Romer D. Advanced Macroeconomics

9.7 Hysteresis 443

employment that follo~\sa random walk with drift. Blanchard and Sulmncrs argue thar this latter prediction accords well with Europe's experience in the 1980s, and that the mechanism ourlincd here provides a likely explanation.

Extensions

Forward-looking behavior by thc insiders and the firm does not alrer the central result of the model. The howledge that this period's hiring affects next period's number of insiders increases the firm's luring for a given wagc (SO that workers set lower wagcs in the future), and moderates the insiders' wage-setting for a given labor demand curve (to ensurc that they remain insiders). But changes in rhe number of insiders still cause shocks to have permanent effects.

Similarly, more complicated rules for insider status lead to more interesting dynamics but do not eliminate the permanent component of employmcnt fluctuations. Suppose, for example, that it rakes two periods of unemployment to lose one's position as an insider. 'Then a negative shock to labor demand does not imme&ately lead to a higher wage. (Indeed, if the insiders are forward-looking,ir leads to a fall in the wage as the unemployed insiders try to keep their insider status.) But a second negative shock leads to a fall in the number of insiders, whlch has a permanent effect on thc paths of the wage and employment. Formally, the wage and employment still have a unit root. One implication of this discussion is that a fall in aggregate demand that is only modcrately long-such as the one expericnced

Other plausible changes in the model, however, eliminate the strong result that one-time shocks have permanent effects on employment. Suppose, for example, we modify the insiders' objecrivc function, (9.63),to include positive utility in the event of unemployment. Then it is less attractive for the insiders to reduce the wagc to increase the probability of e m p l o p e n t when the number of insiders is large and the wage is low than it is when the number of insiders is small. Similarly, if the firm has some bargaining power or the outsiders have some weight in the insiders' objective function, the wage does not rise to fully offset reductions in the number of insiders.

Under plausible assumptions, introducing considerations like thcsc causes employment to return gradually to its initial level after a one-time demand shock. Without membership dynamics, however, cmployment returns immediately to its initial level. Thus makmg the number of insiders endogenous still has important implications for the dymamics of employmcnt.

Situations I\-here one-timc disturbances permanently affect the path of the economy are said to exhibit hy,~teresis.In the context of unemployment, two sources of hysteresis other than the insidcr-outsider considcrations we have been examining have receiled considerable attenrion. One is

444 Chapter 9 UNEMPLOYMENl

deterioration of skills: workers who are unemployed do not acquire additional on-the-jobtraining, and their existing human capital may decay or become obsolete. As a result. workers who lose their jobs when labor demand falls may have difficulty finding rvork when demand recovers, particularly if the downturn is extended. The second additional source of hysteresis is throughlabor-forceattachment. Workers who areunemployedfor extended periods may adjust their standard of living to the lower level pro\ided by income maintenance programs; in addition, a long period of hlgh unemployment may reduce the social stigma of extended joblessness. Because of these effects, labor supply may be permanently lower when demand returns to normal.

The possibility of hysteresis has received considerable attention in the conrcxr of Europe. European unemployment fluctuated around veT low levels in the 1950s and 1960s,rose fairlysteadily to more than 10percent from the mid-1970s to the mid-1980s, and has fluctuated around the 10 percent level since then. Thus there is no evidence of a stable natural rate that unemployment returns to after a shock. Loosely speaking, views of European uncmploymcnt fall into two camps. One emphasizes shlfts in the natural rate as a result of European labor-market institutions. Since most of the major features of those institutions were in place well before the rise in unemployment, this view requires that institutions' effects operate with long lags. For example, because the social stigma of unemployment changes slowly, the impact of generous unemployment benefits on the natural rate may he felt only very gradually. The other view emphasizes hysteresis. In this view, the labor-market institutions convcrtcd what would ha\^ otherwise been shortlived increases in unemployment into very long-lasting ones through union wage-setting, skill deterioration, and loss of labor-force attachment. For more on these issues, see Bean (1994);Siebert (1997);L j u n y s t and Sargent (1998);Ball (1999b);and Blanchard and Wolfers (1999).

9.8 Search and Matching Models

The final departure of the labor market from Walrasian assumptions that we consider is the simple fact that worGers and jobs are heterogeneous. In a frictionlcss labor market, firms are indifferent about losing their workers, since identical workers are cnstlessly available at the samc wage; like\$ise, workers are indifferent about losing their jobs. These implications do not appear to be accurate descriptions of actual labor markets.

When workers and jobs are highly heterogeneous, the labor market has little resemblance to a Walrasianmarket. Rather thanmeeting in centralized markets where employment and wages are determined by the intersections of supply and demand curves, workers and firms meet in a decentralized, one-on-one fashion, and engage in a costly process of trying to match up idiosyncratic preferences, slalls, and needs. Since this process is not in-

9.8 Search and Matching Models 445

stantaneous, it results in 5ome unemployment. In addition, it may have implications for how \\.ages and employment respond to shocks.

