Parameter constancy is a fundamental requirement for empirical models to be useful for forecasting, analysing economic policy, or testing economic theories. However, there are surprises in defining a constant-parameter model, such that models with time-varying coefficients, and expansion of the parameterisation over time are both compatible with constancy, yet unbiased forecasts may not entail a sensible model choice. In-sample tests cannot determine likely post-sample predictive failure. A c...