Ut = E

(10.63)

Note that we are implicitly assuming that the unemployed get no utility; the effects of relaxing this assumption are discussed below.

Implications

To analyze the model, begin by substituting (10.61) for I, and (10.62) for Ct into (10.63). This yields

Ut = E

0 ,.,-/3

Clstw, Nit

(10.64)

Next, define Xf = (Cf/JV/f)Wf"; Xf is the ratio of employment to the number of insiders if ff = 1. With this definition, w/ equals ~"{ }/NitfP. Thus (10.64) becomes

Uf = £[min{ffXf,l}]x-

(10.65)

Njt, 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 Xf that maximizes the objective function. The insiders therefore choose the same value of x each period. If x* denotes this optimal value, the definition of x implies that the insiders choice of Wt is

(Nnx*\

-l/jS

(10.66)

\ /

The labor-demand equation, (10.61), then implies that employment is

If = ffJV/fX*. (10.67)

Equations (10.66) and (10.67) imply that insiders adjust to changes in labor demand and to the number of insiders (that is, to changes in C° and Ni) only by adjusting the wage, and not by altering the probability of employment. Concretely, consider the effects of a low realization of f. The unexpectedly low level of labor demand causes the firm to hire relatively few workers, and so the number of insiders falls. Wlien 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

insiders. These assumptions imply that the period-t objective function is

Extensions

Forward-looking behavior by the insiders and the firm does not alter the central result of the model. The knowledge that this periods hiring affects next periods number of insiders increases the firms hiring for a given wage (so that workers set lower wages in the future), and moderates the insiders wage-setting for a given labor demand curve (to ensure that they remain insiders). But the changes in the number of insiders, given the functional forms for utUity and profits, still cause shocks to have permanent effects.

Similarly, more complicated rules for insider status lead to more interesting dynamics but do not ehminate the permanent component of employment fluctuations. Suppose, lor example, that it takes two periods of unemployment to lose ones position as an insider. Then a negative shock to labor demand does not immediately lead to a higher wage. (Indeed, if the insiders are forward-looking, it 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, which has a permanent effect on the paths of the wage and employment. Formally, the wage and employment StiU have a unit root. One imphcation of this discussion is that a faU in aggregate demand that is only moderately long-such as the one experienced by the United States in the early 1980s-may not have a permanent effect on unemployment, but an extended one- such as those experienced by many European countries in the same period-may.

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 objective function, (10.63), to include positive utility in the event of unemployment. Then it is less attractive for

one-time shock to labor demand-the low value of f-has a long-lasting effect on employment. With workers objective function and the firms profit function taking the specific functional forms we have assumed, the effect is permanent: as (10.67) 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 fs-that have permanent effects, the model impUes that employment is a random 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[t) plus an unpredictable component. If insiders determine wages only in some sectors, only employment in these sectors behaves this way. But if insiders set wages in virtually aU of the labor market, then it is aggregate employment that follows a random walk with drift. Blanchard and Summers argue that this latter prediction accords well with Europes experience in the 1980s, and that the mechanism outlined here provides a likely explanation.

the insiders to reduce the wage to increase the probabiUty of employment when the number of insiders is large and the wage is low than it is when the number of insiders is smaU. 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 these causes employment to return gradually to its initial level after a one-time demand shock. Without membership dynamics, however, employment returns immediately to its initial level. Thus making the number of insiders endogenous stiU has important implications for the dynamics of employment.

Situations where one-time disturbances permanently affect the path of the economy are said to exhibit hysteresis. In the context of unemployment, two sources of hysteresis other than the insider-outsider considerations we have been examining have received considerable attention. One is deterioration of skiUs: workers who are unemployed do not acquire additional on-the-job training, 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 work when demand recovers, particularly if the downturn is extended. The second additional source of hysteresis is through labor-force attachment. Workers who are unemployed for extended periods may adjust their standard of living to the lower level provided by income-maintenance programs; in addition, a long period of high unemployment may reduce the social stigma of extended joblessness. Because of these effects, labor supply may be permanently lower when demand returns to normal.

10.8 Search and Matching Models

The final departure of the labor market from Walrasian assumptions that we consider is the simple fact that workers and jobs are heterogeneous. In a frictionless labor market, firms are indifferent about losing their workers, since identical workers are costlessly available at the same wage; likewise, 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 Walrasian market. Rather than meeting 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, skiUs, and needs. Since this process is not instantaneous, it results in some unemployment. In addition, it may have implications for how wages and employment respond to shocks.

This section presents a model of firm and worker heterogeneity and the matching process. Because modeling heterogeneity requires abandoning