Economic Dynamics

1. Economic Dynamics Miloslav S Vosvrda IES FSV UK

2. Macroeconomic Dynamics Economics dynamics has recently become more prominent in mainstream economics. One feature of significance that grew out of both the closed economy modeling and the open economy modeling was the stock-flow aspects of the models. Keynesian economics had emphasized a flow theory.

3. The stock-flow aspects The balance of payments is a flow. The money resource is a stock. The adjustment required both a change in the flows and a change in the stocks. Such stock-adjustment flows became highly significant and needed for modeling processes. Models had to become more dynamic if they were to become more realistic or better predictors.

4. Two fundamental ways of Economic Dynamics • The fact that the present depends upon the past. • The fact that the economic agents in the present have expectations(or beliefs) about the future. It is the future lag in rational expectations.

5. An area for future research A future lag enters and a model it becomes absolutely essential to model expectations, and at the present time there is no generally accepted way of doing this. This does not mean that we should not model expectations, rather it means that at the present time there are a variety of ways of modeling expectations, each with its strengths and weaknesses.

6. Interlinkes in Economic Dynamics • Nonlinearities • Multiple Equilibria • Local stability Let be a simple nonlinear difference equation. An equilibrium or a fixed point exists, if . A sequence of points {xt } beginning at x0 , and if for a small neighborhood of a fixed point x* the sequence {xt } converges on x* , then x* is said to be locally asymptotical stable.

7. Nonlinearity The crucial element leading to aperiodic or chaotic behavior is the fact that the system is nonlinear. For a linear system a small change in a parameter value does not affect the qualitative nature of the system. For a nonlinear system this is far from true. For a nonlinear system some small change in a parameter value can affect both the quantitative and qualitative nature of the system dramatically.

8. Chaos Theory The fact that nonlinear system can lead to a periodic or chaotic behavior has meant a new branch of study.

9. Characteristics of the system Any deterministic system is analyzed from the following items: • The time-evolution values • The parameter values • The initial conditions A system for which all three are known is said to be deterministic.

10. If such a deterministic system exhibits chaos then it is very sensitive to initial conditions. Since there is always some imprecisions in specifying initial conditions the system is unpredictable, and therefore the future path of the system cannot be known in advance. The future path of the system is said to be indeterminable even though the system itself is deterministic.

11. The question The presence of chaos raises the question of whether economic fluctuations are generated by • the endogenous propagation mechanism -suggests strong government stabilization policies or • from exogenous shocks to the system -suggests no government stabilization policies because business cycles are caused by exogenous shocks

12. New Classical Economicsassumes that the macroeconomy is asymptotically stable so long as there are no exogenous shocks. If chaos is present the it is not true. On the other hand New Keynesian Economics assumes that the economic system is inherent unstable. What is not clear is whether this instability arises from random shocks or from the presence of chaos.

13. What is pervasive in Economics • Nonlinearity • Chaos represented by the following models • The Solow growth model • The optimal growth • The overlapping generations model

14. The Solow growth model where for example f(k) has the following form

15. The optimal growth

16. The overlapping generations model