The effects of wage indexation on macroeconomic fluctuations

Journal of Monetary Economics 6 (1980) 147 -17(?. 0 North-Holland Publishing Company

THE EFFECTS OF WAGE INDEXATION (;rN MACROECONOMIC FLUCTUATIONS A Generdization Alex CUKIERMAN* Carnegie-Mellort Unitvrsity, Pittsburgh. PA 15213, ZJSA This paper investigates the effects of wage indexation on fluctuations in employment, output. investment and the price level within a more general framework than that used in recent literature. The generalization involves: (a) a more general labor contract which allows labor supply as well as labor demand to affect actual employment in disequilibrium, and (b) a regular ISLM framework which includes the previously used monetarist framework as a particular case. It is found that the effects of wage indexation on fluctuations in various economic variables depend in many cases on whether demand or supply dominates the labor market in disequilibrium. The exact dependence is characterized and used to reappraise recent results and develop new results. -

1. introduction

The purpose of this paper is to extend and generalize some of the recent discussion on the effects of wage indexation on macroeconomic fluctuations, within a framework which acknowledges the existence of labor contracts.’ The extensions concern mainly the investigation of the effects of wage indexation on fluctuations in the real rate of interest and the levels of involves relaxing two investment and employment. The generalization particular assumptions made in this literature: (1) that the labor contract determines employment along the labor demand curve, and (2) that aggregate demand may be described only by an equilibrium condition in the money market which amounts to assuming a zero elasticity of the demand for real money balances with respect to the interest rate.2 With the recent acceleration of inflation, the extent of wage indexation in *On leave from the University of Tel-Aviv, A previous version of this paper, written while 1 was at New York University, was presented at the September 1977 meeting of the Econometric Society in Vienna. I would like to thank without implicating Don Patinkin and several anonymous referees for useful suggestions on the previous version. ‘See Bernstein (1974) Friedman (1974). Gray (1376). Fischer (1977b). The last two explicitly incorporate labor contracts into the analysis. For an investigation of some of these issues within the context of instantaneous market clearing, see Barre (1976). ‘See . in particular, Gray and Fischer, op. cit.

Western countries increased markedly.” However, no similar indexation of capital m;arkets developed in most of those, including most notably tile U.S. It is therefore of some interest to investigate the effects of wage indexation on fluctuations in investment and the real rate of interest for an economy which does not have similar indexation in the capital market. This is done here within an extended framework which incorporates an IS as well as an LM curve into the analysis and recognizes that the labor contract may determine employment along either labor demand, labor supply or some combination of those two functions. The first extension is a must when the effects of wage indexation on investment and the real rate of interest are investigated. The second extension is an attempt to deal somehow with the assumption that in disequilibrium. employment is demand determined, which is one unexplained but (as it turns out) crucial feature of the contract postulated in previous literature? The extended framework is also used in order to examine the robustness of previous results concerning the effects of wage indexation on output and price level fluctuations to the introduction of an IS curve and a more general employment behavior in the labor contract. It turns out that while the first extension does not make too much difference, the second one does make a lot of difference, parGcularly as far as the effects of wage indexation on stability in the face of real shocks are concerned. For example. when employment is supply determined, wage indexation may in many cast‘s reduce fluctuations in real variables like output, employment and investment as well as in the price level, even when shocks are exclusively real. Since wage indexation always decreases fluctuations in tho5.c variables when shocks are monetary. one of the main argtiment~~ against it disappears when employment is supply determined.” Section 2 presents the extended macro and contract framework. It incorporates in addition to a monetary and a real supply shock. real demand shocks to consumption and investment as well. It also includes a more general contract employment rule. In section 3 the effect of indexing on output and employment is taken up. Section 4 investigates the effects of wage indexation on fluctuations in investments and the real rate of interest. Its “In the U.S., for example. the proportion of workers under major agrcemcnts with cscalat~v prokiisions rose from about 20 percent in 1960 to SX percent at the bcpinninp of 197(~ SW Kosters ( 19%. p. 132). ‘See Gray and Fischer. op. cit. Barro (1977) critic& this assumption and suggc‘sts th;\t rational individuals should agree on a contract that will always maintain employment at the cx post clearing point of the labor market. He does acknowledge. however. that moral hazard may prevent the formation of such contracts. In an) case. as pointed out by Fischer (1977~). real life contracts do not seem to conform to Barro ( 1977) specificat ion. However. tl lis still lea\es the assumption that employment is demand determined in disequilibrium. uncxvlaincd and rather poorly documented. ‘More preci!;e results appear in the conclusion section.

effect on price level stability is treated briefly in section 5. The results and their implications are summarized in the concluding section. 2. The model The model is a hybrid of those presented by Sargent (1973) and Gray (1976) with a new extended contract employment determination for disequilibrium situations which stipulates that employment is determined by some combination of the demand and supply of labor. The Gray and Fischer case, the other extreme case in which employment is solely supply determined. and the short end rule all emerge as particular cases of this more general contract form.”

Aggepate demand is given by i’, =

K + lS_r, + p [ I’,

-

(, + 1 pf”- p,11+ I:‘*, +

t:;(.

04<

1,

/kO,

(1) where 0, ;wd ~9,are the loparit hms of aggregate demand and real income respectively. I’, is the nominal interest rate. p, the logarithm of the general level of prices. and , + , r)l* is the logarithm of the price level expected to pwail bq the public in period t + I as of period t. Eq. (1) states that total aggregate demand depends positively on real income and is inversely related to the real rate of interest. which in turn equals the nominal rate, I-,. minus the rate of inflation expected by the public. , + , /I: --pr_’ It is assumed that when real income changes. it changes only the consumption component of aggregate demand and that when the real interest changes it affects only the investment component of aggregate demand. c~,,and l+, are random shocks to consumption and investment demands respectively. Each such shock has a xro expected value and a constant variance.

