Alternative models of the supply side. Slide set I.
Ragnar Nymoen
Department of Economics, UiO
10 November 2009
ECON 3410/4410 Lecture 11
Introduction I
In IAM, the Phillips curve relationship is derived from a theory
of wage bargaining and monopolistic price setting.
Expectations errors (see slide set II to lecture 5), Pt 6= Pte , are
the explanation for in‡ation, and for departures of GDP from
full employment GDP.
Easy to imagine that wage and price adjustment are driven by
other factor than just expectations errors.
In particular, this seems reasonable in modern economies with
unions, and with price setting …rms, where there are
con‡icting aims about the real wage.
In order to formalize this intuition, IDM ch 3.2 takes the
starting point that
the theoretical models of wage-bargaining and monopolistic
price setting give propositions about the steady-state
relationships for wage and price.
ECON 3410/4410 Lecture 11
Introduction II
A system with (one or more) error-correction equations can be
used to model the dynamics.
We embed this in a model with two sector: an exposed and a
sheltered sector.
This trait of the model makes it possible to show how close
the modern model of wage bargaining is related to a much
older theory called the Norwegian model of in‡ation, which
continues to play a role in the economic policy debate about
wage settlements.
The qualitative implications for the medium macroeconomic
equilibrium does not hinge on the distinction between an
e-sector and a s-sector, and in slide set II we will discuss those
implications more closely in an “one sector” macro model,
which is comparable to the AD-AS model in IAM.
ECON 3410/4410 Lecture 11
Static long-run relationships. I
In log-linearized form the model is
web = me0 + ae + qe +
p = qs + (1
ws = we =
)qe ;
e1 u,
0<
0
(1)
< 1;
(2)
e1
web ;
qs = ln( ) + ws
(3)
as :
(4)
Equation (1) represents the bargaining theoretical relationship
for e-sector wages, i.e., web = ln(Web ).
(2) is a stylized de…nition of the consumer price index,
p = log(consumer price index).
(3) says that the s-sector is a wage follower, and that in the
long-run, the e-sector wage is equal to the bargained wage.
(4) represents mark-up pricing in the s-sector.
ECON 3410/4410 Lecture 11
Static long-run relationships. II
The four equations determine web ,we , ws , qs and p, for given
exogenous values of ae ; as , qe and u.
If the wage level in period t, wet , approaches web when the
b , the static
initial situation is in disequilibrium: we0 6= we0
model corresponds to a stable steady-state solution.
There are several equilibriating mechanisms that can secure
dynamic stability, and these mechanism are not exclusive of
each other.
In the conventional AD-AS model, it is (implicitly) assumed
that adjustment of ut is the only mechanism that can stabilize
in‡ation.
In order to focus on another possible mechanism, we assume
…rst that unemployment in exogenous, so that it cannot serve
as an equilibrating mechanism.
ECON 3410/4410 Lecture 11
Wage dynamics I
wet is determined by the dynamic model
wet =
0 + 11 mct + 12 mct 1 + 21 ut + 22 ut 1 +
wet
1 +"t :
(5)
with mct de…ned as
mct = aet + qet ;
mct is assumed to be exogenous in the following. This
involves:
exogenous productivity
and price taking behaviour,
and a nominal exchange rate that does not respond to we;t ,
either directly or indirectly. Simplest to assume a …xed
exchange rate.
ECON 3410/4410 Lecture 11
Wage dynamics II
Error-correction transformation:
wet =
+(
0
+
11
+
11
mct +
12 )mct 1
21
ut
+(
21
(6)
+
22 )ut 1
+(
1)we t
1
+ "t
For the bargaining theory to correspond to a long-run model
for the wage level, it is necessary that (5) has a stable
solution.
Since wages usually show a smooth evolution through time,
we state the stability condition as
0<
< 1;
ECON 3410/4410 Lecture 11
(7)
Wage dynamics III
Subject to (7), equation (6) can be written as
wet =
0
(1
+
11
mct +
) wet
21
11
1
ut
+
(8)
12
1
mct
1
21
1
+
22
ut
To reconcile this with the steady-state relationship (1), we
de…ne
21 + 22
,
e;1 =
1
and impose the unit long-run multiplier for mc
11
+
12
= (1
)
ECON 3410/4410 Lecture 11
1
+ "t .
Wage dynamics IV
(8) then takes the form
wet =
0
+
11
(1
mct +
) fwet
1
21
mct
ut
(9)
e1 ut 1 g
1
The short-run multiplier with respect to mct is
typically < 1:
+ "t
11 ,
which is
(9) can be expressed as
wet =
0
0
(1
with
0
0
=
0
(1
+
mct + 21 ut
o
n
+ "t
) we web
11
t 1
)me0 and
web = me0 + ae + qe +
e1 u
as above.
