Ranking of Job Applicants, On-the-job Searchand Persistent Unemployment*

by

Stefan Eriksson and Nils Gottfries†

7 March 2000

We formulate an efficiency wage model with on-the-job search where wages depend on

turnover and employers may use information on whether the searching worker is

employed or unemployed as a hiring criterion. We show theoretically that ranking by

employment status affects both the level and the persistence of unemployment and

numerically that these effects are substantial. More prevalent ranking in Europe compared

to the US – because of more rigid wage structures etc. - could potentially help to explain

the high and persistent European unemployment.

Keywords: Efficiency wage, Turnover, On-the-job search, Persistence, Ranking,

Unemployment, Unions.

JEL classification: E24, J64.

* We are grateful to Peter Diamond, Per-Anders Edin, Peter Fredriksson, Bertil Holmlund, TorstenPersson and seminar participants at the Institute for International Economic Studies, Stockholm, andUppsala University for very helpful comments. Financial support from the Office of Labor MarketPolicy Evaluation is gratefully acknowledged.† Department of Economics, Uppsala University, Box 513, SE-751 20 Uppsala, e-mail:Stefan.Eriksson@nek.uu.se and Nils.Gottfries@nek.uu.se.

1

1. Introduction

When one compares European and US labor markets, several differences are apparent.Unemployment rates are much higher, turnover is much lower, and the adjustment backto equilibrium after a shock appears to be much slower in Europe. While highunemployment may plausibly be blamed on unions and labor market rigidities, and lowturnover may be due to cultural differences, the last observation is especially intriguing.In several European countries, temporary cyclical shocks have raised unemployment andthen it has remained high for a long time. Adjustment costs may be one explanation forsluggish employment adjustment, but it can hardly be the whole story. Why isunemployment so persistent in Europe?1 In this paper we take a new look at thisquestion, emphasizing two aspects of the labor market.

The first is that turnover considerations are important in wage determination.Voluntary turnover is substantial, and when workers quit, firms firm incur significanttraining costs to replace them. Consequently, firms consider the implications for turnoverwhen they set wages.

The second important starting point is that unemployed seem to be at adisadvantage compared to employed workers when they compete for jobs. This may bebecause workers lose some of their human capital in unemployment or becauseunemployment is taken as a signal of unobserved personal characteristics. If employersperceive unemployed workers to have lower average productivity, they will be reluctantto hire them, and this is especially true if wage structures are rigid, preventingdifferentiation of wages according to perceived productivity differentials.

If turnover is important then the firm’s optimal wage should depend on theprobability that a worker looking for another job will actually find one; if this probabilityincreases the firm will respond by raising its wage to prevent costly turnover. If, inaddition, unemployed workers do not compete for jobs on an equal basis with employedapplicants, this must raise the probability for employed workers to get the jobs they applyfor and this in turn will tend to raise the wage. In other words, we should expect aninteraction between the turnover considerations that affect wage decisions and the fact

1 We realize that we are not the first ones to ask this question; we comment below on alternativeapproaches. By “persistence” we mean a high serial correlation in unemployment.

2

that outsiders have a disadvantage compared to insiders when applying for the same jobs.The bigger this disadvantage, the higher is the chance for employed workers to get a newjob, and the higher is, ceteris paribus, the ”efficiency wage” that is optimal from the firm’spoint of view.

To formalize this intuition, we formulate a model where a fraction of all employedworkers apply for new jobs while maintaining their current jobs. Whether a personapplies for a new job or not depends both on the relative wage offered by the firm and ona stochastic non-pecuniary job satisfaction factor which affects the utility gain fromswitching jobs. The wage may be set by the firm or in a bargain with a union. In eithercase, the wage setters take the effect of the wage on turnover into account. We firstconsider the case when employers chose whom to hire randomly (no ranking). We showthat even without ranking unemployment will be persistent. Because of the fear of costlyturnover, a permanent negative shock is not fully accommodated in the next wagecontract, and hence employment remains low for some time after a negative shock.

