Wage Indexation and Output Stability Revisited
Author(s): Esteban Jadresic
Source: Journal of Money, Credit and Banking, Vol. 34, No. 1 (Feb., 2002), pp. 178-196
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ESTEBAN JADRESIC
Wage Indexation and Output Stability Revisited
Since Gray (1976) and Fischer (1977), the accepted view is that
wage indexation stabilizes output when shocks are nominal and
destabilizes output when shocks are real. This paper examines this
proposition's validity when wage indexation is based on lagged inflation. It shows that (i) in a Gray-Fischer economy with plausible
parameters, indexing wages to lagged inflation destabilizes output
regardless of the type of shocks; (ii) the Gray-Fischer result may be
restored if nominal shocks have a strong direct effect on prices,
given wages; (iii) wage indexation to lagged inflation can be neutral for output stability if monetary policy is accommodative.
SINCE THE MID-1970S, there has been considerable research
on the macroeconomic consequences of wage indexation. Starting with the seminal
papers by Gray (1976) and Fischer (1977), the academic literature has studied the effects of wage indexing on the behavior of the economy in response of alternative
types of shocks, its effects on the costs of disinflation and the level of inflation, the
relationship between wage indexation and exchange rate policy, the type of indexation indicator best suited for macroeconomic stability, and several other issues.1 Despite the sizable literature cumulated on the topic, the best-known proposition on
wage indexation has continued to be the one originally stated by Gray and Fischer:
that indexing wages stabilizes output when shocks are nominal and destabilizes output when shocks are real.
Following the analysis in Gray (1976), the standard model used in the academic
literature to show this proposition hinges on the assumption that the cost of living adjustments due to wage indexation are based on current inflation. This assumption directly implies that wage indexing helps to stabilize the real wage, which in standard
macroeconomic models helps to protect employment and output when shocks are
nominal and exacerbates the movements in the same variables when shocks are real.
Intuitively, it captures the notion that indexation would speed up the response of
The author thanks Mike Devereux, Stanley Fischer, Nelson Mark, Peter Wickham, and two anonymous
referees for helpful comments. A preliminary version of this paper entitled "Wage Indexation and
Macro-economic Stability: The Gray-Fischer Proposition Revisited" was issued as IMF Working Paper
96/121 (Washington: International Monetary Fund) in November 1996.
1. Surveys can be found in Carmichael, Fahrer, and Hawkins (1985), Aizenman (1987), Devereux
(1994), Van Gompel (1994), Landarretche, Lefort, and Valdes (1997), and Jadresic (1998a).
ESTEBAN JADRESIC is Director of International Affairs of the Central Bank of Chile. E-mail:
ejadresi@bcentral.cl
Journal of Money, Credit, and Banking, Vol. 34, No. 1 (February 2002)
Copyright 2002 by The Ohio State University
ESTEBAN JADRESIC
:
179
nominal wages to nominal shocks, while it would make the adjustment of the real
wage to real shocks more difficult.
While the assumption that wage indexation is based on current inflation is attractive because of its simplicity, the typical costs of living adjustments granted by actual
indexed wage contracts are based on lagged inflation. This fact has been emphasized
by many authors, including among others Fischer (1977,1986, and 1988), Simonsen
(1983), Bonomo and Garcia (1994), and Jadresic (1996, 1998a, 1998b). In Chile, for
instance, where most wage contracts are indexed, the overwhelming majority of cost
of living adjustments are granted semiannually according to 100 percent of the inflation cumulated during the previous six months ending in the month prior to the date
of the adjustment (see Jadresic 1992; Maturana 1992; Garcia 1995). In Canada and
the United States, in turn, the type of indexed wage contracts observed in practice are
more varied, but typically they specify a quarterly, semiannual, or annual cost of living adjustment, with the size of the noncontingent component of the contract's wage
depending on the difference between the price level observed two or three months
prior to the adjustment and a base price level which usually corresponds to the price
level in some month before the beginning of the contract (see Ehrenberg, Danziger,
and San 1983, p. 239; Hendricks and Kahn 1985; Kaufman and Woglom 1986, pp.
442-3; Card 1986, p. S146; and Christofides 1990, p. 396). As a result, in Chile,
Canada and the United States, the size of the cost of living adjustments granted in indexed wage contracts directly depend on the magnitude of past inflation.2
Fischer (1977) was concerned about the lack of realism of the assumption that
wage indexation is based on current inflation, and, in a section that he considered to
provide the major theoretical innovation of his paper, he formally studied the effects
of a certain type of lagged indexation rule. However, the indexing formula he considered is not the usual indexation rule by which current wages are adjusted according to past inflation; rather, it is a rule by which current wages are adjusted according
to the difference between the one-period-ahead expectations on the current and past
price level. Fischer (1977) acknowledged that the indexing rule he studied may be a
far cry from the one used in practice and noted that indexing to lagged inflation could
modify the conclusion that wage indexation stabilizes output in response of nominal
shocks. He conjectured, however, that if the nominal shocks were permanent, his
basic conclusion would be preserved. He did not formally address this issue.
