The first law of motion is of the type of a dynamic IS-equation, see also Rudebusch
and Svensson (1999) in this regard, here expressed in terms of the growth rate of the
rate of capacity utilization of firms and linearized around the steady state of the model.
It reflects the dependence of excess goods demand on aggregate (income) supply and
thus on the rate of capacity utilization by assuming a negative, i.e., stable dynamic
multiplier relationship in this respect, it shows the joint dependence of consumption
and investment on the real wage (which in the aggregate allows for positive or negative
signs before αω depending on whether consumption or investment is more responsive to
real wage changes) and shows finally the negative influence of the real rate of interest
on the evolution of economic activity. Note here that we have generalized this law of
motion in comparison to the original baseline model of Asada, Chen, Chiarella and
Flaschel (2004), since we now allow for the possibility that also consumption, not only
investment, depends on income distribution as measured by the real wage.
In the second law of motion, for the rate of employment, we assume that the employment
policy of firms follows their rate of capacity utilization (and the thereby implied rate of
over- or underemployment of the employed workforce) with a lag (measured by 1 /βvι ).
Employment is thus assumed to adjust to the level of current activity in delayed form
which is a reasonable assumption from the empirical point of view. We also include
(via the parameter βV2l ) an influence of income distribution on the rate of change of the
employment rate. The last term finally, βv∣ Vc, is added to take account of the possibility
that Okun’s is to be formulated in level form rather than by a law of motion, since this
term is equivalent to the use of const (V c)βV2l , the form of Okun’s law in which this law
was originally specified by Okun himself.
The above two laws of motion therefore summarize the static IS-curve and the employ-
ment this curve implies of the paper of Asada, Chen, Chiarella and Flaschel (2004) in a
dynamic form. They also reflect the there assumed influence of smooth factor substitu-
tion in production and the measurement of the potential output this implied in Asada,
Chen, Chiarella and Flaschel (2004) in an indirect form, as another positive influence
of the real wage on the rate of capacity utilization and its rate of change. This helps to
avoid the estimation of separate equations for consumption and investment C, I and for
potential output Y p as they were discussed and used in detail in Asada, Chen, Chiarella
and Flaschel (2004).
Finally, we have no longer to employ a law of motion for real balances as still was the case
in Asada, Chen, Chiarella and Flaschel (2004). Money supply is now accommodating to
the interest rate policy pursued by the central bank and thus does not feedback into the
core laws of motion of the model. As interest rate policy we here assume the following
type of Taylor rule:
^ = -Yr (r - Го) + Yp( P - ∏) + YVc (Vc - V'c) + Yω (ω - ωo)
Note that we allow for interest rate smoothing in this rule. Furthermore, the actual
(perfectly foreseen) rate of inflation p is used to measure the inflation gap with respect
to the inflation target π of the central bank. There is next a positive influence of the
output gap in this law of motion for the rate of interest, here measured by the rate
of capacity utilization of firms. Note finally that we have included a new kind of gap