- Email: [email protected]
Labor contracts and monetary policy
Journal of Monetary Economics 6 (1980)241-255. 0 North-Holland
LABOR CONTRACTS
Publishing Company
AND MONETARY
POLICY*
Matthew B. CANZONERI University qf lllinois. Urhmu. IL 61801, USA Fischer and others have shown that the very existence of long-term contracts can imply a role for monetary policy in models that incorporate the natural rate hypothesis and rational expectation formation. The present paper examines some of the factors that determine the length of labor contracts and how they are affected by monetary policy. It is argued that a successful stabilization policy might be expected to increase the length of contracts. The net
stabilization
effect of the imposition of such a policy would therefore be to dampen the amplitude of business cycles. but to make them more inertia ridden.
1. Introduction This paper is concerned with the interaction between monetary policy and contracting in labor markets. Recently, Fischer (1977a). Aoki and Canzoneri (1979), and others have shown that the existence of long-term labor contracts can imply a stabilization role for monetary policy in models that incorporate both the ‘natural rate’ hypothesis and the ‘rational expectations’ hypothesis. However. these analyses are incomplete, for they do not explain how the lengths of labor contracts are determined. The lengths of labor contracts affect the cyclical behavior of employment and output. If a change in monetary policy prompts a change in the lengths of contracts, then this reaction should be embodied in a policy evaluation model. Here an attempt will be made to close the model. Briefly, risk averse unions will be assumed to impose wage contracts on profit maximizing firms. In these contracts, unions specify nominal wage rates and the contract’s length. Then firms employ the amount of labor that maximizes profits, period by period. In setting the nominal wage rates, unions form ‘rational’ predictions of future prices and try to hit predetermined real wage tarsets: these targets represent preferred points on real wage -employment trade-offs offered by the firms. In choosing contract lengths, unions weigh the benefit of more accurate price predictions against the cost of more frequent *1 would like to thank an arionymous referee for a number of helpfc suggestions. After this paper was written, an interesting paper by Jo Anna Gray \cas hrou$t to my attention. In it. she addresses the same basic problem that I discuss here; however. her setting and fc~us both differ from what is presented here.
242
M.B. Cammeri,
Labor contracts and monetary policy
contracting. This choice will be seen to depend upon the extent to which monetary policy is offsetting instability in the price level. Generally, monetary policy will be seen to be more potent than the analysis of Sargent and Wallace (1975) would seem to indicate, but more complicated than the ‘fixed wage’ version of the Keynesian model would seem to indicate.’ It should be noted at the outset that in this paper the form of labor contracts and the employment policy of firms are taken as given. Should a change in monetary policy induce, say, the use of indexing, or the agreement upon some scheme whereby unions trade expected wages for employment security, then the present analysis would also be incomplete.2 So what follows must be viewed as an initial (or at least provisional) attempt at closing the model. 2. The model The model will be presented in three stages. In section 2.1, the basic structure of the model will be outlined. Initially, it will be assumed that the length of labor contracts is fixed and that unions set wages in these contracts according to a simple ‘certainty equivalence’ rule. Under these assumptions, equilibrium conditions for employment, output and the price level will be derived. The equilibrium conditions will contain expectation terms since the unions’ wage setting rule involves predictions of future price levels. Expectation formation will be assumed to be ‘rational’, and in section 2.2, the equilibrium conditions will be solved for reduced forms describing the paths of price and output. These reduced forms are, of course, predicated upon the assumed wage setting rule, and the cyclical characteristics of price and output will be seen to depend upon the length of labor contracts. In section 2.3, the unions’ contracting behavior will be discussed in more detail. The ‘certainty equivalent’ wage setting rule (which makes the solution of the model in section 2.2 mathematically tractable) can be justified for risk averse unions if the unions are assumed to have quadratic utility functions. The ‘In particular, standard control algorithms do not appear to be very useful for this type of model. See Aoki and Canzoneri (1979), especially their ‘Case 2: p > 1‘. 2The basic scenario in this paper has come under attack recently, The ‘implicit contract’ theory of Bailey (1974) and Azariadis (1975) suggests that :*isk averse laborers would be willing to trade expected wages for employment security. If so, the equilibrium labor contract would probably not specify an employment rule that is consistent with period by period profit maximtzation. Barro (1977) has also characterized the profit maximizatron rule as pareto inferior. [Fischer’s (1977b) reply to Barro is relevant in the present context.) However. the basic scenario outlined above does seem to be consistent with certain stylized facts about actual labor markets. These markets are characterized by long-term contracts (one to three years in length) and (in the U.S. anyway) a minimal amount of indexing. It would, of course, be preferable to allow the form of the contract (including the employment rule and the possibility of indexing) to be endogenous, and perhaps varying with changes in government policy. This ambitious task is beyond the scope of the present paper.
unions’ risk aversion will be seen to manifest itself in the determination of contract length. In this section, the stochastic processes describing monetary policy, capital formation and aggregate demand disturbances will be left unspecified. The equilibrium paths of price and output will, of course, depend upon the actual specification of these processes. Section 3 provides examples of how the model operates under various specifications.
2.1. The structure of’the model
The supply side of the economy consists of competitive firms and wage setting unions. Unions quote nominal wage rates for a specified length of time in a labor contract. Firms are free to hire any amount of labor they choose at the given wage rates; they are assumed to maximize profits period by period. The typical firm is assumed to have a log-linear production function, (1) where y, is the log of output produced in period t, II, is the log of labor employed in period t. and k, is the log of the capital stock at the beginning of period t. The firm takes prices from the market and wages from the labor contract and hires labor up to the point where the cost of the marginal unit of labor just offsets its product, so
where W,is the log of the nominal wage rate and p, is the log of price. The typical union imposes a labor contract that reflects a compromise between real wage and employment goals. Eq. (2) represents a wageemployment trade-aff for the union. It is assumed that the union has decided upon a set of real wage targets -.-- 2,. . . ., a+--- that represent its wageemployment preferences for a T period horizon. Since the union specifies nominal wages in the labor contract, it must predict future price levels and set nominal wage rates accordingly. The union also specifies the length of the contract. Suppose the length of the contract is T periods; that is, only one contract is negotiated for the T period horizon. As time progresses, actual real wages are likely to deviate more and more from their target values, for predictions of more distant price levels are less accurate. On the other hand, the T period horizon could be broken into two contract periods of length T,i2. Better predictions of the last T/2 price levels can be made half way through the T period horizon, so this JhlunE
I)
244
procedure would produce real wage rates that deviate less on average from their target values. Similarly, the T period horizon could be divided into three, [our or T separate contract periods. However, more frequent contracting is a costly endeavor; resources must be committed to reestimating futt”tre price levels and re-negotiating new contracts. Generally, there will be an optimal number of contracts for the T period horizon and there will be an optimal way of using the price predictions to specify nominal wage rates in the ccjntract. Initially. it ~91 be assumed that the length of the contracts is fixed and that wages are set according to the ‘certainty equivalent’ rule (3) where pp is the price predicted by the union at the time the contract is negotiated. The rest of the economy is represented by a single equation explaining aggregate demand for output, y, =
d, + d k, + d, (y - pt ) + 1
$3
d, >O,
d,>O,
(4)
where 111,is the log of the money supply at the beginning of period t and II, is a random demand disturbance. Eq. (4) may be viewed as the reduced form for income from an IS-LM’ mode1.3 The capital term represents both wealth effects in consumption and the autoregressive part of investment. The disturbance term -epresents disturbances in consumption, investment, fiscal policy and financiar’ markets. It is assumed that the time paths of k, III and t4 are determined by some as yet unspecified stochastic processes. It is quite possible that the time paths of k and 111are coupled with each other and depend upon the time paths of .Y or p. A countercyclical monetary ,policy may, for example, depend upon past values of J and p. Eqs. (I ), (2), (3) and (4) and the stochastic processes for k, 111and II determine the time paths of J, p, II, and NVonce expectation formation is specified. It will be assumed that expectation formation is ‘rational’: If the labor contract is negotiated at the end of period t,, then
3The reduced form of an WLM model should include the expected rate of inflation. Adding the term prlr- 1-p,_ 1 to eq. (4) would not complicate matters much, and it should not change the qualitative results reported in section 3, see, for example, Canzoneri (1978). However, modeling expected i;lflation bs p, + , ,, _ I - I),,~_ 1 as is more usual would produce some familiar non-uniqueness problems, see, for example, Taylor (1977). For simplicity, expected inflation has been left out of eq. (e).