This paper reexamines the effects of wage indexation on output stability taking
into account that actual indexation typically is based on lagged inflation. Following
Gray (1976) and Fischer (1977), the analysis focuses on a simple economy where
prices are set equal to marginal costs, output is determined by real money balances,
nominal shocks are unanticipated monetary shocks, and real shocks are unanticipated productivity shocks. The key innovation is to model wage indexation as a contract clause that specifies periodic wage adjustments according to a lagged value of
2. Note that the typical cost-of-living adjustment observed in Chile, Canada, and the United States
makes wages contingent to lagged inflation rather than to lagged surprises in inflation (despite the fact that
indexing to the latter seems easier to justify on purely theoretical grounds). The effects of indexing wages
to lagged surprises in inflation are briefly reported in section 3.
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inflation incurred since the last wage revision. The effects of contracts with these
clauses are compared with the effects of preset time-varying wage contracts, that is,
contracts in which the sequence of each contract's nominal wage can vary according
to the information available at the time when the agreement is signed. The paper also
briefly reports on the implications of using as standard of comparison the effects of
short-term, fixed-wage contracts.
The analysis reveals that the conventional view on the effects of wage indexation
on output stability does not hold when wages are indexed to lagged inflation. In a
Gray-Fischer economy with plausible parameter values, wage indexation to lagged
inflation destabilizes output not only when shocks are real but also when shocks are
nominal. More generally, when alternative settings are considered, the effects of
wage indexation to lagged inflation on output stability depend on the structure of the
economy and the nature of monetary policy. In particular, the Gray-Fischer result
may be restored if the structure of the economy is such that nominal shocks have a
strong direct effect on prices, given wages. Also, wage indexation to lagged inflation
can be neutral for output stability if monetary policy is accommodative. The general
implication is that a definite evaluation of the effects of wage indexation on output
stability depends on the specific characteristics of the economy under consideration.
The rest of this paper is organized as follows. Section 1 presents the building
blocks for the analysis. Section 2 examines the effects of wage indexation to lagged
inflation in a base case similar to that considered by Gray (1976) and Fischer (1977),
except that it acknowledges the stylized fact that the elasticity of prices with respect
to changes in output, given wages and production conditions, is small. Section 3
studies the effects of considering alternative economic structures, monetary policies,
and indexed and nonindexed contracts. Section 4 provides concluding remarks. An
unpublished Appendix with mathematical derivations and some extensions is available from the author upon request.
1. AN ECONOMY WITH ALTERNATIVE WAGE CONTRACTS
A. Determination of Output and Prices
We consider an economy in which the rate of change of aggregate output yt is a
linear function of the rate of change of real money balances and a nominal shock vt
that is independent and serially uncorrected with mean zero and variance a^.3 Denoting the rate of growth of nominal money supply by mp this specification implies
that
yt = mt - nt + v, ,
(1)
3. Unless otherwise mentioned, level variables are measured in logs and represented with capital letters, and rate-of-change variables are measured as first differences of log levels and represented with
lower case letters and a hat O on top of the corresponding letter.
ESTEBAN JADRESIC
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181
where nt is inflation in period t. Interpreting (1) as a money-market equilibrium condition, the nominal shock vt can be understood as an unexpected and permanent
reduction in money demand. The rate of change of prices in any given period is
determined by the relationship
nt = wt - ut + a(yt - ut),
(2)
where wt is the rate of change of the aggregate wage at period t and ut a real shock in
the same period, assumed to be independent and serially uncorrelated with mean
zero and variance a^. Equation (2) can be interpreted as a price equal marginal cost
condition in rate of change form, where the marginal cost depends on the aggregate
wage, the level of output, and the parameters of the underlying production function.
By construction, the real shock can be interpreted as an unexpected and permanent
positive shift in the latter. The parameter a corresponds to the elasticity of prices or
marginal costs with respect to changes in output, given wages and production conditions. If the good's market is perfectly competitive, a is equal to the inverse of the
elasticity of supply for given wages and production conditions, and must be
non-negative.4
Equations (1) and (2) are implicit in Gray (1976) and Fischer (1977), except that
in this paper the variables in these equations are expressed in terms of rate of
changes rather than in terms of levels. This implies that, by definition, the real and
nominal shocks considered in this paper are permanent in levels. This makes no difference with respect to Gray's (1976) analysis, since in the context of her one-period
model permanent and transitory shocks are equivalent. In comparison with Fischer
(1977), who considers shocks in levels that follow first-order autoregressive stochastic processes, this paper focuses on the limiting case where the autoregressive coefficients on those processes are equal to one. This is the most interesting case to
examine, as Fischer (1977) concedes that in the alternative case that shocks are temporary in levels, indexing wages to lagged inflation could reverse his conclusion that
wage indexation stabilizes output when shocks are nominal.
