Organization of this part:
Wage-price dynamics (the complete set)
B&Ws specification of the Phillips curve (Ch 12 of B&W).
The Norwegian main-course model (Ch 2.2 of IDM)
The Phillips curve, the main-course specification (Ch 2.3 of IDM)
Ragnar Nymoen
University of Oslo, Department of Economics
Norwegian evidence (Ch. 2.5 of IDM)
March 4, 2005
1
1
2
Hyperinflation: a result of crisis and disorganization in the economic and political system of a country. Collapse of monetary institutions.
Introduction
‘Inflation’: the prevailing annual rate at which the prices of goods and services
are increasing.
All prices tend to rise at broadly the same rate, because, when prices of domestic
goods are rising fast this will generally be true also of wages, and of the price
of imported goods.
This is because inflation in one sector of the economy permeates rapidly into
other sectors.
Towards the end of last century, the governments of the “Western world”
invested heavily in curbing moderately high inflation. High European unemployment a potentially big cost.
Were there other ways to curb inflation, as lower cost?
Given that inflation has now become a prime target of economic policy, what
is the inflation outlook and how can inflation be controlled using the policy
instruments that are recognized as legitimate in liberalized economies?
The phrase, a ‘high rate of inflation’ therefore usually describes a situation in
which the money values of all goods in an economy are rising at a fast rate.
Answers to any of these important questions are model dependent. By model
dependency we mean that, before the answer is given, a view has been formulated, either explicitly or implicitly, about the major determinants of inflation
and about which instruments are available for controlling inflation, and so forth.
In this part of the lectures we therefore discuss inflation models.
3
4
2
B&W’s specification of the Phillips curve
Ch 12.3: The Battle of the mark-ups as a framework.
Nominal anchor (here) means something like: “Having fixed P e the nominal
path of the economy is determined”.
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.
But notice how stylized this story is. For example:
Why not W e, also in price setting?
Are these static equations really meant to hold in the short run? Or are they
interpreted as long-run equations?
If we substitute W in (12.4’) from (12.5), we obtain
P = (1 + θ)(1 + γ)P e,
(12.6)
the price level depends only on the price expected by wage negotiators–which
B&W calls the nominal anchor.
5
B&W side-step the whole issue by performing a trick that allows them to go
from level to dynamics:
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
Introducing:
P
−1
π=
P−1
for inflation, and
for core inflation we obtain:
Pe
π̄ =
−1
P−1
6
Next B&W hypothesize that the mark-up moves pro-cyclically:
θ + γ = a(Y − Ȳ )
= −b(U − Ū )
a≥0
(12.7)
b≥0
where Ȳ is the trend component of output (or GDP), whereas Ū is the equilibrium level of the unemployment rate. The second 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.
B&W add (additive) supply shocks, denoted s, hence we have
π = π̄ + a(Y − Ȳ ) + s
(12.11)
π = (1 + θ)(1 + γ)π̄ + θ + γ + θγ
= π̄ + θ + γ + θπ̄ + γ π̄ + θγ
≈ π̄ + θ + γ
= core inflation + sum of mark-up coefficients
In either form,core inflation, denoted π̄, is another term for the expected rate
of inflation.
7
8
= π̄ − b(U − Ū) + s
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. 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.
In this part of the lectures we build 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. We will
concentrate on wage and price setting of small open economies.
3
The Norwegian model of inflation was formulated in the 1960s, by economist
Odd Aukrust. It became (and still is) as much used framework for both medium
term forecasting and normative judgements about “sustainable” centrally negotiated wage growth in Norway.
In modernized form, the model is consistent with today’s models of wage formation, and of the inflation process of small open economies. Specifically, we
show that the model can be formulated as a set of propositions about long-run
relationships and error-correction dynamics, using the models and concepts of
Ch 1 of IDM.
9
10
3.1
Another name for the model is the main-course model, since a joint trend made
up of productivity and foreign prices define the scope for wage growth in an
open economy (the main-course for wage development over time).
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.
An open economy Phillips curve can be derived as a special case of the framework.
11
The main-course model of open economy inflation
A framework for 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 long-run propositions are, i) that e-sector wage growth will follow
a long run tendency defined by the exogenous price and productivity trends in
that sector. ii), If relative wages are to be constant in the long-run, the wage
level of the s-sector needs to follow the same tendency. iii) The development of
the domestic price level will also be influenced by trend growth in international
prices and the productivity trend.
