Romer D. Advanced Macroeconomics
.pdf9.5 Implicit Contracts 433
ers. Firms do not hire !\orkers afresh each period. Instead, many jobs involve long-term attachnlents and considerable firm-specific skills on the part of workers. Akerlof and \lain (1981)and Hall (19821,for example, find that the average worker in the Trnited States is ia a job that will last about 10 years.
The possibility of long-termrelationships implies that the wage does not have to adjust to clear the labor market each period. Workers are content to stay in their current jobs as long as the income streams they expect to obtain are preferable to their outside opportunities; because of thcir long-term relationships with their employers, thcir current wages may be relatively unimportant to this comparison. This section and the next two explore the consequences of this observation. This section considers the case where the pool of workers dealing hlth the firm is fixed; Sections 9.6 and 9.7 investigate the effects of relaxing this assumption.
The Model
Consider a firm dealing \nth a group of workers. The firm's profits are
where L is the quantity of labor the firm employs and w is the real wage. A is a factor that shifts the profit function. It could rcflcct technology (so that a higher value means that the firm can produce more output from a given amount of labor),or economy-wideoutput (sothat a higher value means that the firm can obtain a higher relative price for a given amount of output).
Instead of considering multiple periods, il is easier to consider a single period and assume that A is random. Thus, for example, when workers decide whether to work for the firm, they consider the expected utility they obtain in the single period given the randomness in A, rather than thc average utility they obtain over many periods as their income and hours vary in response to fluctuations in A.
The distribution of A is discrete. There are K possible values of A, indexed by i; pi denotes the probability that A = Ai. Thus the firm's expected profits are
where L , and w,denote the quantity of labor and the real wage if the realization oC A is A,. The firm maximizes its expected profits; thus it is risk-neutral.
Each worker is assumed to work the sanlc amount. The represenlalive worker's utility is
434 C h a ~ t e 9r UNEMPLOYMENT
where lI(.) gives the utility from consumption and V(.) the disutility fro= working. Since U 8 ' ( . )is negative, workers are risk-averse."
Workers' consumption, C, is assumed to equal their labor income, wL." That is, workers cannot purchase insurance against en~plo)mcntand wag? fluctuations. In a more fully developed modcl, this might arise becau? workers are heterogeneous and have private information about their labor^ market prospects. In the present model, however, thc absence of outside insurance is simply assumed.
Equation (9.43)implies that the representative worker's expected utilin
is
'There is some reservation level of expected utility-, uo, rhat workers mu%- attain to be willing to work for thc firm. Thcre is no labor mobility onc? workers agrcc to a contract; thus the only constraint on the contract involte thc average level of utility it offers, not the level in any individual state.
Wage Contracts
One simple type of contract just specifics a wage and then lets the firrr choose employnent once A is determined; many actual contracts at lea" appear to take this form. Under such a contract, unemployment and r e i wage rigidity arise immediately. A fall in labor demand, for example, causes the firm to reduce employment at the fixed real wage while labor suppl; does not shift, and thus creates unemployment (or, if all workers work the same amount, underemployment). And the cost of labor does not responi because, hy assumption, the real wage is fixed.
But this is not a satisfactoryexplanationof unemployment and real w a g rigidity. The difficulty is that this type of a contract is inefficient (Leontiei 1946;Barro. 1977h;Hall, 1980). Since the wage is fixed and the firm choosei employment taking the wage as given, the marginal product of labor is i n d t pendent of A. But since employment varies with A , the marginal disutilih of working depends on A. 'Thus the marginal product of labor is general\ not cqual to the marginal disutility of work, and so it is possible to makt both parties to the contract better off. And if labor supply is not very elac-
tic, the inefficiency is large. When labor demand is low. for example, the
*
" Because the firm's owners can diversify awa) Iirm~specificrisk by holding a broai portfolio, the assumption that tht. firm ia riak~nrulralis rcasonablc for firm-specific shuchs For aggregate shucks, ~ U M C VrhrCTassumption, That the firm is less risk-averse than the nmrkers is harder to justify. Sinrr the main goal of the theory is to e x p l t n thc cffrrts o! dggrrgatc shocks, thls is a weak point of the model. One possihiiit) is rhat thc owners are wealthier than the workers and that risk aversiun is drclining in ~vcalth.