Unions’ price predictions are identical to the model’s mathematical expectation. conditional upon all of the information available at the time the contract is negotiated. This implies. of course, that unions know the stochastic process governing monetary policy. The supply side - eqs. (1). (2), (3) and (5) --- may be solved for a supply function. .1’,=s,j +s, k, - yg, +gp,
-?,,,,,I
s,
>o,
s,>O,
(6)
where the si are functions of the /ii. The supply function can be separated into t&o components,s Jr =!‘JX,*
y&,.
k,,,J+s* (k, - h(,(,)+ s2 (P,-
Prp,, 19
k,,,,,)=*Q + s, k,,,,)-.s’Z,.
(7)
The first component is the output that is supplied if there are no prediction errors: j-n will be called the ‘natural’ rate of output. The second component shows how prediction errors result in deviations from the ‘natural’ rate. If unions predict the price level and the capital stock accurately. then the wage rate they specify in the labor contract produces the desired real wage employment combination: ‘natural’ rates of employment and output result. If. however, the price level is higher than predicted, the wage will be too low; the real wage will be lower than desired and employment and output will be higher than their ‘natural’ rates.
The supply and demand functions can be solved for the equilibrium paths of price and output in terms of the stochastic processes for k, 111and II. Using (4) to eliminate output in (6). I), =
( 1 112 ,[d,, - s,, +
- (s2iti, Hp,-
sg , - (s
I), I,,, )*
1
-
ill )k, + II,] + 111, (8)
All that remains is to relate the price prediction error to the stochastic processes for k. 111and 11. Since these stochastic proctsses are the only ‘This supply function bears a formal mathematical resembIcnce to the supply function used by Sargent and Wallace (1975). it incorporates the ‘natural rate’ hypothesis: Perfectly anticipated price changes have no effect upon employment or output. However. the model does not specify a competitive labor supply with a search theory of unemployment or with hous~~holds basing work leisure decisions on expectations of future prices and wages. features often i&ntified with the ‘natural rate’ hypothesis. Instead it is more closely related to the ‘fixed wage’ acrsio:l of tllc Keynesian model.
M.B
246
Cumzoneri,
Labor
contracts
and monetas”
policy
random elements inI the model, it should not be surprising that the price prediction error can be explained in terms of the prediction errors for k, m and u. It can be shown that” PC-Ptlr,”
0, = 6,
-el(k,-k,l,o)+62(mt-m,,,,)+B,(u,-u,l,,),
-n, P,,
02= d,B,,
oJ=(sJ+dJ1.
(9)
Using this expression rn eqs. (7) and (IQ,
Yn=sg+sl ~~,~()-S2Q,,
(lOa)
Pr=Pn-e1(kl-kl(l,)+eZ(m,-m,(,,)+8,(U,--,((~), P”= (4 --%+S2~t&-C(%
+ w~,)u,,,o*
-4W21~,,ro+mr,to Wb)
Both price and output have ‘natural’ and ‘prediction error’ components. Once the stochastic processes for k, 122 and u are specified, eqs. (lOa) and (lob) determine the equilibrium paths of price and output. Notice that a fully anticipated increase in the money supply (an increase in m,,,J produces a pvoportional increase in the ‘natural’ or expected’ price level; it has no effect upon output. An unanticipated increase in the money supply (an increase in m, - mtlto) produces an unanticipated increase in the price level and thus an output greater than the natural rate. Similar statements can be made about aggregate demand disturbances. 2.3.
Ut2ion
contract decisions
The union is assumed to have already decided upon a s,et of real wage-employment goals for a T period horizon: these goals are represented by the set of real wage targets - dc, , a2,, , ., o+ The union tries to achieve these goals by setting nominal wages in a series of labor contracts, More frequent contracting allows more accurate predictions of the price level, for the average prediction will be based upon more recent information. But contracting is a costly activity, and more frequent contracting adds to these costs. How does a risk averse union with a quadratic utility function choose nominal =Jvagerates and contract lengths‘? ‘Taking the conditional expectation of (8) produces an expression for ,Q,, which can then be I*-ed in conjunction with (8) to derive (9).
M.B.Cunroneri,
Labor
contracts und monetary
polic_t
247
Letting C represent the disutility of recontracting, the utility of negotiating one contract for the entire T period horizon is to+T
U(T)=
-Et0
1 ~wt-pr~~)2--c, to+ 1
where I!&,( ) denotes the mathematical expectation operator conditional upon information available at the end of period t,. If II consecutive contracts are negotiated, each of length T/n, then l
W( T/u) = -
nEto
y
(w, -p,
-zt)2
-nC.
to+ 1
The union chooses the contract length and the nominal wage rates that maximize utility. As is well known, the quadratic terms above can be split into mean and variance components,
&)w,
-
Pf -Tr)2=E,,[(w,
= bt
-Ptpo
-p,,fo-q)-
(Pr-Pt,r,,)12
-x,)2 +&)wt-Pf,t,)2*
Since Et,(pt-p,,t,)2 is not influenced by the choice of nominal wage rates, the optimal wage strategy is to set the mean squared term equal to zero, no matter what the contract length; wages should be set by the ‘certainty equivalent’ rule (3) suggested in section 2.1. This is, of course, the same wage strategy a risk neutral union would use; risk aversion influences contract lbngth, but not the wage strategy.
