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

π^m = β∏m (P - π^m)

in the presentation of the full model below. Besides demand pressure we thus use (as cost
pressure expressions) in the two PC’s weighted averages of this economic climate and
the (foreseen) relevant temporary cost pressure term for future wage and price setting.
In this way we get two PC’s with very analogous building blocks, which despite their
traditional outlook will have a variety of interesting and novel implications. Somewhat
simplified versions of these two Phillips curves have been estimated for the US-economy
in various ways in Flaschel and Krolzig (2004), Flaschel, Kauermann and Semmler (2004)
and Chen and Flaschel and Chen (2004) and found to represent a significant improvement
over single reduced-form Phillips curves, with in fact wage flexibility being greater than
price flexibility with respect to their demand pressure item in the market for goods
and for labor, respectively. Note that such a finding is not possible in the conventional
framework of a single reduced-form Phillips curve.

We have added here to these earlier studies Blanchard and Katz type error correction
mechanisms (the second β terms in each equation) not only in the wage inflation equa-
tion, but also in the price inflation equation. The minus sign in front of βw₂ is motivated
as in the article of Blanchard and Katz (2000), see also Flaschel and Krolzig (2004) in
this regard, while the plus sign in front of βp₂ simply represents a second measure of
cost pressure, in addition to the weighted average of inflation rates shown thereafter. To
simplify steady state calculations we measure these error correction terms in deviation
from their steady state values.

Note that for our current version, the inflationary climate variable does not matter
for the evolution of the real wage ω = w/p , the law of motion of which is given by
(κ = 1/(1 - κ_w κ_p)):

^ω = ^{κ[(1 - κ}P)(^βw 1 ⁽Vl ^— Vl^{) - β}w2 ^{(ω - ω}θ⁾⁾ - ⁽¹ - ^KW^)(βp 1 (Vc ^- Vc^{)+ β}p2 ^{(ω - ω}o^))]

This follows easily from the following obviously equivalent representation of the above
two PC’s:

w — π^m = βw 1 ( V l — V l ) — βw 2 ( ω — ωo, ) + κ_w (p — π^m ),

^{p — π}m = ^βp 1 ⁽ Vc ^— Vc) ^{+ β}p2 ^{(ω — ω}o)) ^{+ κ}p ^{( w — π}m) ^,

by solving for the variables Wj — π^m and p — π^m. It also implies the two across-markets
or reduced form PC’s given by:

^p =    ^{κ [ β}p 1 ⁽ V c ^— V c ) ^{+ β}p 2 ^{( ω — ω}o ) ^{+ κ}p ^{( β}w 1 ⁽ V l ^— V l ) ^{— β}w 2 ^{( ω — ω}o ))] ^{+ π}m^,

^w =    ^κ[βw 1 ⁽Vl ^— Vl) ^{— β}w2 ^{(ω — ω}o)) ^{+ κ}w ^(βp 1 ⁽Vc ^— Vc) ^{+ β}p2 ^{(ω — ω}o))] ^{+ π}m^,

which represent a considerable generalization of the conventional view of a single-market
price PC with only one measure of demand pressure, the one in the labor market.

The remaining laws of motion of the private sector of the model are as follows:

Vc  =  —avc(Vc — Vc) ± αω(ω — ωo) — αr((r — p) — (ro — ∏))

V = ^βv^{l (} V ^— V ) ^{— β}v2, ^{(ω — ω}o ) + ^βv₃^l V

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