12
Ye: output, measured as value added (fixed prices) in the exposed (e) sector,
Qe: price (index) of output.
The first hypothesis, regarding wage formation in the e-sector is the heart of
the framework.
Le: labour input (total number of hours worked),
We: the hourly wage.
The wage share of value added output is
We concentrate on developing that proposition in detail.
WeLe
We
Ye
=
, where average labour productivity is given as Ae =
QeYe
QeAe
Le
Conversely, the rate of profit is
QeYe − WeLe
We
=1−
.
QeYe
QeAe
If there is there exists a long-run rate of profits “needed” to sustain investment
and employment in the e-sector, there is also a long-run sustainable wage-share.
14
13
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:
Let lower case letters denote logs, so for example we = log(We).
Assume that both qe and ae are exogenous variables with a trend-like growth. If
the long-run sustainable wage share is constant, me, we can write the long-run
wage equation for the e-sector as:
H1mc:
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
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).
(1)
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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16
Aukrust goes on to specify “three corrective mechanisms”, namely wage negotiations, market forces (wage drift, demand pressure) and economic policy.
log wage level
"Upper boundary"
We return to these when we discuss dynamics below.
Main course
Note how close Aukrust’s model 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.
"Lower boundary"
0
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 states
that the mark-up γ is a function of the rate of unemployment, a plausible
generalization of H1mc is represented by
time
Figure 1: The ‘Wage Corridor’ in the Norwegian model of inflation.
H1gmc
we∗ = me,0 + mc + γe,1u,
where u is the rate of unemployment (or its log). We use H1gmc in the following.
18
17
The main-course model and the Battle of the Mark-ups
As we have seen, Chapter 12.3 in the book by B&W contains a general framework where.
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
qs∗ = ws∗ − as + ms
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.
The Norwegian model of inflation fits right into this (modern) framework.
Hence, using H1mc−H3mc above we have that
which is similar to B&W’s mark-up equation for price setting:
W
P = (1 + θ)
,
(Y /L)
1. firms typically attempt to mark-up up their prices on unit labour costs,
(12.4’)
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’).
with qs∗ in place of ln(P ).
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20
3.2
There are 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: that real-world wages and prices are
better described by a dynamic models.
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.
There are now two explanatory variables (“x-es”): the main-course variable
mct and ut.
We first assume that both mct and ut are exogenous variables. We will see that
corrective forces are at work even at any constant rate of unemployment. This
is a thought-provoking contrast to the Phillips-curve models that dominate
the macroeconomic policy debate, and which take it as a given thing that
unemployment has to adjust to a certain number called the natural rate or
NAIRU in order to bring about inflation stabilization.
21
22
For the main-course theory to be a realistic model of long term wage behaviour,
it is necessary that (2) has a stable solution. Hence, we assume:
0 < α < 1.
(3)
Use the error correction transformation to obtain
∆we,t = β0 + β11∆mct + β21∆ut
(2)
(4)
+ (β11 + β12)mct−1 + (β21 + β22)ut−1 + (α − 1)wet−1 + εt
and
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
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
(5)
½
¾
β11 + β12
β21 + β22
− (1 − α) we,t−1 −
mct−1 −
ut−1 + εt
1−α
1−α
To reconcile this with the hypothesized long-run relationship H1gmc, we make
use of
β + β22
, the long-run multiplier wrt u,
γe,1 = 21
1−α
23
∆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.
24
rate of
unemployment
Exercise 3.1 Is β22 > 0 a necessary and/or sufficient condition for path b to
occur?
t
0
time
wage level
Exercise 3.3 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
Exercise 3.2 What might be the economic interpretation of having β21 < 0 ,
but β22 > 0?
time
Figure 2: The main course model: A permanent increase in the rate of unemployment, and possible wage responses.
26
25
Below we will show that also the Phillips curve too 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.
The main-course and the price level
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,
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
27
0 < φ < 1.
28
pt = φ(qs,t − qs∗) + qe,t + φ(ae,t − as,t) + φγe,1ut
3.3
A simulation model of the main-course
+ 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
We can use computer simulation to confirm 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:
2. development of foreign prices
3. development of productivity (differential)
we,t = 0.1mct + 0.3mct−1 − 0.06 ln Ut−1 + 0.6we,t−1 + εw,t,
mct = 0.03 + mct−1 + εmc,t
4. domestic unemployment
We will not specify the dynamics here, but note that if a steady state exist,
with ∆qe,t = gqe and ut = constant then
Ut = 0.005 + 0.01 · S1989t + 0.8Ut−1 + εU,t
(8)
(9)
(10)
∆pt = gqe + φ(gae − gas )
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29
Change in ln U t to a regime shift in 1989, that raises the equilibrium rate.