This section presents a model of firm and worker heterogeneity and the matching process. Because modeling heterogeneily requires abandoning many of our usual tools, even a basic model is relatively complicatcd. As a result, the model here onl) introduces some of the issues in~ulved . '~

The Model

The economy consists of workers and jobs. Workers canbe either employed or unemployed, and jobs can be either filled or vacant. The numbers of employed and unemployed workers are denoted E and U , and the numbers of filled and vacant jobs arc denoted F and V. Each job can have at most one worker. 'Thus F and E must be equal. The labor force is fured at i;thus E + I / = i.Throughout. we consider only stcady states.

The number of jobs is endogenous. Specifically,vacancies canhc created or eliminated freely; there is a fixed cost of C per unit timc, however, of maintaining a ,job (either filled or vacant). C can be lhought of as reflecting the cost of capital.

The model is set in continuous timc. When a worker is employed, he or she produces output at rate A per unit time and is paid a wage of w per unit timc. A is exogenous and is assumed to be greater than C; w is determined endogenously. For simplicity, costs of effort and of job search are ignored. Thus a worker's utility per unit time is w if employed and 0 if unemployed. Sirmlarly, profits per unit timc from a lob are A - w - C if it is filled and - C i f it is vacant. Workers' objective function is the expected present discounted value of their lifetime utility; firms' objective function is the expected present discounted value of lifetime profits. The bscount rate, r, is exogenous and constant.

I h c key assumptions of thc model concern how workers become employed. Positive levels of unemployment and vacancies can coexist without being immediately eliminated by hiring. Instead, unemployment and vacancies are assumed to yield a flow of new ,jobs at some rate per unit rime:

The matching function, (9.681, proxies for the complicated process of employer recruitment, worker search, and mutital evaluation. It is not assumcd to exhibit constant returns to scale. hen it exhibits increasing returns (6+ y > 11, there are thick-murket eflritx increasing the level of search makes the matching process operate rnore effectively, in the sense that it

For examples uf scarrh and matching ~ ; ' ; r ~ b ,ree Uiarnund (1982); Pissarides (1985);

446 Chapter 9 UNEMPLOYMENT

yiclds more output (matches) per unit of input (uncmploymcnt and vacancies). When the matching [unction has decreasing returns ( 6+y < 11, there are crowding effects.

In addition to the flow of new matches, there is turnover in exisling jobs. As in the Shapiro-Stiglitz model, jobs end at an exogenous rate b per unit timc. Thus the dynamics of the number of employcd workcrs are given b) E = M(U,V ) - b E . Since we are focusing on steady slates, M and E must satisfy

Let a denote the rate per unit time that unemployed workers find jobs, and a thc rate per unit time that vacant jobs are filled. a and a are given by

As in the Shapiro-Stiglitr model, we use dynamic programming to describe thc valucs of thc various states. The "remn" on being employcd is a "dividend" of w per unit time minus the probability b per unit time of a "capital loss" of VE - Vr,. Thus,

where r is the interest rate (see equation [9.30] for comparison). Similar reasoning implies

Two conditions complete the model. First, when an unemployed worker and a firm with a vacancy meet, they must choose a wage. It must be high enough that the worker wants to work in the job, and low enough that the employer wants to hire the worker. Because neither party can find a replacement instantaneously, howcvcr, thcsc requirements do not uniquely determine the wage. Instead, there is a range of wages that makes both parties better off than if they had not met. We assume that the worker and

-~ -~

2i See Problem 9.15 for the implicar~onsof alrrrnativc assumptions about how the sur~ plus is divided.

costlessly. Thus the valui. of a \ acancy must be zero.

Without the frict~on,.the model is simple. Labor supply is perfectly inelastic at i,and labor demand is pcrfcctly claitic at A C. Thus, since A - C > 0 by assumption, there is full employment at t h s wage. Shifts in labor demand-changes m 4-lead to immediate changes in rhe wagc and leave employment unchanged.

Solving the Model

We solve thc model by Cocusing on two variables, employment ( E ) and the value of a vacancy (VV).Our procedure will he to find the value of V,! implied by a given level of crnployment, and then to impose the free-entry condition rhar VL,must be 0.

We begin by considering thc determination of the wage and the value of a vacancy givcn a and cw. Subtracting (9.74)from (9.72) and rearranging llelds

Similarly, (9.73)and (9.75)imply

Since our splitting-the-surplus assumption (equation [9.76]) implies that VE- VUand V,: - V,! are equal, (9.77)and (9.78)imply

Solving this condition for w llclds

Equation (9.80)implies rhar when a and a are equal, the firm and the worker di\,ide the outpur from the job equall). When a exceeds n,workers can find new jobs more rapidly than firms can find new employccs, and so more than half of the output goes to thc worker. When n exceeds a , the reverse occurs.

