Alternative models of the supply side. Slide set II.
Ragnar Nymoen
Department of Economics, UiO
16 November 2009
ECON 3410/4410 Lecture 11
Summary of last lecture I
In Lecture 11 we summarized a formal bargaining model of
wage formation, which we interpreted as a theory of the
steady-state wage in the e-sector of an open economy.
The e-sector wage (we;t ) will be dynamically stable if we;t
depends negatively on the deviation between the real wage
target (web ) and the actual real-wage.
we;t ! web = me0 + ae + qe +
t!1
e1 u
This wage error correction mechanism is active at any given
rate of unemployment.
The interpretation is that the wage is directly in‡uenced by
the pro…tability— and bargaining is about the sharing of
pro…ts.
ECON 3410/4410 Lecture 11
Summary of last lecture II
In the steady state, with constant growth rates ga;e and
gq;e for productivity and price:
we =
|
ae + qe = ga;e + gq;e
{z } | {z }
mc
g mc
We also saw that the short-run change in the consumer price
index depend on “imported in‡ation”, productivity growth,
the change in the rate of unemployment, and the error
correction variable in the dynamic wage equation.
We showed that these implications were the same as in the
older main-course theory.
In particular: mc is the slope of the long-run main-course
which is the centre of the “wage-corridor” that gives the
growth path followed by e-sector wages over time.
ECON 3410/4410 Lecture 11
Summary of last lecture III
Permanent changes in u would shift the level of the
main-course.
This will a¤ect we;t temporarily, but not permanently since
the wag growth rate is independent of u in the long-run.
The level of we is of course permanently a¤ected by the shift
in the level of u.
ECON 3410/4410 Lecture 11
This lecture:
Review the steady-state properties of the Norwegian model.
Show another mechanism than bargaining, which can stabilize
the in‡ation process in the open economy.
De…ne the wage-price curve NAIRU, in a one sector model
with wage-bargaining and monopolistic wage setting.
Show example of simulations of dynamic models with error
correcting wage and price equations, and compare with
simulations with Phillips curve equations instead of wage and
price error correction.
Implications for the medium term macroeconomic equilibrium,
with reference to AS-AD with Phillips curve.
Lecture 11 and 12 will then have covered IDM Ch 3.1-3.2.7
and 3.3. There will be no speci…c exam questions from the
other sections in Ch 3 in IDM.
ECON 3410/4410 Lecture 11
Steady state in the main-course/wage bargaining model I
The system of equations for the long-run steady state is
we = me0 + ae + qe +
p = qs + (1
e1 u,
)qe ;
0
(1)
< 1;
(2)
e1
0<
ws = we ;
(3)
qs = ln( ) + ws
as :
(4)
The exogenous u is constant.
Di¤erentiation of the steady-state system gives:
we
=
p =
=
ws = ga;e + gq;e
qs + (1
) qe
(ga;e + gq;e
= gq;e + (ga;e
ga;s ) + (1
ga;s )
ECON 3410/4410 Lecture 11
)gq;e
Steady state in the main-course/wage bargaining model II
Note that, if ga;e = ga;s , we get the same long-run property as
in IAM: p = foreign in‡ation
But note also that if ga;e increases, the implication of this
theory is that steady-state in‡ation is increased,and that his is
due to the wage-follower hypothesis that we have imposed.
ECON 3410/4410 Lecture 11
The main-course unemployment rate I
It is the direct link between pro…tability wage setting that
stabilizes wage dynamics in the bargaining model.
What happens if the link breaks down? Can wages still follow
a main-course in a wage corridor?
The answer is yes: To see this, start from
wet =
+(
0
+
11
+
11
mct +
12 )mct 1
21
ut
+(
21
(5)
+
22 )ut 1
+(
1)we t
as a general model for wage dynamics. In lecture 11 we
obtained the wage bargaining consistent dynamic model by
assuming 0 < < 1.
Assume instead that
ut is exogenous!
= 1. Then (5) is unstable as long-as
ECON 3410/4410 Lecture 11
1
+ "t
The main-course unemployment rate II
However, = 1 de…nes a wage Phillips curve if we set
( 21 + 22 ) < 0 and ( 11 + 12 ) = 0:
If, in addition ut is an endogenous variable, that depends on
we;t 1 mct 1 either directly or indirectly (through pt as in
an AD curve interpretation), wages may be stabilized, as in
the main-course model, but through another mechanism, we
can thing of it as indirect error-correction working through
adjustments,of ut .
