Inflation denotes the prevailing annual rate at which prices of goods and services
are increasing.
Lecture 4: Open Economy Wage-Price
Dynamics (Ch 3 of IDM)
All prices tend to rise at broadly the same rate, because, when prices of domestic
goods are rising, 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.
Ragnar Nymoen
University of Oslo, Department of Economics
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.
September 11, 2007
1
Hyperinflation (> 100% per year or quarter): a crisis in the monetary and
political system of a country. Usually both internal and external causes. Not
an issue here.
Towards the end of last century, the governments of the “Western world”
sought to curb moderately high inflation. High European unemployment a big
cost.
Were there other ways to curb inflation, at a 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?
Answers to any of these important questions are model dependent: before an
answer can be is given, a view has to been formulated of the major determinants
of inflation and about which instruments are available for controlling inflation,
and so forth.
3
2
Hence our main-focus is this lecture are models of wage and price setting,
because those theories represent the modern understanding of inflation (among
decisions makers for example).
Models of wage-and-price setting also represent the supply side of the macroeconomic models that are in use for policy analysis, and for forecasting the
macroeconomy.
In Ch 3 of IDM we emphasize two important models that are relevant to the
inflation process of small open economies: the bargaining model, Ch 3.2, and
the Phillips curve model, Ch 3.3.
The main premise of the bargaining model is that firms and their organized
workers are engaged in a partly cooperative and partly conflictual sharing of
the rents generated by the operation of the firm.
In Norway, a system of bargaining based wage setting has been the framework
both for analysis and policy decisions for decades. It represents a main element
in the socio-economic system.
4
We give a balanced assessment of the wage bargaining approach and the Phillips
curve.
Wage bargaining and incomplete competition (Ch 3.2
of IDM)
We note from the start that there are similarities and differences:
The wage bargaining theory can be interpreted as hypotheses of the steady
state.
Theoretical developments during the last 20 years of the last century developed
a supply-side model based on incomplete competition.
The Phillips-curve is a short-run model, from the outset.
Wages was modelled as determined by bargaining, allowing coordination on
both sides of the bargain. Specifically, wages were not assumed to be determined (completely) by decentralized contracts between individual workers
and any single firm (as in efficiency wage models, or in older models assuming
perfect competition).
Hence, the two models “attack” wage-and price setting from different ends of
the short-run/long-run spectrum.
Nevertheless, we can embed both models in an ECM (equilibrium correction
model), which will help us see the real differences and similarities between the
models. Specifically, their different implications about the long-run.
Prices are set by monopolistically competitive firms (each firm faces “its own”
demand schedule).
The newest variant of the Phillips curve, the New Keynesian Phillips curve,
contain some new traits relative to the old Phillips curve, but some important
properties carry over to the New Keynesian Phillips.
The whole framework is referred to as the incomplete competition model of
wage and price setting.
5
6
A bargaining theory of the steady-state wage
Since price formation plays a role for how wages are bargained, we have to start
by a stating our assumptions about price setting.
Two sectors: the exposed (e) and sheltered (s) sector. e-sector firms are price
takers. In the s-sector there is monopolistic competition among firms.
Qe and Qs denote the producer prices in the two sectors. We assume that the
consumer price index P is a weighted average of the two prices:
(1−φ)
P = Qφ
s Qe
0<φ<1
(1)
where φ is a coefficient that reflects the weight of non-traded goods in private
consumption.
Assuming a stationary environment, profit maximizing behaviour among firms
in the s-sector gives:
Ws
. >1
(2)
Qs =
As
Ws is the hourly wage cost. As is the average labour productivity, As = Ys/Ls
where Ys denotes output (measured as value added) in the sheltered sector,
and Ls denotes labour input.
The mark-up coefficient is determined by the elasticity of demand facing each
firm.
Reference: next slide.
7
8
The wage level in the sheltered sector is determined by the following equation:
Memo: s-sector price setting
Ws = We
(3)
saying that the sheltered sector wage is proportional to the wage in the exposed
sector of the economy.