If thrrv arr 1 \\orkrrs, rhr rcprcscntativc ~ m r k e r ' hours and consumptiun arr ir fact LIT and w l / i ,and sourilitv takes the torm ~ ( c I L-) ~ ' ( L I Z l) u. vliminatc I., drfinc
( I ( ( ' ) = IJ(CIL) and V ( L )- V I L I i ) .
L
9.5 Implicit Contracts 435
marginal disutility of work is lo\\, and so the firm and the workers could both be made better off if the ~rorkersworked slightly morc.
Thus we can appeal to Iiled-wage contracts with employment dctcrmined at the firm's discretion as a potential explanation of unemploynent and real wage rigidity only if n.e can explain why a firm and its workers would agree to such an arrangement. The remainder of this section shows, however, rhat our assumptions imply that they will in fact agree to a very different contract. Section 9.6 then suggests a variation on our model that could give rise to something much'closer to this type of a contract.
Efficient Contracts
To see how it is possible to improve on a wage contract, suppose the firm offers the workers a contract specifying the wage and hours for each possible realization of A. Since actual contracts do not explicitly specify cmployment and the wage as functions of the state, such contracts are known as implicit contract^.'^
Recall rhat the firm must offer the workers at least some minimum level of expected utility, uo, but is otherwise unconstraincd. In addition, since Li and w, determine C,, we can think of the firm's choice variables as L and C in each state rather than as L and w . The Lagrangian for the firm's problem is therefore
( = I |
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(1 |
I ) |
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h |
i r ~ , ~ -( ci]~ , t) A |
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L = x p |
p i r u ( c , ) - V ( L , ) I |
- uu . |
(9.45) |
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The first-order condition for C, is |
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p , + Apiil'(C,) = 0, |
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(9.46) |
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or |
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1 |
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(9.47) |
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U ' ( C i ) = - |
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A' |
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Equation (9.47)implies that the marginal utility of consumption is constant across states, and thus that consumption is constant across states. Thus rhc risk-neutral firm fully insures the risk-averse workers.
The first-ordcr condition for L, is
p i A , F ' ( L , ) = hp,V'(L,). |
(9.48) |
Equation (9.47)implies A = l / U ' ( C ) ,where Cis sumption. Substituting this fact into (4.48) and yields
r11e curIstrtrIt level of condividing both sides by p,
\ ' ( L , ) |
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A,F'(l.i) = r.:,,Ci' |
(9.49) |
'"The rheur? or implicit contracts is due to A / a r ~ a d ~(1975);s Baily (1974); and Gordon
(1074).
436 Chapter 9 UNEMPLOYMENT
Implications
Under efficient contracts, workers' real incomes are constant. Thus thc model appears to imply strong real wage rigidity; in fact,because L is highe when A is higher, the model implies that the wagc per hour is countercycLcal. Unfortunately, however, this result does not help to account for t k puzzle that shfts in labor demand appear to result in large changes in employment. The problem is that with long-term contracts, the wagc is n: longer playng an allocative role. That is, firms do not choose employmentaking the wage as given. Rather, the level of employment as a function c! the state is specified in the contract. And, from (9.49),t h s level is the le\ t. that equates the marginal product of labor blth the marginal disutility oi additional hours of work.
As a result, the model implies that the cost to the firm of varying the amount of labor it uses changes greatly with its level of employment. S u p pose the firm wants to increase emp1o)mcnt marginally in state i. To dc this, it must raise workers' compensation to make them no worse off thx. before. Since the expected utility cost to workers of the change is piV'(L, j . C must rise by p i V ' ( L ,jIU'(C1. Thus the marginal cost to the firm of increasing employment UI a given state is proportional to C"(L,). If labor supplx is relativcly inelastic, V ' ( L i j is sharply increasing in L,, and so the cost o: labor to the firm is much highcr when employment is hlgh than when I- is low. Thus, for cxample, embedding this modcl of contracts in a mode: of price determination like that of Section 6.8 would not alter the resulthat relatively inelastic labor supply creates a strong incentive for firms rc cut priccs and increase employment in recessions, and to raise priccs ant reduce employment in booms.