Another difference with respect to Fischer (1977) is that his analysis assumed implicitly and without justification that a=l. Such assumption differs from the one
used by Fischer (1986) and most of the literature on nominal wage rigidities (for example, Taylor 1980), which maintains that a=0. Since the stylized fact is that output
changes do not have strong effects on prices, given wages and production conditions
(see Blanchard and Fischer 1989, pp. 464-67), the analysis below first uses the plausible value a=0 as benchmark case, and then explores the effects of considering alternative values for a.
4. If the good's market is monopolistically competitive, a can take negative values between zero and
minus one. The macroeconomic literature, however, hardly ever has considered the case of a negative a to
be relevant. The reader interested on the implications of a negative a on the issues discussed in this paper
may easily derive them by using the equations derived below, which remain valid for values of a in the
above mentioned range.
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B. Determination of Wages
The central innovation in this paper with respect to the analysis in Gray (1976)
and Fischer (1977) is on the modeling of wages. This subsection first presents the
model used to characterize indexed wage contracts, and then the model used to typify nonindexed wage contracts.
Indexed Wage Contracts. To examine the effects of indexing wages to lagged inflation in the simplest possible way, it is assumed that indexed wage contracts have a
duration of two periods, and that, in the second period, they grant a cost of living adjustment equal to 100 percent of the inflation observed in the first period (the effects
of considering partial indexation to lagged inflation and indexation to lagged surprises in inflation are reported below).5 Assuming also that wage negotiations are
uniformly staggered, it follows that in any period half of the wages are renegotiated,
while the other half are adjusted according to past inflation. The rate of change of the
aggregate wage implied by the indexed contracts is thus
where t_xxf is the initial wage adjustment granted in the indexed contracts beginning
at time t, that is, the wage increase agreed for the first period of those contracts. The
subscript t— 1 indicates that, by assumption, this variable is set on the basis of information available at the end of t— 1.
To model aggregate wage behavior, one needs to specify what determines the initial wage adjustment t-xxj. Applied discussions of wage indexation often assume
that this variable is simply a function of past inflation and the unemployment rate or
the output gap. If contracts are revised, however, the initial wage adjustments must
be agreed upon in the wage negotiations between firms and workers. It is postulated
here that, as an outcome of these negotiations, the initial wage adjustment is set so as
to make the expected value of the average real wage of the contract equal to a target
real wage, where the latter is established on the basis of information available at the
time of the negotiation. This specification can be interpreted as the outcome of an
optimization problem where wage setters maximize the expected value of a quadratic function of the average real wage implied by each contract.6 If contracts that
begin at time t are negotiated with information on events occurred up to time t— 1,
this can be written as
5. For the more general case where the indexed contracts last for N periods and the cost of living adjustments are granted every n periods, see Jadresic (1998a).
6. The goal of maximizing a nonlinear function of a contract's real wage is implied by different
mi-croeconomic models of wage determination, including the union wage model and the efficiency
wage model. The specification of the maximand as a quadratic function of the real wage permits to
introduce expected variables in a log-linear manner and can be interpreted as a second-order
approximation to the actual objective function. The assumption that the average real wage rather than its
present value matters simplifies the algebra.
ESTEBAN JADRESIC
:
183
Z.I
xt is such that Et_x(Contract's average real wage) =
Et_x\
Qr + Qi+i
, (4)
where E is the standard expectational operator, and the right hand side of the equation corresponds to the target real wage for the contracts signed for the period t to
H-l, given the information available at the end of t— 1. To simplify comparisons
made below, this target real wage is specified as an average of period-specific target
real wages, Et_xQt and Et_lQt+l. The determination of the latter is addressed below. To
derive the initial wage adjustment implied by this condition, let XJ be the nominal
wage that wage negotiators agree for the first period of the contracts beginning at
period t. Taking into account that the wage for the contract's second period will be
adjusted according to lagged inflation, (4) implies
^t-\
|(*/-*?)+{(*/+*,-^i)
=^,-i(",+",-i)
(5)
where Pt+S is the price level in period t+s (with s = 0,1). Using the fact that Pt+S =
Pt+s-\ + rcf+j and rearranging terms to solve for die initial nominal wage leads to:
XJ ==P,_, +±£,_,(Q, +fl,+1 +n, +*„,).
(6)
The initial wage adjustment can then be obtained as the difference between XJ and
the value achieved in period t— 1 by the wages of the contracts that began in period
f-2; that is,
xt - Xt
Pt_3)
(7a)
(Xt_2 + Pt_2
= n,_l+(l-L2)Et_A
fl,+fl(+1+7I,+7I(+1
(7b)
where L is the standard lag operator. Finally, replacing (7b) in (3) leads to the following expression for aggregate wage behavior when contracts are indexed:
w/=7t,_,
+ ±(l-L2)Et_l
fl,+flf+1 + n, + 7i,+1
(8)
Equation (8) distinguishes two components in me behavior of me aggregate wage
when contracts are indexed. The first one is inertial and stems partly from the indexation rule mat grants non-negotiated wages an adjustment equal to lagged inflation, and
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MONEY, CREDIT, AND BANKING
partly from a catch-up revision that compensates negotiated wages for the inflation observed in the previous period. The second one represents the aggregate effect of the initial wage adjustments granted in the renegotiated contracts, measured relative to past
inflation. This effect depends on the wage-setters' expectations about the target real
wage and inflation during the life of the new contracts, as compared to the expectations
they held on those same variables when they signed the expiring contracts.
