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.