Detecting chaos in the cash-in-advance model using the two-pass-fold method

In monetary economics, models with multiple equilibria abound, especially in the case of models with overlapping generations such as the Cash-In-Advance model. Using inverse limits, [KS] establish a topological classification of the arising multiple equilibria and analyze the backward dynamics of the model. However, their work remains strictly theoretical and lacks any relevant examples supporting the theory. In this paper we corroborate the classification by presenting a family of examples that illustrate all possible cases from the classification. Moreover, using a numerical method called the Two-Pass-Fold detection, we examine each category and analyze the presence of chaos for a range of plausible monetary policy decisions