In addition to failing to predict relatively acyclical labor costs, the mode: fails to predicl unemploymmt: as emphasized aboue, the implicit contracr equates the marginal product of labor and the marginal disutilily of work The modcl does, however, suggest a possible explanation for apparcnt unemployment. In the efficientcontract, workers are not free to choose the^- labor supply given the wage; instead the wage and employment are simuitancously speciried to yield optimal risk-sharing and allocarive cfficienc) When employment is louv, the margina! disutility of work is low and the hourly wage, CILi, is high. Thus workers wish that they could work more at the wage [he firm is paymg. As a rcsult, even though employment and the wage arc choscn optimally, workers appear to bc constrained in their labor supply.
9.6 Insider-Outsider Models
The analysis in Section 9.5 assumes that the firm is dealing with a fixed pool of workers. In reality, thcrc are two groups of potential workers. The first group-the insiders-are workers who havc some connection with the firm at the time of the bargaining, and whose interesls are therefore taken
9.6 Insider-Outsider Models 437
into account in the contract. The second group-the outsiders-are workers who have no initial connection uith the firm but who may be hired after the contract is set. This distinctioll may be important for both fluctuations and ~ n e m ~ 1 o ) m e n t . ~ "
Insiders and Outsiders and the Cyclical Behavior of
Labor Costs
Consider a firm and a set of insiders. The Cirm and the insiders bargain over the w-age and employmenl as functions of the state. Hours are fixed, so labor input can vary only through changes in the number of workers. The firm's profits are
rr = A F ( L I + L o ) - wlLI - w ~ L ~ , |
(9.50) |
where LI and Lo are the numbers of insiders and outsiders the firm hires, and wi and wo are their wages. As before, A is random, taking on the value A, with probability p,. The insiders have priorityin hiring; thus 1.0 can be positive only if L, equals the number of insiders. i,.
Oswald ( 1 9 9 3 )and Gottfries (1992 ) argue thar labor markets have two features that critically affect the problem facing the firm. The first is that, because of normal employment growth and turnover, most of the time the insiders are fully employed and the only hiring decision concerns how many outsiders to hire. Talung this to the extreme, here we assume that L1 always equals ii.Since the insiders are always employed, their utility depends only on their wage:
The second feature of labor markets emphasized by Oswald and Gottfries is that the wages paid to the two types of workers cannot be set independently: in practice, the higher the wage that the firm pays to its existing employes, the more it must pay to its new hires. Again adopting an extreme form for simplicity, we assume that w,, rises one-for-onewith w,:
Finally, we assume that the insiders have sufficient bargaining power and that the gap between insider and outsider wages (c) is sufficiently small thar the firm is always able to hire as many new workers at w1 - c as it wants. Thus the model applies most clearly to a firm that faces a strong union or that must pay a high wage for some other reason.
It is convenient to think of the firm's choice variables as wi and Lo in each stare. wo is determined by wi and equation (9.52);Li is h e d at &. As in the previous section, the firm must provide the insiders wlth expected
- "'Important contr~hutionsto the insider-outsider literature indud? Shakrd and Sutton (1984); solo>$^ 1 l Y X j : Grcjiory ( I 986); Llndbeck and Snower (1988);Blanrhard and Sulnmers (1985, 1987); Olixdld 8 1'193); and Gottfries (IYYZ).
438 Chapter 9 UNEMPLOYMENT
utility of at least uu. The Lagrangian for the firm's problem is thus
'The first-order condition for Lei is
Equation (9.55) implies that, just as in a conventional labor demand problem, but in sharp contrast to what happens with implicit contracts, employment is chosen to equate the marginal product of labor ~ l t the M-ageThe. reason is that outsiders, who are the workers relevant to the marginal employment decision, are not involved in the original bargaining. The insiders and the firm maximize their joint surplus. They therefore agree to hire outsiders up to the point where their marginal product equals the wage they must be paid; the outsiders' preferences are irrelevant to this calculation.
The first-order condition for wri is
This implies
Since Loi is hgher in good states, (9.57) implies that U'(wl,) is higher. Thls requires that WI, is lower-that is, that the wage is countercyclical. Intuitively, the firm and the insiders want to keep the expenses of hiring outsiders down; they therefore lower the wage in states where emplorment is high. In short, this model implies that the real wage is countercychcal and that it represents the true cost of labor to the firm.
