We reconsider the issue of the (non-)equivalence of period and continuous time analysis in macroeconomic theory and its implications for the existence of chaotic dynamics in empirical macroeconomics. We start from the methodological precept that period and continuous time representations of the same macrostructure should give rise to the same qualitative outcome, i.e. in particular, that the results of period analysis should not depend on the length of the period chosen. A simple example where this is fulfilled is given by the Solow growth model, while all chaotic dynamics in period models of dimension less than 3 are in conflict with this precept. We discuss a typical example from the recent literature, where chaos results from an asymptotically stable continuous-time macroeconomic model when it is reformulated as a discrete-time model with a sufficiently long period length.