Recall that we want to focus an the valuc of a vacancy. Equation (9.75) states that rVv equals C + a ( \ ) - 1, I . Expression (9.78) for VF - Vv therefore gives us

448 Chapter 9 UNEMPLOYMENT

Substituting expression (9.80)for w into this equation yields

Equation (9.82) expresses r\/,/l.In termc of C, A, r, b, a, and cw. a and n . however, are endogenous. Thus the next step is to express them in terms of E. The facts that a = M(U,V)/U (equation [9.701),that M = bE (equation 19.691),and that E + U = Limply

Similarly, we know from (9.71)that

To express n in terms of E , we therefore need to express M(U,V) and 1. in terms of E. In stcady state, M(U,V) equals bE (see [9.691). From the matching function, (9.68).this implies bE = KUPVJ',or

Substituting this expression and thc fact that M(U,V) equals b E into (9.84) gives us

Equations (9.83) and (9.86) imply that a is increasing in E and that or is decreasing. Thus (9.82) implies that rV1. is a decreasing function of E. As E approaches Z, a approaches infinity and ~u approaches 0; hence rVLr approaches -C. Similarly, as E approaches 0, a approaches 0 and n approaches infinity. Thus in'this case rV1 approaches A - C, which we have assumed to be positive. This information is summarized in Figure 9.6.

The equilibrium level of employment is determined by the intersection of the rVv locus with the free-entry condition, which implies rl.; = 0. Imposing this condition on (9.82)yields

FIGURE 9.6 The determination of equilibrium employment in the search and matching model

where the functions u(E1 and a(b)are givcn by (9.83)and (9.86).This expression implicitly defincs E, and thus compleles the solution of the model.

The Impact of a Shift in Labor Demand

We now want to ask our usual question of whether the impcrfection we arc considering-in this case, thc absence of a centrali~edmarket-affects thz cyclical behavior of the labor market. Specifically, wc are interested in whcther it causes a shift in labor demand to have a larger impact on employment and a smallcr impact on the wage than it does in a Walrasian market.

Kecall that we do not observe any long-run trcnd inunemploymenl. Thus a successful model of thc labor market should imply that in response to long-run productivity growth, there is no change in unemployment. In this modcl, it is natural to model long-run productivity growth as increases of the same proportion in the output from a job (A) and its nonlabor costs

(C). From Figure 9.6, it is not immed~atel!clear how such a change affecls the point where the rVv linc crosses the hori~onlalaxis. Instead we must examine the equilibrium condition, 19s; 8 . Inspecting t h s condition shows that if A and C change by the same proportion, the value of E for whch the condilion holds does not change. Tku>the model implies that long-run productiblty growth does not aKect tnlpIo\rnent. This means that a and a do nor change, and thus that the wag< ,::znges by the same proportion as A (see 19.801).In short, thc model's 1i.r.;-:~.m implications are reasonable.

450 Chapter 9 UNEMPLOYMENT

FIGURE 9.7 The effects of a fall in labor demand in the search and matching model

We will model a cyclical change as a shift in A with no change in C. To analyze this change, begin by considering the steady-state effects of a fall in A. From (9.82),this shifts the rVv locus down. Thus, as F i y r e 9.7 shows, employment falls. In a WaLrasianmarket,in contrast, employment is unchanged at 1.Intuitively, in the absence of a frictionless market, workers are not costlessly avadable at the prevailing wage. The decline in A, with C fixed, raises firms' costs of searching for a worker relative to the profits they oblain when they find one. Thus the number of firms-and hence employment-falls.

In addition, the matching function (9.68),together with the fact that M ( U ,V ) equals b E in steady state, implies that steady-state vacancies are ( ~ E / K ) ~ ~ Y / ( L - E )ThusP I Y .the decline inA and the resulting decrease in the number of firms reduce vacancies. The model therefore implies a negative relation between unemployment and vacancies-a Beveridge curve.

'The model docs not imply substantial wage rigidity, however. From (9.83) and (9.841, the fall in E causes a to fall and a to rise: hen unemploynent is hlgher, workers cannot find jobs as easily as before, and firms can fill positions more rapidly. From (9.801,this implies that the wage falls more than proportionately wlth A . ~ ~

The dynamics of the transition between the two steady slates are also of interest. Sincc there is no reason for firms whose positions are filled

26 Sincc rv = A C in the il'alrasian market, the same result holds there. I hus it is not clear which case exhibits greater wage adjustment. Nonetheless, simply adding heterogeneity and matching does not appear tu gt.nerare slrung wage rigidity.