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A note on wage indexation in a model with staggered wage setting
Economics Letters North-Holland
19
17 (1985) 19-22
A NOTE ON WAGE INDEXATION
IN A MODEL WITH STAGGERED
WAGE SETTING
Felipe G. MORANDE University of Santiago, Santiago, Chile Received
5 March
1984
The purpose of this note is to show that, in the staggered wage setting B la Taylor, exogenous indexation of wages is destabilizing in terms of both prices and output. In a small open economy, the simultaneous application of an exchange rate policy aimed at maintaining purchasing power parity would help in eliminating output variability.
1. Introduction The use of wage indexation as a tool for stabilizing output and prices was first analyzed by Gray (1976) and later by Fischer (1977) and Cukierman (1980). The overall conclusion from these works seems to be that wage indexation will be destabilizing (in terms of output) under real shocks and stabilizing under monetary shocks, and that prices will be always more unstable with than without wage indexation. The underlying assumption in this comparison is that, with no indexation of wages, labor contracts will prevent the nominal wage from adjusting quickly to monetary or real shocks. Moreover, in disequilibrium situations employment will adjust along the labor demand curve. However, no attention is paid in the papers cited above to the fact that most contract decisions are not made at the same time. As Taylor (1979) shows, the dynamics of wage (and price) as well as output adjustments are very much depending on this real-life property of wage contracts. Therefore, placing the Gray-Fisher-Cukierman discussion into a context of staggered wage setting seems an interesting extension of their work.
2. The model Following Taylor (1979), we assume that wage contracts last one year and that decisions dates are evenly staggered; for example, one-half of contracts are set in January and the other half in July. Defining ‘period’ as a six month interval, and x, as the deviation of the log of the contract wage to be in effect for periods t and t + 1, then an equation for contract wage determination would be x, =
+x,_~ ++Ez_,x,+I +t(~/2)(E,~,y,+E,~ty,+t)+f,,
where y, represents excess demand in period t, y is a parameter greater than zero, and c, is a random shock. As usual, E,_, is expected value conditional on period t - 1 information. The overlapping nature of contracts makes the wage adjustment set at the start of period t depend on adjustments to wages in effect during t and t + 1. Also, since x, will be prevailing in t and t + 1, any excess demand in those periods will also affect the wage adjustment at t. 0165-1765/85/$3.30
0 1985, Elsevier Science Publishers
B.V. (North-Holland)
20
F.G. Morande /
Wage indexation in staggered setring
The model needs a specification of the excess demand variable and a policy rule. Assuming that ours is a small open economy - as most countries that have experienced exogenous wage indexation of the type described below - we state that aggregate demand depends on the real exchange rate, like
e>
yt=8(e,-w,)+u,,
(2)
0,
where e, and w, are the logs of the nominal exchange rate and the aggregate wage, both measured as deviations from trend; U, is a random shock. In eq. (2) the term e(e - w) represents the substitution between foreign and domestic goods, the price of the latter being proxied by the aggregate wage rate. The policy rule is assumed, in log-linear form, e, = hw,, where the policy parameter h indicates the degree of accommodation of the exchange rate to changes in wages, or how far the Central Bank is from maintaining purchasing power parity. With this and assuming, like Taylor, that wr is the geometric average of contract wages outstanding at t, such as w, = 0.5(x, + x~_~), we are able to close the model. If expectations are formed rationally, we can find a solution for x, like x,=hx,_1
+E *,
where
x = (1 + 0.5~0(1 -h) - ~viyBo)~(l
(31
+ o.wo- h)),
which is less than or equal to one if ye(l - h) -c2. For w,, it will be w, =
xw,_,+ 0.5(<,
3.1,ntroduction
+ Et_,).
(4)
of exogenous wage indexation
Note that the type of solution for x, in eq. (3) and for w, in eq. (4) implies a sort of endogenous indexation. 1 In spite of this, suppose the government decides to guarantee workers that their contract wages will keep pace with inflation. A law is passed establishing that contract wage adjustments at time t must be at least as great as the average wage fluctuation in the previous period t - 1. So, formally, the following constraint is imposed on wage negotiations: ’ x, 2 wt-l.
