Keynesian Dynamics and the Wage-Price Spiral:Estimating a Baseline Disequilibrium Approach

which finally gives

sition, also for all values of γr = γω which are chosen sufficiently small.

Proposition 2:

Assume in addition that the parameters βw₂ ,βp₂ ,αω,γω and βπm are all set
equal to zero which decouples the dynamics of V ^c,V^l ,r from the rest of the
system. Assume furthermore that the partial derivative of the first law of
motion depends negatively on V ^c , i.e., the dynamic multiplier process, char-
acterized by αVc , dominates this law of motion with respect to the impact of
V ^c.⁶ Then: The interior steady state of the implied 3D dynamical system

^ - .- — -. ..     .. ..             ..

V  =  -αv c ( V — V) — αr (( r — p) — ( Го — π))          (6)

V l  =  β_vι( V^c — V^c )                                      (7)

Г  =  —Yr ( r — Го ) + Yp ( p> — ∏) + YV c ( V^c — V^c )           (8)

is locally asymptotically stable if the interest rate smoothing parameter γr and
the employment adjustment parameter β_Vl are chosen sufficiently small.

Sketch of proof: In the considered situation we have for the Jacobian of these reduced
dynamics at the steady state:

J=

The determinant of this Jacobian is obviously negative if the parameter Yr is chosen
sufficiently small. Similarly, the sum of the minors of order 2: a2 , will be positive if β_Vl
is chosen sufficiently small. The validity of the full set of Routh-Hurwitz conditions then
easily follows, since trace J = —a1 is obviously negative and since det J is part of the
expressions that characterize the product a 1 a2.                                        ■

Proposition 3:

Assume now that the parameter αω is negative, but chosen sufficiently small,
while the error correction parameters βw₂ ,βp₂ are still kept at zero (as is the

⁶i.e., αVc > αpκκpβ_w .

13

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