ECON 3410/4410 Lecture 11
(10)
Wage bargaining and in‡ation I
To simplify we assume that adjustments of s-sector wages and
prices are instantaneous.
The in‡ation model is then (10) and
wst =
wet ,
qst =
wet
p=
(11)
aet ,
qs + (1
(12)
) qe :
(13)
4 equations that determine we (t), ws (t), qs (t) and p(t) as
functions of initial conditions, and given processes for the
exogenous variables mc(t), u(t) and "(t).
The model is a recursive system of equations: The wage
growth rate in the exposed sector is determined …rst, and then
the other growth rates follow recursively.
ECON 3410/4410 Lecture 11
Wage bargaining and in‡ation II
The reduced form equation for the rate of in‡ation,
0
0
pt =
+(
+
pt , is:
11
11
(1
+ "t
(14)
+ (1
)) qe;t +
21
ut
aet
ast
n
o
) wet 1 web
implying following explanatory variables for in‡ation:
“Imported in‡ation”: (
11
+ (1
Shock to unemployment:
21
Productivity growth:
aet
11
e-sector equilibrium correction:
)) qet
ut
ast ,
(1
n
) we:t
ECON 3410/4410 Lecture 11
1
b
we;t
o
1 .
Wage bargaining and in‡ation III
The point is that we obtain a “richer theory” of in‡ation
determinants (in the short-run!).
Clearly, one can use error-correction formulation both for
ws ;t and qst , and the list will be even longer.
Can also introduce expectations variables, which we have
abstracted from above in order to concentrate on the new
element,
ECON 3410/4410 Lecture 11
Size of e¤ects I
Set the share of non-traded goods in consumption to 0:4.
Then = 0:67, and setting 11 = 0:5 gives a coe¢ cient of
qet of 0:66.
Foreign in‡ation in the range of 1% 5% in our model implies
that a 3% in‡ation abroad imputes for example 2% “imported
in‡ation”.
The coe¢ cient of
aet is 0:33, and for
ast we obtain
0:67.
The net-e¤ect of productivity growth rates at around 2% may
therefore be rather small.
Note the implication that increased productivity in the
exposed sector of the economy increases in‡ation. It occurs
because e-sector productivity growth increases the bargained
wage in that sector, which in‡icts price increases in the
sheltered sector via the assumption of relative wage
stabilization.
ECON 3410/4410 Lecture 11
Size of e¤ects II
Equilibrium correction in wage setting:
With the above parameter values, and = 0:7, the coe¢ cient
of wet 1 web in equation (14) becomes 0:2. The
interpretation is that a 1 percentage point deviation from the
the steady-state wage in period t 1 leads to a reduction of
the period t in‡ation rate of 0:2 percentage points.
ECON 3410/4410 Lecture 11
Including of cost-of-living e¤ects in the theory I
In real world wage bargaining, compensation for increases in
cost-of-living is always a main issue.
One way to bring this into the model is to include
dynamic equation for e-sector wage setting:
wet =
0
0
(1
+
11
mct +
) fwet
1
ut +
21
mct
1
31
pt
e1 ut 1
pt in the
(15)
me0 g + "t :
Since in‡ation can be expressed as:
pt =
wet
ast + (1
) qet
we can derive the following “semi-reduced form” for
ECON 3410/4410 Lecture 11
wet :
Including of cost-of-living e¤ects in the theory II
0
wet = ~ 0 + ~ 11 mct + ~ 21 ut +
(1^) fwet
mct
1
41
ast +
e1 ut 1
1
51
qet
(16)
me0 g + ~"t :
where the coe¢ cient with aneare the original coe¢ cients of
(15) divided by (1
31 ), and
41
51
=
=
31
31 (1
=(1
)=(1
31
),
31
)
By using (16) instead of (15) in the system-of-equations, the
recursive solution method of the original model is re-installed.
ECON 3410/4410 Lecture 11
The Norwegian model of in‡ation I
The idea that wage bargaining can stabilize wage growth and
in‡ation directly, and also when the rate of unemployment is
…xed exogenously, goes back to the 1960s.
For example Norwegian economist Odd Aukrust formalized
the “main-course model of in‡ation”, also known as he
Norwegian Model of In‡ation.
As above, there is an e-sector where …rms are price takers,
and a sheltered sector where …rms set prices as mark-ups on
wage costs.
A …xed exchange rate is assumed.
ECON 3410/4410 Lecture 11
The Norwegian model of in‡ation II
The model’s long-run propositions are:
1
that e-sector wage growth will follow a long run tendency
de…ned by the exogenous price and productivity trends in that
sector.