It is easy to think of changes that wfaken these results. For example, if there are states in which some insiders are laid off, for those states the contract would equate the marginal product of labor with the opportunit). cost of insiders' time rather than with the wage. Similarly, if there is not an unlimited supply of outsiders, this would tend to make the wage increasing rather than decreasing in 4. Such changes, however, do nor entirely undo the result that insider-outsider considerations reduce the cyclical sensitivit) of the marginal cost of labor to firms.
The critical assumption of the model is that the outsiders' and insiders' wages are linked. Without this link, the firm can hire outsiders at the prevailing economy-hide wage. With inelastic labor supply, that wage is low in recessions and high in booms, and so the marginal cost of labor to the firm is highly procyclical.
9.6 Insider-Outsider Models 439
Unfortunately, the in51dt.r-outs~derlitcrature has not made a strong case that outsiders' and insiders' w g e s are linked. Gottfries argues thal such a link arises from the facts that the firm must be given some freedom to discharge insiders who are incompetent or shirlung i n d that an excessive gap between insidcrs' and outsiders' Isages would give the firm an incentive to take advantage of this freedom. Blanchard and Summers (1986)arguc that the insiders are reluctant to allo!\- the hiring of large numbers of outsiders at a low wage because they realize that, over time, such a policy M-ouldre- sult in the outsiders controlling the' bargaining process. Rut it is far from clear that tymg insiders' and outsiders' wages is the best way of dealing with these problems. If the economy-widewage is sometimes far below w, - c, bing the insiders' and outsiders' wages is \,cry costly. ?'he firms and the insiders might therefore be better off if they instead agreed to some limitation on the firm's ability lo hire outsiders, or if they charged ncw hires a fee (and let the fcc vary with the gap between w, and the economy-widewage). Thus we can conclude only thal i f a link between insiders' and outsiders' wages can be established, insider-outsider considerations havc potentially important implications.
Unemployment
If the entire labor market is characterized by insider power, grcater insider power reduces employment by raising the wage and causing Cirms to move up their labor demand curves. Thus in this case the insider-outsider distinction pro~ldesa candidate explanation of unemploylnent.
The more realistic case, however, is for there to be insider power only in part of the labor market, with the rest relatively competitive. But evenin this case, insider power can increase average unemp1o)mcnt. When some sectors offcr higher wagcs than others, workers have an incentive to try to obtain.jobs in those sectors. New entrants to the labor market arc therecore slower to accept jobs in the competitive sector, and n70rkcrswho have been laid off from the high-wage sector accept longer spells of unemplo)mcnt before they give up hope of returning to their old jobs."
T h s reasoning suggests that the contracting considerations investigated in Section 9.5 may also increase average unemploymenL. In the modcl analyzed there, the employment of the workcrs represented in thc contracts is efficient. But we ignored the issues of \\I-.ether such arrangements cover the entire economy, and of how workers rome to he represented in such arrangcmenls. If there are two sectors, one with explicit or implicit contracts and one with employment and wages large11determined competitively, and if workcrs fare better in the contract sector, then again they have an incentive to accept grcater unemplo)mcnt to increase their chances of obtaining these high-quality Jobs.
" See I'mblems 9.11 through g.13 tor esan?~;: i: rhc rffccts of wage dispersion
440 Chapter 9 UNEMPLOYMENT
There is relativclylittlc c~ldcnccconcerning how important these mcchanisms are to acLual unemployment. Summers (1986b)argues that such wail unemployment is central to the determination of average unemplo~ment. He presents evidence both across U.S. states and ovcr timc that general measures of wage dispersion and measures of wage dirrerences between "highquality" and "low-quality"jobs are strongly associated with differences in average unemployment rates. This is precisely what one would expect if workers' efforts to obtain jobs paling more than the market-clearing wage are an important sourcc of unemployment. Thus the limited etidcnce we have suggests these models may offer a promising route to understanding unemployment.
9.7 Hysteresis
One of the building blocks of the previous model is the assumption that the insidcrs arc alwal-semployed. 'This assumption is likely to fail in some situations, however. Most importantly, if the insidcrs' bargaining power is sufficiently great, they will set the wage high enough to risk some unemplo) - ment: if the insiders arc fully cmployed with certainty, there is a bencfit but not a cost to them of raising the wage further. In addition, unusually large ncgativc shocks to labor demand are likely to lead to some unemplo\ment among the insiders.