Using the optimal wage strategy, utility will be to+1
ii(l)= - u-/q)
1 (p,-l),,J2 - VW. 1()+ 1
if T,‘l contracts of length I are negotiated sequentially. The optimal contract length is determined by calculating the marginal utility of increasing the contract length. Letting t, equal 0 for notational simplicity,
248
0(2)-O(l)=
- V/2)&i
h4-Pr,d2
-(T/2)C+TE,(P,-P,,“)2
1
+TC =(T/2)~C-[E,(p,-P2,~)‘-E!,(P~-P1,0)tl)~ i’(3)-t?(2)=(T/6){C-[fi,(p~-p~,~)~-&(P1
-P,,d21
*
-[E,(p,-P,,,)2-E,(P2-P2,~)21~~
o(T)-
t(T;:2)=C-E,
y [’ 1
(pl+Tz,-pt+~
2,d2-(lit-P,,o)2
1 .
Going from one- to two-period contracts saves the (cltility) cost of recontracting every even period, but it also increases the prediction errors in the even periods. Similarly, going from two- to three-period contracts saves one cost of re-contracting in each six year group, but it also increases prediction errors. As the union increases contract length, it saves recontracting costs. but it increases prediction errors. The marginal utility calculations show that the prediction error component increases faster than the cost savings component as the length is increased. The marginal utilities decrease as contract length is increased; the optimal length is, of course, the longest length for which the marginal utility is positive. If U(T)- U( T/2) is positive, then there will be only one contract for that whole time horizon. It is important to realize that the optimal contract Pengch depends upon monetary policy. fc;r _.
3. ‘Examples
The model outlined in section 2 is quite general in the sense that capital formation, monetary policy and the struckre of the aggregate demand disturbance were left unspecified. It provides a general structure within which to study causes of business cycles and stabilization policy. Estrrnplv I.
Passive monetary policy, exogenous capital formation, serially correlated demand disturbances. Suppose aggregate demand disturbances ace generated by the first-order autoregressive process
u,=PU,-
1
+e,,
OQ
where Y, is a serially uncorrelated random variable with zero mean and variance 6:. Suppose capital grows along a non-stochastic trend path, k,, and suppose the money supply fluctuates randomly about a non-stochastic trend,’ M,, so
q
=iii,+c,.
(13)
where C, is a serially uncorrelated random variable, independent of c’,. with . mean zero and variance a:. Given (11). (12) and (13). the price prediction error in period t a:an be calculated from eq. (9).* b
The marginal utilities derived in the last section may be used to determine the length of labor contracts,
if2
C(T)-Q-l-- Z)=C-cry$
1 (p2i+...+p2’i
- “+ I’).
The length of the labor contract depends upon the sizes of p and a: relative to C, the utility cost of recontracting. If p = 0, then o(T) - o( T,2) r 0 and there is only one contract for the entire 7’ period horizon. If aggregate demand disturbances are not serially correlated, then h;lvine more recent information does not help in predicting future prices: the Lbor contract should be made as long as possible to avoid the costs of recontracting. If 0: und /) #re large, demand disturbances are both large and predictable. and it is worth the extra costs to negotiate a series of contracts. If (rf and 11are large “Thr: randomness in monetary policy IS due to the fact that the FED sets the lekcl of reserges in the banking system rather than the actual money supply: differential reserve requirements and bank‘s fluctuating demand for excess reserves imply an inherent randomness in monetary policy, the magnitude of which can Se measured by the variance of the money supply. cf. The FED may be able to control this randomness to some extent through its regulation of the banking system. ‘Again. f,,. the time the existing labor contract was negotiated. has been set equal to zero for notational convenience.
M.B. Canzoneri, Labor contracts and monetary policy
250
enough, o(2) - o( 1) will be negative and unions will recontract every period. In this example the parameters of monetary policy do not enter the marginal utility calculations: the FED can change @ and a: without changing the length of labor contracts. This will not be true for countercyclical policies. If unions negotiate new contracts each period, then their price prediction errors will be serially uncorrelated random variables, and price, employment and output will fluctuate randomly, in a serially uncorrelated manner, about their ‘natural’ components. Output, for example, will be
This is, of course, not consistent with the observed cyclica’i, behavior of employment and output. However, the notion of unions recontracting each period is equally inconsistent with observed behavior: The typical union contract covers a three year period, while the Federal Open Market Committee meets monthly. Thus it appears that unions have found it too expensive to recontract each period. If unions negotiate longer contracts, then [from eq. (lo)] in the tth period after the contract is negotiated,
F” =so+s*kr-S#,,
Pt=Pn+82&t+e,(e,-tpe,_, p, =
+...+y'-'e,),
(&_I -. so+ s&/d2 - [(St -d,)/d,]k,+~~+(lld,)y'u,.
Unions are losing useful (but too costly) information when they do not make period by period price predictions. Their prediction errors are serially correlated, and price and output fluctuate about their natural components in a serially correlated manner. The model produces business cycles. Asymptotic variances measure the amplitude of the cycling,
Yrhe amplitude of the cycles increases as time progresses and the unions price 1iredictions become less accurate. So how does monetary policy - the choice of m, and at - affect price, output and employment in this example? Since monetary policy does not itrfluence capital formation, it has no control over the trend paths or ‘natural r;ates’ of employment and output. In fact, the systematic P* planned part of
M. B. Cantoneri, Labor contracts and ntonutar~*polic!+
251
monetary policy, PH$,has no effect on output at all; systematic increases in the money supply are reflected in proportionately higher ‘natural’ components of the price level. The random element in monetary policy simply adds instability to the economy. A decrease in a:, assuming that this is possible, diminishes the amplitude of the price, output :nd employment cycles. Exogenous capital formation, countercyclical serially correlated demand disturbances. 2.
Exm1pk?
monetary policy,
Let the processes generating capital and aggregate demand disturbances be the same as in the first example, but add a counter-cyclical element to the monetary policy rule,” 111,=
m,- hu, -
1
(14)
,
where hu,_ 1 is a feedback term that enables the FED to offset expected demand disturbances in eq. (4).9 The expected disturbance is pu, _ l, so h should be set at p/d, if the FED wants to try to wholly offset the disturbance. A more conservative policy would set h somewhere between zero and p/dz. The price prediction error in this example is -
-d2U3hiu,
Pr-Pqo=
_ -u,_ 1
l
,o)+U3(ut-~r,0)
=0,~~,+I),(p-4i,h)(e,_,+pe,_,+...+p'-~e,),
and the marginal utilities that determine the length of labor contracts are
ir(z)-o(l)=
(T/2)[C-a,ZUS(p-d21t)'],
ir(3)-ri(2)=(T,'d)[C-a,ZUS(p-d,h)2(1+2p2)1.