Total prodLIck 1;. is produced with a neoclassical aggregate production t‘unction. The aggregate capital stock is assumed fixed.H so aggregate output can be written ala Function of total labor input and a productivity factor. 2. “I Jo

to explain the contract fawn or its length within the rnod~l [for s~nnt’ SUCK SW Alariadls (1975) and Gray : 19711)]. However. this limitati~~n 13 at knst part!> cWllpt3lsiitcd by presentation of the results here for a fairly general con:rad form. ‘TIC rate. I’,. is taken to bc the yield to maturity on a one period bond. “I abstract from the long-run effects of investment on capital accumulatiw.

dtcmpts.

not try

A. Cukicrman, kVage indexation on mucroeconomic Juctuations

150

x =Qwt),

a,= 1 +u,,

(2)

term where G(L,) is homogeneous of degree less than one and u, is a with zero mean. L, is labor input? Production is assumed to be a discrete process that takes place once each period. All contracts have a duration of one period and establish a base nominal wage rate, W*, and an indexing parameter, y. Contracts for any period t are written at the end of period t ‘i - 1, so these two variables must be set with less than full information on the other variables relevant to production decisions in period t. The nominal wage rate for period t is set at the level that would clear the labor market if the price level expected for that period in the previous one, ,p,*_1 actually materializes. * O This level is designated by an asterisk and is referred to as the contract wage rate.’ ’ In addition, the value of the indexing parameter is specified in the contract independently of W*.’ 2 The demand and supply for labor are, as in the neoclassical model, cgiven bY (3) and

respectively. Note that demand for labor depends on the ratio of the real wage to the productiv\,ty factor.’ z 2.3. The money market The demand for money is positively related to nominal income and ‘Whenever either of output, employment, the price level and the nominal money supply appear both as themselves and in log form, a capital letter is used for the variable itscllf and a lower case letter for the logarithm of that variable. An exception to this rule is the rcul wage rate, w, which denotes the level of the real wage rate rather than its logarithm. “This assumed behavior is consistent with the rational expectations hypothesis, 1‘Gray (1976, p. 224), refers to it as the certainty equivalent of the nominal wapc rate, However, since this term has a specific meaning in the uncertainty literature, which will ho c:qu;~l to the contract wage only under restrictive forms of the utility function (Le., risk ncutrul), I prefer to use a Iliore neutral terminology. j21n reality the indexing parameter, the contract length, and W* will probably not be set independently. However, since the main objective of this paper is to investigate the effects of the degree cf indexing on macroeconomic fluctuations, these interactions are abstracted from, For a discussion of the relation between the degree of indexing and contract length. see Gray (197X). 13This can be seen by differentiating the production function with respect to labor, equating the resulting marginal productivity of labor with the real wage rate and solving for the quantity of labor demanded.

A. Cukiermun, Wuge index&ion on mucroeconomic fluctuations

151

inversely related to the nominal rate of interest. Its specific form is

where md stands for the natural logarithm of nominal money demand, V is a constant element of the demand for money, akin to the ‘Cambridge K’, and t]& is a random shock to money demand with a zero mean. Money supply is assumed exogenously given by 111;= m + qs,

(W

T

where t15’ is a given constant and qsr is a random shock to money supply with a zero mean. Let E,=

&a, + &it,

% =qdr

-%f*

where caf. citv11,and II, are assumed to be mutually and serially uncorrelated. 2.4. No sltocks This equilibrium is the one the parties to the wage contract in the labor market assume will prevail during the period of the contract. It determines simultaneously both the nominal wage rate of the contract, W*,” as well as the expected price level P*. * 5 The next period expected price level is assumed to be formed rationally,” using all the systematic information about the model. Formally, the equilibrium values of labor, the nominal interest rate, the price level and the contract nominal wage rate can be obtained by requiring that the labor, commodity and money markets are all in equilibrium for the particular case in which all shocks are set equal to their expected value which is 0. Using eqs. ( 1) --(S), In G(Llr)= k+cBr*,

“Note that W* is . both the contract nominal wage rate the base nominal wage rate for the indexed case.

(6)

when there is no indexation as well as

‘“Since it turns out that this expected price level is time independent in this model, I deleted the time indices. “The concept is originally due to Muth (1961) but has been used in the context of macro models by Barre ( 1976). Lucas ( 1973 ), Sargent ( 1973), Sargent and Wallace (1975 ). and several others.

L*=,(;+o-),

(W

where

&K *=*-6

and

c

B

3i3
Eqs. (6) to (8) describe the no shocks equilibrium of the economy which determines L*. I’*. P* and W*. Th e no shocks equilibrium level of output can be obtained by substituting L* into the production function (2) and setting II at zero. ’ ’

When the. random shocks which affect the various markets are not identically zero the equilibrium values of the price level, the interest rate. employment and output will usually deviate from their no shocks counterparts. Clearly in such cases the labor market will be thrown out of equilibrium which raises an important question regarding the way actual employment is determined in disequilibrium. Gray (1976) and Fischer f1977a, b) resolve that issue by assuming that in disequilibrium actual employment is demand determined. Barro (1977) makes the point that rational optimizing individuals should agree to a pattern of employment determined at the intersection of the supply of and the ex post demand curve for labor, thus reaching a Pareto superior position. However, as he recognizes, there may be moral hazard impediments to the writing of the contingent contracts necessary to achieve this result. In addition. as pointed out by Fischer (1977c), actual labor contracts do not seem to be of the kind suggested by Barro. This leaves the theory of employment behavior in disequilibrium in a rather unsatisfactory state of affairs, This is further complicated by the observation that there seems to be no particular reason to assume that employment is determined along the demand curve. Ilt is possible to assume, probably with equal justification, that it is set accorL ing to the supply curve or at the minimum of the supply and demand quantities for any given real wage which happens to prevail in the market. I wil; therefore, assume an eclectic rule for the determination of employment in disequilibrium situations. III particular. 1 will assume that for ‘-Note that for the no shocks equilibrium previously anticipated price level since the equilibrium value of the price level under random shocks equal t&ir mathematical consequence, the expected rate of inflation is the nominal interest rate.

there is no difference between the actual and the public computes this anticiijation by solvine the the assumption that the rl4izations of the ihrw expectatiois respectively, kvhich are all 0. As a zero and there is no difference between the real and

.4. (‘14h itwim.