2
If relative wages are to be constant in the long-run, the wage
level of the s-sector needs to follow the same tendency.
3
The development of the domestic price level therefore be
in‡uenced by trend growth in international prices and the
productivity trend.
The …rst hypothesis, about wage formation in the e-sector, is
in many ways the de…ning characteristic of the whole
framework. It plays the same role in the theory as
Nash-bargaining stage in modern formulation.
ECON 3410/4410 Lecture 11
The Norwegian model of in‡ation III
The wage share of value added is
We Le
We
=
, where Ae
Qe Ye
Qe Ae
Ye
Le
where Le and Ye denoted employment and output.
By de…nition, the rate of e-sector pro…ts is
Q e Ye W e L e
=1
Qe Ye
We
:
Q e Ae
(17)
If we assume that there is a long-run rate of pro…t which is
required to sustain investment and employment in the
e-sector. Then (17) says that there is also a required long-run
wage-share.
ECON 3410/4410 Lecture 11
The Norwegian model of in‡ation IV
Assume that both Qe and Ae are exogenous variables with a
trend growth. We can then formulate the main-course
proposition:
We = Me Qe Ae ;
(18)
where We denotes the long-run equilibrium wage level
consistent with the twin assumptions of exogenous price and
productivity trends and a constant required wage-share,
denoted Me in (18).
Using logs, the long-run wage equation for the e-sector
becomes:
H1mc : we = qe + ae + me ;
where an asterisk, denotes a long-run equilibrium value, and
we = ln(We ).
The marker H1mc indicates that this is the …rst hypothesis of
the Norwegian Model of In‡ation.
ECON 3410/4410 Lecture 11
The Norwegian model of in‡ation V
qe and ae both increase over time. we is therefore also
trending upwards along a path determined by the main-course
variable:
mc = ae + qe
(19)
The graphical representation of the main-course theory shows
the actual time series of the wage level,we;t , ‡uctuating
around a growing main-course, but always inside a wage
corridor.
ECON 3410/4410 Lecture 11
The wage-corridor
The actual wage
will ‡uctuate
around the
main-course,
log wage level
"Upper boundary"
Main course
and, inside the
walls of the
corridor.
This is the same
wage dynamics
that we
developed from
the modern
bargaining
approach.
"Lower boundary"
0
time
ECON 3410/4410 Lecture 11
A shift in the main-course I
There is nothing in the Norwegian model hindering that the
long-run wage level can change as a result of changes changes
to the economy.
Among other thing. the main course can shagne if there is a
permanent change u (shifts from one mean to a new oner)
If me is a function of the rate of unemployment, a
generalization of H1mc becomes
H1gmc
we = me;0 + mc +
e;1 u,
H1mc has the same interpretation as the “bargained wage” in
the modern approach: If wet follows a stable dynamic process,
then its steady-state is given by we .
ECON 3410/4410 Lecture 11
A shift in the main-course II
As noted there are two other long-run propositions which
complete Aukrust’s theory: a constant relative wage between
the sectors (denoted mes ) and the existence of a normal
sustainable wage share also in the s-sector:
H2mc
H3mc
we
ws
ws = mes ,
qs as = ms
as is the exogenous productivity trend in the sheltered sector.
Re-arranging H3mc , gives
qs = ws
as + ms
which is similar to the ‘price equation’in the wage bargaining
model above!
ECON 3410/4410 Lecture 11
Simulating the main-course
We can use computer simulation to con…rm our conclusions
about the dynamic behaviour of the main-course model.
The following three equations make up a representative
main-course model of wage-setting in the exposed sector:
we;t = 0:1mct + 0:3mct
mct = 0:03 + mct
1
1
0:06 ln Ut
1
+ 0:6we;t
+ "mc ;t
1
+ "w ;t ;
(20)
(21)
Ut = 0:005 + 0:005 S1989t + 0:8Ut
1
+ "U ;t
(22)
S1989t is an indicator variable which is 0 before 1989 and 1
afterwards.
ECON 3410/4410 Lecture 11
Simulated solution
2.25
extended main-course
2.20
upper-boundary
2.15
solution for we,t
2.10
2.05
lower-boundary
2.00
1.95
2003
2004
2005
2006
2007
2008
2009
ECON 3410/4410 Lecture 11
2010
2011
Solution with an exogenous shift in u
Change in ln U t to a regime shift in 1989, that raises the equilibrium rate.
-3.0
-3.2
-3.4
-3.6
1990
1.9
1995
2000
Solution of we,t
Without regime shift U
int
1.8
With regime shift U
int
1.7
1990
1995
ECON 3410/4410 Lecture 11
2000