Using identification-robust methods, the authors estimate and evaluate for Canada and the United States various classes of inflation equations based on generalized structural Calvo-type models. The models allow for different forms of frictions and vary in their assumptions regarding the type of price indexation adopted by firms. Point and confidence-set parameter estimates are obtained based on the inversion of identification-robust test statistics. Focus is maintained on the structural aspect of the model with formal imposition of the restrictions that map the theoretical model into the econometric one. The results show that there is some statistical merit to using indexation-based Calvo-type models for inflation. However, some identification difficulties are also uncovered with considerable uncertainty associated with estimated parameter values. In particular, we find that implausibly-high frequency of price re-optimization values cannot be ruled out from our identification-robust confidence sets.