-3.0
2.25
-3.2
extended main-course
2.20
-3.4
upper-boundary
2.15
-3.6
solution for we,t
1990
1.9
1995
2000
Solution of we,t
2.10
Without regime shift in U t
1.8
2.05
With regime shift in U t
lower-boundary
1.7
2.00
1990
1995
2000
1.95
2003
2004
2005
2006
2007
2008
2009
2010
2011
Figure 3: Simulation of calibrated model
Figure 4: Unemployment and wage resonse to a regime shift in the equilibrium
rate of unemployment in 1989. Simulation of the calibrated model
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4.1
4
The main-course and the Phillips curve
In the 1970s, the Phillips curve and the main-course models were seen as
alternative, representing “demand side ” (Phillip) and “supply side” models of
inflation! However, the difference between viewing the labour market as the
important source of inflation, and the Phillips curve’s focus on product market,
is more a matter of emphasis than of principle, since both mechanism may be
operating together.
Moreover, as we have seen, there has been a complete change in the profession’s
interpretation of the Phillips curve: it is now given a supply side interpretation!
We next show formally how the two approaches can be combined within an
error-correction framework.
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The Phillips curve version of the main-course model
We focus on the wage Phillips curve, and recall that according to main-course
theory it is assumed that
1. we∗ = me,0 + mc, i.e., H1mc above.
2. the causal structure is “one way” as represented by H4mc and H5mc above.
3. Unemployment, ut has a stable long-run mean.
A Phillips curve system which is consistent with this is
∆wt = βw0 + βw1∆mct + βw2ut + εw,t,
βw2 < 0,
ut = βu0 + αuut−1 + βu1(w − mc)t−1 + εu,t βu1 > 0
0 < αu < 1,
(11)
(12)
We have simplified the notation by dropping the “e” sector subscript. On the
other hand, since we are now considering a 2 equation system, we have added
a w in the subscript of the coefficients.
34
(4) and (11) make up a dynamic system.
Note that compared to (4) the autoregressive coefficient αw is set to unity
in (11). It represent an important restriction since it rules out that wages
error-correct with respect to deviations from the main-course directly. Instead,
unemployment now corrects, as captured by the second equation (12).
Equation (12) represents the idea that low profitability leads to high unemployment (if the wage share is too high relative to the main-course unemployment
will increase in most situations, i.e., βu1 > 0.)
35
For known initial conditions (w0,u0, mc0), the systems determines a solution
(w1, u1), (w2, u2), ...(wT , uT ) for the period t = 1, 2, ...., T . The solution also
depends on the values taken by mct, εw t, εu,t over that period.
Without further restrictions on the coefficients, it becomes too complicated
to derive the final equation of for example wt. This is frequently the case for
systems!
However, we are usually able to characterize the steady-state, assuming that it
exists (that a solution is stable). Usually we can also discuss the dynamics in
qualitative terms (i.e., words and graphs rather than maths). We follow this
approach in the following.
36
Assume that the system has a stable solution
The solution based on εw t = εu,t = 0 and ∆mct = gmc (the constant growth
rate of the main course) approaches the following steady state:
∆wt = gmc,
ut = ut−1 = uphil , the equilibrium rate of unemployment.
Substitution into (12) and (11) gives the following long run system:
gmc = βw0 + βw1gmc + βw2uphil
Given (13), the second line in the long run system can be solved for the equilibrium wage
1 − αu phil
−βu0
+ mc +
u
w=
βu1
βu1
uphil = βu0 + αuuphil + βu1(w − mc)
The first equation gives
βw0
β −1
+ w1
gmc),
(13)
−βw2
−βw2
which is the natural rate of unemployment in this model. We can also call
the “main-course rate of unemployment”, since it is the rate of unemployment
required to keep wage growth on the main course.
uphil = (
37
38
Qualitative discussion of dynamics and stability.
Consider the solution based on ∆mct = gmc, and εw t = εu,t = 0 in all periods.
