Mode‐locking and entrainment of endogenous economic cycles

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Abstract
We explore the robustness of aggregation in Sterman's model of the economic long wave. The original model aggregates all capital‐producing firms into a single sector and generates a large‐amplitude self‐sustained oscillation with a period of roughly 50 years. We disaggregate the model into two coupled industries, one representing production of plant and long‐lived infrastructure and the other representing short‐lived equipment and machinery. While holding the aggregate equilibrium characteristics of the model constant, we investigate how mode‐locking occurs as a function of the difference in capital lifetimes and the strength of the coupling between the sectors. Disaggregation allows new modes of behavior to arise: In addition to mode‐locking, we observe cascades of period‐doubling bifurcations, chaos, intermittency, and quasi‐periodic behavior. Despite the introduction of these additional modes, the basic behavior of the model is robust to the aggregation assumption. We consider the likely effects of finer disaggregation, the introduction of additional coupling mechanisms, such as prices, and other avenues for the exploration of aggregation in system dynamics models.