(5)
Table 1 reports the effects of constraint (5) on the stability of wages and output and on the purchasing power of contract wages, when a shock to contract wages occurs. As can be seen there, there are substantial differences between effects depending on whether the shock is positive or
For C, > 0 and cl+, = 0, i > 1, we have that at time 1, x is greater than W, so there is a gain for the real contract wage negotiated at r. This gain vanishes steadily starting at period t + 1, since from then on w is greater than x. Naturally, the higher X is, the longer it will take w to catch up with the initial advantage of x. If h = 1, then w will never be able to recuperate the initial real gain of x. As we will see later, the same result is obtained with an exogenous indexation of the type in eq. (5). This could explain why this latter policy is so appealing to labor unions during inflationary periods. A more realistic indexation rule would also include W,_ *, since both wl_, and w,_* are accounting for the inflation between t -2, the time of the last negotiation for people bargaining at t, and t. But qualitative results are not affected if we simplify by just using w,_ 1.
21
F.G. Morande / Wage indexarion in staggered setting
Table 1 Shock
X
Wage indexation binding
0 < A < 0.5
from
f = 2 on
Stability of contract wages
Stability of average wages
not convergent
not convergent
not convergent
Solution
(see x,)
Y, = - 8(1-
for xc:
Stability output
Y, + -
x, = X,-L
of
e(l-
Change in real wage: cx, - cw, positive h)w, + or
= (c, - w,) - fC,
h)$,
ast+w
+ 0,
* XI --*SC1 r,>O r,=o,
0.5
fromt=3on
not convergent Solution for x,:
not convergent (see x,)
not convergent Y, -+ - e(lh)ac, + U,
1 ;c,
x, = x r-1 x, * aq, $
r>l
X=1
0 < X < 0.5
c, i 0
positive = (0.5 + X)r, - w,
0.5 < h -=z1
never
never
only at
t=2
c, = 0, rzl X=1
only at
t=2
not convergent Solution for x,: x, =x,_, = c,
not convergent (see x,)
Y, = VI
convergent Solution for x,: x, = xx,_,
convergent (see x,)
convergent y,=--6’(1-h)w,+u,
convergent Solution for x,: x, =0.5Xx,+,
convergent (see x,)
convergent
not convergent not convergent Solution for x,: (see x,) x,=x,_, = 0.5c,
stable
positive = 0.5c,
0
xx,=-Xw,=r,/l-h
0
zx, = - cw, = Il.5 - X/l - X].c, stable Yz= WY
negative = 0.25~~
negative. If C, > 0 and A < 1, then wage indexation is binding after a few periods (one or two) and implies a great deal of instability in both price and output. In other words, in trying to assure a ‘real’ wage to workers in an inflationary situation, the government is destabilizing both prices - a self-fed inflation appears - and output, which persistently declines (with respect to its trend). There is, however, a gain in the real contract wage due to the initial greater increase in x compared to w. This gain grows with X, achieving a highest value of 0.5 E, when A = 1. If the initial shock is negative and no further shocks occur in the future, wage indexation will help to stabilize wage and price when 0.5 < X < 1, compared to the situation without wage indexation. With or without indexation, if X < 1 there is no change in real contract wages in the long run after a negative shock. An exchange rate policy of maintaining PPP (i.e., h = 1) will make wage indexation non-binding with an initial positive shock, and practically non-binding with a negative shock (except at t = 2), provided that no further shocks occur. This policy completely stabilizes output and destabilizes wages and prices, in both cases. It also reduces the real wage in the long run in the negative shock case, and increases it the most in the positive shock case. All in all, the results in terms of how destabilizing wage indexation is seem to be mixed. However, these results are valid when the shock, either positive or negative, only occurs once (for example, at the beginning of the periods). In a more realistic situation, shocks can happen at any time and in any direction. In this case, wage indexation would turn out to be very destabilizing. Actually, it is enough that only one positive shock occurs at some time in order to obtain a persistent, self-fed inflation (and