Uirgt* itick nit iottdvu tt~l4c~rot~~~otlo)ITi(’ flrrc-trctrtiom

153

any given real wage rate, employment is a weighted average of the demand and supply quantities corresponding to the real wage rate.

!!Y+(1 -#)g(1\*),

L=fy’

0x

The Gray and Fischer case will obtain as a particular case for 0 = 1. Determination CA’employment along the supply curve is obtained for 0 =0 and the short-end rule by using 0 = 1 for any w > W*= W*/p* and 0 = 0 for any XC w*. However, more generally eq. (9) states that in disequilibrium, actual employment wiii be affected by both supply and demand where 0 measures the extent to which one or the other is a more dominant factor in the determination of employment. The advantage in this formulation i:; that it may be used. economically. to find which of the results concerning the effects of wage indexation on stability. previously published in the literature. depend on the assumption that employment is demand determined. More importantly, the new results to be presented here will therefore have more generality. In view of (9) the values of I*. P. L and w for the case of no indexation (NI) will be determined from zr,+lnG(L,)=k+t*[re,-(p*-p,)]+I:,. 1~1=

1”+ 11,+ II,+ In G (L, ) + br*,+ r/,,

L=(!f‘ (,(:“+*11,1>+(1 -- -+W$g* \\‘,=

CV*

(7a) (9%‘) (lo\‘)

-

p,

(W

l

So the disequilibrium values of I’, P. I, and N*will depend. in general. on the realizations of the three random shocks: C, 11and II. Furthermore. since the nominal wage rate is fixed at z;t‘*. the real wage rate will [as suggested by ( lO”‘)] become a function of P, and so will employment through (9”). For the indexed (I) case I’. P. L and w will bc determined bq conditions (6a) and (RI) with the following two equations replacing (9”‘) and (lo”): L, = (,I’ * (

“‘*

1 + II,>

+

(1 -4)g(\t*” ).

\\‘Z \I’*s M;‘*p*. The real wage is now fixed [through (lo’)] at its contracted value.

(9’)

110’)

154

A. Cuicierman, Wage indexation 011macroeconomic jluctuutions

3. The effxts of wage indexation on fluctuations in output and employment Recent literature on the effects of wage indexation on fluctuati6n in output concludes that wage indexation will decrease fluctuations in output when shocks are predominantly monetary and that it will exacerbate those fluctuations when shock.s are predominantly real.” This conclusion is obtained within a framework in which the labor contract stipulates that employment is always determined along the labor demand curve. This characteristic of the labor contract is one unexplained but crucial aspect of the contract form. Pending a fuller understanding” of labor contracts, it is therefore desirable to know the extent to which the above result depends on this specific assumption. Furthermore, since this conclusion is reached within an extreme monetarist framework2* it is also desirable to check its robustness within a more general framework like the one presented here. The model presented here also rnakes it possible to determine the effects of wage indexation in the face of real aggregate demand shocks. The effects of various shocks on output are preseeted in table 1.21 bgl is the partial elasticity of output with respect to labor input from the production function which is positive. c$,., is the absolute value of the elasticity of labor demand with respect to the real wage rate. c&, is the elasticity of labor supply with respect to the real wag4~9rate and is assumed to be positive. YI,,, is defined at the bottom of the table. It measures the disequilibrium response of employment to a change in the real wage rate. The table suggests that monetary and real demand shocks do not affect either employment or cjutput when the**eis wage indexation, but that they do cause changes in 50th of those variab‘.es in the absence of wage indexation. This is summarized in the following proposition: Proposition 1. Ia the face c-rf’either morzetarq, or real demand shocks, wge indexation irons out jluctuations in emploj~ment and output.22 This proposition is basically a threefold generalization of the results obtained by Gray and Fischer. It suggests that their result is independent of whether employment is determined along the supply of labor, the demand for labor or by some linear combination of these two schedules. It also does not depend on their monetarist assumption that the elasticity of the demand for money with respect to the interest rate is zero. 23 In addition, it suggests that ‘%ee Gray (1976) and Fischer (1977b). “For an interesting discussion of optimal labor contract, see Hail and Liiien (1979). “‘I-he Gray (1976) model will obtain here as a particular case when b =0 and 0 = 1. “For a derivation of the various multipliers in the table, see appendix section A.1. 22The proof follows trivially by comparing the relevant multipliers in table 1. 23This however is pointed out by Fischer (1977b) in the appendix to his paper in which indexatidn is invesiigated within a standard IS-LM framework.

A. Cukierman, Wage indexation on macroeconomicfluctuatio~ts

155

Table 1

Percentage changes in output, employment and prices for various shocks with and without wage indexation.”

Non-indexed

Indexed

d_s Monetary shocks

1 - b “uy,Y,w’l

0

0

Real demand shocks Real supply shocks

1 0

c( 1 - h)( 1 + oa,,a;Jrc

( + I(1 + Ba,,&)u

dl M<$netaryshocks

1 - C&J

*-

0

D

0

Real demand shocks 1

Real supply shocks

-r,

Monetary shocks

1 --cq

(-)-i-b)I

Real demand shocks

1 _ b _t-.

