Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems
AbstractThis paper is a follow-on to our earlier paper, "Bifurcations in Continuous-Time Macroeconomic Systems." In this paper, we determine the stability properties of the UK continuous time macroeconometric model on its bifurcation boundaries and we test the null hypothesis that the model's parameters are inside the model's unstable region. We then attach to the model Bergstrom's recommended stabilization policy rule. We find that for most settings of his policy rule's parameters, the model's stable region becomes smaller. Hence the policy may be counter- productive. To the degree that "stabilization policy" is interesting, its intent must be to stabilize a system that is not stable. This is bifurcation. Hence stabilization policy only can be understood as bifurcation selection. We find that selection of a policy that will produce successful bifurcation from the model's unstable region to its stable region is much more difficult than previously believe. If in fact the economy is unstable without policy, the selection of successful stabilization policy is an exercise in a very difficult area of complex dynamics. Since Berstrom is one of the originators of the Bergstrom-Wymer-Nowman model, Bergstrom's choice of stabilization policy cannot be viewed as uninformed. We do find that a policy produced from optimal control theory is capable of bifurcating the system successfully from its unstable region to the stable region. But the form of the resulting policy rule is far too complicated to be of practical use. In addition, such a policy, even if implemented, cannot reasonably be viewed as robust to model specification error, since issues regarding the Lucas critique and time inconsistency (Kydland and Prescott) suggest the need for caution in any assumption of robustness to specification error, when such experiments condition upon a structural model.
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Bibliographic InfoPaper provided by EconWPA in its series Macroeconomics with number 9901002.
Length: 29 pages
Date of creation: 21 Jan 1999
Date of revision:
Note: Type of Document - pdf and ps zip; prepared on UNIX Sparc, pdf and ps; pages: 29 ; figures: included. Using the UK continuous time macroeconometric model, we explore its stability properties, its bifurcation boundaries, and its properties under stabilization policy. Earlier work by Grandmont and others has shown that complex dynamics of various forms can be produced by simple models that have no policy relevancy. We use the UK continuous time macroeconometric model to permit similar analysis with a model that has policy relevancy.
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bifurcation stabilization policy instability;
Other versions of this item:
- William Barnett & Yijun He, 2012. "Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201227, University of Kansas, Department of Economics, revised Sep 2012.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-02-15 (All new papers)
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