Organization of this part:
Wage and price setting. Slides for 5 February
lecture
1. B&W motivation for the Phillips curve (Ch 12 of B&W).
2. The Norwegian main-course model (section 8 of Dynamic models)
3. The Phillips curve
Ragnar Nymoen
University of Oslo, Department of Economics
4. Some evidence (optional and cursory)
February 2, 2004
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1
1
B&W’s motivation for the Phillips curve
From level to dynamics:
Ch 12.3: The Battle of the mark-ups as a framework for understanding inflation.
Using the notation in B&W we have
P = (1 + θ)
W
(Y /L)
price setting
(12.4’)
Y
W/P e = (1 + γ) , wage setting
(12.5’)
L
θ represents firms setting prices as a mark-up on unit labour costs, and γ
represents workers and union strive to set the “expected real wage” as a markup on average productivity.
(12.6)
the price level depends only on the price expected by wage negotiators–which
hence becomes a nominal anchor in this model.
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Introducing:
π=
P
−1
P−1
π̄ =
Pe
−1
P−1
for inflation, and
for core inflation we obtain:
π = (1 + θ)(1 + γ)π̄ + θ + γ + θγ
If we substitute W in (12.4’) from (12.5), we obtain
P = (1 + θ)(1 + γ)P e,
P
Pe
− 1 = (1 + θ)(1 + γ)(
− 1) + (1 + θ)(1 + γ) − 1
P−1
P−1
Pe
P
− 1 = (1 + θ)(1 + γ)(
− 1) + θ + γ + θγ
P−1
P−1
= π̄ + θ + γ + θπ̄ + γ π̄ + θγ
≈ π̄ + θ + γ
= core inflation + sum of mark-up coefficients
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Next B&W hypothesize that the mark-up moves pro-cyclically:
θ + γ = a(Y − Ȳ )
= −b(U − Ū )
a≥0
b≤0
(12.7)
Are the static equations (12.4’) and (12.5) meant to be interpreted to hold
in each time period (behavioural relationships) or as long-run steady state
relationships? Either interpretation has its inconsistencies.
(1)
where Ȳ is the trend component of output (or GDP), whereas Ū is the equilibrium level of the unemployment rate. The first equality in (12.7) is referred to
as Okun’s Law by economists (cf Ch 11). It is a representation of an empirical
regularity (finding on many data sets).
Thus we can draw this Phillips curve either in a π, Y diagram (AS schedule)
or on a π, U (Phillips curve) diagram, see Fig 12.5.
1. Behavioural equations: But then, for given expectations, prices and wages
are reacting without lags to changes in productivity (and changes in the
mark-up). We know that this is not even approximately true: In the real
world there are long lags.
2. Long-run steady state relationships: Inconsistent then to include price expectations. In a steady-state, there is no room for expectation errors.
B&W add (additive) supply shocks, denoted s, hence we have
In either form,core inflation, denoted π̄, is another term for the expected rate
of inflation.
Before we return to B&W we will take a detour into a more coherent approach
to wage-price dynamics, where we build on the insight that relationships between wage and price levels are best interpreted as hypothetical long-run
relationships. At the same time we will concentrate on wage and price setting
of small open economies.
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6
π = π̄ + a(Y − Ȳ ) + s
(12.11)
= π̄ − b(U − Ū) + s
2
The Norwegian main-course model
The Scandinavian model of inflation was formulated in the 1960s, by the Norwegian economist Odd Aukrust. It became (an still is!) the framework for
both medium term forecasting and normative judgements about “sustainable”
centrally negotiated wage growth in Norway.
In its day the Scandinavian model and the Phillips curve were views as alternative models. No doubt that the Phillips curve “won”.
Pity, since Odd Aukrust’s (1977) model can be reconstructed as a consistent
set of propositions about long-run relationships and causal mechanisms. The
reconstructed Norwegian model of inflation serves as a reference point for, and
in many respects also as a corrective to, the modern models of wage formation
and inflation in open economies. The Phillips curve is a special case!
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2.1
A model of long-run wage and price setting
Central to the model is the distinction between an exposed sector where firms
are price takers, and a non-tradables and sheltered sector where firms set prices
as mark-ups on wage costs.
The model’s main propositions are, first, that e-sector wage growth will follow
a long run tendency defined by the exogenous price and productivity trends
in that sector. Second, if relative wages are to be constant in the long-run,
the wage level of the s-sector needs to follow the same tendency. Third, the
development of the domestic price level will also be influenced by trend growth
in international prices and productivity trend.
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e-sector wage formation: the profit share and the wage-share
Let lower case letters denote logs, so for example we = log(We).