Assume common technology Fs(Lsi). Firm i maximizes:
Πi = QsiDi(Qsi/Qs) − WsFs−1(Di(Qsi/Qs)
The hourly wage level We is determined by bargaining between labour unions
and organizations representing firms. We define real profits, π, as
with respect to own price Qsi given demand function Di(Qsi/Qs). 1 oc:
Qsi(1 + 1/ElQsi D) = Ws/Fs0
= (1 + 1/ElQsi D)−1 and Fs0 = As in a symmetric equilibrium with
Setting
Qsi = Qs gives (2).
We
We 1
Le = (1 −
)Ye.
Qe
Qe Ae
For simplicity, we assume that Ye is a non-increasing function of real unit labour
costs:
We/Qe
Ye = Ye(
), Ye0 ≤ 0.
(4)
Ae
π = Ye −
9
10
The core of the theory is that We is settled in accordance with the principle of
maximizing the Nash-product denoted N :
Using the specifications of the profit and the utility functions, the Nash-product
can be expressed as
N =(ν − ν0)fπ 1−f
(
(5)
where ν denotes union utility and ν0 denotes the fall-back utility or reference
utility.
We specify union utility as
We
, U, Zν )
P
0 > 0 and ν 0 ≤ 0. Z represents other factors in union preferences. The
νW
ν
U
fall-back or reference utility:
ν(
W̄
, U)
P
where W̄ is the average level of nominal wages. Assume in following that
0 − ν 0 < 0.
νU
0U
)f (
or
⎧
⎨
⎫f
½
⎬
W̄
N = ν( P , U, Zν ) − ν0( , U)
⎩
⎭
P
Q
Wq
e
(1 − Wq
)1−f
¾1−f
1
)Ye
Ae
where Wq = We/Qe denotes the producer real wage.
We assume that (1), (2) and (3) are taken into account during the bargaining.
Note that P can be written in terms of Wq :
ν0 = ν0(
11
We 1
(1 −
)Ye
Qe Ae
We
W̄
N = ν(
, U, Zν ) − ν0( , U)
P
P
P =
Ã
We
Qe
!φ
Qe
µ
¶
µ
¶φ
1 φ
= WqφQe
,
As
As
(6)
and that the two relative prices P/Qe and W̄ /P are also functions of the real
12
wage Wq :
µ
P
= Wqφ
Qe
As
(7)
We
Wq 1−φ
Qe
´φ = ³
´φ ³ ´φ = ³ ´φ
We
e As
Qe
As
As
W̄
We
= ³ ´φ
³
We
P
Q
Qe
¶φ
(8)
Using (6)-(4), the N becomes:
⎧ ⎛
⎞
⎛
⎞⎫
¶
µ
¶¾
1−φ φ
1−φ φ ⎬f ½µ
⎨
Wq
W
A
W
A
Wq 1−f
q
s
q
s
⎠
⎝
⎠
N = ν⎝
,
U,
Z
−
ν
1
−
Y
ν
e
0
⎩
⎭
εφ
εφ
Ae
Ae
(9)
The 1st oc condition for a maximum is given by NWq = 0 which defines the
bargained real wage Wqb implicitly as
Wqb = F (Ae, As, f, U, Zν ),
In a wider interpretation, union bargaining power f is negatively related to U ,
meaning that the total derivative of Web with respect to U is negative even
though the partial derivative might be positive.
By choosing a log-linear functional form for the G-function in (11), we can
write
web = me0 + ae + qe + γe1u, γe1 ≤ 0
(12)
where web = ln(Web), and ae, qe and u likewise denote the logs of the corresponding variables in (11). For simplicity, we regard As, and Zv as constants,
(10)
and they are therefore subsumed in me0.
(11)
Equation (12) represents the hypothesized long-run or steady-state relationship
for e-sector wages.
Equivalently, for the bargained nominal wage Web:
Web = AeQe G(As, f, U, Zν ).
The expected non-negative sign of the partial derivative of the G function
with respect to U can be shown to depend on the specification of the utility
functions.
14
13
Wage bargaining and dynamics
For completeness we also express the relationships (1), (2) and (3) in logarithmic form:
p = φqs + (1 − φ)qe,
0 < φ < 1,
(13)
ws = web,
(14)
qs = ln( ) + ws − as.