7.2 ir(TP-O1’TiZ)=C-af05(r)-d?h)2
c
@2”-
‘)+,,,+p2”-2’+7+
1
If h is set equal to zero, then these marginal utilities are, of course, identical to those in the first example. As 12 is increased to p/d, more and more of the “The stochastic . term representing inherent randomness in the money supply has been omitted for simplicity. It would play the same role in this example that It played in the first. ‘The feedback rule does not involve unobserved variables, for il,
, =?‘,
,
-d,--d,k,_,
-lL~??l,
1
-p,
,I.
252
expected demand disturbances are offset by monetary policy; price prediction errors become smaller and contract lengths become longer. t periods after a contract is negotiated, price and output are
lf labor contracts cover more than one period, then price and output cycle about their ‘natural’ paths. If there is no counter-cyclical policy (CB =O), price and output behave in much the same way as in the first example. The introduction of a countercyclical policy (0 < II 5 p/d, ) decreases the coefficients in front of the lagged terms. making the amplitude of the cycles smaller. The variances
2 G2 yt =s20pt
2
illustrate the dampening effects of the counter-cyclical policy. Since prices will be more predictable, unions will make contracts longer and so the cycling will become more inertia ridden, but dampened. If the FED were able to completely offset expectec’ demand disturbances (II= pi& ). output would simply fluctuate about its ‘natural’ rate in a serially uncorrelated manner, price prediction errors would be serially uncorrelated, and contracts would be as long as possible. Endogenous
capital formation, serially uncorrelated
demand
disturbances. In this examl:Je, monetary policy will be assumed to have some effect upon capital formation. Let ’
k,=R,+m,_
00,
1,
(15)
where R, is again a non-stochastic trend term. Last period’s money supply is a proxy ror the credit conditions that helped to determine this period’s capital stock. For simplicity, the aggregate demand disturbance is assumd to be serially uncorrelated or p =0 in (11); the implications of a serially correlated demand disturbance were discussed in detail in the first two examples. Monetary policy is assumed to take the form ill, =q
+hm,_,
+&,.
(16)
253
The randomness in the money supply is re-introduced because it will be seen to play a new role in tGs example. Since the current capital stock depends upon last period’s money supply, price and output depend upon both current and past values of the money supply. This causes a cycling in price and output. The money feedback term, It 111, _ t, can be used to offset this new instability. Since in this example
111,-ll~,(()=h(nt,_,
111,_
1 -
‘4 -
1 IO
=c,_1
-!rn,_
I(o)+‘:,.
+Itr:,_,+...+I?‘-)Ei.
the price prediction error is [again, from (9)]
(‘bnsider first the case in which the money feedback term is not used. With It =Q the price prediction error is
The marginal utilities could crgain be calculated to determine the length of labor contracts. but the experience of the last two examples suggests what the rt’sults would be. Since the price prediction error is serially correlated, shorter contracts lead to better price predictions. Monetary policy does not influence the length of contracts except through control over the random element in the money supply; a smaller a: causes longer labor contracts. If the contracts cover more than one period, output and the price level will fluctuate in a serially correlated manner about their ‘natural’ components. The only effect monetary policy has upon this instability is through c:; a lower a,.?leads to smaller fluctuations. While monetary policy does not play a powerful stabilization role (with h ==Q),it can play an important growth role, since
By controlling capital formation, monetary policy (here, the choice of affect the ‘natural’ rates of employment and output.
rfi,) can
254
M.B. C’mzoncri, Labor contracts
and monetctlry policy
If the money feedback term is used, then monetary policy plays a strong stabilization role as well. If h is set equal to 9,c/O, the price prediction error reduces to &E, + &e,; the entire lagged effect is offset. In this case, labor contracts will be as long as possible, and the cycling of price, employment and output about their ‘natural’ paths will be dampened. The variance of output, for example, will fall from &6: +O:c2)c$ + O$& when h=Q, to s;e$0,2+eg0:, when h=elc/e2. 4. Conclusion This paper presents a policy evaluation model that focuses upon the relationship between monetary policy and contracting in labor markets. Risk averse labor unions are assumed to impose labor contracts on competitive firms. These unions are assumed to have quadratic utility functions. Quadratic utility functions lead to ‘certainty equivalent’ wage setting rules and a mathematically tractable model: The time paths of price, output and employment can be expressed in terms of means and deviations from means of the stochastic processes for capital formation, monetary policy and exogenous disturbances. Cyclical characteristics turn out to depend upon the lengths of labor contracts, and these lengths depend on the risk aversion of unions and monetary policy. Examples were provided in which business cycles are caused by the existence of long-term contracts (in conjunction with serially correlated disturbances) or by monetary policy itself. In either case, monetary policy is able to offset sonz: of the instability through the use of feedback control. Generally speaking, if monetary policy takes instability out of the economy, contract lengths become longer (for the benefits of more frequent contracting no longer outweigh the costs) and cyclical components of price, output and employment will have longer lags. The net result of a more ambitious counter-cyclical policy is a more inertia ridden cyclical structure with a dampened amplitude. Thus monetary policy has a stabilization role in a model tha.t incorporates both ‘rational’ expectations and the ‘natural rate’ hypothesis. Monetary policy also plays a growth r( ’ if it affects capital formation. While the model does appear to capture many stylized features of actual labor markets, there are a number of aspects that lack a sound theoretical foundation. For example, the contracting procedure itself is not described in any detail. Why does the labor contract take this particular form with period by period profit maximization and no indexing? Why do not various types of contingent contracts appear when the economy becomes more unstable? Until these microeconomic aspects can be dealt with in a satisfactory manner, one must view both positive and normative implications of models such as the one outlined above with a certain amount of skepticism.
References Aoki, M. and M. Canzoneri, 1979, Reduced forms of rational expectations models, Quarterly Journal of Economics, forthcoming. Azariadis, C.. 1975, Implicit contracts and underemployment equilibria, Journal of Political Economics, Dec.
Bailey, M.,1974, Wages and employment under uncertain demand, Review of Economic Studies, Jan. Barre, R., 1977, Long-term contracting, sticky prices, and monetary policya Journal of Monetary Economics 3. Canzoneri, M., 1978, The role of monetary and fiscal policy in the new neoclassical models, Southern Economic Journal, Jan. Fischer, S., 1977a. Long term contracts, rational expectations and the optimal money supply rule, Journal of Political Economics, Feb. Fischer, S., 1977b, Long-term contracting, sticky prices and monetary policy: A comment, Journal of Monetary Economics 3. Gray, J., 197BfOn indexation and contract length. Journal of Political Economics, Feb. Sargent, T. and N. Wallace, 1975, Rational expectations, the optimal monetary instrument, and the optimal money supply rule, Journal of Political Economics. April. Taylor. J.. 1977. Conditions for unique solutions in stochastic macroeconomic models with rational expectations. Econometrica. Sept.
