We re-examine the empirical evidence concerning a well-known class of one-factor models for the short rate process (cf. Chan et al. [Journal of Finance 47 (1992) 1209] (CKLS)) and some recent extensions allowing for a nonlinear drift and for changing parameters with a new statistical methodology based on robust statistics, the Robust Generalized Method of Moments (RGMM). We find that standard GMM model selection procedures are highly unstable in these applications. When testing the CKLS models with the RGMM we find that they are all clearly misspecified and we identify a clustering of influential observations in the 1979–1982 subperiod, a time span that is well known to coincide with a temporary change in the monetary policy of the Federal Reserve. This clustering of influential observations does not disappear when we introduce a non-linearity in the drift and allow for a parameter shift during the 1979–1982 period. Moreover, a Cox–Ingersoll–Ross model (selected by the RGMM) might offer a satisfactory data description for the period after 1982, since there only a few isolated outliers are found. Comparable results are obtained for the Euro-mark case.