F.G. Morande / Wage indexation in staggered setrrng
22
so a continuously negative output gap for h < l), with no subsequent negative shock being able to alter that inflation. Let’s illustrate this. Suppose that there is, at time 1, a positive shock c, and wage indexation had been previously imposed. After a little while with no further shocks, x, stabilizes at x, = x,_ ,. Now, if at time 11, say, a negative shock occurs (E,, < 0), it will not affect x, at all nor its path after 11. Why? Because xi, and x,+i, are restricted by (5) such that x,, 2 w,~ = t(.x,,, + x9) = as in (5) is imposed, the economy is condemned to Xi0 = xg. In other words, if wage indexation inflation, after the first positive shock occurs, for as long as such an indexation is prevailing, ’ with the subsequent negative output gaps. If wage indexation must be present for political reasons, the economic authority could opt for simultaneously enforcing an exchange rate policy of maintaining PPP. By doing so, it will be validating the self-fed inflation caused by the wage indexation and therefore the persistent decline in output from trend will be avoided. 4
3. Conclusions We have seen that, with staggered wage setting, wage indexation would be destabilizing in terms of output and prices in most cases analyzed. The only case in which it would help to stabilize output and prices is when there are only negative shocks; however, this is ruled out by construction of the model which assumes that shocks to x, are zero-mean shocks; otherwise, any true mean will be incorporated by rational agents as part of the wage trend. If wage indexation is politically inevitable, a simultaneous exchange rate policy of keeping PPP would be helpful in eliminating output variability.
References C&ierman, A., 1980, The effects of wage indexation on macroeconomic fluctuations, Journal of Monetary Economics 6, no. 2, 147-170. Fischer, S., 1977, Wage indexation and macroeconomic stability, Journal of Monetary Economics, supplementary series 5, 107-147. Gray, J.A., 1976, Wage indexation: A macroeconomic approach, Journal of Monetary Economics 2, no. 2, 221-235. Taylor, J., 1979, Staggered wage setting in a macro model, The American Economic Review, Papers and Proceedings, May.
3 Ifh
the rate of inflation
will be higher.
19
17 (1985) 19-22
A NOTE ON WAGE INDEXATION
IN A MODEL WITH STAGGERED
WAGE SETTING
Felipe G. MORANDE University of Santiago, Santiago, Chile Received
5 March
1984
The purpose of this note is to show that, in the staggered wage setting B la Taylor, exogenous indexation of wages is destabilizing in terms of both prices and output. In a small open economy, the simultaneous application of an exchange rate policy aimed at maintaining purchasing power parity would help in eliminating output variability.
1. Introduction The use of wage indexation as a tool for stabilizing output and prices was first analyzed by Gray (1976) and later by Fischer (1977) and Cukierman (1980). The overall conclusion from these works seems to be that wage indexation will be destabilizing (in terms of output) under real shocks and stabilizing under monetary shocks, and that prices will be always more unstable with than without wage indexation. The underlying assumption in this comparison is that, with no indexation of wages, labor contracts will prevent the nominal wage from adjusting quickly to monetary or real shocks. Moreover, in disequilibrium situations employment will adjust along the labor demand curve. However, no attention is paid in the papers cited above to the fact that most contract decisions are not made at the same time. As Taylor (1979) shows, the dynamics of wage (and price) as well as output adjustments are very much depending on this real-life property of wage contracts. Therefore, placing the Gray-Fisher-Cukierman discussion into a context of staggered wage setting seems an interesting extension of their work.
