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

• H0 : P = 11 v.s. H1 : P =12

Chi-Squared(25)= 42.86003 with Significance Level 0.20055

• H0 : P = 10 v.s. H1 : P =11

Chi-Squared(25)= 52.30518 with Significance Level 0.03868

According to these test results we use VAR(12) to represent a general model that should
be an approximation of the DGP. Because in the dynamic system of (1) - (5) the variable
ukbpt is treated as exogenous, we factorize the VAR(12) process into a conditional process
of dwt ,dpt ,V_t^l ,V_t^c ,rt given ukbpt and the lagged variables, and the marginal process of
ukbpt given the lagged variables:

dwt
dpt
^Vt^l^Vt^crt

C ci ∖

c₂

c₃

V5 /

pl
b2
I₁b₃b4

∖

d74 +

)

ai
a2

a3	ukpbt
a4
a5

(14)

a ailk

P ^a2l k

+ ∑ α3ι k

^k=¹^a41 k

^a51 k

^al2 k
^a22 k
^a32 k
^a42 k
^a52 k

^al3 k
^a23 k
^a33 k
^a43 k
^a53 k

^al4 k
^a24 k
^a34 k
^a44 k
^a54 k

^al5 k
^a25 k
^a35 k
^a45 k
^a55 k

al6k ʌ

^a26 k

^a36 k

^a46 k

^a56 k

dwt-k
dpt-k
V^l^Vt-k
V^c^Vt-k
rt-k

elt ʌ
^e21

ukbpt-k

^e3t

^e41

e51 /

P
ukbpt =c6 + a6lk
k=l

^a62k

^a63k

^a64k

^a65k

^a66k

dwt-k
dpt-k
V^l^Vt-k

V^c

^Vt-k
rt-k
ukbpt-k

+ e6t

(15)

Now we examine if ukbpt can be taken as ”exogenous” variable. The partial system (14) is
exactly identified. Hence the variables ut are weakly exogenous for the parameters in the
partial system,⁷ For the strong exogeneity of ukbpt, we test whether dwt,dpt,V_t^l,V_t^c,rt
Granger cause ukbpt .

The test is carried out by testing the hypothesis: H0 : aijk =0, (i =6;j =1, 2, 3, 4, 5; k =
1, 2, ..., 12) in (15) based on likelihood ratio

• Chi-Squared(60)= 69.157150 with Significance Level 0.19572294

⁷For detailed discussion see Chen (2003)

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