Then we consider a situation with ranking, i. e. when some employers prefer tohire employed applicants. Ranking increases the probability that an employed worker getsthe job he applies for and this makes it optimal for firms to set higher wages. The result isboth lower steady state employment and a slower adjustment following a shock.Simulations show that the effects of a limited degree of ranking are substantial forreasonable parameter values.

The model is used to interpret the differences between the US and Europe. Asnoted above, both the level and the persistence of unemployment are much higher inEurope. There are three main factors in our model that might explain these observeddifferences: lower mobility, stronger unions and, perhaps, more ranking in Europe. Wefind that the lower turnover in the European economies should, by itself, lead to lowerunemployment and approximately the same amount of persistence. Since unemploymentis in fact much higher in Europe, this has to be explained either by strong unions or bymore prevalent ranking. Our simulations show that, within this model, wage pressure dueto strong unions can explain high unemployment, but not the high persistence observedempirically. Instead, our analysis points to ranking of job applicants as a potentiallyimportant explanation for the persistence of unemployment observed in most Europeanlabor markets.

The notion that unemployed workers - and especially those who have beenunemployed for a long time - have difficulty competing for jobs has been around for

3

some time (see e. g. Phelps (1972), Layard and Nickell (1986)) but there are fewmicrobased models formalizing the idea. The insider bargaining model developed byBlanchard and Summers (1986) and Gottfries and Horn (1987) emphasizes the distinctionbetween employed and unemployed workers, but can hardly generate the extremeamount of persistence found in the data.2 Other related papers are Huizinga andSchiantarelli (1992) and Gottfries and Westermark (1998), who show that persistencemay arise due to the forward looking nature of wage decisions, but without the interactionbetween on-the-job search and ranking that we emphasize in the present paper.

The paper that is closest in spirit to ours is Blanchard and Diamond (1994). Theyanalyze ranking of unemployed workers by duration in a matching model. The wage isdetermined by Nash bargaining with the expected utility of a recently laid off worker asthreat point. Their main question is how the wage is affected if firms rank job applicantsaccording to the length of unemployment. The result is that ranking has small effects onthe long run wage level, but substantial effects on the wage dynamics following a shock.An expected increase in employment improves the bargaining position of those currentlyemployed - since they will be first in line for the new jobs if they become unemployed -so wages increase.

Our analysis differs in several ways. First, we focus on on-the-job-search and theadvantage of employed job searchers relative to the unemployed rather than thedistinction between short-term and long-term unemployed. Second, while Blanchard andDiamond take employment to be driven by exogenous job creation and destruction rates,we are able to solve the model for employment, calculate persistence, and evaluate theeffects quantitatively. Third, our results differ qualitatively from those of Blanchard andDiamond. In our model, ranking has substantial effects not only on the dynamics, butalso on the long run equilibrium level of wages and employment. We believe that ourfocus on on-the-job search is the key reason why our results differ in this respect.3

2 In univariate models of unemployment, the coefficient on lagged unemployment is close to unity formany European countries (see references below). The Blanchard and Summers (1986) version of theinsider bargaining model generates hysteresis, which is an extreme form of persistence, but only becausethey make very special assumptions concerning union preferences etc. - see the discussion in Blanchard(1991) or Bean (1994).3 Pissarides (1992) considers a related model where long-term unemployment leads to a loss of skill. Thereis no ranking in his model. Instead, firms cannot distinguish long-term and short-term unemployed, so alljob seekers have the same chance to get a job. Persistence arises because long term unemploymentimplies a deterioration of the average quality of unemployed workers which makes it less profitable forfirms to hire workers and fewer vacancies are created. Thus the mechanisms are quite different from thoseconsidered here.

4

In Section 2 we formulate the basic model without ranking, solve it for steadystate employment and show that unemployment is persistent even without ranking. InSection 3 we introduce ranking and show that this increases unemployment andpersistence. Section 4 extends the model to allow for wage contracts spanning severalperiods. In Section 5 we use numerical simulations to examine whether the observeddifferences in turnover, unemployment and persistence between Europe and the US canbe explained by our model and Section 6 concludes.