(+)_-_

Real cupply shocks

(c(b-

1 :;ot&,+ (c+h)Y,,)u

1

D

D

( + )8a;‘,,u

1-S

1 - b It’ + b)( 1 + Oa,,a;‘,)u

b

c(l--6) (-

) -----

c-t h

c(l-b)

E 1-s

(1 +tla,.,a:,)u

All the multipliers are evaluated at :he “D=c(l-b)+(c+b)a,&,, YI,~Ou&(l 4)~;~. point of no shocks equilibrium. For derivations, see appendix. The signs which appear in parentheses on the left-hand side of some of the expressions in the table give the signs of those expressions for positive realizations of the various shocks. No sign appears when it is either ambiguous in general or obvious.

wage indexation neutralizes the effects of real demand shocks on employment and output as well as the effects of monetary shocks. The intuitive reason for this neutralization of both monetary and real demand shocks may be understood by reference to eq. (9’). With no real supply shocks and u’ fixed at w* by indexation, neither employment nor output will be affected by shocks that originate in the money-market or in the components of aggregate demand. Given that output and employment are not affected, these shocks will simply determine [through (6a) and (7a)] new values of r and p. However, when the economy is subject to real supply shocks, the dichotomy between the demand and supply sectors of the economy

A. Cukierman,

156

M/ugeindexution

on mucroeconomic ,fluctutrt ions

disappears even under indexation. Moreover, the effect of indexation on fluctuations in employment and output depends now on whether in disequilibrium situations, actual employment is determined mostly by supply rather than by demand or vice versa. This is made more exact in the following proposition: Prsposit (a)

iolz

decrease

jluctuatiorzs

2.

In

the jtice

fluctuations iu emplomer2t .

of in

real

output

supply [ff’

Y,,,,

disturhmes


and

wge I? <

ifi’ . . either of’ . the .fbllowing thee

indexatioil

will:

2, crrzti (h) &CI’LUSLJ cordit ions holds:

(i) Y,,,>O and B< (B-2)Baf’,,,a,,, (ii) Y,,,.
*

and B>max[l,Ba:,,.a,,(B-2)].

where B = [(c + b)Yl,,,o,,]/[lc((

1 - h)]

l

Prooj: By a comparison of the relevant multipliers from table 1. For details see appendix. In order to understand these results intuitively it will prove useful to understand first the effects of real supply disturbances on the price level for the non-indexed case. A positive supply disturbance causes, at the original level of labor input, an increase in output which creates excess supply in the commodity market and excess demand for money in the money mnrkct. In the labor market, to the extent that the demand for labor has any impact at all on labor in disequlibrium (0 50) the increase in the marginal productivity of labor causes, at the preshock real wage, an increase in labor input which further aggravates the disequilibrium in both the money and the good’s market by causing an additional increase in output. The direction of change in the price level may now be inferred from the requirement that it changes in a way which restores equilibrium in both the commodity and the money market. It turns out that whether the price level should increase or decrease to restore equilibrium in those markets depends to a large extent on whether an increase in the real wage rate decreases or increases labor input in disequilibrium situations. In the first case, YI,,,~0. and labor demand dominates disequilibrium situations. For this case a decrease in the price level will restore equilibrium through the following three channels: (a) by decreasing the real interest rate it will boost up demand for goods to keep up with the increased supply [see (6a)]; (b) by increasing real money supply it will decrease the excess demand in the money market [see (7a)]: (c) by increasing the real wage rate it will choke off some of the increase in labor input and output, causing further reductions in excess demand in the money market and in excess supply in the commodity market. When. however. labor supply dominates actual labor input in disequilibrium (Y,,,.~0) an

ir~r*~st~ in the price level will lay decreasing the real wage rate achieve some of t1.e equilibrating reduction in output. But when the price level increases. its effect through channels (a) attd (b) above on both the money and the commodity markets is disequilibrating. Hence in this case the price level will decrease (as in the case in which demand behavior dominates disequilibrium in the labor market) or increase depending on whether the effects of a change in the price level 4331the economy through channels (a) and (b) dominate or are dominated by the effects of this change through channel (c).~’ Having understood the various effects of real supply shocks on the price level we may turn to its effect on other variables. A positive supply shock affects labor input in the non-indexed case through two channels: First by changing the demand for labor at any given real wage rate. Secondly by changing the real wage rate through the effect that this change has on the price level. The total effect on labor input without indexation can accordingly be rewritten as (11) where the first term on the right-hand side of (11) is the effect on labor input keeping the real wage constant which also happens to equal to the total etTect of a supply shock in the case of wage indexation. The second term on the right-hand side of ( 11) summarizes the additional effects that a change in II has OII employment through its effects on the price level and therefore on the real wage rate and employmenr ? There are three alternative cases in which the absolute value of the change in labor input without iildexation is larger than the absolute value of the chancre in labor input with wa~!t’ indcxation. One of those occurs when demind dominates disequilibriuk behavior in the labor market and the other two when supply dominates disequilibrium behavior in the labor market. For the demand dominated case we know from the previous discussion that the price level goes down causing an Increase in the real wage rate which in turn makes the increase in labor input in the non-indexed case smaller (algebraically) than the increase in labor input with indexation. Hence the only way in which employment can cl~ango more without indexation than with it, in the face of a supply shock is if it $rlls more in the non-indexed case than it r*isc)sin the indexed case. This will be the wsc w1w11conditim (b.i) is satisfied. For the supply dominated case in which the price level goes down. the real wage increases and employment increases more without indexation than with it since the increase in the real wage rate [as can be seen from (11 I] stimulates