LABOR CONTRACTS
Publishing Company
AND MONETARY
POLICY*
Matthew B. CANZONERI University qf lllinois. Urhmu. IL 61801, USA Fischer and others have shown that the very existence of long-term contracts can imply a role for monetary policy in models that incorporate the natural rate hypothesis and rational expectation formation. The present paper examines some of the factors that determine the length of labor contracts and how they are affected by monetary policy. It is argued that a successful stabilization policy might be expected to increase the length of contracts. The net
stabilization
effect of the imposition of such a policy would therefore be to dampen the amplitude of business cycles. but to make them more inertia ridden.
1. Introduction This paper is concerned with the interaction between monetary policy and contracting in labor markets. Recently, Fischer (1977a). Aoki and Canzoneri (1979), and others have shown that the existence of long-term labor contracts can imply a stabilization role for monetary policy in models that incorporate both the ‘natural rate’ hypothesis and the ‘rational expectations’ hypothesis. However. these analyses are incomplete, for they do not explain how the lengths of labor contracts are determined. The lengths of labor contracts affect the cyclical behavior of employment and output. If a change in monetary policy prompts a change in the lengths of contracts, then this reaction should be embodied in a policy evaluation model. Here an attempt will be made to close the model. Briefly, risk averse unions will be assumed to impose wage contracts on profit maximizing firms. In these contracts, unions specify nominal wage rates and the contract’s length. Then firms employ the amount of labor that maximizes profits, period by period. In setting the nominal wage rates, unions form ‘rational’ predictions of future prices and try to hit predetermined real wage tarsets: these targets represent preferred points on real wage -employment trade-offs offered by the firms. In choosing contract lengths, unions weigh the benefit of more accurate price predictions against the cost of more frequent *1 would like to thank an arionymous referee for a number of helpfc suggestions. After this paper was written, an interesting paper by Jo Anna Gray \cas hrou$t to my attention. In it. she addresses the same basic problem that I discuss here; however. her setting and fc~us both differ from what is presented here.
242
M.B. Cammeri,
Labor contracts and monetary policy
contracting. This choice will be seen to depend upon the extent to which monetary policy is offsetting instability in the price level. Generally, monetary policy will be seen to be more potent than the analysis of Sargent and Wallace (1975) would seem to indicate, but more complicated than the ‘fixed wage’ version of the Keynesian model would seem to indicate.’ It should be noted at the outset that in this paper the form of labor contracts and the employment policy of firms are taken as given. Should a change in monetary policy induce, say, the use of indexing, or the agreement upon some scheme whereby unions trade expected wages for employment security, then the present analysis would also be incomplete.2 So what follows must be viewed as an initial (or at least provisional) attempt at closing the model. 2. The model The model will be presented in three stages. In section 2.1, the basic structure of the model will be outlined. Initially, it will be assumed that the length of labor contracts is fixed and that unions set wages in these contracts according to a simple ‘certainty equivalence’ rule. Under these assumptions, equilibrium conditions for employment, output and the price level will be derived. The equilibrium conditions will contain expectation terms since the unions’ wage setting rule involves predictions of future price levels. Expectation formation will be assumed to be ‘rational’, and in section 2.2, the equilibrium conditions will be solved for reduced forms describing the paths of price and output. These reduced forms are, of course, predicated upon the assumed wage setting rule, and the cyclical characteristics of price and output will be seen to depend upon the length of labor contracts. In section 2.3, the unions’ contracting behavior will be discussed in more detail. The ‘certainty equivalent’ wage setting rule (which makes the solution of the model in section 2.2 mathematically tractable) can be justified for risk averse unions if the unions are assumed to have quadratic utility functions. The ‘In particular, standard control algorithms do not appear to be very useful for this type of model. See Aoki and Canzoneri (1979), especially their ‘Case 2: p > 1‘. 2The basic scenario in this paper has come under attack recently, The ‘implicit contract’ theory of Bailey (1974) and Azariadis (1975) suggests that :*isk averse laborers would be willing to trade expected wages for employment security. If so, the equilibrium labor contract would probably not specify an employment rule that is consistent with period by period profit maximtzation. Barro (1977) has also characterized the profit maximizatron rule as pareto inferior. [Fischer’s (1977b) reply to Barro is relevant in the present context.) However. the basic scenario outlined above does seem to be consistent with certain stylized facts about actual labor markets. These markets are characterized by long-term contracts (one to three years in length) and (in the U.S. anyway) a minimal amount of indexing. It would, of course, be preferable to allow the form of the contract (including the employment rule and the possibility of indexing) to be endogenous, and perhaps varying with changes in government policy. This ambitious task is beyond the scope of the present paper.
unions’ risk aversion will be seen to manifest itself in the determination of contract length. In this section, the stochastic processes describing monetary policy, capital formation and aggregate demand disturbances will be left unspecified. The equilibrium paths of price and output will, of course, depend upon the actual specification of these processes. Section 3 provides examples of how the model operates under various specifications.
2.1. The structure of’the model
The supply side of the economy consists of competitive firms and wage setting unions. Unions quote nominal wage rates for a specified length of time in a labor contract. Firms are free to hire any amount of labor they choose at the given wage rates; they are assumed to maximize profits period by period. The typical firm is assumed to have a log-linear production function, (1) where y, is the log of output produced in period t, II, is the log of labor employed in period t. and k, is the log of the capital stock at the beginning of period t. The firm takes prices from the market and wages from the labor contract and hires labor up to the point where the cost of the marginal unit of labor just offsets its product, so
where W,is the log of the nominal wage rate and p, is the log of price. The typical union imposes a labor contract that reflects a compromise between real wage and employment goals. Eq. (2) represents a wageemployment trade-aff for the union. It is assumed that the union has decided upon a set of real wage targets -.-- 2,. . . ., a+--- that represent its wageemployment preferences for a T period horizon. Since the union specifies nominal wages in the labor contract, it must predict future price levels and set nominal wage rates accordingly. The union also specifies the length of the contract. Suppose the length of the contract is T periods; that is, only one contract is negotiated for the T period horizon. As time progresses, actual real wages are likely to deviate more and more from their target values, for predictions of more distant price levels are less accurate. On the other hand, the T period horizon could be broken into two contract periods of length T,i2. Better predictions of the last T/2 price levels can be made half way through the T period horizon, so this JhlunE
I)
244
procedure would produce real wage rates that deviate less on average from their target values. Similarly, the T period horizon could be divided into three, [our or T separate contract periods. However, more frequent contracting is a costly endeavor; resources must be committed to reestimating futt”tre price levels and re-negotiating new contracts. Generally, there will be an optimal number of contracts for the T period horizon and there will be an optimal way of using the price predictions to specify nominal wage rates in the ccjntract. Initially. it ~91 be assumed that the length of the contracts is fixed and that wages are set according to the ‘certainty equivalent’ rule (3) where pp is the price predicted by the union at the time the contract is negotiated. The rest of the economy is represented by a single equation explaining aggregate demand for output, y, =
d, + d k, + d, (y - pt ) + 1
$3
d, >O,
d,>O,
(4)
where 111,is the log of the money supply at the beginning of period t and II, is a random demand disturbance. Eq. (4) may be viewed as the reduced form for income from an IS-LM’ mode1.3 The capital term represents both wealth effects in consumption and the autoregressive part of investment. The disturbance term -epresents disturbances in consumption, investment, fiscal policy and financiar’ markets. It is assumed that the time paths of k, III and t4 are determined by some as yet unspecified stochastic processes. It is quite possible that the time paths of k and 111are coupled with each other and depend upon the time paths of .Y or p. A countercyclical monetary ,policy may, for example, depend upon past values of J and p. Eqs. (I ), (2), (3) and (4) and the stochastic processes for k, 111and II determine the time paths of J, p, II, and NVonce expectation formation is specified. It will be assumed that expectation formation is ‘rational’: If the labor contract is negotiated at the end of period t,, then
3The reduced form of an WLM model should include the expected rate of inflation. Adding the term prlr- 1-p,_ 1 to eq. (4) would not complicate matters much, and it should not change the qualitative results reported in section 3, see, for example, Canzoneri (1978). However, modeling expected i;lflation bs p, + , ,, _ I - I),,~_ 1 as is more usual would produce some familiar non-uniqueness problems, see, for example, Taylor (1977). For simplicity, expected inflation has been left out of eq. (e).
