Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints

The mathematical analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in Lagrangian mechanics. In a differential-algebraic equation framework, households, firms, banks, and the government employ forces to change economic variables according to their desire and their power to assert their interest. These ex-ante forces are completed by constraint forces from unanticipated system constraints to yield the ex-post dynamics. The out-of-equilibrium model combines Keynesian concepts such as the balance sheet approach and slow adaptation of prices and quantities with bounded rationality (gradient climbing) discussed in behavioral economics and agent-based models. Depending on the power relations and adaptation speeds, the model converges to a neoclassical equilibrium or not. The framework integrates different schools of thought and overcomes some restrictions inherent to optimization approaches, such as the problem of aggregating individual behavior into macroeconomic relations and the assumption of markets operating in or close to equilibrium.