We use a previously unexploited data set to calculate the real exchange rate with respect to the U.S. dollar for Mexico for 1930.01-1960.12, and to test for purchasing power parity (PPP). The initial results from the Augmented Dickey-Fuller (ADF) test show weak support for the PPP hypothesis. The Kapetanios, Shin, and Snell test, for a unit root null with an alternative of nonlinear reversion to the mean, indicates substantial support for PPP. However, non-normality and, sometimes, heteroscedasticity are found in the test residuals. Using a wild bootstrap approach, critical values are calculated from the empirical distribution of the residuals. Reevaluating the test statistics with the new critical values, we conclude that there is evidence of nonlinear adjustment to PPP for 1930.01-1951.12 but there is no evidence that PPP held for 1952.01-1960.12, the period of import substitution in Mexico.