and from there back to increases in economic activity, through the real rate of interest
channel. This destabilizing so-called Mundell effect must become dominant as the ad-
justment speed of the climate expression βπm is increased. The Blanchard / Katz error
correction terms in the fourth row of J, obtained from the reduced form price Phillips
curve, that are (as only further terms) associated with the speed parameter βπm , are of
no help here, since they do not appear in combination with the parameter βπm in the
sum of principal minors of order 2. In this sum the parameter βπm thus only enters once
and with a negative sign implying that this sum can be made negative if this parameter
is chosen sufficiently large.
Furthermore, making use of the reduced form expression for the term p — πm one can eas-
ily show - under one mild assumption - that the sign structure in the above 4D Jacobian
can be reduced to the following form without change in the sign of the corresponding
Jacobians:
0—00
J 000+
J = 0 0 — 0 ■
+000
This follows, since we can reduce the first two laws of motion to the use of πm in
the place of p and since the last two laws can be reduced to βw and βp terms solely,
respectively, which in turns implies a further reduction to a negative influence of only ω
on its rate of growth and a positive sole influence of V c on πm , everything without change
of sign in the considered determinants. Assuming then that interest rate smoothing is
sufficiently weak allows for the conclusion that the 4D determinant exhibits a positive
sign throughout.
We therefrom in sum get that the 4D dynamics will be convergent for small speeds
of adjustments βπm , while it will be divergent for parameters βπm chosen sufficiently
large. The Mundell effect thus works as expected from a partial perspective. There will
be a unique Hopf bifurcation point βπHm in between where the system loses asymptotic
stability in a cyclical fashion by the death of an unstable or the birth of a stable limit
cycle. Yet sooner or later purely explosive behavior will be established, where there
is no room any more for persistent economic fluctuations in the real and the nominal
magnitudes.
Remark: The Livingston index for consumer price index inflation may be used to measure
the size of the parameter βπm on the basis of this measure for an inflationary climate.
Comparison with DFP?
Modifying the above model finally in order to incorporate into it a simple dynamic
version of Okun’s law, see (2), gives rise to its following respecification:
Vc = const — αv c Vc — αω ω — αr ( r — p) (39)
Vl = const + βvι Vc + βvι Vc (40)
r = const — Yr r + Ypp> + Yv c Vc + Yω ω (41)
ω = const + κ [(1 — Kp )( βw 1 Vl — βw 2 ω ) — (1 — κw )( βp 1Vc + βp 2 ω )] (42)
π m = β∏m ( P — πm ) (43)
24