Since we now need a two equation model we adopt the
notation from Ch. 3.3 of IDM.
wt
=
w0
+
w1
ut
=
u0
+
u ut 1
0 <
u
mct +
+
w 2 ut ,
u1 (w
mc)t
w2
1,
< 1,
ECON 3410/4410 Lecture 11
< 0,
u1
(6)
> 0 (7)
The main-course unemployment rate III
First we de…ne the steady state solution of the system,
assuming dynamic stability:
wt =
ut = ut
mct = gmc ,
1
= u phil , the equilibrium rate of unemployment.
The long-run model is therefore:
gmc =
w0
+
u phil =
u0
+
w 1 gmc + w 2 u
phil
+ u1 (w
uu
phil
mc)
The …rst equation (alone!) gives the solution for u phil
u phil = (
w0
w2
+
1
w1
gmc );
(8)
w2
which is the NAIRU/natural rate of unemployment implied by
the Phillips curve model.
ECON 3410/4410 Lecture 11
The main-course unemployment rate IV
We may can also call u phil the “main-course rate of
unemployment”, since it is the rate of unemployment required
to keep wage growth on the main-course.
Next: the dynamics of the wage setting with a Phillips curve.
For simplicity: mct = gmc in all periods, starting from any
historically determined initial condition. In this case, (6)
becomes:
wt
gmc =
w0
+(
w1
1)gmc +
w 2 ut ,
or, using (8):
wt
gmc =
w 2 (ut
u phil ).
ECON 3410/4410 Lecture 11
(9)
The main-course unemployment rate V
From the second equation of the dynamic system, (7):
ut =
u0
+
u ut 1
+
u1 (w
it is seen that a higher value of w
unemployment in the next period.
mc)t
1,
u1
>0
mc contributes to higher
This analysis shows that from any starting point on the
Phillips curve, stable dynamics lead to the steady state
solution. This indicates that both w 2 < 0 and u1 > 0 are
important for stability.
How can we give a formal argument?
ECON 3410/4410 Lecture 11
The main-course natural rate
Initial state is
w0 and u0
wage growth
Gradually
wct mct will
increase along
the short-run
wage Phillips
curve
long run Phillips curve
∆ w0
g
mc
And
ut ! u phil =
u
0
u
phil
log rate of
unemployment
ECON 3410/4410 Lecture 11
The long-run
Phillips curve is
de…ned for
w = mc.
Vertical if
w 1 = 1.
Summing up the bargaining and Phillips curve versions of
the Norwegian model of in‡ation
The bargaining version and the PCM version of the theory
have many implications in common:
The wage level follows a main-course, inside a wage corridor.
In steady state, the wage-share is constant, and wage in‡ation
is equal to foreign in‡ation plus productivity growth.
In steady state: CPI In‡ation is equal to foreign in‡ation plus
the di¤erence between e and s productivity growth.
The di¤erence between the models lies in the mechanism that
secures stability of the wage share and in‡ation.
In the wage bargaining case: unions adjust their wage claims
to last year’s pro…tability. In‡ation is stabilized at the given
rate of unemployment
In the PCM case: unemployment serves as a disciplining
device: There is only one level of unemployment at which the
rate of in‡ation is stable, this is the main-course rate of
unemployment above, a variant of the natural rate of
unemployment.
ECON 3410/4410 Lecture 11
Wage-price curves and the NAIRU I
The models and results reviewed so far do not depend on the
distinction between an e- and s-sector.
In a one-sector model of the economy we invoke steady-state
wage and price equations of the form:
q f = mq + w
with mq > 0 and #
a
0, and
w b = mw + q + ! (p
with mw > 0, 0
!
(10)
#u;
1, $
q) + a
$u,
(11)
0.
(10) is …rms’price setting and (11) is wage-bargaining. Both
refer to the total economy.
ECON 3410/4410 Lecture 11
Wage-price curves and the NAIRU II
Compared to the model that focused on e-sector wage
formation, (11) is seen to contain a variable (p q) which is
the di¤erence, or the wedge, between the producer and the
consumer real wage.
The wedge represents the lasting e¤ect of cost living on the
bargained wage.
It is theoretically and empirically relevant for a total economy
wage equation. (! = 0 is rejected in tests)
As above we can add a de…nition for the log of the consumer
price p:
p = qt + (1
)pit ;
(12)
where pi is the log of the import price in domestic currency.
ECON 3410/4410 Lecture 11
Wage-price curves and the NAIRU III
In this model, the NAIRU is de…ned by setting q f = q and
w b = w and solving (10) and (11) for the NAIRU rate of
unemployment u w
uw =
mq + mw
pe
+!
.
#+$
#+$
(13)
where pe denotes a constant steady state value of the relative
price p q.
Note that
p
and that pi
q = (1
)(pi
q)
q is a de…nition of the real-exchange rate.
One much used rationalization of pe is that is is the
real-exchange rate that secures balanced trade in the long run.