(15)
The long-run model therefor consists of (12)-(15). The four static(!) equations
determine web,ws, qs and p. The exogenous variables are ae, qe and u.
Assume that wet is determined by the dynamic model
wet = β0 + β11mct + β12mct−1 + β21ut + β22ut−1 + αwet−1 + εt.
(16)
with
mct = aet + qet,
for simplicity.
mct and ut are exogenous in (16).
The next question to ask is whether this steady state is dynamically stable. As
we have explained in lecture 3, the answer to this question depends on whether
the wage level in period t, wet, approaches web in the case where the initial
situation is characterized by disequilibrium: we0 6= wb.
15
The exogeneity of ut is assumed because we first want to see which stabilizing
mechanisms in wage formation are at work even at a constant and exogenous
rate of unemployment. This is a contrast to “natural rate models” of wage
dynamics which dominates the macroeconomic policy debate, and which takes
it as a given thing that unemployment has to adjust in order to bring about
constant wage growth and, eventually, stable inflation.
16
If we apply the same error-correction transformation as in lecture 3, we obtain:
∆wet = β0 + β11∆mct + β21∆ut
(17)
+ (β11 + β12)mct−1 + (β21 + β22)ut−1 + (α − 1)wet−1 + εt
For the bargaining theory to be a realistic model of long term wage behaviour,
it is necessary that (16) has a stable solution. Since wages usually show a
rather smooth evolution through time we state the stability condition as
0 < α < 1,
saying that the elasticity of wb with respect to the rate of unemployment is
identical to the long—run multiplier of the actual wage wet with respect to ut,
and then impose the following restriction on the coefficient of mct−1:
β11 + β12 = (1 − α)
(20)
since (12) implies that the long-run multiplier with respect to mc is unity. Then
(19) becomes
(18)
Subject to the stability condition in (18), equation (17) can be written as
∆wet = β0 + β11∆mct + β21∆ut
(19)
½
¾
β11 + β12
β21 + β22
− (1 − α) wet−1 −
mct−1 −
ut−1 + εt.
1−α
1−α
To reconcile this with the steady-state relationship (12), we define
β + β22
γe,1 = 21
,
1−α
∆wet = β0 + β11∆mct + β21∆ut
(21)
− (1 − α) {wet−1 − mct−1 − γe1ut−1} + εt
which is an example of the homogenous ECM (with respect to one explanatory
variable, mct). The short-run multiplier with respect to mct is β11, which can
be considerably smaller than unity without violating the long-run relationship
(12).
18
17
(21) can be re-expressed as
0
Wage bargaining and inflation
∆wet = β0 + β11∆mct + β21∆ut
n
− (1 − α) we − web
or
o
t−1
(22)
+ εt
To sketch the theory’s implication for inflation, we need to reconsider the three
equations (13)-(15). Equation (13) is a definition equation that holds not only
in the long run, but also in each time period. Hence, we have
0
∆wet = β0 + β11∆mct + β21∆ut
− (1 − α) {we − mct−1 − γe1ut−1 − me0} + εt,
(23)
we only need to keep in mind that β00 = β0 − (1 − α)me0 as explained.
pt = φqst + (1 − φ)qet
Subject to the condition 0 < α < 1 stated above, wage growth is seen to bring
the wage level in the direction of the bargained wage web. For example, assume
that the sum of price and productivity growth is constant so that ∆mct =
gmc, and that the rate of unemployment isnconstant,o ∆ut = 0 . If there is
disequilibrium in period t − 1, for example we − web
> 0, wage growth
n
t−1o
n
o
from t − 1 to t will be reduced, and this leads to we − web < we − web
t
t−1
in the next period.
19
or in terms of growth rates:
∆pt = φ∆qst + (1 − φ)∆qet.
(24)
The two equations (14), for the s-sector wage, and (15), for the s-sector price
level, have different interpretations. They are hypotheses about the steady
state. Realistically speaking,e there is no reason why adjustment lags and
friction should not be important for wage and price adjustments in the sheltered
20
sector. Hence, it is only in order to simplify the model as much as possible
that we write the equations for ∆wst and ∆qst as
∆wst = ∆wet, and
∆qst = ∆wet − ∆aet.