158

A. Cukierman, Wage iruiexation on macroeconomic fluctuatiorts

employment beyond the level to which it increases with wage indexation. The condition Bc 1 in (b.ii) assures that the price level will indeed decrease in this case. When the price level increases, the consequent decrease in the real wage rate causes (taken by itself) through the dominant supply behavior a decrease in employment. When condition (b.iii) is fulfilled the total resulting decrease in employment without indexation is larger in absolute value than the increase in employment with indexation. Note that in the case of a supply shock the ultimate total change in output must always be in a direction opposite to the ultimate change in the price level.26 An increase in output causes excess supply in the commodity market and excess demand in the money ‘market. A consequent decrease in the price level works to re-equilibrate the commodity market by decreasing the real rate of interest (thus stimulating aggregate demand) as well as the money market by increasing the real quantity of money (thus decreasing excess demand in this market). The total effect of a supply shock on output in the non-indexed economy can be decomposed (as in the case of its effect on employment) into a ‘direct effect’ which disregards the repercussions on output through the price level and the real wage and into a real wage effect which focuses only on those repercussions. This can be achieved by substituting (11) into the expression dy=u+a,,dl, to obtain

=dr’lsa,,!?‘,,,dp, I

(12)

where

(12) suggests that the ‘direct effect’ is identical to the total effect on output with indexation and that the real wage effect on output depends on the change in the price level. Comparison of (11) and (12) suggests that the change in output in the non-indexed economy is larger or smaller (algebraically) than the change in output in the indexed econom! depending on whether the change in employment in the non-indexed economy is larger or smaller (algebraically) than the change in employment in the indexed 26The reader can convince himself of this fact for both the indexed and the non-indexed economies by drawing in the r--P plane two curves, one which describes the combinations of r and P for which the commodity market is in equilibrium for a given _LAnother which describes the combinations of r and P for which the money market is in equilibrium for a given _v.By noting the shifts of those curves caused by a change in y the claim mad: in the text follows.

A. Cu kicmtan, Wage indexut ion on macroeconomic fltrctunt ions

159

economy. This suggests that (dyNII> Idyii, if it occurs at all, will occur under the same circumstances that assure ]d/N,l> Id/,/. We shall therefore re-examine these three cases: (i) When demand behavior dominates disequilibrium in the labor market (Y,, > 0) our previous analysis suggests that the price level must decrease. Hence from (12) dyNI
160

non-indexed cases, wage indexation will increase downward fluctuations output. Part (,b) of Proposition 2 suggests that the effects of wage indexation employment strongly depend on the sig”;lof Yr,,., that is again on whether disequilibrium situations employment is dominated mostly by supply or demand.“*

in on in by

4. The effect of wage indexation on investment’s fluctuations The literature on the macroeconomic effects of wage indexation focuses on the effects of such indexation on fluctuations in output and employment but says virtually nothing about its effects on the variability of investment. However, an increase in the variability of investment, other things being equal, has a negative effect on economic welfare if the typical investor is risk averse. In addition, if it is costly to expand and contract the production of the investment good, these costs will be smaller when the same average level of investment is maintained with smaller variability. In countries which suffer from inflation, wage indexation is usually introduced before indexation of capital markets? It is therefore interesting to ask what the effect of the introduction of wage indexation on fluctuations in investment would be when no c;lpital market indexation exists. Since investment demand varies with the real rate, the absolute value of fluctuations in investments is in most cases directly proportional to the absolute value of iluctuations in the real interest rate, I*,= I*,- (II*- 11,). Hence. in order to compare the fluctuations in investments. with and without wage indexation. it is sufficient to compare the absolute value of fluctuations in the real interest rate in the two economies? In what follows. this comparison is performed for each kind of the shocks that affect the economy. “For the case in which it is only demand determined and using the puriIIIIctCr \iIluch IZ,, =z 3, p= -0.2, y.= 0.X and h = -0.5, condition (h.i) of Proposition 3 hcco~ms 1 2 2( 1 + I 3 nf,, ) which is obviously violated. (c,, = 2: 3 is consistent Nith a Cobb DcJuglas spccit’icut iou of tlw aggregate production function. The other assumed elastlcltics Ure not incon&tcnt \\ ith econometric estimates of these elasticities.) This suggests that when V,,, ~0, wage ilA~si~tlc~ll oh more likely to increase fluctuations in employment in the t’ilcc of 14 supply tti~ttr~ki~l\c~. However, for !&CO it is more likely to decrease fluctuations in cmp)oyment in the face of such disturbances. For example, when employment is solely supply dctcrmincd (0 = 0). V,,, c 0 irI]d H = 2; 3 6,. It follows from Proposition 2 (b.ii) that as hp as the hstkity of Ii~h~~ supply with respect to the real wage is smaller than 1,5. wage indexation will dccrcusc tll~ctuittic~n~ in employment. “An example is Italy in which wage indexution prevails but in whit h there ih IN> simlkrr indexation of financial contracts. In Israel indexation of long-term bonds was introduced in the mid-fifties when wage indexation has been widespread for quite SOIIIC time. The U.S. which is a late comer into the inflation circle. seems to conform to this pattern: with the acceleration of inflation in 1974;75, the proportion of indexed wage contracts increased dramatically. Ho\vefer, no similar shift towards indexed financial contracts was to be found in c:\;bital markets. -U The only exception to this rule occurs when a non-zero random shock, I:,,, affects real investment demand. This case is therefore dealt with separately betoN*.

161

real rate interest may either because a change in the nominal interest rate, or because of a change in the expected rate of inflation p* -pt which in turn changes only because of changes in the actual price level p,. For example, a CVWV~S pctrihtrs increase in

prices as well as the nominal rate of interest. As can be verified from table 2.

Pcrccntagc‘ changw m the rwl

rate of infcre~t for bariou\ shocks with and kvithout \iage indoxuation

_

- - --_-_--_I.

___ ^-. -__- -.___._ -----__

--- _--

_-.l_l-_l___--_-

dr*.”

_--_-L_-_____

Non-inclcxcd

_-

---

1ndexed -

which @es the percentage change in the real interest rate for a given (say. positive) monetary shock with no indexation, the resulting change may be either up or down but will most certainly be non-zero. The intuitive reason is that, as can be seen from (ha). there is a strict negative relationship between output and the real interest rate in the face of monetary shocks. Since without indexation a monetary shock affects output. it must affect the real rate of interest as well. On the other hand when the economy is indexed. a monetary shock does not affect employment and output. It will, however. atTect the nominal interest rate and the price level by acting directly on the money market. However. since total output does not change, total aggregate demand must remain the same. which suggests using the right-hand side of (6a) that the real interest rate does not change: It follows that wage indexation stabilizes fluctuations in investments. in the face of monetary disturbances.

