A simple General Constrained Dynamics (GCD) model for demand, supply and price shocks

Glötzl, Erhard (2022): A simple General Constrained Dynamics (GCD) model for demand, supply and price shocks.

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 equilibrium is obtained as 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 is constitutes a natural extension of GE theory. It 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. GCD models can be seen as an alternative to DSGE models to model the dynamics of economic processes. DSGE models are used in particular to analyse economic shocks. For this reason, the aim of this article is to show how GCD models are formulated and how they can be used to model economic shocks such as demand, supply, and price shocks. Since the goal of this paper is to lay out the fundamental principles to the formulation of such GCD models, very simple macroeconomic models are used for illustrative purposes. All calculations can easily be carried out with the open-source program GCDconfigurator, which also allows for the integration of shocks.

• Item Type: MPRA Paper
• Language: English
• Keywords: macroeconomic models, demand shock, supply shock, price shock, 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

References

Flannery, Martin Raymond. 2011. „D’Alembert–Lagrange analytical dynamics for nonholonomic systems“. Journal of Mathematical Physics 52 (3): 032705. https://doi.org/10.1063/1.3559128. Glötzl, Erhard. 2015. „Why and How to overcome General Equilibrium Theory“. MPRA Paper 66265. https://mpra.ub.uni-muenchen.de/66265/1/MPRA_paper_66265.pdf. ———. 2022a. „General Constrained Dynamic (GCD) models with intertemporal utility functions“. https://www.dropbox.com/s/269ki6287fc8atk/A%20general%20constrained%20dynamic%20model%20with%20intertemporal%20utility%20function%20FINAL%20Version%202%20maten.docx?dl=0. ———. 2022b. „Macroeconomic General Constrained Dynamic models (GCD models)“. https://www.dropbox.com/s/2h8o3rg0r4b008b/Macroeconomic%20GCD%20Modelle%20A%2CB%2CC%20FINAL%20Version%202.docx?dl=0. Glötzl, Erhard, und Lucas Binter. 2022. „GCDconfigurator, GitHub“. https://github.com/lbinter/gcd. Glötzl, Erhard, Florentin Glötzl, und Oliver Richters. 2019. „From Constrained Optimization to Constrained Dynamics: Extending Analogies between Economics and Mechanics“. Journal of Economic Interaction and Coordination 14 (3): 623–42. https://doi.org/10.1007/s11403-019-00252-7. Godley, Wynne, und Marc Lavoie. 2012. Monetary economics: an integrated approach to credit, money, income, production and wealth. 2. Aufl. Basingstoke and New York: Palgrave Macmillan. Richters, Oliver. 2021. „Modeling the Out-of-Equilibrium Dynamics of Bounded Rationality and Economic Constraints“. Journal of Economic Behavior & Organization 188 (August): 846–66. https://doi.org/10.1016/j.jebo.2021.06.005. Richters, Oliver, und Erhard Glötzl. 2020. „Modeling Economic Forces, Power Relations, and Stock-Flow Consistency: A General Constrained Dynamics Approach“. Journal of Post Keynesian Economics 43 (2): 281–97. https://doi.org/10.1080/01603477.2020.1713008. Smale Institute. 2003. „Smale Institute Mathematics & Computation“. 2003. http://www.smaleinstitute.com/problem.html. Smale, Steve. 1991. „Dynamics Retrospective: Great Problems, Attempts That Failed“. Physica D: Nonlinear Phenomena 51 (1–3): 267–73. https://doi.org/10.1016/0167-2789(91)90238-5. ———. 1997. „Mathematical Problems for the Next Century“. Fields Institute, Toronto, Juni. http://www.cityu.edu.hk/ma/doc/people/smales/pap104.pdf. ———. 1998. „Mathematical problems for the next century“, nachgedruckt in V. Arnold, M. Atiyah, P. Lax, B. Mazur: Mathematics: Frontiers and Perspectives 2000, American Mathematical Society 2000, 2: 7–15. Zaman, Asad. 2020. „New Directions in Macroeconomics“. International Econometric Review (IER) 12 (1): 1–23. https://doi.org/10.33818/ier.747603.