(25)
(26)
showing that the bargaining model implies the following explanation of inflation
in a small-open economy:
1. Autonomous inflation: φβ00 ,
Equation (23) for e-sector wage growth and (24)-(26) are 4 equations which
determine the endogenous variables wet, wst, qst and pt as functions of initial
conditions and given values for exogenous variables mct, ut and εt. The exogenous and pre-determined variables are wet−1, mct−1 and ut−1. The model is
a recursive system of equations: The wage growth rate in the exposed sector is
determined first, from (23) and then the other growth rates follow recursively
3. Shock to unemployment: φβ21∆ut
Specifically, the reduced form equation for the rate of inflation, ∆pt, is found
to be:
4. Productivity growth: φβ11∆aet − φ∆ast,
∆pt = φβ00
+ (φβ11 + (1 − φ))∆qe,t + φβ21∆ut
+ φβ11∆aet − φ∆ast
− φ(1 − α) {wet−1 − mct−1 − γe1ut−1 − me0}
+ φεt
2. “Imported inflation”: (φβ11 + (1 − φ))∆qet
(27)
5. e-sector equilibrium correction: −φ(1−α) {we.t−1 − mct−1 − γe1ut−1 − me0}
6. random shocks: φεt
21
22
Set the share of non-traded goods in consumption to 0.4. Then φ = 0.67, and
setting β11 = 0.5 gives a coefficient of ∆qet of 0.66. Foreign inflation in the
range of 1% − 5% is of course not uncommon, and our model implies that a
3% inflation abroad imputes 2% “imported inflation”.
Equilibrium correction in the exposed sector represents a numerically significant
factor in this model. With the chosen parameter values, and setting α = 0.7
in the wage equation, the coefficient of {we.t−1 − mct−1 − γe1ut−1 − me0} in
equation (27) 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 inflation rate of 0.2 percentage points, ceteris paribus.
Size of effects
The coefficient of ∆aet is 0.33, and for ∆ast we obtain −0.67. The net-effect
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 inflation. It occurs because e-sector productivity growth
increases the bargained wage in that sector, which inflicts price increases in the
sheltered sector via the assumption of relative wage stabilization.
23
Practical use of the framework needs to represent ∆wst and ∆qst by separate
ECM equations, to avoid the imposition of instantaneous adjustment. Many of
the properties of (27) will continue to hold true. For example the strong role
of imported inflation, the sign reversal of the two productivity terms, and the
role of equilibrium-correction in exposed sector wage setting.
24
Wage-price spiral
In real world wage setting, compensation for increases in cost-of-living is always
a main issue. Hence, to increase the degree of realism of the model can include
∆pt in the dynamic equation of exposed sector wages setting, with a positive
coefficient. Clearly, with this generalization of the model, the inflation model
is no longer a recursive system, since instead of (23), we have:
∆wet = β00 + β11∆mct + β21∆ut + β31∆pt
(28)
where the coefficient with an e are the original coefficients of (28) divided by
(1 − β31φ), and β41 = −β31φ/(1 − β31φ), β51 = β31(1 − φ)/(1 − β31φ). By
using (29) instead of (28) in the system-of-equations, the recursive solution
method of the original model is re-installed.
− (1 − α) {wet−1 − mct−1 − γe1ut−1 − me0} + εt.
However, since inflation can be expressed as:
∆pt = φ∆wet − φ∆ast + (1 − φ)∆qet
we can derive the following semi-reduced form for ∆wet:
∆wet = β̃00 + β̃11∆mct + β̃21∆ut + β41∆ast + β51∆qet
− (1^
− α) {wet−1 − mct−1 − γe1ut−1 − me0} + ε̃t.
(29)
25
26
The Norwegian model of inflation
The Norwegian model of inflation has a longer history in economics than both
Nash bargaining theory and error correction models. Already in the 1960s, Odd
Aukrust fomulated the main-course model of inflation, or the Norwegian Model
of Inflation.