Nonindexed Wage Contracts. Since wage indexing helps to prevent the cost of too
frequent negotiations, indexed wage contracts are in practice long-term contracts;
for instance, the duration of typical indexed contracts in the unionized sector of the
U.S. labor market is three years or more, and in Chile, two years. In order to assess
the effects of these contracts, it is natural to use as standard of comparison the behavior of the economy under similarly long-term contracts that specify preset
time-varying wages during the life of each contract, such as the nonindexed
contracts observed in the unionized sector of the U.S. labor market, and that have
been modeled by Fischer (1977).
If the preset time-varying wage contracts last for two periods, and there is uniform
staggering of negotiations, it follows that in any period half of the wages are renegotiated on the basis of the information available at the end of the t— 1, while the other
half are adjusted according to the agreements reached with the information available
at the end of f—2. The implied rate of change of the aggregate wage of preset
time-varying wage contracts is
where t_xxp and t_2xp are the wage adjustments agreed for period t on the basis of
the information available at the end of periods t— 1 and t—2.
To model t_xxp and r_2*/\ it is assumed as above that wage setters target a real
wage. Specifically, taking into account that with these type of contracts wage setters
can go beyond the attempt to achieve an average real wage, and rather target a specific real wage for each period, it is posited that
p
t-sxt
is such that £,_5(Contract's real wage at period t)
= Et_flt
for 5= 1,2.
(10)
Using (9) and (10) as for the case of indexed contracts, it is easy to show that the implied expression for the rate of change of the aggregate wage of preset time-varying
wage contracts is:
wp =\(Et-x + Et_2)(&t + nt) +1(1 -£,_3)[o>,_i + «>,-2 + *,-i + *,-2]>
0D
ESTEBAN JADRESIC
:
185
where Et_s&t is the expected change in the target real wage between t—\ and t according to information about variables available at the end of t—s.
The intuition for the terms at the right-hand side of equation (11) is as follows.
The first term contains the adjustment of wages stemming from the changes in expected prices and the target real wage, according to the information available when
the different vintages of current contracts were signed. The second term represents
the effect of the revision of wages in the renegotiated contracts, which depends on
the discrepancies between the inflation rates and target real wages predicted in the
previous negotiation and their actual values.
The Target Real Wage. To complete the above wage-determination models, it is assumed that wage setters target a real wage that is proportional to the expected level
of aggregate output per person in the labor force. Taking the size of the labor force as
given and normalizing units properly, this implies that
£,_A+, = £,-i^
for s = 1 , 2 ,
(12)
where Yt+S is the level of aggregate output in period t+s.
This specification for the target real wage, which captures the intuition that the
real wage tends to increase when the labor market becomes tighter and when the
economy becomes richer, is both theoretically and empirically plausible. From a
theoretical perspective, the assumption that the target real wage is proportional to the
level of output per person in the labor force is consistent with a supply wage relation
linking the real wage negatively with the rate of unemployment. As emphasized by
Blanchard and Katz (1997), such a relationship is implied by all the main modern
approaches to wage determination based on explicit maximization models, including
the matching approach, the efficiency wage approach, and the competitive approach.
From an empirical viewpoint, in turn, the assumption of equiproportionality between
output and the target real wage is broadly in line with the extensive empirical evidence on the wage-curve compiled by Blanchflower and Oswald (1995).7 In addition,
in the model considered in this paper, the assumption that the target real wage is
equiproportional to the expected level of output permits to ensure that the rate of unemployment and the functional distribution of income are constant in the steady
state, features that conform with the long-term evidence on these variables.
C. Completing and Solving the Model
To study the effects of the alternative type of wage contracts, output fluctuations
are measured in terms of output gaps, that is, the distance between the level of output
implied by the type of contracts being considered and the frictionless level of output.
Formally, the analysis focuses on
7. Their central finding with data for a number of regions and periods is that a 1 percent increase in the
unemployment rate typically reduces the real wage by about 0.1 percent (Blanchflower and Oswald
1995). With standard estimates for the Okun's Law coefficient [between 2 and 3; for instance, see Adams
and Coe (1990)], and for an unemployment rate of the order of 5 percent, this implies that a 1 percent increase in output would raise the real wage by the order of 1 percent.
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:
MONEY, CREDIT, AND BANKING
Zt=Yt-Yt ,
(13)
where Zt is the output gap and Y* the frictionless level of output.
The frictionless level of output is defined as the level of output that would be observed if wages were fully flexible and current shocks were observable. In the present model, this corresponds to the level of output that would be observed in a
situation where wage setters set
Wt = E£lt + Pt=Yt + Pt.
or,
(14a)
wt = yt + nt.
