General Constrained Dynamic (GCD) models with intertemporal utility functions

Glötzl, Erhard (2022): General Constrained Dynamic (GCD) models with intertemporal utility functions.

Abstract

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 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 are Dynamic Stochastic General Equilibrium (DSGE) models. 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 constitutes a natural extension of GE theory. This approach is based on the standard method for modelling dynamics under constraints in physics. We therefore call models of this type "General Constrained Dynamic (GCD)" models. In Glötzl (2022b) this modelling method is described for non-intertemporal utility functions in macroeconomics. Since intertemporal utility functions are, however, essential for many economic models, this paper sets out to extend the GCD modelling framework to intertemporal GCD models, referred to as IGCD models in the following. This paper sets out to define the principles of formulating IGCD models and show how IGCD can be understood as a generalisation and alternative to DSGE models.

• Item Type: MPRA Paper
• Language: English
• Keywords: macroeconomic models, intertemporal utility function, constraint dynamics, GCD, DSGE, out-of-equilibrium dynamics, Lagrangian mechanics, stock flow consistent, SFC
• Subjects: A - General Economics and Teaching > A1 - General Economics > A12 - Relation of Economics to Other Disciplines; B - History of Economic Thought, Methodology, and Heterodox Approaches > B1 - History of Economic Thought through 1925 > B13 - Neoclassical through 1925 (Austrian, Marshallian, Walrasian, Stockholm School); B - History of Economic Thought, Methodology, and Heterodox Approaches > B4 - Economic Methodology > B41 - Economic Methodology; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B59 - Other; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C54 - Quantitative Policy Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E10 - General

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