Unions’ price predictions are identical to the model’s mathematical expectation. conditional upon all of the information available at the time the contract is negotiated. This implies. of course, that unions know the stochastic process governing monetary policy. The supply side - eqs. (1). (2), (3) and (5) --- may be solved for a supply function. .1’,=s,j +s, k, - yg, +gp,
-?,,,,,I
s,
>o,
s,>O,
(6)
where the si are functions of the /ii. The supply function can be separated into t&o components,s Jr =!‘JX,*
y&,.
k,,,J+s* (k, - h(,(,)+ s2 (P,-
Prp,, 19
k,,,,,)=*Q + s, k,,,,)-.s’Z,.
(7)
The first component is the output that is supplied if there are no prediction errors: j-n will be called the ‘natural’ rate of output. The second component shows how prediction errors result in deviations from the ‘natural’ rate. If unions predict the price level and the capital stock accurately. then the wage rate they specify in the labor contract produces the desired real wage employment combination: ‘natural’ rates of employment and output result. If. however, the price level is higher than predicted, the wage will be too low; the real wage will be lower than desired and employment and output will be higher than their ‘natural’ rates.
The supply and demand functions can be solved for the equilibrium paths of price and output in terms of the stochastic processes for k, 111and II. Using (4) to eliminate output in (6). I), =
( 1 112 ,[d,, - s,, +
- (s2iti, Hp,-
sg , - (s
I), I,,, )*
1
-
ill )k, + II,] + 111, (8)
All that remains is to relate the price prediction error to the stochastic processes for k. 111and 11. Since these stochastic proctsses are the only ‘This supply function bears a formal mathematical resembIcnce to the supply function used by Sargent and Wallace (1975). it incorporates the ‘natural rate’ hypothesis: Perfectly anticipated price changes have no effect upon employment or output. However. the model does not specify a competitive labor supply with a search theory of unemployment or with hous~~holds basing work leisure decisions on expectations of future prices and wages. features often i&ntified with the ‘natural rate’ hypothesis. Instead it is more closely related to the ‘fixed wage’ acrsio:l of tllc Keynesian model.
M.B
246
Cumzoneri,
Labor
contracts
and monetas”
policy
random elements inI the model, it should not be surprising that the price prediction error can be explained in terms of the prediction errors for k, m and u. It can be shown that” PC-Ptlr,”
0, = 6,
-el(k,-k,l,o)+62(mt-m,,,,)+B,(u,-u,l,,),
-n, P,,
02= d,B,,
oJ=(sJ+dJ1.
(9)
Using this expression rn eqs. (7) and (IQ,
Yn=sg+sl ~~,~()-S2Q,,
(lOa)
Pr=Pn-e1(kl-kl(l,)+eZ(m,-m,(,,)+8,(U,--,((~), P”= (4 --%+S2~t&-C(%
+ w~,)u,,,o*
-4W21~,,ro+mr,to Wb)
Both price and output have ‘natural’ and ‘prediction error’ components. Once the stochastic processes for k, 122 and u are specified, eqs. (lOa) and (lob) determine the equilibrium paths of price and output. Notice that a fully anticipated increase in the money supply (an increase in m,,,J produces a pvoportional increase in the ‘natural’ or expected’ price level; it has no effect upon output. An unanticipated increase in the money supply (an increase in m, - mtlto) produces an unanticipated increase in the price level and thus an output greater than the natural rate. Similar statements can be made about aggregate demand disturbances. 2.3.
Ut2ion
contract decisions
The union is assumed to have already decided upon a s,et of real wage-employment goals for a T period horizon: these goals are represented by the set of real wage targets - dc, , a2,, , ., o+ The union tries to achieve these goals by setting nominal wages in a series of labor contracts, More frequent contracting allows more accurate predictions of the price level, for the average prediction will be based upon more recent information. But contracting is a costly activity, and more frequent contracting adds to these costs. How does a risk averse union with a quadratic utility function choose nominal =Jvagerates and contract lengths‘? ‘Taking the conditional expectation of (8) produces an expression for ,Q,, which can then be I*-ed in conjunction with (8) to derive (9).
M.B.Cunroneri,
Labor
contracts und monetary
polic_t
247
Letting C represent the disutility of recontracting, the utility of negotiating one contract for the entire T period horizon is to+T
U(T)=
-Et0
1 ~wt-pr~~)2--c, to+ 1
where I!&,( ) denotes the mathematical expectation operator conditional upon information available at the end of period t,. If II consecutive contracts are negotiated, each of length T/n, then l
W( T/u) = -
nEto
y
(w, -p,
-zt)2
-nC.
to+ 1
The union chooses the contract length and the nominal wage rates that maximize utility. As is well known, the quadratic terms above can be split into mean and variance components,
&)w,
-
Pf -Tr)2=E,,[(w,
= bt
-Ptpo
-p,,fo-q)-
(Pr-Pt,r,,)12
-x,)2 +&)wt-Pf,t,)2*
Since Et,(pt-p,,t,)2 is not influenced by the choice of nominal wage rates, the optimal wage strategy is to set the mean squared term equal to zero, no matter what the contract length; wages should be set by the ‘certainty equivalent’ rule (3) suggested in section 2.1. This is, of course, the same wage strategy a risk neutral union would use; risk aversion influences contract lbngth, but not the wage strategy.