(14b)
and where output and prices are determined by equations (1) and (2). Using (14b) in
(2), it is easy to check that this definition implies
y* = ut;
(15)
that is, the frictionless level of output moves one for one with the real shocks. 8
The model is completed by specifying a monetary policy rule that describes the
management of money supply by the monetary authority. Unless otherwise mentioned, the analysis below uses Gray's (1976) and Fischer's (1977) assumption that
money supply is fixed:
mt = 0 .
(16)
The solutions to the model—comprised of equations (1), (2), (12), (13), (15), (16),
and the alternative aggregate wage equations (8) and (11)—examined below assume
rational expectations. The derivations of these solutions is detailed in the unpublished Appendix. Assuming that the output gap in the absence of shocks is zero,
these derivations lead to the following solutions for the output gap under each type
of contract:
l
z! -^—zL+^—z'=-±-v.+
5 + 4a^'-1
5 + 4a
'"2
5 +4a
Z,p =—J—v, + ------------ v,_, .
'
1+a'
2(1 +a) ' l
(l + a)(5 + 4a) ' l
1+a'
'
(18)
8. The behavior of the frictionless output also can be derived from the analysis of the labor market in
a frictionless environment. In rate-of-change form, the production function underlying (2) is yt = (1+a)-1/,
+ ut, where lt is the rate of change of labor input. Replacing this expression in (2) and solving
ESTEBAN JADRESIC
:
187
The following sections examine the implications of these equations, as well as some
extensions.
2. WAGE INDEXATION AND OUTPUT STABILITY: BASE CASE
This section examines the effects of wage indexation under the benchmark assumption that the elasticity of prices with respect to changes in output, given wages
and production conditions, is nil. The analysis is based on equations (17) and (18)
for a=0. For simplicity of exposition, the focus is on the response of output to single (unit and positive) nominal and real shocks, in a situation where the economy has
been fully at rest prior to the occurrence of the shock.
A. Nominal Shock
Consider first the effects of a nominal shock. As depicted in Figure 1, the initial response of output to such a shock is the same regardless of the type of wage contracts
in the economy. This result arises because, independently of the type of contracts
considered, wages, prices and inflation in any given period are predetermined. In
consequence, a positive shock vt tends to increase real money balances and output
identically in all cases.
In subsequent periods, the response to the nominal shock depends on the nature of
the contracts in the economy. When preset time-varying wage contracts prevail, 1/2
of the initial expansion of output persists one period following the impact; thereafter
the economy rests in equilibrium [see equation (18)]. In the case of indexed contracts, instead, 3/5 of the initial expansion of output persists one period after the
shock; thereafter output converges to its equilibrium through an oscillatory process
that rapidly fades away [see equation (18)]. 9
These results imply that, contrasting with the Gray-Fischer view, the overall effect
of wage indexation when this economy is hit by a nominal shock is to destabilize the
output gap. This can be confirmed by computing the sum of the squared output gaps
generated by the nominal shock, or equivalently, by computing the unconditional
variance of the output gap when the economy is repeatedly hit by nominal shocks
and there are no real shocks.10 As implied by the results in the unpublished appendix,
for the wage variable implies that the demand-wage is wtD = nt — (1+a)-1/, + ut. Also, replacing it in
(14b) implies that the frictionless supply-wage is wts = nt + (1+a)-1/, + uv It follows that in a friction-less
environment wtD = wts only if lt = 0. Thus, it must be that y* = ut.
9. The oscillatory and convergent nature of the path for output can be verified by computing the roots
of the characteristic equation implied by equation (17). Both are imaginary and have the property that the
multiplication of their inverses is smaller than one.
10. Setting ut = 0 for all t, equations (17) and (18) lead to solutions of the type Xt = 27=q^W-s'
where the Os (5=0,1,2..) depend on the structural parameters of the economy. Using the assumption that
the shocks are independent and serially uncorrelated, it follows that the sequence of Xts in response of a
single unit shock v0 = 1 at t=0 is O0, Ol5 02~, so that the sum of squares of the Xts generated by a unit
nominal shock is equal to the sum of squares of the Os. This is equal to the unconditional variance of the
Xts, normalized by the variance of the v,s.
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1.0
MONEY, CREDIT, AND BANKING
-1
•Indexed Wage Contracts Preset
Time-Varying Wage Contracts
■+■
0.8
|
0.6
I
0.2
0.0
-0.2
2
Period
FIG.1. Response of Output Gap to a Nominal Shock (with Fixed Money Supply)
under indexed wage contracts, the latter is 10 percent larger than under preset
time-varying wage contracts.
These results obtain because wage indexation reduces the response of wages to
the nominal shock in the period following the impact, which under a fixed money
supply and prices determined by wages, slows down the adjustment of the economy.
The dampening effect that wage indexation has on the initial response of wages to
the nominal shock is explained as follows. When contracts are indexed, wage setters
know that any change in wages and inflation today will automatically feedback into
cost of living adjustments and inflation tomorrow. Following a nominal shock that is
perceived to require an adjustment in the level of wages and prices, wage setters thus
anticipate that part of the needed revision of wages will automatically occur at a later
date through the cost of living adjustments. The anticipation of these future adjustments moderates the magnitude of the revision of wages immediately after the nominal shock occurs, reducing the speed of the adjustment of the economy to the
nominal shock.