In this case (4) becomes
wage growth
∆wt − gmc = βw0 + (βw1 − 1)gmc + βw2ut, or, using (13):
∆wt − gmc = βw2(ut − uphil )
Assuming that βw2 < 0, wage growth is higher than the main-course growth
as long as unemployment is below the natural rate.
long run Phillips curve
∆ w0
g
mc
Moreover, from the second equation of the system:
ut = βu0 + αuut−1 + βu1(w − mc)t−1, βu1 > 0
it is seen that growth in w − mc contributes to higher unemployment in the
next period. This analysis suggests that from any starting point on the Phillips
curve, stable dynamics leads to the steady state solution.
u
0
u phil
log rate of
unemployment
Figure 5: Open economy Phillips curve dynamics and equilibrium.
We conclude that the restrictions βw2 < 0 and βu1 > 0 are important for
stability. And that for example βw2 = 0 harms stability.
39
40
Short and long run Phillips curves
The short-run Phillips curve is in this model given by (11). The slope coefficient
is
βw2 < 0
The long run Phillips curve characterizes a steady state situation in which
∆wt = ∆mct. Replacing ∆mct on the right hand side of (11) by ∆wt implies
that the slope of the long run Phillips curve is
βw2
<0
1 − βw1
Showing that the long-run Phillips curve is steeper that the long-run Phillips
curve, i.e., as long as 0 < βw1 ≤ 1.
In textbooks it is often asserted that the long run Phillips curve “has to be”
vertical, which corresponds to βw1 = 1. No such implication in the main-course
model–the hypotheses hold good also for the case of βw1 < 1
In many instances expectations term are included on the right hand side of the
Phillips curve. For example, instead of (11) we might have
∆wt = βw0 + βw1∆wte + βw2ut + εw,t,
e
or ∆wt+1
for that matter. However, as long as expectations are influenced by
the main-course, we get the same conclusion as above. For example
∆wte = ϕ∆mct + (1 − ϕ)∆wt−1, 0 < ϕ ≤ 1
In steady state there are no expectations errors, so
∆wte = ∆wt−1 = gmc
41
42
A relationship between domestic inflation ∆pt and the rate of unemployment
is implied by the main-course model. From the definitional equation
Summary and implications
Two dynamic models of wages which are both consistent with the long run
propositions of the main-course theory.
Price Phillips curve
obtain
pt = φqs,t + (1 − φ)qe,t,
0 < φ < 1.
∆pt = φ∆qs,t + (1 − φ)∆qe,t
In the simplest case, assume that s-sector price growth is always on a steadystate path. From the assumed constant wage-share in the s-sector (H2mc),
and the constant relative wage assumption (H3mc):
∆qs,t = ∆wt − ∆as,t
1. First model (in Ch 2.1): ADL model for wage level: DL part made up of
main-course variable (mct) and the rate of unemployment (ut).
(a) If we assume a stable solution of the ADL (i.e., 0 < α < 1), it can be
transformed to an ECM for wage growth.
(b) For a given (exogenously determined) level of ut, wage growth errorcorrects deviations form the main-course.
Since ∆wt depends on ut, so do ∆qs,t and eventually inflation.
The steady state rate of inflation: ∆qs,t = gmc − gas , ∆qe,t = gqe ⇒
∆pt = φ(gmc − gas ) + (1 − φ)gqe = gqe + φ(gae − gas )
(c) Therefore, there is a steady state level for the ware share wt − mct.
(d) Stability of wage growth and inflation also follows.
since gmc = gqe + gae .
43
44
2. Second model (in Ch 2.2): If there is no stable solution of the ADL (i.e.,α =
1), there is no valid ECM for wages either. Instead, a Phillips curve model
(PCM) for wage growth applies.
(a) As a single equation, the PCM gives an unstable solution for the wageshare wt − mct.
3. Hence both models (ECM and PCM) stabilizes the wage share, and the
rates of wage and price inflation.
4. The difference between the models lies in the mechanism that secures
stability of the wage share
(a) In the ECM case: Collective rationality in wage setting institutions.
For example: Unions adjust their wage claims to the last years profitability. Wage (and price) inflation is stabilized at any given rate of
unemployment (also low ones!)
(b) If the PCM is linked up with a second equation, which explains ut as an
increasing function of the wage share, the two equation system implies
a steady state level for the ware share wt − mct.
(c) The PCM implies a natural rate of unemployment (uphil ) which correspond steady state level of unemployment implied by the 2-equation
system.