ECON 3410/4410 Lecture 11
Wage- and price-curves and the NAIRU
Price setting is
here for # = 0
u w is the NAIRU
Are there other
possible
steady-states?
For example uss ,
with (w q a)
at some point
along A-B?
ECON 3410/4410 Lecture 11
The stability of the wage-price spiral
The question in the previous slide can be rephrased as:
Are the wage-price spiral dynamically stable only at the NAIRU
rate of unemployment u w ?.
Or can in‡ation reach a steady-state conditional on an u which
is di¤erent from the NAIRU u w ?
Based on the analysis of the Norwegian model with bargaining,
we can guess that the answers are "NO", and "YES".
And this turns out to be true: There is a wide set of
parameterization of dynamic wage and price equations that
are stable for any exogenous unemployment process u(t). The
next slide shows an example of what the solution may look
like.
ECON 3410/4410 Lecture 11
Stable wage-price dynamics with exogenous U.
Error correction in wage and price setting.
2. 00
U
U_ss
(w-q-a)
-0. 150
(w-q-a)_ss
-0. 175
1. 75
-0. 200
-0. 225
1. 50
-0. 250
0
20
(pi-q)
40
60
80
0
100
0. 06
-2. 0
20
D4p_ss
D4pi_ss
(pi-q)_ss
40
60
80
100
D4p
0. 04
-2. 2
0. 02
-2. 4
0
20
40
60
80
100
0
20
40
60
ECON 3410/4410 Lecture 11
80
100
Endogenous U
Even though the wage-price spiral is stable for exogenous
u(t), there is no reason for not investigating the behaviour of
the extended system where ut is endogenous in the dynamic
model.
In the extended model, we supplement the error correction
equations for wages and prices, with an equation for ut of the
type:
ut = cu0 +cu1 Dut + ut
>0
(14)
where gt takes the interpretation of exogenous expenditure, so
g > 0. The real-exchange rate can be motivated in the same
way as IAM do for the AD schedule.
w-p equations take role of AS curve, and (14) takes role of
AD shedule.
Next, give examples of simulations of extended (AD-AS)
system with di¤erent speci…cations of AS.
1
re
(pit
1
qt
1 )+ g gt +"u;t ;
ECON 3410/4410 Lecture 11
re
Stable wage-price dynamics with endogenous U
Error correction in wage and price setting
-0.150
U
U_ss
(w-q-a)
1.8
(w-q-a)_ss
-0.175
-0.200
1.6
-0.225
1.4
0
20
40
60
80
-0.250
100
0
20
40
60
80
100
60
80
100
-2.0
(pi-q)
(pi-q)_ss
D4p
D4pi
0.075
D4p_ss
-2.1
0.050
-2.2
0.025
-2.3
0.000
0
20
40
60
80
100
0
20
40
ECON 3410/4410 Lecture 11
Wage-price Phillips curves, with endogenous U
2. 8
U
0. 0
U_ss
(w-q-a)
(w-q-a)_ss
-0. 1
2. 6
-0. 2
2. 4
-0. 3
2. 2
0
20
(pi-q)
40
60
80
100
0
20
40
60
D4p
D4pi_ss
(pi-q)_ss
80
100
D4p_ss
0. 10
-3. 0
0. 05
-3. 5
0. 00
-0. 05
-4. 0
0
20
40
60
80
100
0
20
40
60
ECON 3410/4410 Lecture 11
80
100
Implications for medium-run macrodynamics I
In IAM and other texts,the unemployment rate, is determined
from the AS function alone.
Unless unemployment adjusts towards the supply side
determined natural rate, the rate of in‡ation will not become
constant, and there will be no steady-state equilibrium.
But with a di¤erent theory of wage and price formation it no
longer follows logically that natural rate unemployment
dynamics is necessary for in‡ation stabilization.
The reason is that for example the nominal wage may adjusts
directly, and not only via unemployment (or output-gap as in
IDM). We have referred to this property as direct wage error
correction.
In these model there is a range of unemployment rates that
are consistent with stable in‡ation.
ECON 3410/4410 Lecture 11
Implications for medium-run macrodynamics II
Possible implications of replacing the Phillips curve in the
AD-AS model with a model with error-correction in wage and
price setting:
1
2
Supply side shocks may be stabilized faster.
Demand shocks may hit GDP and unemployment harder than
in the reference model: In‡ation stabilization alone is not
enough to bring unemployment back to “before shock” level.
Hence: more stabilization of wages and prices, and less
stabilization of GDP and unemployment may be one tentative
conclusion.
We use “possible” and “may” because these are issues that
call for more work!
And they are empirically relevant because econometric studies
of wage formation …nd evidence of direct wage error
correction, for many countries and for di¤erent sample
periods.
ECON 3410/4410 Lecture 11