B. Real Shock
As shown in Figure 2, a real shock such as the one considered here has no effect
on the output gap at the period it impacts on the economy, whatever the type of contracts being considered. Indeed, given that in any single period wages are predetermined, a positive real shock reduces prices proportionally and increases real money
balances and output exactly by the same magnitude as the size of the shock. Since
output and the frictionless level of output increase by the same amount, the output
gap thus remains unaltered.
ESTEBAN JADRESIC
:
189
0.6 -i— ------------------------------------------------------------------------------------------ ,
------ Indexed Wage Contracts
---- Preset Time-Varying Wage Contracts
0.4 4-
o
&
4-
0.2
3
I
o
0.0
-0.2 -I ------------- 1 ---------- 1 ----------- 1 ---------- 1 ----------- 1----------- 1 ----------- 1 ----------- 1
-
2
-
1
0
1
2
Period
3
4
5
6
FIG. 2. Response of Output Gap to a Real Shock (with Fixed Money Supply)
After the real shock occurs, however, while output with preset time varying wage
contracts remains in equilibrium if there are no further shocks, output with indexed
wage contracts increases. The reason is that with indexation the reduction in the inflation rate that occurred in the period of the shock is transmitted automatically into
lower-than-trend inflation in the next period. This effect raises real money balances
and expands output despite the fact that no additional shocks have occurred. In subsequent periods, due to a dynamics that is driven by the cost-of-living adjustments
mandated by the indexed contracts, output converges to its equilibrium after a sequence of oscillations that gradually fade away. In consequence, wage indexation to
lagged inflation destabilizes output when a real shock hits the economy under consideration.
It is important to note that, while this result is qualitatively similar to the one implied by the assumption that indexation is based on current inflation, its logic is substantially different. The reasoning here is not that indexation prevents real wages
from adjusting, but rather that with wage indexation the initial impact of a real shock
on inflation is transmitted mechanically to wage adjustments and inflation in subsequent periods; with a fixed money supply, this feedback effect from past to current
inflation destabilizes output.
C. Summary
Since the above analysis implies that wage indexation to lagged inflation destabilizes the response of output both to real and to nominal shocks, it directly follows
that, in the base case considered in this section, the overall effects of wage indexation to lagged inflation is to destabilize output. This result can be shown formally by
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computing the unconditional variance of the output gap and inflation implied by the
alternative type of contracts when both real and nominal shocks coexist and occur repeatedly through time (see the unpublished Appendix).
3. WAGE INDEXATION AND OUTPUT STABILITY: ALTERNATIVE SETTINGS
A. Alternative Economic Structures
Consider the case when the elasticity of prices with respect to changes in output,
given wages and production conditions, is larger than zero. The evolution of the output gap in response of a real and a nominal shock in this case is summarized in Table
1 [obtained directly from equations (17) and (18)].
In the case of a real shock, it is easy to see that a positive and finite a reduce the
magnitude of the movements in the output gap following the period of the shock, but
it does not change the qualitative behavior of the output gap following the shock.
This is because, regardless of the value of a, it continues to be the case that the indexation clauses automatically transmit the initial effect of the shock on inflation
into the following periods.
Regarding the effects of a nominal shock, three results stand out. First, in the period when the shock hits the economy, real money balances and output increase by
the same amount under the different type of contracts, just as in the base case exam-
TABLE1
RESPONSE OF OUTPUT GAP TO UNIT SHOCKS (WITH FIXED MONEY SUPPLY)
Type of Shock and Wage Contracts:
Nominal Shock
Period
Zero
One
Two
Three
Sum
Sum of Squares
1
(1+oc) 3
(5+4a)(l+a)
(l-4a)
(5+4a)2(l+a)
-(13+20a)
(5+4a)3(l+a)
(3+2ot) 2(1
+oc)2
(22+45a+32a2+8a3)
8(2+5a+4a2+a3)(l+a)2
1
(1+a)
1 2(1
+a)
0
0
(5+4a)
4
(5+4a)2
-2(1+4a)
(5+4a)3
1
2(1 +a)
5 4(1
+a)2
NOTE: "I" stands for indexed wage contracts, "P" for preset time-varying wage contracts.
2(1 +a)
(3+2a)
8(2+5a+4a2+a3)
ESTEBAN JADRESIC
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191
ined above. The novelty is that now inflation rises on impact due to the direct effect
of demand and output on prices. With a fixed money supply and predetermined
wages, this effect dampens the expansion of output during the first period by a factor
equal to (l+a)_1. Second, in subsequent periods, the speed of adjustment of the
economy when contracts are nonindexed is exactly as in the base case. Indeed, as implied by the effects in Table 1, if preset time-varying wage contracts prevail, 1/2 of
the initial expansion of output persists one period following the impact; thereafter
the economy rests in equilibrium. Third, when contracts are indexed, a positive a
speeds up the adjustment of the economy. As shown in Table 1, a proportion
3(5+4a)_1 of the initial expansion of output persist one period after the shock. Thus a
positive a reduces the persistence of the initial disequilibrium in the first period
after the shock. In addition, since the damping factor associated to the subsequent
oscillations of output is (5+4a)_t, a larger a also speeds up the adjustment of the
economy in subsequent periods.