162

A. Cukierman, Wage indexation on macroeconomic jluctuations

4.2. Real shocks to investment demand When the economy is affected only by real investment demand shocks, Eitq indexation unambiguously decreases fluctuation in investment to 0. This can be understood intuitively as follows; We know from the previous section that, with wage indexation, any real demand shock and in particular a shock to investment demand does not affect output. Hence, consumption must remain the same and therefore investment is unchanged as well. The real rate of interest increases in this case by -E&? which is exactly the increase necessary to maintain investment demand at its preshock level. However without indexation the change in investment, di,,, as a result of a shock to investment demand is3’ (13) which suggests that in the non-indexed case investment changes iff output changes. Since in the absence of indexation output always changes in the face of any real demand shock it follows ihat investment must change. Hence wage indexation stabilizes fluctuations in investment caused by shocks to investment demand. Unfortunately, this simplicity* disappears as soon as we turn to real consumption demand and supply shocks. An exact evaluation of the effects of wage indexing in investment’s fluctuations requires now a more precise determination of a.‘leeffects of real consumption demand and supply shocks on t! with and wiGlout wage indexation. This is supplied in table 2 which gives the percentage changes in the real rate of interest caused by various shocks with and without wage indexation. 4.3. Reti/ shocks to consumption demand or to supply

The effect of wage indexation on fluctuations in investments or the real rate of interest in the face of real supply and consumption disturbances is summarized in the following proposition: Proposit ion 3. (u) In an economy which is jbced with reul demnrrd disturbance in consumptioil, Ed,, wage indexa t ion will decrease jluct utit iorrs in 31The first equality follows by differentiating (1) totally with respect to t+,. The second by noting from tables 1 and 2 that du,, =dc, + ( l/c)dxNI. Substituting this last expression instead of dr,, in (13) and noting that di, =/I dt!,+ Q,= 0 the extreme right-hand side of (13) follows. Note that unlike dr,. dl etc. di is not a proportional rate of change but rather the ratio between the change in investment demand and total aggregate demand at the no 5hocks equilibrium of the economy. However since the denominator of this expression is the sa-\ilefor the indexed and the non-indexed case, the proportional rate of chal:ge in investment without indexation will be larger than with it if and only if IdiN,1 > [dill.

A. Cukiermait,

Wage indexcrticln

on macroe~onnrnic‘.fllic’tuntic?~ts

163

investments if and onfy if V,, < 0, urzd either qf the two johvirzg holds:

(i) Bc 1, OY

Proofi By comparing the appropriate ex ressions with and without L indexation for given values of the shocks Go,and u from table 2. The details are fvorked out in the appendix. Interpretat iort. In the case of real supply shocks only, there is a strict one to one negative relationship between total output and the real rate of interest as can be seen from (6a). Any change in output must be accompanied by a change in the real interest rate in the opposite direction in order to enable demand to absorb the change in output. Hence whenever the absolute value of the change in output is larger without indexation than with it, the absolute value of the change in the real rate of interest must be larger without indexation than with it. ft is therefore not surprising that condition (b) of Proposition 3 is identical with condition (a) of Proposition 2. In order to understand the conditions in Proposition 3(a) it is useful to decompose the total effect of a real demand shock for the non-indexed case into two components: (a) One which holds output constant and records only the direct effect of a real demand shock on the real rate of interest, This is the change in the real rate of interest that is necessary to keep the commodity market in (6a) in equilibrium in the face of a change in c:,. (b) The additional effect on the real interest rate of the change in output caused by the changes in employment brought about by the change in the real wage rate as a result of the change in the price level. Formally

where N 5 (I~)a,,c,, and is positive or negative as C, is positive or negative. Note that the direct effect - (I,$)c,,, is identical with the total effect of a real consumption demand shock on real interest in the case of indexation and must be positive if c;, is positive. This is not surprising since with wage indexation the real rate of interest has to ch:lnge only in order to equate total aggregate demand to a given C’OILS~M~ level of output. However, when there is no indexation, the real interest rate has to change also in order to

keep

aggregate demand in line with the c*hangud level of output. The fundamental question is whether this additional change in interest reenforces or works against the change in it under wage indexation. When (as can be checked from table 1) D 4, a positive real demand shock increases the price level which causes a decrease in the real wage rate and for VI,,,~0 (dominant supply behavior in the labor market) a decrease in output. Therefore in the non-indexed case, the real interest rate has to increase not only in order to reduce aggregate demand to the preshock level of output but to reduce it to the smaller size of output supplied as well. By noting that the conditions B < 1 and D CO are equivalent it is apparent that this is the case when condition (a.i) of Proposition 3 is satisfied. In case (a.ii) of Proposition 3 the real interest rate in the non-indexed case actually decreases more as a result of a positive real demand shock than the amount by which it rises in the indexed case. This can be understood as follows: When B > 1 (which is equivalent to D >O) the price level decreases as a result of a positive real demand shock.32 The real wage rises and since supply disequilibrium behavior dominates in the labor market. employment and output rise which, taken in isolation, has a depressing effect on the real rate of interest. If this last effect dominates the direct positive effect on the real rate of interest by enough to make the decrease in it without indexation larger than the increase in it with indexation, the effect of indcxation will be stabilizing. When the last two conditions in part (a.ii) of Proposition 3 arc fulfilled this turns out to be the case. To sum up, the Discussion of this s&on suggests that wapc indexation unambiguously decreases fluctuations in investment if t!le economy is affected bv either monetary_ or real investment demand shocks. When. however. the eionomy is affectlbd by either shocks to consumption demand or to supply the (de)stabilizing effects of wage indexation on investment depend to a large extent on whether demand or supply behavior dominates the labor market during disequilibrium episodes. As suggested by Proposition 3 when the effect of demand on employment during disequilibrium episodes is dominant ((II,,,.>O), either because the absolute value of demand elasticity for labor is sufficiently larger than the absolute wluc of the elasticity of I;~lx~ supply. or because 0 is sufficiently near to 1, or both, wage indexation will increase fluctuations in investments for any real supply or consumption demand shock. However. when If’,,,, c 4). the opposite result cannot ho rul,.bd ouL3” -“This can be verified from table 1. 33To illustrate such a possibility, consider again the values for the various ehwticities from footnote 28; t,, = 2’3, fl= -0.2, z=O.8 and h =O.S. Assuming the extreme case in which employment is solely supply determined Y‘,,,~0. The !_ondition B < I Implies now c;,~< 3 2. Hence. for the above parameter values, a labor supply elasticity whtlh is smaller than 3 Z implies that wage indexation will reduce fluctuations in investments III the face of both 14 supply and consumption demand shocks.

