Christian Haxholdt

Mode locking and entrainment of endogenous economic cycles

We explore the robustness of aggregation in Stermans 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.

Entrainment in a disaggregated economic long wave model

This paper investigates how mode-locking and other nonlinear dynamic phenomena arise through the interaction of two capital-producing sectors in a disaggregated economic long wave model. Each sector in isolation produces a self-sustained oscillation with a period and amplitude determined by the characteristics of that sector. However, the sectors interact through their mutual dependence on each others output for their own production. When this coupling is accounted for, the two sectors tend to synchronize or lock together with a rational proportion between the periods. While keeping the aggregate equilibrium characteristics of the system constant, we study how this locking occurs as a function of the difference in capital lifetimes and as a function of the strength of the coupling between the sectors. Besides mode-locking and quasi-periodic behavior, the observed phenomena include cascades of period-doubling bifurcations, chaos, and intermittency. When the difference in capital lifetimes is very large, the coupled system tends to behave like a one-sector model with a reduced capital content of production.

Clubs as status symbol: would you belong to a club that accepts you as a member?

Abstract We present a stylised model that goes beyond traditional analyses involving crowding and exclusiveness, and addresses the status issue by asking ‘Do I want to be associated with those individuals?’ rather than ‘Do I want to be associated with that many individuals?’. As the population cares more about status, exclusion from well-defined groups/clubs occurs: less desirable individuals are refused. Inability to exclude induces the most desirable individuals to leave, and the club collapses. Offering honorary membership to the most desirable potential members is not only a commercially optimal strategy when exclusion is not allowed, it even outperforms exclusion as a revenue maximisation strategy.

Phase-Locking in a Goodwin Model

Mode-locking is a phenomenon that arise in nonlinear dynamical systems, when two or more cyclic motions interact with one-another. In the first place mode-locking means that the oscillations adjust to each other so as to get in step. However, the adjustment is more complicated than this because each mode contains harmonics and subharmonics which may also try to get in step. Many economic phenomena can be thought of as coupled oscillators. Examples are the interaction between seasonal fluctuations and the business cycle, the interaction between different sectors in an economy (Lorenz, 1987a), and the interaction between different national or regional economies (Lorenz, 1987b).