(b) In the PCM case: Little collective rationality. Instead unemployment
serves as a diciplining device: There is only one level of unemployment
at which the rate of inflation is stable.
46
45
5
Norwegian evidence on the main-course model
Using annual data 1965-1998 for manufacturing sector.
5. Important implications for policy: For example:
(a) If PCM is the true model, then self-defeating policy to try to target
“full unemployment” below the natural rate.
(b) If ECM is the true model then it is not only possible to target full
unemployment, it may also be advisable in order to maintain collective
rationality (avoid breakdown in the bargaining system/institutions)
5.1
A Phillips curve model
\t = − 0.0683 + 0.26 ∆pt−1 + 0.20 ∆qt + 0.29 ∆qt−1
∆wc
(0.01)
(0.11)
(0.09)
(0.06)
− 0.0316 tut − 0.07 IPt
(0.004)
(0.01)
(14)
ûphil = 0.0313
47
48
Note how few times the actual rate of unemployment crosses the line of the
estimated natural rate.
0.08
Actual rate of unemployment
0.07
This suggest very sluggish adjustment of actual unemployment to the purportedly constant equilibrium rate.
0.06
0.05
+2 se
0.04
To investigate the dynamics more formally, we have grafted the Phillips curve
equation (14) into a system that also contains the rate of unemployment as an
endogenous variable.
u p hil
0.03
−2 se
0.02
1985
1990
1995
2000
Figure 6: Sequence of estimated main-course natural rates, uphil in the figure
(with ±2 estimated standard errors), and the actual rate of unemployment.
The endogeneity of the rate of unemployment is just as much a part of the
natural rate framework as the wage Phillips curve itself, since without the
“unemployment equation” in place one cannot show that the natural rate of
unemployment obtained from the Phillips curve corresponds to a steady state
of the system.
50
49
∆p t
tu t
0.10
5.2
−3
0.05
An error correction model
−4
1970
1980
1990
2000
∆wc t
0.20
1970
1980
1990
2000
wc t −a t −q t
−0.2
0.15
− 0.835 ∆ht − 0.0582 IPt
(0.13)
(0.01)
−0.3
0.10
0.05
−0.4
1970
1980
1990
tu t : Cumulated multiplier
0.050
2000
1970
0.000
0.025
−0.005
0.000
−0.010
1980
1990
2000
wc t −a t −q t : Cumulated multiplier
−0.015
−0.025
0
10
20
30
d
∆w
t = − 0.197 − 0.478 ecmw,t−1 + 0.413 ∆pt−1 + 0.333 ∆qt
(0.01)
(0.03)
(0.05)
(0.04)
0
10
20
30
Figure 7: Dynamic simulation of the Phillips curve model. Panel a)-d) Actual
and simulated values (dotted line). Panel e)-f): multipliers of a one point
increase in the rate of unemployment
51
(15)
The first explanatory variable is the error correction term ecmw,t−1 which
corresponds to we,t − we∗ in section 3.2. The estimated we∗ is a function of
mc, with the homogeneity restriction imposed. The estimated value of γe,1 is
−0.01, hence we have:
ecmw,t−1 = wct−1 − mct−1 − 0.01 tut−1
52
∆p t
tu t
0.10
-3
0.05
-4
0.20
∆wc t
1970
1980
1990
2000
1970
wc t −a t −q t
-0.2
1980
1990
2000
1990
2000
0.15
-0.3
0.10
0.05
-0.4
1970
1980
tu t : Cumulated multiplier
0.04
1990
1970
1980
wc t − a t −q t : Cumulated multiplier
2000
0.000
-0.001
0.03
-0.002
0.02
-0.003
0
10
20
30
40
0
10
20
30
40
The two last panels in the figure show the cumulated dynamic multiplier of an
exogenous shock to the rate of unemployment. The difference from figure 7,
where the steady state was not even “in sight” within the 35 year simulation
period, are striking. In figure 8, 80% of the long-run effect is reached within 4
years, and the system has reached a new steady state by the end of the first
10 years of the solution period. The conclusion is that this system is more
convincingly stable than the Phillips curve version of the main-course model.
Note also that the estimated model, which uses real data of the Norwegian
economy, has the same dynamic properties as the calibrated theory model of
section 3.3.
Figure 8: Dynamic simulation of the ECM model Panel a)-d) Actual and simulated values (dotted line). Panel e)-f): multipliers of a one point autonomous
increase in the rate of unemployment
53
54