Variations in employment can give rise to dynamics in the number of insiders. Under many institutional arrangements, workers who become unemployed eventually lose a say in wage-setting; likewise, workers who are hircd cvcntually gain a role in bargaining. Thus a fall in employment caused by a decline in labor demand is likely to rcducc thc numhcr of insiders, and a rise in employment is likely to increase the number of insiders. These changes in the number of insiders then affect future wage-setting and employment.
These ideas are developed formally by Blanchard and Summers (1986).?' Blanchard and Summers focus on Europe in the 1980s, where, rhcy arguc, the conditions for these effects to be relevant were satisfied: workers had a great dcal of powcr in wage-setting, there were large negative shocks, and the rules and institutions led to some extent to the disenfranchisement from the bargaining process of workers who lost their jobs.
Assumptions
We considcr a simplified version of Blanchard and Summers's model. The wage is set unilaterally by the insidcrs, and employment is choscn by the
lL See also Gregor) (1986)
|
9.7 Hysteresis 441 |
1 |
firm. The number of insldcrs in one period is dcrcrinined by the prcvious |
!period's employment: thu5
For simplicity, both the insiders and the firm neglect the impact of their decisions on the future number of insiders; thus they miwimize their currentperiod ob,iectivefunctions each period.
The representative firm's profits are
where we assume for simplicity-that all workers are paid the same wage, regardless of whether they are insiders.13 The first-order condition for thc firm's choice of employment is
Solving (9.6O) for L yields the labor demand curve,
Shocks to labor demand arc modeled by assuming that A is random, which implies that Cis random. Specifically,C, is assumed to rakc the form
where Cf is a component of C, that is known when workers set the wagc and E , is an i.i.d. random shock that is determined after w, is set.
In setting the wage, the insiders facc a tradeoff between the expected fraction of thc membership that is employed and the wage conditional on being employed. To sce the consequences of endogenous changes in the number of insidcrs in the strongcst possible form, assume that the insiders' period-r objective function is the expected fraction of the insiders who are employed times utility conditional on being employed, and that this utility takes the form w: (0 < b < 1). Since the insiders arc assumed to be hired first and the number of insiders hired cannot exceed the number available, insidcr cmploymenr is the smaller of total employment and rhc number of insiders. Thesc assumptions imply that the period-t objective function is
Note that we arc implicitly assunung that the unemployed get no utility; thc effects of relaxing this assumption arr discussed below.
?i Assuming that insiders' and o u t c ~ d e r :::zges differ by a ronr;tant, as in Seclion 9.6. has no impurranr implications fur t h r anal, i:i
442 Chapter 9 UNEMPLOYMENT
Implications
To analyze the model, begin by substituting (9.61) for L, and (9.62) for C, into (9.63).T h s ylelds
Next, define xt = (CPINI~~W;';xt is the ratio of employment to the number of insiders if E , = I . With this definition, w/'equals Thus (9.64) becomes
N,,,the number of insiders, and C:, the expected position of labor demand, affect the objective function only multiplicatively. Thus they cannot affect the value of xt that maximizes the objective function. The insiders therefore choose the same value of x each period. If x* denotes this optimal valuc, the definition of x implies that the insiders' choice of w, is
The labor-demand equation, (9.61),then implies that employment is
Equations (9.66)and (9.67)imply that insiders adjust to changes in labor demand and to the number of insiders (thatis, to changes in Coand N I )only by adjusting the wage, and not by altering the probability of emplo~ment. Concretely, consider the effects of a low-realization of E.I'he unexpectedly low level of labor demand causes the firm to hire relatively few workers, and so the number of insiders falls. When the remaining insiders decide on the wage for the following period, they can afford to set a higher wage, since there are fewer of them for the firm to employ. Thus the one-time shock to labor demand-the low value of 6-has a long-lasting effect on employment. With workers' objective function and the firm's profit function taking the specific functional forms n-e have assumed, the effect is permanent: as (9.67) shows, the fall in employment is passed fully into reduced employment in the following period-and hence in all subsequent periods as well.
Since it is the unpredictable movements in demand-the E'S-that have permanent effects, the model implies that employment is a vundum walk with drift. That is, the change in employment equals a constant term (reflecting the fact that expected employment can be either more or less than N I , )plus an unpredictable component. If insiders determine wages only in some sectors, only employment in thcsc sectors behaves this wa)-. But if insiders set M-agesin \irtually all of the labor market, then it is aggregate