Resumé

SUMMARY: The paper offers a simple graphic illustration of a joint approach to the problem of equilibrium unemployment, encompassing an unemployment-inflation trade-off well as history dependencies, but without a long-run equilibrium. We decompose unemployment, as well as actual, into two parts, one which interacts with wage changes and one which does not. The latter responds to deviations from equilibrium by the former and also to exogenous variables. A common framework is needed in order to understand the variations of unemployment, across countries as well as across labour markets within the countries.

1. Introduction

The co-existence of two quite different explanations of involuntary unemployment - the NIRU (non inflationary rate of unemployment)¹ and the hysteresis approach makesthe between means and ends Somewhat obscure, when discussing labour market policy. This is so, although there are examples where the analysis containselements both approaches, e.g. Layard and Nickell (1987a), 1987b), Jackman, Layard and Nickell (1991), and others and most authors emphasize that explaining the history of unemployment takes more than one theory. However, these approaches still operate with a (unique) long-run NIRU and hysteresis is only considered smoothing or obstructing the adjustment process towards the long-run equilibrium. Whereas, the presentnote a (simple graphic) illustration of a joint NIRU and hysteresis approach to the problem of equilibrium unemployment, which does not involve a long-run equilibriumin traditional way. Rather, we model a whole range of levels where, for a givenhistory, unemployment can remain. In this approach equilibrium unemployment, as well as actual, is decomposed into two parts, one which interacts with wage changes and one which does not. The latter responds to deviations from equilibrium by the former and also to exogenous variables. The decomposing of the

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I wish to thank Professor Peter Birch Sørensen for helpful comments and encouragement. Unfortunately, I am the one to blame for the remaning errors and shortcomings.

1. This expression is from a draft version of Jackman, Layard and Nickell (1991). We use it instead of the usual NAIRU (non-accelerating inflation rate of unemployment) as accelerating inflation has become somewhat old-fashioned.

unemployment facilitates a characterization of the various parts of the overall unemploymentby
particular accounts (as offered in the literature).

A common (general) framework, rich enough to encompass an unemployment-inflation and history dependencies, is needed in order to understand the variations of unemployment, across countries as well as across labour markets within the countries. we shall touch upon in the closing discussion with a reference to the Danish unemployment problem.

2. Decomposing the unemployment

In a traditional Phillipscurve context the rate of wage change is a function of the rate of unemployment. But the group of unemployed people is not homogeneous, and due to differences in skills and average durations of unemployment spells, the same rate of unemployment might affect the wage change differently in two otherwise identical labor Hence, let us define the effective unemployment, U_e, as the number of unemployed persons, U, weighted by their level of skills, search intensity, and duration of unemployment. That is, we calculate the number of fully skilled, fully searching and briefly unemployed persons according to some normalization:

(1)

where /n is the quality of the unemployed labor force and X the average search intensity.
The quality is a function of the average level of skills q and average duration of unemployment
d\

(2)

Total unemployment is the labor force L minus employment N, U = L - N and U =
Ue+ Ur, where the subscript r indicates residual unemployment. Small u's are unemployment
The Phillipscurve is then:

(3)

where w is the wage rate. The literature offers a number of different foundations of the
Phillipscurve, such as union bargaining, efficiency wage, etc. They apply here as well
of cause. The decomposition is illustrated in figure 1.

The level of effective unemployment corresponding to no wage inflation we will called institutional unemployment, u*. This is the long-run level of effective unemploymentwhich on the institutional set-up, first of all the institutions for wage formations;the of unionization, the degree of decentralization in wage bargaining,

etc. Further, u* includes unemployment due to the matching procedure such as spells of involuntary spells of search during which the worker might meet employers but is rejected.The obtainable long-run unemployment rate over all possible institutions is u* min, which will be called frictional unemployment.

