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Economic Dynamics
Miloslav S Vosvrda
IES FSV UK
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.
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.
Two fundamental ways of
Economic Dynamics
• The fact that the present depends upon the past.
yt  f ( yt 1 )
• The fact that the economic agents in the present
have expectations(or beliefs) about the future.
yt  g ( E[ yt 1 ])
It is the future lag in rational expectations.
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.
Interlinkes in Economic Dynamics
• Nonlinearities
• Multiple Equilibria
• Local stability
Let xt  f ( xt 1 ) be a simple nonlinear
difference equation. An equilibrium or a fixed
*
*
point exists, if x  f ( x ) . 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.
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.
Chaos Theory
The fact that nonlinear system can lead to
a periodic or chaotic behavior has meant a
new branch of study.
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.
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.
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
New Classical Economics
assumes 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.
What is pervasive in Economics
• Nonlinearity
• Chaos
represented by the following models
• The Solow growth model
• The optimal growth
• The overlapping generations model
The Solow growth model
kt 1
1     kt  s  f (kt )


1 n
where for example f(k) has the following form
f  kt   s  a  kt   n     kt

The optimal growth
kt 1  f (kt )  (1   )  kt  ct
u(ct )    u(ct 1 )  [ f (kt 1 )  (1   )]
The overlapping generations
model
(1  n)  kt 1  z  [ f (kt 1 )  (1   )  w(kt )]