The first hypothesis, about wage formation in the e-sector, is in many ways
the defining characteristic of the whole framework. It takes the place of Nashbargaining in the model set out above.
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 wage share of value added is
The model’s long-run propositions are,
1. that e-sector wage growth will follow a long run tendency defined 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.
WeLe
We
Ye
=
, where average labour productivity is given as Ae =
QeYe
QeAe
Le
By definition, the rate of e-sector profits is
QeYe − WeLe
We
=1−
.
QeYe
QeAe
If there is there is a long-run rate of profit which is needed to sustain investment
and employment in the e-sector, there is also a long-run sustainable wage-share.
The development of the domestic price level will also be influenced by trend
growth in international prices and the productivity trend.
27
28
Assume that both Qe and Ae are exogenous variables with a trend-like growth.
We can then formulate what we might call the main-course proposition:
We∗ = MeQeAe,
(30)
where We∗ denotes the long-run equilibrium wage level consistent with the twin
assumptions of exogenous price and productivity trends and a constant normal
wage share, denoted Me in (30).
Using logs, the long-run wage equation for the e-sector becomes:
H1mc:
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:
we∗ = qe + ae + me,
where an asterisk,∗ denotes a long-run equilibrium value, and we∗ = ln(We∗)
etc.
The marker H1mc indicates that this is the first hypothesis of the theory.
The normal situation is that both qe (foreign price adjustments) and ae (technical progress) increase over time. According to H1mc we∗ is also trending
upwards along a path determined by the so called main-course variable:
mc = ae + qe
(31)
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).
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 .
29
30
log wage level
"Upper boundary"
Main course
There is nothing in Aukrust’s theory which rules out that the long-run wage
level can change as a result of shocks to the economy. Hence, me 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). We use H1gmc in the following.
"Lower boundary"
0
time
Figure 1: The ‘Wage Corridor’ in the Norwegian model of inflation.
31
Clearly H1mc has the same interpretation as the “bargained wage” in the incomplete competition model: If wet follows a stable dynamic process, then its
steady-state is given by we∗.
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 we∗ − ws∗ = mes,
H3mc ws∗ − qs∗ − as = ms
32
as is the exogenous productivity trend in the sheltered sector. Re-arranging
H3mc, gives
qs∗ = ws∗ − as + ms
2.25
which is similar to the ‘price equation’ in the incomplete competition model
above!
2.20
extended main-course
upper-boundary
2.15
A simulation model of wage dynamics
solution for we,t
2.10
2.05
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:
lower-boundary
2.00
1.95
2003
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
Ut = 0.005 + 0.005 · S1989t + 0.8Ut−1 + εU,t
(32)
(33)
(34)
2004
2005
2006
2007
2008
2009
2010
2011
Figure 2: Simulation of calibrated model
33
34
Change in ln U t to a regime shift in 1989, that raises the equilibrium rate.
-3.0
Empirical performance of ECM wage equation
-3.2
Norwegian manufacturing 1970—2004 data. OLS estimation results
-3.4
-3.6
1990
1.9
1995
2000
Solution of we,t
∆wt = + 0.25 ∆qt −
(4.2)
0.31 (w − w∗)t−1
(10.3)
+ 0.43 ∆pt − 0.04 IPt − 0.79 ∆ht
(3.9)
(4.1)
(4.4)
Without regime shift in U t
1.8
With regime shift in U t
1.7
1990
1995
2000
IP , is an incomes-policy indicator. ht is the length of the working day. The
(modified) main-course variable wt∗ is:
w∗ = mct − 0.1ut + me
Figure 3: Unemployment and wage resonse to a regime shift in the equilibrium
rate of unemployment in 1989. Simulation of the calibrated model
35
36
The main-course model and the Scandinavian model of inflation
0.175
Δwt
Fitted
The “Scandinavian model” specifies the same three underlying assumptions as
the main-course model: H1mc (we do not need the extended version of the
hypothesis for the point we wish to make here), H2mc and H3mc.
0.150
0.125
But the distinction between long-run and dynamics is blurred in the Scandinavian model. Hence, for example, the dynamic equation for e-sector wages in
the Scandinavian model is usually written as:
0.100
0.075
∆we,t = β0 + ∆mct,
(without a disturbance term for simplicity) which is seen to place the restriction
of α = 1 on the ECM for e-sector wage dynamics.
