The purpose of this comment is to demonstrate that their theoretical result concerning the first order derivative of relative inflation persistence with respect to the degree of accommodation is incorrect. As a consequence, the sign of the first derivative becomes ambiguous. We provide an economic explanation of this result, elaborating on the three distinct transmission mechanisms in the AS (relative) model. Moreover, we propose an economically meaningful modification of the original AS model that restores a strictly positive relation between exchange rate accommodation and relative inflation persistence.international economics and trade ;

Kool,C.J.M.

Lammertsma,A.

English

Research Papers in Economics

1
The Phillips Curve, the Persistence of Inflation, and the Lucas Critique:
Evidence from Exchange-Rate Regimes: Comment
by Clemens J.M. Kool and Alex Lammertsma
1
November 1997
                                               
1 LIFE and Department of Economics, University Maastricht, Maastricht, the Netherlands. We thank Roel
Beetsma, Kees Koedijk, Joan Muysken, and Tom van Veen for useful discussions and comments. Any
remaining errors are our own.2
The Phillips Curve, the Persistence of Inflation, and the Lucas Critique:
Evidence from Exchange-Rate Regimes: Comment
In a recent paper in this Review, Alogoskoufis and Smith (1991) - henceforth AS -  make an
important contribution with respect to the theory on the effectiveness of systematic monetary
policy under different exchange rate regimes. In particular, they use a symmetric two-country
macro-model with forward-looking price-setters, to show first that higher monetary
accommodation increases the persistence of average inflation across countries, and second that
higher exchange rate accommodation increases the persistence of inflation differentials between
countries.
The purpose of this comment is to demonstrate that their theoretical result concerning the
first order derivative of relative inflation persistence with respect to the degree of accommodation
is incorrect.
2 As a consequence, the sign of the first derivative becomes ambiguous. We provide
an economic explanation of this result, elaborating on the three distinct transmission mechanisms
in the AS (relative) model. Moreover, we propose an economically meaningful modification of the
original AS model that restores a strictly positive relation between exchange rate accommodation
and relative inflation persistence.
                                               
2 Alogoskoufis (1992) uses a related model under alternative assumptions about price- and wage-setting
to come up with the same conclusion about the positive link between exchange rate  accommodation and
relative inflation persistence as do AS. That result is flawed too.5
In equations (3) and (4), l is the firm=s intertemporal discount factor, while q measures the firm=s
marginal adjustment cost of prices relative to the cost of deviating from the optimal steady-state
price. a and b measure the responsiveness of output demand to the real interest rate and the real
exchange rate respectively. d is the share of domestic goods in consumption and g is the
responsiveness of real wages to unemployment.
Install Equation Editor and double-
click here to view equation. is a composite
exogenous  variable that depends on the relative reservation wage (
Install Equation Editor and double-
click here to view equation. ),
relative labor supply (
Install Equation Editor and double-
click here to view equation. ), relative labor productivity
(
Install Equation Editor and double-
click here to view equation. ), a relative demand shock (
Install Equation Editor and double-
click here to view equation. ), and
firms= relative benchmark inflation rate (
Install Equation Editor and double-
click here to view equation. ).
5
For further analysis, note that (3) is a second order difference equation that may be
rewritten as:
Install Equation Editor and double-
click here to view equation.
where z1 and z2 are real positive roots on either side of unity under the (sufficient) assumption that
f<1. Then, relative (expected) inflation can be shown to follow an AR(1) process with
autoregressive parameter z1 (< 1), which depends on f. Solving z1 from the characteristic equation
(5) and taking the first derivative with respect to the degree of exchange rate  accommodation (f)
yields:
Install Equation Editor and double-
click here to view equation.
                                               
5 Note that equation (4) deviates from AS due to some computational errors on their side.6
with
Equations (3)-(6) significantly differ from AS due to a mistake in their derivation of the relative
wage equation. The sign of the first derivative now becomes ambiguous instead of strictly positive
as claimed by AS.
6 Ultimately, the sign in (6) depends on c. Since the expression (1+b(b
2-4c)
-1/2)
can be shown to be negative, the first derivative in (6) is positive if c exceeds some small negative
number. For c large and negative, the sign becomes negative.
AS explain their results in quite general terms only, referring to the interaction of the
wage- and price-setting behaviour. Contrary to Dornbusch (1982), they fail to precisely discuss
the various transmission mechanisms. In our discussion, we add to the intuition of our result by
focusing on the three components of c, which each correspond to a distinct transmission channel:
2l(1-d), 2lgb, and ga respectively. We try to explain the link from higher accommodation (f) to
higher persistence (z1) through each channel individually.
The first channel 2l(1-d) is related to the indexation of wages to expected prices. Since
both domestic and foreign wage-setters consume a mix of domestic and foreign goods, a positive
domestic price shock puts upward pressure on wages in each of the two countries (with wage
responsiveness d and (1-d) for the home and foreign country respectively). However, an increase
in exchange rate accommodation reduces this wage pressure for the foreign country (higher prices
                                               