Ye: output, measured as value added (fixed prices) in the exposed (e),
Qe: price (index) of output.
Le: labour input (total number of hours worked),
Assume that both qe and ae are exogenonus variables with a trend-like growth.
If the long-run sustainable wage share is constant, me, we can write the longrun wage equation for the e-sector as:
H1mc:
We: the hourly wage.
The wage share of value added output is
WeLe
We
Ye
=
where Ae =
QeYe
QeAe
Le
Conversely, the rate of profit is
QeYe − WeLe
We
=1−
QeYe
QeAe
Assume that there exist a long-run rate of profits “needed” to sustain investment and employment in the e-sector. Correspondingly, there is also a long run
sustainable wage-share.
we∗ = qe + ae + me,
where an asterisk,∗ denotes a long-run equilibrium value. The marker H1mc
indicates that this is the first hypothesis of the theory!
The normal situation is that both qe (due to inflation) and ae (due to technical
progress) are increasing over time. Then we is also trending (upwards) along
a path determined by the so called main-course variable:
mc = ae + qe
(2)
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9
It is easy to prove (by citation) that Aukrust meant equation H1mc as a long-run
relationship between the e-sector wage level and the main-course:
log wage level
"Upper boundary"
The relationship between the “profitability of E industries” and the
“wage level of E industries” that the model postulates, therefore, is
certainly not a relation that holds on a year-to-year basis”. At best it is
valid as a long-term tendency and even so only with considerable slack.
It is equally obvious, however, that the wage level in the E industries is
not completely free to assume any value irrespective of what happens
to profits in these industries. Indeed, if the actual profits in the E
industries deviate much from normal profits, it must be expected that
sooner or later forces will be set in motion that will close the gap.
(Aukrust, 1977, p 114-115).
Main course
"Lower boundary"
0
time
Figure 1: The ‘Wage Corridor’ in the Norwegian model of inflation.
Therefore, the graphical representation of the main-course theory shows the
actual time series of the wage level,we,t, fluctuating around a growing maincourse, but always inside a wage corridor .
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12
Aukrust goes on to specify “three corrective mechanisms”, namely wage negotiations, market forces (wage drift, demand pressure) and economic policy.
The profitability of the E industries is a key factor in determining the
wage level of the E industries: mechanism are assumed to exist which
ensure that the higher the profitability of the E industries, the higher
their wage level; there will be a tendency of wages in the E industries
to adjust so as to leave actual profits within the E industries close to
a “normal” level (for which however, there is no formal definition).
(Aukrust, 1977, p 113).
We discuss these corrective mechanism in the section on dynamics below!
Note how close Aukrust models comes to B&W’s modern mark-up equation
for wages (again using their notation and numeration):
Y
W/P e = (1 + γ) ,
(12.5’)
L
the main difference being that Aukrust’s model is more precise about the time
horizon, and that his theory is for the e-sector of the economy.
There is nothing in Aukrust’s theory that rules out that the long run wage
level can change as a result of shocks to the economy. Hence, just as B&W
speculates that the mark-up γ is a function of the rate of unemployment, a
plausible generalization of H1mc is represented by
H1gmc
we∗ = me,0 + mc + γe,1u,
where u is the rate of unemployment (or its log).
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14
The two remaining main-course propositions
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 we∗ − ws∗ = mes,
H3mc ws∗ − qs∗ − as = ms
as is the exogenous productivity trend in the sheltered sector. Re-arranging
H3mc, gives
which is quite similar to B&W mark-up equation for price setting:
W
,
(Y /L)
Causality
The main-course model also specifies the following three hypotheses about
causation:
H4mc mc → we∗,
H5mc we∗ → ws∗,
H6mc ws∗ → qs∗,
where → denotes one-way causation. In his 1977 paper, Aukrust sees the
causation part of the theory (H4mc-H6mc) as just as important as the long
term relationships (H1mc-H3mc).
qs∗ = ws∗ − as + ms
P = (1 + θ)
2.2
(12.4’)
with qs∗ in place of ln(P ).
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2.3
The Norwegian model and the Battle of the Mark-ups
In a way,...,the basic idea of the Norwegian model is the “purchasing power doctrine” in reverse: whereas the purchasing power doctrine
assumes floating exchange rates and explains exchange rates in terms
of relative price trends at home and abroad, this model assumes controlled exchange rates and international prices to explain trends in
the national price level. If exchange rates are floating, the Norwegian
model does not apply (Aukrust 1977, p. 114).
As we have seen Chapter 12.3 in the book by B&W contains a general framework where.
From a modern viewpoint this is something of a strait-jacket, in that the steady
state part of the model can be valid even if one-way causality is untenable.
For example H1mc, the main-course proposition for the exposed sector, makes
sense also when the nominal exchange rate, together with wage adjustments
are stabilizing the wage share around a long-run mean.
The Norwegian model of inflation fits right into this (modern) framework.
Hence, using H1mc−H3mc above we have that
1. firms typically attempt to mark-up up their prices on unit labour costs,
2. workers and unions on formulate real wage claims which are a mark-up on
productivity.
Hence, there is a conflict between workers and firms: both care about the real
wage, but they have imperfect control: Workers influence the nominal wage,
while the nominal price is determined by firms.
w∗ = me + qe + aq ,
qs∗ = ms + w∗ − as.
The desired wage level is a mark up on prices and productivity, exactly as in
equation (12.5’) in B&W. The s-sector price level is a mark-up on unit-labour
costs (as in B&W’s equation (12.4’).
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18
2.4
There are however two differences:
First: don’t have the full “circular process” emphasized by B&W (see p 287),
but if the Norwegian model is extended to incorporate also effects of consumer
prices (which would be an average of qe and qs), in e-sector wage setting, full
circularity would result.
Second, B&W present the battle of mark-ups model in a static setting. This
of course runs against our main message, namely that actual wage and prices
are better described by a dynamic system.
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Dynamic adjustment
If e-sector wages deviate too much from the main-course, forces will begin
to act on wage setting so that adjustments are made in the direction of the
main-course.
We can use the autoregressive distributed lag model, ADL, to represent this:
we,t = β0 + β11mct + β12mct−1 + β21ut + β22ut−1 + αwe,t−1 + εt.
(3)
There are now two explanatory variables (“x-es”): the main-course variable
mct and ut.
Assume (first) that both mct and ut are exogenous variables. We will then see
that corrective forces are at work even at any constant rate of unemployment.
This is a thought provoking contrast to “natural rate models” which dominates
modern macroeconomic policy debate, and which takes it as a given thing
that unemployment has to adjust in order to bring about wage and inflation
stabilization.
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Using the same error correction transformation:
∆we,t = β0 + β11∆mct + β21∆ut
(4)
(7) embodies that the long-run multiplier implied by (3) is unity. The short-run
multiplier is β11, which can be considerably smaller than unity without violating
the main-course hypothesis H1gmc.
+ (β11 + β12)mct−1 + (β21 + β22)ut−1 + (α − 1)wet−1 + εt
and
∆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
Using H1gmc, this can be expressed as
The formulation in (6) is an ECM for short, hence we can write
0
∆we,t = β0 + β11∆mct + β21∆ut
− (1 − α) {we. − w∗}t−1 + εt
where we∗ is given by the left hand side of the extended main course relationship
H1gmc.
∆we,t = β0 + β11∆mct + β21∆ut
n
o
− (1 − α) we,t−1 − mct−1 − γe,1ut−1 + εt
(6)
β11 + β12 = (1 − α)
(7)
as long as also the following restriction is imposed in (3)
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
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!
a
b
t0
time
Figure 2: The main course model: A permanent increase in the rate of unemployment, and possible wage responses.
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Three final remarks
3. The main-course and the price level
1. First, looking back at the consumption function example, it is clear that
the dynamics there also has an equilibrium correction interpretation.
2. Below we will show that also the Phillips curve has an ECM interpretation.
The main difference is the nature of the corrective mechanism: In Aukrust’s
model there is enough collective rationality in the system to secure dynamic
stability of wages setting at any rate of unemployment (also very low rates).
Wage growth and inflation never gets out of hand or out of control. In
the Phillips curve model on the other hand, unemployment has to adjust
to a special level called the “natural rate” and/or NAIRU for the rate of
inflation to stabilize.
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pt = φ(qs,t − qs∗) + qe,t + φ(ae,t − as,t) + φγe,1ut
+ terms with me,0, ms and me,s
saying that, the change from pt to pt+1, and hence inflation will depend on
1. Equilibrium correction in s− sector pricing
2. development of foreign prices
3. development of productivity (differential)
4. domestic unemployment
We will not specify the dynamics here, but note that if steady state exist, with
∆qe,t = gqe and ut = constant then
∆pt = gqe
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So far we have looked at e-sector wage formation in detail. To sketch the theories implication for the overall price level, we introduce a simplified definitional
equation for the log of the price level, p:
pt = φqs,t + (1 − φ)qe,t,
0 < φ < 1.
φ is a coefficient that reflects the weight of non-traded goods in private consumption. Starting from
pt = φ(qs,t − qs∗) + qs∗ + (1 − φ)qe,t,
and using H1gmc, H2mc and H3mc, we have
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