165

5. The effect of wage indexation on price level fluctuations S. 1 . Tlte

tgkt

cff’ w4

ge idextrt iorl 012 price let-e1jluctuat ions

Fischer (5977b) finds that irrespective of the origin of the shock which affects the economy, wage indexation will increase fluctuations in the price level. As suggested by the following proposition, this result too depends on the assumption that employment is demand determined: Propwit iorr 4. Wctge irtdescrtim will docreuse jluctuatiom in the price 1ereI dttrtever the sourc*eof’ the shock thut q@cts the eco12on2)'@' Y,,.
See appendix.

The proposition suggests that as long as employment is dominated by the demand for labor schedule. wage indexation will indeed increase fluctuations in the price level. However. when actual employment is dominated by labor supply. there is a good chance that wage indexation will decrease fluctuations in the general level of prices. For the specific parameter values used in footnote 25 and O=O. this result will obtain for any labor sl~pply elasticity which is smaller ahan 3.

Gray (1976) derives an optimal degree of indexation by using as an optimality criterion the minimization of the expected value of the square deviation of actual from desired output, where desired output is the level of output which would have been produced if the labor market was allowed to clear c#~ the realization of the random shocks became known? She finds the optin!al degree of indexing to depend on the elasticities of labor supply and demiind and to be an increasing function of the variance of monetary shocks and a decreasing function of the variance of supply shocks, Using the same optimality criterion within the present more general framework it is possible to show that the optimal rate of indexation will ~~l.s(~~~ depend on the elasticity of consumption demand with respect to income, the elasticity of aggrugutc demand with respect to the real rate of interest. the elasticity of real money demand with respect to the nominal rate of interest and the wrirtrw of real demand shocks. At least for the case 0 = 1 the optimal degree of indexation is still an increasing function of the variance of monetary shocks and a decreasing function of the variance of real supply shocks.

166

A. Cukierman, Wage indexation on macroeconomic fluctuations

Furthermore, shocks.

it is an increasing function of the variance of real demand

6. Conclusion This paper investigates the effects of wage indexation on fluctuations in employment and investment. t also checks the robustness of previous results regarding the effects of wage indexation on fluctuations in output and the price level to assumptions regE&rdingthe labor contract employment rule and the sensitivity of the demand fQ>rmoney with respect to the interest rate. It is found that in the face of monetary shocks or shocks to investment demand, wage indexation always irons out fluctuations in investment. However, in the face of either consumption demand or supply shocks, wage indexation increases fluctuations in investments when the labor contract employment rule reflects mostly the behavior of the demand for labor. But when it reflects mostly the behavior of labor supply, it is likely that wage indexation will decrease fluctuations in investment even in the face of shocks to consumption demand and supply. Wage indexation always irons out fluctuations in employment and output in the face of either monetary or real demand shocks and increases them under most circumstances in the face of supply shocks when the employment rule is demand do:ninated.. However, when the employment rule is supply dominated, wage in
A. Cukierman, Wage indexation on macroeconomicfluctuations

167

Appendix A.I. Dericatiort

of table

I

By taking the no shocks equilibrium system given by eqs, (6), (7), and (8) as a point of departure and by introducing non-zero shocks into all markets, it is possible to compute the resulting proportional deviations of each of the endogenous variables from this equilibrium by performing a standard comparative statics experiment. For given non-zero values of the random shocks E, q and U, logarithmic differentiation of the non-indexed system given by #a), (7a) and (gN’)yields

cdr+cdp-a,,dl=

-E1 _g+tl,

UW

-V-U,

(A.3

bdr+ 1 l dp+a,,dl=

- Y’,,dp+ I l dl=0c&u,

(A.31

where

and

) ,t,*> a:,=- .fw* L*

0

aSH

T

g’w* 1 ,=------w*> 0, _

LS

and CQ is the partial elasticity of output with respect to labor supply computed from the production function evaluated at the no shocks equilibrium. dr, dp and dl are all logarithmic differentials. They therefore represent the percentage deviation of each of those variables from r*, p* and I*. respectively. Performing an identical comparative static experiment on tht’ indexed system given by (6a), (7a) and (9’) in the text yields an identic;il system of equations as in (A.1) through (A.3), except that in (A.3) Vi,,. is replaced by zero. This reflects the fact that under indexation, a change in the price Ievel does not affect employment by changing the real wage rate since this last variable is fixed, The percentage changes in labor, the price level and output for any combination of shocks can be obtained by solving the system (AS)--(A.3) for dl and dp and by using the relation dy= (1 + a,+dl)u. Setting alternatively each of the shocks q, e, and u to be non-zero while the other two are set equal to zero, it is possible to obtain all the multipliers in table 1 for the non-indexed case. The same multipliers for the indexed case are obtained by a substituting Y,, = 0 in each of the multipliers for thy *fir ‘- ’

A. Cukierman, Wage indexation on macroeconomic

168

jlucttratiorls

A.2. Proo$ of*Propcsitioft 2 Proof

oj(a).

