Using the same error correction transformation:
and
(4)
∆we,t = β0 + β11∆mct + β21∆ut
+ (β11 + β12)mct−1 + (β21 + β22)ut−1 + (α − 1)wet−1 + εt
∆we,t = β0 + β11∆mct + β21∆ut
(5)
½
¾
β + β12
β + β22
− (1 − α) we,t−1 − 11
mct−1 − 21
ut−1 + εt
1−α
1−α
To reconcile this with the hypothesized long run relationship H1gmc, we make
use of
β + β22
γe,1 = 21
(the l-r multiplier of wage with respect to u),
1−α
and impose the following restriction on the coefficient of mct−1:
β11 + β12 = (1 − α)
(6)
∆we,t = β0 + β11n∆mct + β21∆ut
o
− (1 − α) we,t−1 − mct−1 − γe,1ut−1 + εt
(7)
since the long-run multiplier with respect to mc is unity. Then (5) becomes
(Note that the short-run multiplier wrt mc is β11, which can be considerably
smaller than unity without violating the main-course hypothesis H1gmc).
The formulation in (7) is an ECM. We can write
0
∆we,t = β0 + β11∆mct + β21∆ut
− (1 − α) {we − we∗}t−1 + εt
where we∗ is given by the left hand side of the extended main course hypothesis
H1gmc.
Stable dynamics: Assume ∆mct = gmc and ∆ut = 0 (constant rate of unemployment). Assume disequilibrium in period t − 1:
{we − we∗}t−1 > 0 reduces ∆we,t, which leads to {we − we∗}t < {we − we∗}t−1
in the next period, hence error-correction.
22
21
rate of
unemployment
Exercise 2.1 Is β22 > 0 a necessary and/or sufficient condition for path b to
occur?
t
0
time
wage level
a
Exercise 2.2 What might be the economic interpretation of having β21 < 0 ,
but β22 > 0?
Exercise 2.3 Assume that β21 + β22 = 0. Try to sketch the wage dynamics (in
other words the dynamic multipliers) following a rise in unemployment in this
case!
b
t0
time
Figure 2: The main course model: A permanent increase in the rate of unemployment, and possible wage responses.
23
24