There are numerous ways in which a given labor market institution can be utilized. Thus, there might be unemployment due to the way the institution is operating or brought operate. This is called functional unemployment v*. Thus, w* is the minimum obtainable level of equilibrium unemployment given the institution, while u* is the additional amount of equilibrium unemployment due to the fact that the institution is not exploited optimally with respect to employment. Functional unemployment might be caused by skill mismatch, lack of skills among the unemployed, benefit opportunities do not induce incentives for the unemployed to search sufficiently intensive and other incentive problems not due to the wage setting institution. Hence, voluntary spells of search is functional unemployment.

It is not obvious that the goal of public policy should be to eliminate functional unemployment completely. For instance, som voluntary search unemployment might be a good idea, if it is due to the fact, that skilled workers are not being forced away from their area of experience during short unemployment spells.

The NIRU is the sum of institutional and functional unemployment. That is, the
equilibrium unemployment given the labor market institution and given how this is
brought to function. Hence, there isn't much natural about the NIRU, as we see it.

3. The sliding NIRU.

In our framework so far, the long run equilibrium unemployment which is observable constant over time as long as institutions and their performance are unchanged. This might not be the whole story. First, changes in the educational standard of the unemployed and/or the average duration due to entry and exit will change the scene. Secondly, if the effective unemployment differs from «*, this might have an impact on the average quality of the unemployed and thereby influence the level of functional unemployment.

EXAMPLE 1: For simplicity, look at the following asymmetric steady state equilibrium,
entry and exit are assumed to match each other by number and quality,
and where uc = u* means no change in labor force quality. First define quality as

(2')

and assume the following:

(5)

The situation is illustrated in figure 2 where the initial equilibrium unemployment is u*(t). After a recession, causing an increase in the effective unemployment to u_e(t +\), the economy does not return to the same level of equilibrium unemployment but to a higher level u*(t+r), say after tperiods. However u* has not changed, while u*_{F (t)} has increased to w* (t+x) due to the decaying quality of the unemployed labor force. Thus, NIRUfr) = uf+ u*_F(t), and NIRU (t+r) = uf+ u*_{F (t+r).}

In this example, entry and exit ware assumed to match each other by number and quality, and without the recessive shock both levels of unemployment, m* and u_F(t), would have remained constant. A given constant mismatch would not change this. But a change in the rate of growth of a variable which influences the supply of labor, by number or quality, might have an impact on the level of equilibrium unemployment. The explanation is, that the level of functional unemployment is a measure of how well the institution is brought to cope with a given characteristic of entry and exit. If the

characteristic changes, then the task changes and an uncharged degree of functioning will cope differently with this new task. In other words: A given set of structural problemsand given characteristic of entry and exit yield a certain level of functional unemployment. Thus, if the current characteristic becomes more difficult to match, and the amount of structural problems remains the same - the level of functional unemploymentwill rise.

Nevertheless, the kind of relationship between variables should be thought of as endogenous
some extent. If unemployment becomes very high, the relationship between
the variables will come under pressure.

The framework discussed above suggest that the current equilibrium level of unemployment
not necessarily the one where wage inflation is zero. Consider the following
description.

EXAMPLE 2: Let the characteristic of entry-exit match, by number and quality, be such that the system is drifting towards a steadily higher level of functional unemployment institutional unemployment and wages are constant. Hence, the degree of functioning of the labor market cannot quite manage the changes in characteristics of labor supply. This is illustrated in figure 3 by the horizontal arrows. Suppose further the following symmetric version of (5), where c is a constant representing the mismatch entry and exit characteristics.

(6)

Now, by keeping the effective unemployment (sufficiently) below the level of institutional (constantly or steadily increasing demand policy and/or employment as long as they reduce the effective unemployment) the government create a constantly positive hysteresis effect. This is illustrated by the points ujt) and u(t) in figure 3, where backward pointing arrows represent the hysteresis effect, and arrows pointing up represent the effect of the public policy. The rates u_e(t) and u(t) will move as time passes, u_e(t) down along the Phillipscurve and u(t) as showed the resulting effect, the dashed arrow. Consequently, if the hysteresis effect is assumed increase (strictly monotonic), as the effective unemployment advances (sufficiently) the level of institutional unemployment, there would be a unique point where the system can remain. This tense "equilibrium" is illustrated by u*_e and u* in figure The equilibrium implies a constant rate of wage inflation.