Using the output multipliers from table 1, the condition

becomes equivalent to the condition

For YI, > 0, (AS) is equivalent to 1c+ b~Y,,.a,,, < 0 which is violated. Therefore, (AS) holds only if Y,, 1, (AS) t?olds iff B < 2, which establishes 2(a). ProoJef (b).

Using the employment multipliers from table 1, the condition

is equivalent to the condition

For W,, >O and B > --0o~,~~~,,, (A.7) becomes equivalent to - 1~+ hl( 1 + Bof’,,,a,,)Y,,>O, whit,“1 is violated since Y,,,,> 0. For YI,V>O and B < - 0a;‘,.a,.,, (A.7) is equi\vJent to the condition B c (B - 2 )IJc#,,,Q. It follows that when YI,, >O, (A.7) is fulfilled iff

I-Iowever, since for Y,,,>O, B ~0 it follows that the last expression on the right-hand side of (AS) is the smallest which establishes Proposition 2(b.i). For Yi,O, which must be the case when Yy,,,~0, thus proving 2 (b.ii), * For Y,, 1, (A.7) holds iff B > &#,,,a,@ - 2). which proves 2(b.iii). A.3. Derivation oj’ the rnultipkrs

in tdde 2

By solving the system (A.l)--(A.3) for dp and dr both for Y,,,.+ 0 (no indexation) and Y,, = 0 (indexation), setting alternatively each of the shocks: q, E, and u, to be nori-zero while the other two are set equal to zero, it is possible to obtain dr and dp for the various cases. The percentlige changes in table 2 are then obtained by using the relationship ‘dLy =dy 3 dp.

169

Prooj‘ of. (a).

Using the multipliers

for a change in c, from table 2. the

condition

is equivalent to

For Y,, r 0. (A. 10) is equivalent to IhiY,,,.a,, c 0 which must be violated since Y,,. >O. Hence. Idrx,I > ldr,l only if Y,,,.< 0.’ If. in addition, IYl,,,~,,lI> 1 - h. [DI =Ihcc*IIYt,.la,,-l~~)(l -4). and condition (A. 10) becomes equivalent to lhl ]Y,,,.a,.,< 0. which must be violated. Hence. (A. 10) holds only if YIr,.< 0 M/ 1 -h > Yt,,.~,.,.If in addition. B < 1 : (A. 10) holds iff IhY,,,.l>O which is always the case. When Be 1,

D = d 1- h + ‘h,, nst ) + hlfllr,qt co.

t.

Since Y,,,.1 - h is redundant in this case. This establishes Proposition 3(a.i). If B > 1. (A.lO) holds iff Ilc*l(1 - II - IY,,,,c,,.,() > IhY,,,,((T,.,.which establishes 3(a.ii ). P WO/’of’ (1~). Using the multipliers for a change in ~1from table 2, (A.9) become’s equiwlent to condition (AS) which as has been demo&rated in section A.2 of this appendix will hold iff Y,,,.c 0 and B < 2.

Comparison of the price multipliers indexution suggests that the requirement

(dPNII ’ IdPll

from table

1

with and without

(A.1 1)

is equivalent (whatever the source of the shock) to condition (A.S). above. However. the argument immediately following this expression in the proof of Proposition 2(a) suggests that it is fulfilled if Y/,,,~0 and B < 2.

170

A. Cukier:nun, Wuge indexation on macroecorlomic fluctuations

References Aaria&. C., 1975, Implicit contracts and underemployment equilibria, Journal of Pohticaf Economy 83, Dec., 1183-1202. Barre, R.J., 1976, Indexation in a rational expectations model, Journal of Economic Theory 13, 229 -244. Barro, R.J., 1977, Long term contracting, sticky prices and monetary policy, Journal of Monetary Economics 3, 305-3 16. Bernstein. E.M., 1974, Indexing money payments in a large and prolonged inflation, in: Giersch et al.. eds., Essays on inflation and indexation (American Enterprise Institute). Fischer, S., 1977a, Long term contracts, rational expectations and the optimal money supply rule, Journal of Political Economy 85, Feb., 191-206. Fischer. S., 1977b, Wage indexation and macroeconomic stability, in: Stabilization of the domestic and international economy, Carnegie-Rochester Conference Series on Public Policy 5 (A supplementary series to the Journal of Monetary Economics), 107-148. Fischer, S., 1977c, Long term contracting, sticky prices and monetary policy: A comment, Journal of Monetary Economics 3, 317-323. Friedman, M., 1974. Monetary correction, in: Giersch et al., eds., Essays on inflation and indexation (American Enterprise Institute). Gray, J-A., 1976, Wage indexation: A macroeconomic approach, Journal of Monetary Economics 2,221-235. Gray, J-A.. 1978. On indexarion and contract length. Journal of Political Economy 86, Feb.. 1 . 18. Hall, R.E. and D. Lilien, 1979, Efficient wage bargains under uncertain supply and demand, American Economic Review 69, Dec., 868-879. Rosters. M., 1976, Wages, inflation and the labor market, in: W. Fellner, ed., Contemporary economic problems, 109- 162. Lucas. Jr. R., 1973, Some international evidence on output-inflation trade-offs, American Economic Review 63, June, 326-334. Muth. J., 1961, Rational expectations and the theory of prise movements, Econometrica, July, 315-335. Sargent. T.J., 1973, Rational ,‘xpecti;iions, the real rate of interest and the natural rate of unemployment, Brookings Papers on Economic Activity 2, 429-480. Sargent. T.J. and N. Wallace, 1975, Rational expectations. the optimal monetary instrument and the optimal money supply rule, Journal of Political Economy, April.