stability analysis of the DAS-DAD dynamics.
We note that the rate of employment, if above the NAIRU level, may also act negatively
on the growth rate of capacity utilization, i.e., on the first law of motion, when the
Kaleckian view of the political business cycle (bosses do not like full employment) is
taken into account in addition. There may of course also be derivative influences (time
derivatives of the considered variables) added to the considered equations, which indeed
should have the same sign as the level influence, since they add to the impact of high
levels if the considered change is positive. Such extensions of the present dynamics must
here however be left for their future investigation.
We have employed reduced-form expressions in the above system of differential equations
whenever possible. We have thereby obtained a dynamical system in five state variables
that is in a natural or intrinsic way nonlinear. We note however that there are many
items that reappear in various equations or are similar to each other implying that
stability analysis can exploit a variety of linear dependencies in the calculation of the
conditions for local asymptotic stability. This dynamical system will be investigated
in the next section in somewhat informal terms with respect to the stability assertions
it gives rise to. A rigorous proof of local asymptotic stability and its loss by way of
Hopf bifurcations can be found in Asada, Chen, Chiarella and Flaschel (2004) for the
original baseline dynamic AS-AD form of the considered disequilibrium AS-AD growth
dynamics. For the present model variant we shall supply more detailed stability proofs
in Asada, Chiarella, Flaschel and Hung (2004) and also detailed numerical simulations
of the model.
3 Feedback-guided stability analysis
In this section we illustrate an important method to prove local asymptotic stability of
the interior steady state of the dynamical system (1) - (5) through partial motivations
from the feedback chains that characterize this baseline model of Keynesian dynamics.
Since the model is an extension of the standard AS-AD growth model we know from
the literature that there is a real rate of interest effect typically involved, first analyzed
by formal methods in Tobin (1975), see also Groth (1992). Instead of the stabilizing
Keynes-effect, based on activity-reducing nominal interest rate increases following price
level increases, we have here a direct steering of economic activity by the interest rate
policy of the central bank. Secondly, if the correctly expected short-run real rate of
interest is driving investment and consumption decisions (increases leading to decreased
aggregate demand), there is the activity stimulating (partial) effect of increases in the
rate of inflation that may lead to accelerating inflation under appropriate conditions.
This is the so-called Mundell-effect that normally works opposite to the Keynes-effect,
and through the same real rate of interest channel as this latter effect.
Due to our use of a Taylor rule in the place of the conventional LM curve, the Keynes-
effect is here exploited in a more direct way towards a stabilization of the economy and
it works the stronger the larger the parameters γp ,γV c are chosen. The Mundell-effect
by contrast is the stronger the faster the inflationary climate adjusts to the present level
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