Standard autocorrelation corrections applied to cointegrating regressions can lead to erroneous first-differencing. Such outcomes are shown to be possible under a range of environments, including cases with autocorrelation coefficients substantially less than 1. First-differencing of a cointegrating regression results in estimates that may bear little relation to the parameters in the original untransformed relation, resulting in misinterpretation of the parameter estimates. These results are proved analytically and demonstrated with simulations and empirical examples.