2. The model Following Taylor (1979), we assume that wage contracts last one year and that decisions dates are evenly staggered; for example, one-half of contracts are set in January and the other half in July. Defining ‘period’ as a six month interval, and x, as the deviation of the log of the contract wage to be in effect for periods t and t + 1, then an equation for contract wage determination would be x, =
+x,_~ ++Ez_,x,+I +t(~/2)(E,~,y,+E,~ty,+t)+f,,
where y, represents excess demand in period t, y is a parameter greater than zero, and c, is a random shock. As usual, E,_, is expected value conditional on period t - 1 information. The overlapping nature of contracts makes the wage adjustment set at the start of period t depend on adjustments to wages in effect during t and t + 1. Also, since x, will be prevailing in t and t + 1, any excess demand in those periods will also affect the wage adjustment at t. 0165-1765/85/$3.30
0 1985, Elsevier Science Publishers
B.V. (North-Holland)
20
F.G. Morande /
Wage indexation in staggered setring
The model needs a specification of the excess demand variable and a policy rule. Assuming that ours is a small open economy - as most countries that have experienced exogenous wage indexation of the type described below - we state that aggregate demand depends on the real exchange rate, like
e>
yt=8(e,-w,)+u,,
(2)
0,
where e, and w, are the logs of the nominal exchange rate and the aggregate wage, both measured as deviations from trend; U, is a random shock. In eq. (2) the term e(e - w) represents the substitution between foreign and domestic goods, the price of the latter being proxied by the aggregate wage rate. The policy rule is assumed, in log-linear form, e, = hw,, where the policy parameter h indicates the degree of accommodation of the exchange rate to changes in wages, or how far the Central Bank is from maintaining purchasing power parity. With this and assuming, like Taylor, that wr is the geometric average of contract wages outstanding at t, such as w, = 0.5(x, + x~_~), we are able to close the model. If expectations are formed rationally, we can find a solution for x, like x,=hx,_1
+E *,
where
x = (1 + 0.5~0(1 -h) - ~viyBo)~(l
(31
+ o.wo- h)),
which is less than or equal to one if ye(l - h) -c2. For w,, it will be w, =
xw,_,+ 0.5(<,
3.1,ntroduction
+ Et_,).
(4)
of exogenous wage indexation
Note that the type of solution for x, in eq. (3) and for w, in eq. (4) implies a sort of endogenous indexation. 1 In spite of this, suppose the government decides to guarantee workers that their contract wages will keep pace with inflation. A law is passed establishing that contract wage adjustments at time t must be at least as great as the average wage fluctuation in the previous period t - 1. So, formally, the following constraint is imposed on wage negotiations: ’ x, 2 wt-l.
(5)
Table 1 reports the effects of constraint (5) on the stability of wages and output and on the purchasing power of contract wages, when a shock to contract wages occurs. As can be seen there, there are substantial differences between effects depending on whether the shock is positive or
For C, > 0 and cl+, = 0, i > 1, we have that at time 1, x is greater than W, so there is a gain for the real contract wage negotiated at r. This gain vanishes steadily starting at period t + 1, since from then on w is greater than x. Naturally, the higher X is, the longer it will take w to catch up with the initial advantage of x. If h = 1, then w will never be able to recuperate the initial real gain of x. As we will see later, the same result is obtained with an exogenous indexation of the type in eq. (5). This could explain why this latter policy is so appealing to labor unions during inflationary periods. A more realistic indexation rule would also include W,_ *, since both wl_, and w,_* are accounting for the inflation between t -2, the time of the last negotiation for people bargaining at t, and t. But qualitative results are not affected if we simplify by just using w,_ 1.