These results imply that allowing for an a that is large enough can revert the ranking of the effects of wage indexation on the variability of output in response of a
nominal shock. Indeed, consider first the effects of wage indexation during the first
period after the shocks occurs. As implied by Table 1, for a smaller than 1/4, the proportion of the initial expansion of output that persists during that period is larger with
indexed contracts than with preset time-varying wage contracts [since 3(5+4a)-1 is
larger than a]. This result is qualitatively similar to the one obtained in the base case.
For a larger than 1/4, however, the opposite result obtains: the magnitude of the output gap one period after the shock occurs is smaller with indexed contracts than with
preset time-varying wage contracts [since 3(5+4a)-1 is smaller than 1/2]; that is, indexed contracts speed up the adjustment of output in the first period after the shock
occurs. To get the intuition behind this result, recall that a positive a implies that
prices rise at the time of the impact. The advantage of indexed contracts over preset
time-varying wage contracts when a is large is that, in the period immediately after
the shock occurs, the initial price increases lead to automatic increases in the wages
of the contracts not yet open to renegotiation. These increases complement the stabilizing effect of the increases in the wages of the renegotiated contracts, leading to a
faster adjustment of wages, prices, real money balances, and output in the period
after the shock occurs.
The above analysis refers only to the output gap observed during the first period
after the nominal shock hits the economy. To compare the effects of indexed contracts with those of preset time-varying wage contracts more generally, one has to
take into account the effects that these contracts have both in the first period after the
impact and in subsequent periods. Using the standard criteria by which aggregate
output fluctuations are measured according to the sum of squared output gaps—or
equivalently, comparing the unconditional variances of the output gap when all
shocks are nominal—the results in the unpublished Appendix imply that indexed
wage contracts raise or reduce output instability relative to preset time-varying wage
contracts depending on whether a is respectively larger or smaller than approximately 0.2728.
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To conclude, if nominal shocks have a strong and direct effect on prices, given
wages, then the Gray-Fischer result may be restored. This result is of interest because, although it does not seem empirically plausible in the context of the Gray
(1976) and Fischer (1977) type of economy considered here, the existence of a
strong and direct effect of nominal shocks on prices is more plausible in the context
of a small open economy. Indeed, in a small economy open to trade and financial
transactions, a nominal shock similar to the one considered here can lead to a quick
nominal depreciation of the domestic currency and increase in the price of foreign
goods, and by this mechanism, to a direct increase in the aggregate price index, without any changes in wages. As shown in a companion paper (Jadresic 1998b), if this
effect is strong enough, the Gray-Fischer result can obtain with wages indexed to
lagged inflation even if the elasticity of domestic prices with respect to output
changes, given wages, is small.
B. Alternative Monetary Policies
Following Gray (1976) and Fischer (1977), the above analysis assumes that
money supply is fixed. If under such a policy wage indexation destabilizes output,
however, it is valid to question whether the monetary authority of an economy with
indexed wages would want to follows such a policy. In fact, in applied discussions of
highly indexed economies, it often has been argued that monetary authorities accommodate shocks in order to avoid the unemployment costs of resisting them (for
example, see Williamson 1985).
We now examine how the results for the case of indexed wage contracts change
when monetary policy accommodates shocks by indexing money supply to lagged
inflation, that is, when
rht = nt_x .
(19)
As shown in the unpublished Appendix, replacing in the model equation (16) with
equation (19) leads to the following solution for the output gap:
Zj =^—vt + --------------- v,_, .
'
1+a'
2(1 +a) ' x
(20)
This is the same expression obtained above for the output gap in the case of preset
time-varying wage contracts and fixed money supply [compare equation (20) with
equations (18)]. Therefore, indexing money supply when contracts are indexed reduces the variability of output in response of nominal shocks and leads to the same
the variability of output observed under preset time-varying wage contracts with
fixed money supply.
By depriving the economy of a nominal anchor, however, indexing money supply
has dramatic consequences on the variability of inflation. Indeed, under such a policy
rule, equations (19), (1), (13), and (15) lead to zt = 7Cr_1 - nt + vt — ut. Differentiating
equation (20), using on it this expression for £,, and rearranging terms leads to
ESTEBAN JADRESIC
a
K = rcL +
f
fl
v, + ------- (v,_ 1 + vt_2) - ut,
fl
f2
(1 + a) f
2(1 +a)
:
193
(21)
%
which implies that the variance of inflation in this case is infinite.
