Accelerators in Macroeconomics: Comparison of Discrete and Continuous Approaches
Valentina V. Tarasova and Vasily E. Tarasov
DOI : 10.3844/ajebasp.2017.47.55
American Journal of Economics and Business Administration
Volume 9, 2017
We prove that the standard discrete-time accelerator equation cannot be considered as an exact discrete analog of the continuous-time accelerator equation. This leads to fact that the standard discrete-time macroeconomic models cannot be considered as exact discretization of the corresponding continuous-time models. As a result, the equations of the continuous and standard discrete models have different solutions and can predict the different behavior of the economy. In this study, we propose a self-consistent discrete-time description of the economic accelerators that is based on the exact finite differences. For discrete-time approach, the model equations with exact differences have the same solutions as the corresponding continuous-time models and these discrete and continuous models describe the same behavior of the economy. Using the Harrod-Domar growth model as an example, we show that equations of the continuous-time model and the suggested exact discrete model have the same solutions and these models predict the same behavior of the economy.
© 2017 Valentina V. Tarasova and Vasily E. Tarasov. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.