21
F.G. Morande / Wage indexarion in staggered setting
Table 1 Shock
X
Wage indexation binding
0 < A < 0.5
from
f = 2 on
Stability of contract wages
Stability of average wages
not convergent
not convergent
not convergent
Solution
(see x,)
Y, = - 8(1-
for xc:
Stability output
Y, + -
x, = X,-L
of
e(l-
Change in real wage: cx, - cw, positive h)w, + or
= (c, - w,) - fC,
h)$,
ast+w
+ 0,
* XI --*SC1 r,>O r,=o,
0.5
fromt=3on
not convergent Solution for x,:
not convergent (see x,)
not convergent Y, -+ - e(lh)ac, + U,
1 ;c,
x, = x r-1 x, * aq, $
r>l
X=1
0 < X < 0.5
c, i 0
positive = (0.5 + X)r, - w,
0.5 < h -=z1
never
never
only at
t=2
c, = 0, rzl X=1
only at
t=2
not convergent Solution for x,: x, =x,_, = c,
not convergent (see x,)
Y, = VI
convergent Solution for x,: x, = xx,_,
convergent (see x,)
convergent y,=--6’(1-h)w,+u,
convergent Solution for x,: x, =0.5Xx,+,
convergent (see x,)
convergent
not convergent not convergent Solution for x,: (see x,) x,=x,_, = 0.5c,
stable
positive = 0.5c,
0
xx,=-Xw,=r,/l-h
0
zx, = - cw, = Il.5 - X/l - X].c, stable Yz= WY
negative = 0.25~~
negative. If C, > 0 and A < 1, then wage indexation is binding after a few periods (one or two) and implies a great deal of instability in both price and output. In other words, in trying to assure a ‘real’ wage to workers in an inflationary situation, the government is destabilizing both prices - a self-fed inflation appears - and output, which persistently declines (with respect to its trend). There is, however, a gain in the real contract wage due to the initial greater increase in x compared to w. This gain grows with X, achieving a highest value of 0.5 E, when A = 1. If the initial shock is negative and no further shocks occur in the future, wage indexation will help to stabilize wage and price when 0.5 < X < 1, compared to the situation without wage indexation. With or without indexation, if X < 1 there is no change in real contract wages in the long run after a negative shock. An exchange rate policy of maintaining PPP (i.e., h = 1) will make wage indexation non-binding with an initial positive shock, and practically non-binding with a negative shock (except at t = 2), provided that no further shocks occur. This policy completely stabilizes output and destabilizes wages and prices, in both cases. It also reduces the real wage in the long run in the negative shock case, and increases it the most in the positive shock case. All in all, the results in terms of how destabilizing wage indexation is seem to be mixed. However, these results are valid when the shock, either positive or negative, only occurs once (for example, at the beginning of the periods). In a more realistic situation, shocks can happen at any time and in any direction. In this case, wage indexation would turn out to be very destabilizing. Actually, it is enough that only one positive shock occurs at some time in order to obtain a persistent, self-fed inflation (and
F.G. Morande / Wage indexation in staggered setrrng
22
so a continuously negative output gap for h < l), with no subsequent negative shock being able to alter that inflation. Let’s illustrate this. Suppose that there is, at time 1, a positive shock c, and wage indexation had been previously imposed. After a little while with no further shocks, x, stabilizes at x, = x,_ ,. Now, if at time 11, say, a negative shock occurs (E,, < 0), it will not affect x, at all nor its path after 11. Why? Because xi, and x,+i, are restricted by (5) such that x,, 2 w,~ = t(.x,,, + x9) = as in (5) is imposed, the economy is condemned to Xi0 = xg. In other words, if wage indexation inflation, after the first positive shock occurs, for as long as such an indexation is prevailing, ’ with the subsequent negative output gaps. If wage indexation must be present for political reasons, the economic authority could opt for simultaneously enforcing an exchange rate policy of maintaining PPP. By doing so, it will be validating the self-fed inflation caused by the wage indexation and therefore the persistent decline in output from trend will be avoided. 4
3. Conclusions We have seen that, with staggered wage setting, wage indexation would be destabilizing in terms of output and prices in most cases analyzed. The only case in which it would help to stabilize output and prices is when there are only negative shocks; however, this is ruled out by construction of the model which assumes that shocks to x, are zero-mean shocks; otherwise, any true mean will be incorporated by rational agents as part of the wage trend. If wage indexation is politically inevitable, a simultaneous exchange rate policy of keeping PPP would be helpful in eliminating output variability.
References C&ierman, A., 1980, The effects of wage indexation on macroeconomic fluctuations, Journal of Monetary Economics 6, no. 2, 147-170. Fischer, S., 1977, Wage indexation and macroeconomic stability, Journal of Monetary Economics, supplementary series 5, 107-147. Gray, J.A., 1976, Wage indexation: A macroeconomic approach, Journal of Monetary Economics 2, no. 2, 221-235. Taylor, J., 1979, Staggered wage setting in a macro model, The American Economic Review, Papers and Proceedings, May.
3 Ifh
the rate of inflation
will be higher.