Let us here emphasize, that the set-up is highly partial apparently: The consequencesfor
real wage, for the tax burden, etc. are not modeled. For the real wage to be

determined for instance, we need to specify the wage-price relation and assume somethingabout growth. It might be that in this "equilibrium" price changes will match wage-changes and thus in equilibrium the real wage would remain constant. If so, we have pointed at positive hysteresis as the reason for unemployment to be low in equilibrium with inflation. Note further, that there do not exist equilibria in this modelunder inflation.

In these two examples, there is no long-run equilibrium or history independent NIRU. does not, of course, imply that we consider all rates between zero and one to be likely levels of current equilibrium unemployment. On the contrary, we consider equilibrium unemployment to be bounded and further that there exist a range of rates, which the equilibrium unemployment hardly can exceed. This we can model by specifying e function from (1), for a given search intensity A, as illustrated in figure 4, where fx is normalized to take positive values only.

4. Discussion

The difference between unemployment among (low paid) unskilled and (high paid) qualified/skilled workers can be characterized by using the suggested decomposing of the overall unemployment.² The main problem of the Danish market for unskilled labor is functional unemployment due to the lack of outside pressure. Such pressure would presumably lower unemployment, because unskilled labor is a "standard good", and demand for such labor service is wage-elastic. Whereas, on the Danish market for qualifiedlabor

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2. What follows is nothing more than conjectures, really, partly deduced from the design of the Danish benefit system, and partly from some preliminary and indirect empirical observations about the firm's hiring and firing behaviour.

lifiedlaborthe main problem is institutional unemployment. Here, there is a considerableoutside but it is of such importance to the hiring firms, that they get the right manpower. Therefore, they do not consider taking the risk (not even a small one) of hiring unemployed labour. Thus, even a considerable outside pressure has only a vagueimpact wage setting, wherefore the problem with unemployed qualified labour should not be attacked by increasing outside pressure but rather by working on the institution;the the firms behavior of recruiting, retaining and motivating workers, etc.

The case given by example 1 seems to illustrate the trend of Danish unemployment over the last 2 decades: It seems that the economy has drifted towards steadily higher equilibrium unemployment, and the explanation could be that during each recession decay has increased the functional unemployment as illustrated (shifted the w-curve towards

The problem in example 2, dealt with by letting the government create positive hysteresis could alternatively have been approached by working on the functioning the labor market, the so-called structural problems. But in the short run, doing so might not be possible for political or other reasons.

In practice both the choice of institution and the choice of the more detailed setup surrounding the institution are bounded by conditions from outside the standard analysis. instance, a corporative institution with centralized wage bargaining might be the right institution as far as unemployment is concerned, but on the other hand, it might leave too little room for local "motivating-by-wage" management so that productivity growth ends up on an inefficiently low level. This is the real dilemma concerning the Swedish situation, we believe. Here, the "employment principle" is not a direct problem, its aim is to prevent residual unemployment from developing by constantly positive hysteresis effects (the drawback being wage inflation). Concerning programmes; if the poorest equipped of the unemployed are reached, this part of the programme will not yield inflationary pressure but probably not a significant effect either (if any).

Generally, our understanding of such trade-off in the choice of institution (and in the
more detailed structural set-up) is insufficient, which should encourage labor-market
studies emphasizing the role and formation of institutions.

References

Jackman, R., R. Layard and S. Nickell. 1991.
Unemployment - Macroeconomic Performance
the Labour Market. Oxford.

Layard, R. and S. Nickell. 1987a. Unemployment Britain. In The Rise in Unemployment, by C. Bean, R. Layard and S. Nickell, London, reprinted from Economi-

ca, August 1986, Special issue on Unemployment.

Layard, R. and S. Nickell. 1987b. The Labour In The performance of the British Economy, ed. by R. Dornbusch and R. Layard, Oxford.