Using the optimal wage strategy, utility will be to+1
ii(l)= - u-/q)
1 (p,-l),,J2 - VW. 1()+ 1
if T,‘l contracts of length I are negotiated sequentially. The optimal contract length is determined by calculating the marginal utility of increasing the contract length. Letting t, equal 0 for notational simplicity,
248
0(2)-O(l)=
- V/2)&i
h4-Pr,d2
-(T/2)C+TE,(P,-P,,“)2
1
+TC =(T/2)~C-[E,(p,-P2,~)‘-E!,(P~-P1,0)tl)~ i’(3)-t?(2)=(T/6){C-[fi,(p~-p~,~)~-&(P1
-P,,d21
*
-[E,(p,-P,,,)2-E,(P2-P2,~)21~~
o(T)-
t(T;:2)=C-E,
y [’ 1
(pl+Tz,-pt+~
2,d2-(lit-P,,o)2
1 .
Going from one- to two-period contracts saves the (cltility) cost of recontracting every even period, but it also increases the prediction errors in the even periods. Similarly, going from two- to three-period contracts saves one cost of re-contracting in each six year group, but it also increases prediction errors. As the union increases contract length, it saves recontracting costs. but it increases prediction errors. The marginal utility calculations show that the prediction error component increases faster than the cost savings component as the length is increased. The marginal utilities decrease as contract length is increased; the optimal length is, of course, the longest length for which the marginal utility is positive. If U(T)- U( T/2) is positive, then there will be only one contract for that whole time horizon. It is important to realize that the optimal contract Pengch depends upon monetary policy. fc;r _.
3. ‘Examples
The model outlined in section 2 is quite general in the sense that capital formation, monetary policy and the struckre of the aggregate demand disturbance were left unspecified. It provides a general structure within which to study causes of business cycles and stabilization policy. Estrrnplv I.
Passive monetary policy, exogenous capital formation, serially correlated demand disturbances. Suppose aggregate demand disturbances ace generated by the first-order autoregressive process
u,=PU,-
1
+e,,
OQ
where Y, is a serially uncorrelated random variable with zero mean and variance 6:. Suppose capital grows along a non-stochastic trend path, k,, and suppose the money supply fluctuates randomly about a non-stochastic trend,’ M,, so
q
=iii,+c,.
(13)
where C, is a serially uncorrelated random variable, independent of c’,. with . mean zero and variance a:. Given (11). (12) and (13). the price prediction error in period t a:an be calculated from eq. (9).* b
The marginal utilities derived in the last section may be used to determine the length of labor contracts,
if2
C(T)-Q-l-- Z)=C-cry$
1 (p2i+...+p2’i
- “+ I’).
The length of the labor contract depends upon the sizes of p and a: relative to C, the utility cost of recontracting. If p = 0, then o(T) - o( T,2) r 0 and there is only one contract for the entire 7’ period horizon. If aggregate demand disturbances are not serially correlated, then h;lvine more recent information does not help in predicting future prices: the Lbor contract should be made as long as possible to avoid the costs of recontracting. If 0: und /) #re large, demand disturbances are both large and predictable. and it is worth the extra costs to negotiate a series of contracts. If (rf and 11are large “Thr: randomness in monetary policy IS due to the fact that the FED sets the lekcl of reserges in the banking system rather than the actual money supply: differential reserve requirements and bank‘s fluctuating demand for excess reserves imply an inherent randomness in monetary policy, the magnitude of which can Se measured by the variance of the money supply. cf. The FED may be able to control this randomness to some extent through its regulation of the banking system. ‘Again. f,,. the time the existing labor contract was negotiated. has been set equal to zero for notational convenience.
M.B. Canzoneri, Labor contracts and monetary policy
250
enough, o(2) - o( 1) will be negative and unions will recontract every period. In this example the parameters of monetary policy do not enter the marginal utility calculations: the FED can change @ and a: without changing the length of labor contracts. This will not be true for countercyclical policies. If unions negotiate new contracts each period, then their price prediction errors will be serially uncorrelated random variables, and price, employment and output will fluctuate randomly, in a serially uncorrelated manner, about their ‘natural’ components. Output, for example, will be
This is, of course, not consistent with the observed cyclica’i, behavior of employment and output. However, the notion of unions recontracting each period is equally inconsistent with observed behavior: The typical union contract covers a three year period, while the Federal Open Market Committee meets monthly. Thus it appears that unions have found it too expensive to recontract each period. If unions negotiate longer contracts, then [from eq. (lo)] in the tth period after the contract is negotiated,
F” =so+s*kr-S#,,
Pt=Pn+82&t+e,(e,-tpe,_, p, =
+...+y'-'e,),
(&_I -. so+ s&/d2 - [(St -d,)/d,]k,+~~+(lld,)y'u,.
Unions are losing useful (but too costly) information when they do not make period by period price predictions. Their prediction errors are serially correlated, and price and output fluctuate about their natural components in a serially correlated manner. The model produces business cycles. Asymptotic variances measure the amplitude of the cycling,
Yrhe amplitude of the cycles increases as time progresses and the unions price 1iredictions become less accurate. So how does monetary policy - the choice of m, and at - affect price, output and employment in this example? Since monetary policy does not itrfluence capital formation, it has no control over the trend paths or ‘natural r;ates’ of employment and output. In fact, the systematic P* planned part of
M. B. Cantoneri, Labor contracts and ntonutar~*polic!+
251
monetary policy, PH$,has no effect on output at all; systematic increases in the money supply are reflected in proportionately higher ‘natural’ components of the price level. The random element in monetary policy simply adds instability to the economy. A decrease in a:, assuming that this is possible, diminishes the amplitude of the price, output :nd employment cycles. Exogenous capital formation, countercyclical serially correlated demand disturbances. 2.
Exm1pk?
monetary policy,
Let the processes generating capital and aggregate demand disturbances be the same as in the first example, but add a counter-cyclical element to the monetary policy rule,” 111,=
m,- hu, -
1
(14)
,
where hu,_ 1 is a feedback term that enables the FED to offset expected demand disturbances in eq. (4).9 The expected disturbance is pu, _ l, so h should be set at p/d, if the FED wants to try to wholly offset the disturbance. A more conservative policy would set h somewhere between zero and p/dz. The price prediction error in this example is -
-d2U3hiu,
Pr-Pqo=
_ -u,_ 1
l
,o)+U3(ut-~r,0)
=0,~~,+I),(p-4i,h)(e,_,+pe,_,+...+p'-~e,),
and the marginal utilities that determine the length of labor contracts are
ir(z)-o(l)=
(T/2)[C-a,ZUS(p-d21t)'],
ir(3)-ri(2)=(T,'d)[C-a,ZUS(p-d,h)2(1+2p2)1.
