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.
33
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
-3
0.05
-4
0.20
∆wc t
1970
1980
1990
5.2
2000
1970
wc t −a t −q t
-0.2
1980
1990
2000
0.15
-0.3
0.10
-0.4
1970
1980
tu t : Cumulated multiplier
1990
1970
1980
wc t − a t −q t : Cumulated multiplier
2000
0.000
1990
2000
-0.001
0.03
-0.002
0.02
-0.003
0
10
20
30
40
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)
− 0.835 ∆ht − 0.0582 IPt
(0.13)
(0.01)
0.05
0.04
An error correction model
0
10
20
30
40
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