2 On-the-Job Search, Wage Determination and Unemployment Persistence without Ranking of Job Applicants

The model is intended to capture the fact that job-to-job flows are substantial and turnoverconsiderations are important for firms when they set wages. The importance of voluntaryturnover is well documented. Holmlund (1984), Akerlof, Rose and Yellen (1988) reportquit rates around two percent for the U. S., Sweden and Japan and Boeri (1999) finds thatquits from one job to another constitute around 50 per cent of all hiring in severalEuropean economies. According to Holmlund (1984), about 8 percent of employedworkers in Sweden engaged in job search during a year and Pissarides and Wadsworth(1994) report that around five per cent of all employed workers in Britain do search for anew job. Lane, Stevens and Burgess (1996) show that worker reallocation is two to threetimes as great as job reallocation. Another indication of the importance of quits is the factthat total worker turnover is procyclical – reflecting the procyclicality of quits (Andersonand Meyer (1994)). Also, survey evidence shows that firms care about turnover. Fear oftraining/ hiring cost as a result of quits, as well as fears that the most productive workerswould quit, deter firms from wage cuts (Blinder and Choi (1990), Campbell and Kamlani(1997)). Moreover, as emphasized by Akerlof, Rose and Yellen (1988), both wages andnon-pecuniary factors seem to influence quit decisions.

We first consider a case when there is no ranking of job applicants. There are a largenumber of workers and a large number of identical firms, but the number of firms is muchsmaller than the number of workers. Events take place in discrete time and the sequence ofevents in each period is the following. Near the end of every period a fraction s of theworkers leaves employment and enters the pool of unemployed. This fraction is exogenouslygiven and represents workers quitting or being laid off for exogenous reasons. Then wages

5

are set – either by the firm or in a bargain - and the remaining workers decide whether to lookfor a new job or not, considering the wage offered by the firm, the wage offered elsewhereand a non-pecuniary “job satisfaction” factor. All unemployed workers also search and everysearcher submits one application to a randomly chosen firm.4 Firms receiving the applicationsthen make their choices of whom to hire.

We have three distinct decisions: firms set wages, workers decide whether tosearch and firms decide whom to hire. We now proceed by first analyzing search andturnover in a specific firm for a given wage, then analyzing the firm’s optimal decisionabout the wage, and then we consider the case when the wage is set in a bargain betweenthe firm and the workers. Finally we turn to employment dynamics in a symmetricgeneral equilibrium and calculate long-run unemployment and persistence.

SearchEvery worker who remains employed when a new period begins has to decide whether tolook for a new job or not. We assume that every employed worker draws a number νthat determines his job satisfaction from continuing to work at his present job. Thenumber ν is drawn from a random distribution with cdf G(ν). Given ν, his expectedutility from the current job is ν/i

tw ; the expected utility from a randomly chosen new job

is tw . To keep the model simple, we assume that every worker makes a new

independent draw of ν every period.5 Furthermore, G(ν) is assumed to be unimodal andhave a mean smaller than unity, so if the wage is the same most workers prefer the jobthey have.

The employed workers decide whether to search or not given the wage offered bythe firm, i

tw , the wage expected elsewhere in the economy tw and the parameter ν . On-

the-job search is costless, so a worker will start searching if iitt ww ν/> . Then the

fraction of workers searching in a given period is

4 Whether workers send in one or more applications is less important. The important assumption is thatsearch intensity is taken as given for all searchers. This assumption is discussed in the final section.5 The assumption that the gain from switching jobs is purely temporary is made to simplify the analysis.In practice, we would expect high serial correlation in ν. Such a model would be very complicated,however, since we would need to keep track of a distribution of workers with different levels of jobsatisfaction. Also, the workers would have to consider effects on utility in future periods when theyconsider switching jobs.

6

)/(1)/( titt

it wwGwwS −= , (1)

where S is decreasing and our assumptions about the distribution imply that S’’(1) > 0.All searching workers apply for one job each period and submit their applications

randomly. The fraction of previously employed workers quitting to take another job isthen tt

it awwSs )/()1( − , where ta is the probability that an employed searcher finds a job

(to be determined later).