Note that in the right-hand side of equation (20) only nominal shocks appear. In
other words, by indexing money supply to lagged inflation, a real shock has now no
effect on the output gap despite the fact that wages are indexed. The reason, of
course, is that, under such a policy, the automatic increases in wages and prices due
to indexation following the period of the shock are fully accommodated. This result
illustrates the crucial importance that the fixed money supply assumption has for deriving the above result that wage indexation destabilizes output when real shocks
occur. It also illustrates how misleading it can be to use the assumption that wage indexation is based on current inflation, according to which wage indexation destabilizes output when a real shock occurs regardless of the monetary policy in place.
C Alternative Nonindexed Contracts
As noted in the introduction, an alternative benchmark to assess the effects of indexed contracts is provided by the behavior of the economy under contracts that
specify a fixed nominal wage during the contract's lifetime, such as the ones considered by Taylor (1980). Since, in practice, fixed-wage contracts tend to be shorter in
duration than indexed and preset time-varying wage contracts—typically lasting for
one year instead of two, three or more years—it seems most relevant to consider the
case of short-term fixed-wage contracts that last for one period. The consequences of
using the effects of these types of contracts as the standard of reference to assess the
effects of contracts indexed to lagged inflation is examined in the unpublished Appendix. The main finding is that wage indexation to lagged inflation always destabilizes output when the alternative to the indexed wage contracts is short-term
fixed-wage contracts. The intuition is simple: the adjustment of nominal wages is
fastest under short-term fixed wage contracts.
D. Alternative Indexed Contracts
The above analysis also assumes that indexed contracts involve full indexation of
wages to lagged inflation. This assumption captures closely the type of wage indexation observed in some countries such as Brazil (in the 1980s) and Chile (in the
1980s and 1990s), as well as the stylized characterization of actual wage indexation
made by many previous authors (see the references provided in the introduction). In
other countries such as the United States and Canada, however, typical indexed wage
contracts involve only partial indexation to lagged inflation, and in some cases, indexed contracts index wages to lagged surprises in inflation rather than to lagged inflation (again, see the references in the introduction).
The unpublished appendix examines the effects of allowing for these alternative
types of indexation when money supply is fixed. Not surprisingly, it finds that indexing wages partially rather than fully to lagged inflation dampens the differences between the effects on output stability of indexed contracts and nonindexed contracts,
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but does not change the basic conclusions derived above. Regarding the effects of indexing wages to lagged surprises in inflation, it finds that indexed contracts of this
type (i) always destabilize output when shocks are real, (ii) are neutral for output stability when shocks are nominal and oc=0, and (iii) stabilize output when shocks are
nominal and a is positive. Therefore, unlike wage indexation to lagged inflation, indexing wages to lagged surprises in inflation does not destabilize output when
shocks are nominal. However, it is easy to see that in an economy where some indexed contracts index wages to lagged inflation and others index wages to lagged
surprises in inflation, it continues to be true that wage indexation destabilizes output
when shocks are nominal and oc=0. Also, it is even more likely that, if a is large
enough, then wage indexation stabilizes output when shocks are nominal. Thus, as
long as some indexed contracts index wages to lagged inflation, the fact that some indexed contracts may instead index wages to lagged surprises in inflation does not
modify the basic conclusions derived above.
4. CONCLUDING REMARKS
Since the seminal work by Gray (1976) and Fischer (1977), the major proposition
of the wage indexation literature has been that indexing wages stabilizes output
when shocks are nominal and destabilizes output when shocks are real. That proposition, however, has been based on the assumption that wage indexation is based on
current inflation, or is determined according to a peculiar lagged indexation rule unlike most seen in practice. As emphasized by many authors, including Fischer (1977,
1985, and 1988) himself, the evidence indicates that a more usual type of indexation
rule is to establish periodic wage adjustments on the basis of lagged inflation.
The analysis in this paper shows that in a Gray-Fischer economy with plausible
parameter values, wage indexation to lagged inflation destabilizes output regardless
whether shocks are real or nominal. The conventional view does not hold in such an
economy because wage indexation to lagged inflation tends to reduce the magnitude
of the initial wage revisions in response of a nominal shock, which slows down
rather than speeds up the adjustment of the economy to such a shock. The smaller
initial responsiveness of indexed wages is due to the fact that, immediately after a
nominal shock occurs, wage setters anticipate that part of the needed adjustment of
wages will automatically occur at a later date through the cost of living adjustments.
This paper also shows that, in more general settings, wage indexation to lagged inflation can stabilize or destabilize output depending on the structure of the economy
and the nature of monetary policy. In particular, wage indexation to lagged inflation
can be less damaging or even beneficial for output stability when nominal shocks
have a strong direct effect on prices, given wages. As noted above, while such an effect may not be empirically plausible in an economy like the one considered by Gray
(1976) and Fischer (1977), it may be more plausible in the context of a small open
economy. Also, it appears that if monetary policy is accommodative, indexing wages
to lagged inflation may have no consequences on output stability—and rather desta-
ESTEBAN JADRESIC
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195
bilize inflation. A key implication for future studies is that assessing whether wage
indexation hampers or enhances output stability is largely an empirical matter.
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