6 AS claim that Dornbusch (1982) also finds a strictly positive link between exchange rate
accommodation and inflation persistence. This is incorrect. Dornbusch distinguishes two offsetting
channels: one works through the demand side and increases persistence, the other through the supply
(cost) side, which decreases persistence. The net effect is uncertain, similar to our conclusion.
Install Equation Editor and double-
click here to view equation.7
on domestic goods are compensated partly by a depreciating domestic currency), while it increases
wage pressure at home: not only domestic goods become more expensive, but imported foreign
goods as well. As a result, the relative wage differential increases and becomes more persistent due
to the interaction of forward-looking price- and wage-setters.
The second effect 2lgb comes from the real exchange rate effect on relative output. A
domestic real appreciation through a positive domestic price shock, leads to a decline in relative
output (b) and thus higher relative unemployment and lower relative wages (g), which in turns
leads to lower relative prices, that moderate the initial price shock. Increasing exchange rate
accommodation lowers the real exchange rate effect on output, unemployment and wages. Thus,
less compensation of the initial price shock occurs and persistence increases.
The third channel ga counteracts the first two effects. A positive price shock implies
higher expected inflation through the interaction of wage- and price-setters. Lower relative real
interest rates result, which stimulate relative output (a) and via lower unemployment increase
relative wages (g) and prices. However, higher exchange rate accommodation increases expected
depreciation. Because of intereste rate parity, relative nominal interest rates then increase, so that
the real interest rate effect is decreased and persistence is lowered.
In summary, higher exchange rate accommodation unambiguously leads to higher relative
inflation persistence only when the first two transmission channels dominate the last one. In
practice, this may well be the case.
7 Also, additional coefficient restrictions may be imposed to
obtain a positive first derivative in (6). For example, sufficient conditions are the absence of a real
interest rate effect on output (a=0), or the absence of an unemployment effect on real wage-
setting (g=0).  When these assumptions seem to far-fetched, weaker but intuitively appealing
                                               
7 The empirical results in AS provide supportive evidence of a positive link between real exchange rate
accommodation and relative inflation persistence.8
assumptions may do the job as well. The discount rate l probably is close to one. Then, if output
is about half as responsive to real exchange rate shocks as it is to real interest rate shocks, the
second and third transmission channels approxiately cancel, so that the wage-indexation effect
dominates. Arbitrarily low values of g (or a) will suffice as well, given the positive wage-
indexation effect.
II Expected real exchange rate mean reversion
In this section we propose a modification of the original model to find a strictly positive link
between exchange rate accommodation and relative inflation persistence, instead of imposing
additional coefficient restrictions. One of the peculiarities of the original model are the implications
for real exchange rate developments. Under positive relative inflation persistence and zero
exchange rate accommodation, domestic and foreign price levels can diverge without bounds.
Consequently, real exchange rates are allowed to display persistent trends as well. This is at odds
with both theoretical real exchange rate models and empirical work on real exchange rates. The
latter category generally points to slow mean reversion of real exchange rates. Here, we modify
the AS model in an admittedly ad hoc way to reflect the stylized facts on real exchange rate
behavior. More precisely, we impose expected real exchange rate mean reversion by adding the
following equation to the original model:
Install Equation Editor and double-
click here to view equation.9
where the real exchange rate ert is defined as 
Install Equation Editor and double-
click here to view equation. . Without loss of
generality, the equilibrium real exchange rate 
Install Equation Editor and double-
click here to view equation. is set to zero.
8 Using
the same procedure as before, the following second-order equation for relative prices results:
                                               
8 The inclusion of equation (7) only affects the relative model. Since the average model actually comprises
the whole two-country world, it becomes a closed economy model in which all exchange rate terms
disappear anyway.
Install Equation Editor and double-
click here to view equation.
1
Install Equation Editor and double-
click here to view equation.
with
Install Equation Editor and double-
click here to view equation. defined in equation (4). After rewriting equation (8) in the
general second-order form of (5), expression (6') for the first derivative may be obtained:
Install Equation Editor and double-
click here to view equation.
The same three transmission channels can be distinguished as in (6). However, the first derivative
is unambiguously positive again. The crucial difference is the positive sign on the real interest rate
channel ga(1+h). This effect may be explained as follows.
For a given degree of exchange rate accommodation, a domestic price shock raises  the
relative price level. The real exchange rate then appreciates away from its equilibrium level, giving
rise to expected real home depreciation. In turn this requires higher relative real interest rates. Via
the goods market, lower relative output and higher relative unemployment put downward pressure
on relative wages. In the end a moderating effect on relative prices results, through the interaction
of wage- and price-setters. Suppose now that the degree of exchange rate accommodation10
increases. The real exchange rate then appreciates less in real terms, because the nominal exchange
rate is allowed to do part of the job, relative real interest rates rise less and the impact of the
transmission mechanism described above decreases. That is, the moderating effect diminishes and
relative inflation persistence increases.
REFERENCES
Alogoskoufis, George S., AMonetary Accommodation, Exchange Rate Regimes and Inflation
Persistence@, The Economic Journal, May 1992, 102, 461-480.
Alogoskoufis, George S. and Ron Smith, AThe Phillips Curve, the Persistence of Inflation, and the
Lucas Critique: Evidence from Exchange-rate Regimes@, The American Economic Review,
December 1991, 81, 1254-1275.
Dornbusch, Rudiger, APPP Exchange-Rate Rules and Macroeconomic Stability@, Journal of
Political Economy, February 1982, 90, 158-165.
Lammertsma, Alex, AInflation-Output Trade-Offs and the Implications for Monetary Policy@,
1997, University Press Maastricht, chapters 5 and 6.

AInflation-Output Trade-Offs and the Implications for Monetary Policy@,

AMonetary Accommodation, Exchange Rate Regimes and Inflation Persistence@, The Economic Journal,

APPP Exchange-Rate Rules and Macroeconomic Stability@,

AThe Phillips Curve, the Persistence of Inflation, and the Lucas Critique: Evidence from Exchange-rate Regimes@, The American Economic Review,

The Phillips Curve, the Persistence of Inflation, and the Lucas Critique:Evidence from Exchange-Rate Regimes: Comment

http://edocs.ub.unimaas.nl/loader/file.asp?id=469

The Phillips Curve, the Persistence of Inflation, and the Lucas Critique:Evidence from Exchange-Rate Regimes: Comment

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics