mean of the series prior to July 1976 is −3.89, and the mean afterwards is −3.94, a difference of 1.3%. The variance is 0.0236 prior to the break and 0.0462 afterwards, an increase of 95% (results using the other series are almost identical). These calculations (heuristically) suggest that the shift in the variance provides a more plausible explanation for the break than a shift in the mean. We also compute the Bai and Perron (1998, 2003) test allowing for one break, in congruence with the other tests, and employ the SupF test having a null of no-level break against an alternative of one-level break. We are unable to reject the null of level break for RER 1, although it can be rejected or RER 2 and RER 3 at the 5% level. For both these cases, the Bai and Perron test endogenously locates the break in April 1991, that is, 15 years after the break identified by KLN. These results imply that the July 1976 break revealed by the KLN test was not a level break, which should have been uncovered by the Bai-Perron test. This counterfactual evidence from the Bai–Perron test suggests that the variance shift as found by the KLN test was the cause of the July 1976 break.