0.050
0.025
1970
1975
1980
1985
1990
1995
2000
This implies unstable dynamics. If the wage path is ever pushed off the main
course, it never returns.
2005
Figure 4: Actual wage growth, and fitted according to main-course ECM.
In terms of the Typology of Lecture 2, the Scandinavian model is a Differenced
data model.
37
38
Wage and price curves
The standard exposition sets we = we∗ and p = p∗ in each time period. The
implication is that actual wages and prices are determined by a static model!
Models that feature mark-up behaviour in price and wage setting are not uncommon in textbooks.
They are presented as equations for a wage-curve and a price curve.
In our framework these equations take the form:
we∗ = me0 + qe + ae + γe1u, and
(35)
p∗ = φ(mse − ms) + φ(we∗ − as) + (1 − φ)qe
(36)
This procedure also raises an issue about which variables are determined by
the wage-curve and the price curve. To look into this issue a little further,
we simplify the notation by setting as = ae = a, and mse = 0, so that
we∗ = ws∗ = w∗. In the case of w = w∗ and p = p∗ (35) and (36) can then be
re-expressed as:
w − qe − a = me0 + γe1u,
1
w − qe − a = ms + (p − qe)
φ
(37)
(38)
where we have utilized the s-sector wage and price setting to derive (36) for
the desired price p∗ as a mark-up on bargained unit-labour costs (we∗ − as).
Due to the openness of the economy, p∗ depends on foreign prices, qe.
where (38) is simply (36) in the (e-sector) wage share on the left hand side of
the equation.
39
40
Equation (37) can be represented graphically as downward sloping line in a
graph with w−qe−a along the vertical axis and u along the horizontal axis. This
is the wage-curve. Equation (38) defines a horizontal line in the same graph.
This is the price-curve. The intersection point between the curves is often
viewed as the determination of the wage-curve natural rate of unemployment
(or NAIRU).
However there are logical problems with this approach:
The price-curve depends on the relative price p − qe, so an unique intersection
point does not exist unless we can fix p − qe at a certain value. Put differently:
(37) and (38) are two equation in three unknown variables, and it is not clear
why it is that u should be regarded as endogenous, and not p − qe.
Most commonly: The requirement that the trade balance (or the current account) is balanced in the long term.
However, the properties of the dynamic wage and price setting system imply
that if a steady state exists for the wage share wt − qet − at, a unique steadystate also exists for pt − qet. Hence, there is an internal inconsistency in the
approach which determines the long-run or steady state value of the rate of
unemployment from static wage and price curves.
The argument is that p − qe can be regarded as determined from outside the
system of wage and price setting equations.
42
41
∗ denotes the (log of) foreign prices in foreign currency, and E is the
where qet
t
nominal exchange rate (kroner/euro).
Role of exchange rate regime
Later in the course, a main focus will be the choice of exchange rate regime,
and how that choice conditions macrodynamics. So far we have implicitly
assumed that the rate of foreign exchange is exogenous, corresponding to a
fixed exchange rate regime. In order to make this explicit, we need to expand
the notation a little. For example, the sum of the logs of productivity and
foreign price
The reason why we have suppressed the nominal exchange rate Et from the
model so far, is that in a fixed exchange rate regime, the Et has no separate
influence on wage growth.
Clearly if We and E are endogenous, as in the case of a floating exchange rate
regime, the main-course model is incomplete: we need more theory to be able
to explain E.
mct = ∆aet + ∆qet + mct−1,
(39)
Ch 3.2.8 in IDM shows that if there is perfect capital mobility and depreciation expectations are perfect, then the main-course becomes modified by the
(exogenous) difference between the domestic and foreign interest rate, but the
dynamic wage equation is still stable.
∗ + ∆ ln E + mc
mct = ∆aet + ∆qet
t
t−1.
(40)
Hence, what we have learnt about stability of wages, for a given level of unemployment may hold for a floating exchange rate regime as well.
mct = aet + qet
which can be written as
or
43
44