Macroeconomic General Constrained Dynamic models (GCD models)

In economics balance identities as e.g. C+K'-Y(L,K) = 0 must always apply. Therefore, they are called constraints. This means that variables C,K,L cannot change independently of each other. In the general equilibrium theory (GE) the solution for the equilibrium is obtained as an optimisation under the above or similar constraints. The standard method for modelling dynamics in macroeconomics is DSGE. Dynamics in DSGE models result from the maximisation of an intertemporal utility function that results in the Euler-Lagrange equations. The Euler-Lagrange equations are differential equations that determine the dynamics of the system. In Glötzl, Glötzl, und Richters (2019) we have introduced an alternative method to model dynamics, which is a natural extension of GE theory. It is based on the standard method in physics for modelling dynamics under constraints. We therefore call models of this type "General Constrained Dynamic (GCD)" models. In this paper we apply this method to macroeconomic models of increasing complexity. The target of this labour is primarily to show the methodology of GCD models in principle and why and how it can be useful to analyse the macroeconomy with this method. Concrete economic statements play only a subordinate role. All calculations, even for GCD models of any complexity, can be easily performed with the open-source program GCDconfigurator.