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

4.3 Estimation of the Structural Model

As discussed in section 2, the law of motion for real wage rate, eq. (4), can be considered
as the reduced form of two structural equations for dwt and dpt . Assuming that the
inflation climate variable is a function of past price inflation rates, the dynamics of the
system (1) - (5) is equivalently presented by the following equations:

dwt = βw 1 ( V^l — V^l ) t-1 + Kw dpt-1 + (1 — Kw ) dp 12t-1 — β_ww ukbpt + e 1t     (16)

dpt = βp 1 ( V c — V c ) t-1 + Kpdwt + (1 — Kp ) dp 121-1 + β_wpukbpt + e 21       (17)

Vl = ^βVl ⁽Vc ^- Vc)t-1 ^{- β}V^{l (ω — ω}oo)t-1 ^{+ β}Vl ⁽Vl ^— Vl)t-1 ^{+ e}31        ⁽¹⁸⁾

^rt = ^— Yr ^{(r — r}o) t-1 ⁺ Yp ^{(p — π}) t-1 ⁺ Yvc ^{( V}c ^{— V}c) t-1 ⁺ Yω ^{(ω — ω}o) ^{+ e}51      ⁽²⁰⁾

Obviously the model (16) and (20) is nested in the VAR(12) of (14). Therefore we can
use (14) to evaluate the empirical relevance of the model (16) to (20). First we test
whether the parameter restrictions on (14) implied by (16) to (20) are valid. If the null
of these restrictions cannot be rejected, we will estimate (16) and (20) and then calculate
the empirical estimates for the model (1) to (5).

The structural model (16) to (20) puts 408 restrictions on the unconstrained VAR(12)
of system (14). Applying likelihood ratio method we can test the validity of these
restrictions. We get the result:

• Chi-Squared(408)= 536.377763 with Significance Level 0.00001921

Obviously, for the period from 1955:1 to 2000:4, the structural model is too restric-
tive. However, for the period from 1965:1 to 2000:4 we can not reject the null of these
restrictions. The test result is the following:

• Chi-Squared(408)= 414.104639 with Significance Level 0.39322678

Obviously, the specification from (16) to (20) is a valid one for the data set from 1965:1
to 2000:4. The estimation results are listed in the appendix. This result shows strong
empirical relevance of the law of motions described in (1) - (5) as a model for the
economy from 1965:1 to 2000:4. It is worthwhile to note that altogether 408 restrictions
are implied through (1) - (5) on the VAR(12) model. A p-value of 0.39 means that (1) -
20

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