7.2 ir(TP-O1’TiZ)=C-af05(r)-d?h)2
c
@2”-
‘)+,,,+p2”-2’+7+
1
If h is set equal to zero, then these marginal utilities are, of course, identical to those in the first example. As 12 is increased to p/d, more and more of the “The stochastic . term representing inherent randomness in the money supply has been omitted for simplicity. It would play the same role in this example that It played in the first. ‘The feedback rule does not involve unobserved variables, for il,
, =?‘,
,
-d,--d,k,_,
-lL~??l,
1
-p,
,I.
252
expected demand disturbances are offset by monetary policy; price prediction errors become smaller and contract lengths become longer. t periods after a contract is negotiated, price and output are
lf labor contracts cover more than one period, then price and output cycle about their ‘natural’ paths. If there is no counter-cyclical policy (CB =O), price and output behave in much the same way as in the first example. The introduction of a countercyclical policy (0 < II 5 p/d, ) decreases the coefficients in front of the lagged terms. making the amplitude of the cycles smaller. The variances
2 G2 yt =s20pt
2
illustrate the dampening effects of the counter-cyclical policy. Since prices will be more predictable, unions will make contracts longer and so the cycling will become more inertia ridden, but dampened. If the FED were able to completely offset expectec’ demand disturbances (II= pi& ). output would simply fluctuate about its ‘natural’ rate in a serially uncorrelated manner, price prediction errors would be serially uncorrelated, and contracts would be as long as possible. Endogenous
capital formation, serially uncorrelated
demand
disturbances. In this examl:Je, monetary policy will be assumed to have some effect upon capital formation. Let ’
k,=R,+m,_
00,
1,
(15)
where R, is again a non-stochastic trend term. Last period’s money supply is a proxy ror the credit conditions that helped to determine this period’s capital stock. For simplicity, the aggregate demand disturbance is assumd to be serially uncorrelated or p =0 in (11); the implications of a serially correlated demand disturbance were discussed in detail in the first two examples. Monetary policy is assumed to take the form ill, =q
+hm,_,
+&,.
(16)
253
The randomness in the money supply is re-introduced because it will be seen to play a new role in tGs example. Since the current capital stock depends upon last period’s money supply, price and output depend upon both current and past values of the money supply. This causes a cycling in price and output. The money feedback term, It 111, _ t, can be used to offset this new instability. Since in this example
111,-ll~,(()=h(nt,_,
111,_
1 -
‘4 -
1 IO
=c,_1
-!rn,_
I(o)+‘:,.
+Itr:,_,+...+I?‘-)Ei.
the price prediction error is [again, from (9)]
(‘bnsider first the case in which the money feedback term is not used. With It =Q the price prediction error is
The marginal utilities could crgain be calculated to determine the length of labor contracts. but the experience of the last two examples suggests what the rt’sults would be. Since the price prediction error is serially correlated, shorter contracts lead to better price predictions. Monetary policy does not influence the length of contracts except through control over the random element in the money supply; a smaller a: causes longer labor contracts. If the contracts cover more than one period, output and the price level will fluctuate in a serially correlated manner about their ‘natural’ components. The only effect monetary policy has upon this instability is through c:; a lower a,.?leads to smaller fluctuations. While monetary policy does not play a powerful stabilization role (with h ==Q),it can play an important growth role, since
By controlling capital formation, monetary policy (here, the choice of affect the ‘natural’ rates of employment and output.
rfi,) can
254
M.B. C’mzoncri, Labor contracts
and monetctlry policy
If the money feedback term is used, then monetary policy plays a strong stabilization role as well. If h is set equal to 9,c/O, the price prediction error reduces to &E, + &e,; the entire lagged effect is offset. In this case, labor contracts will be as long as possible, and the cycling of price, employment and output about their ‘natural’ paths will be dampened. The variance of output, for example, will fall from &6: +O:c2)c$ + O$& when h=Q, to s;e$0,2+eg0:, when h=elc/e2. 4. Conclusion This paper presents a policy evaluation model that focuses upon the relationship between monetary policy and contracting in labor markets. Risk averse labor unions are assumed to impose labor contracts on competitive firms. These unions are assumed to have quadratic utility functions. Quadratic utility functions lead to ‘certainty equivalent’ wage setting rules and a mathematically tractable model: The time paths of price, output and employment can be expressed in terms of means and deviations from means of the stochastic processes for capital formation, monetary policy and exogenous disturbances. Cyclical characteristics turn out to depend upon the lengths of labor contracts, and these lengths depend on the risk aversion of unions and monetary policy. Examples were provided in which business cycles are caused by the existence of long-term contracts (in conjunction with serially correlated disturbances) or by monetary policy itself. In either case, monetary policy is able to offset sonz: of the instability through the use of feedback control. Generally speaking, if monetary policy takes instability out of the economy, contract lengths become longer (for the benefits of more frequent contracting no longer outweigh the costs) and cyclical components of price, output and employment will have longer lags. The net result of a more ambitious counter-cyclical policy is a more inertia ridden cyclical structure with a dampened amplitude. Thus monetary policy has a stabilization role in a model tha.t incorporates both ‘rational’ expectations and the ‘natural rate’ hypothesis. Monetary policy also plays a growth r( ’ if it affects capital formation. While the model does appear to capture many stylized features of actual labor markets, there are a number of aspects that lack a sound theoretical foundation. For example, the contracting procedure itself is not described in any detail. Why does the labor contract take this particular form with period by period profit maximization and no indexing? Why do not various types of contingent contracts appear when the economy becomes more unstable? Until these microeconomic aspects can be dealt with in a satisfactory manner, one must view both positive and normative implications of models such as the one outlined above with a certain amount of skepticism.
References Aoki, M. and M. Canzoneri, 1979, Reduced forms of rational expectations models, Quarterly Journal of Economics, forthcoming. Azariadis, C.. 1975, Implicit contracts and underemployment equilibria, Journal of Political Economics, Dec.
Bailey, M.,1974, Wages and employment under uncertain demand, Review of Economic Studies, Jan. Barre, R., 1977, Long-term contracting, sticky prices, and monetary policya Journal of Monetary Economics 3. Canzoneri, M., 1978, The role of monetary and fiscal policy in the new neoclassical models, Southern Economic Journal, Jan. Fischer, S., 1977a. Long term contracts, rational expectations and the optimal money supply rule, Journal of Political Economics, Feb. Fischer, S., 1977b, Long-term contracting, sticky prices and monetary policy: A comment, Journal of Monetary Economics 3. Gray, J., 197BfOn indexation and contract length. Journal of Political Economics, Feb. Sargent, T. and N. Wallace, 1975, Rational expectations, the optimal monetary instrument, and the optimal money supply rule, Journal of Political Economics. April. Taylor. J.. 1977. Conditions for unique solutions in stochastic macroeconomic models with rational expectations. Econometrica. Sept.