Wage settingIn this section we assume that the wage can be changed every period.6 When setting thewage, the firm takes account of the fact that labor turnover is costly. For every workerthe firm hires, it incurs a hiring cost equal to c times the average wage tw . The

production function is )( itt lFθ , where tθ may be interpreted as productivity, price, or

product demand. If wages are set in nominal terms, θt will be a composite variable includingboth real and monetary factors.7

To simplify, we assume that voluntary quits are sufficiently large that all employmentadjustment can be made by variations in hiring,8 and subjective certainty; the firm optimizes asif the future was known with certainty.9 The firm solves the following maximizationproblem:

6 In Section 4 we generalize this to the case when the wage is set for N periods7 If, for example, each firm faces a demand curve of the form pmppq ii /)/( η−= , where p i is thefirm’s price, p is the price level and m is money supply, and produces under constant returns to scale withproductivity θ, revenue of the firm can be written

( ) ( ) ηηηθ/11/1/11 /

−− ipm l .

With predetermined prices, an unexpected monetary shock clearly affects employment. Withpredetermined nominal wages but fully flexible prices, the situation is more complicated. Prices are setwith a fixed markup on marginal cost, which is w plus the hiring cost minus the hiring cost that is savednext period, all divided by θ. Still, fixed nominal wages imply that prices adjust less than fully to monetaryshocks. As we will see below, only unexpected changes in θt affect employment.8 This assumption simplifies, but it is not crucial for the present analysis. It is important for the optimalityof nominal wage contracts, however – see Gottfries (1982). Note that we could include some random(exogenous) closure and birth of some firms – creating microeconomic job destruction – without changingthe macroeconomic analysis.9 Hence the dynamic analysis below refers to the adjustment of employment after an unexpected once andfor all shock to θ.

7

( ))))/()1(1(()( max 1i

jt0j

j

,

ijtjtjt

ijt

ijtjt

ijt

ijtjt

lwlawwSsslcwlwlF

ijt

ijt

−++++++++++

∞

=

−−−−−−∑++

θβ

(2)The first order conditions are

0)1)(/(' 1 =−−− −ittt

it

it laswwcSl (3)

0)/()1()(' 1111 =−+−− ++++ ttittt

it

itt awwSscwcwwlF βθ . (4)

Equation (4) defines the labor demand function ) , , , ,,( 111 +++= titttt

it

it wwawwll θ . Inserting

this into (3) we get the following equation, which implicitly determines the firm’s optimalwage, the “efficiency wage”, e

tw :

ittt

ett

etttt

et lawwcSswwawwl 111 )/(' )1() , , , ,,( −++ −−=θ . (5)

The optimal wage is such that the direct cost of a marginal wage increase equals thereduction in turnover costs associated with a wage increase. The optimal wage dependspositively on the average wage level, the hiring cost, and the probability that a searchergets a job.

Unions and BargainingIn most European labor markets, and some parts of the US labor market, the wage is setin negotiations between employers and a union. Even if there is no formal unionorganization, workers may have bargaining power because they could potentially takecollective action against the firm. The negotiation process is modeled as in Gottfries andWestermark (1998). The firm and the union make alternate offers. After a bid is rejected,it may turn out that workers are unable to continue the strike, and if this situation occurs,the firm sets its optimal wage, e

tw , defined above. Otherwise, bargaining continues until

one party accepts a bid made by the other party. This wage setting mechanism generatesa wage that is approximately equal to a “union markup factor” µ times the wage that thefirm would set if it was free to set the wage:

et

it ww µ= . (6)

8

The size of the markup depends on the workers’ ability to last a conflict, the impatienceof the parties etc. (see Appendix 1). Substituting into (5) we get the following equationwhich determines the wage when workers have bargaining power:

ittt

itt

itttt

it lawwSscwwawwl 111 )/(' )1() ,/ , , ,,/( −++ −−= µµθµ . (7)

The Level and Persistence of UnemploymentSince we are interested in aggregate employment, we consider a symmetric generalequilibrium where all firms set the same wage. This is the natural situation since all firmsand workers are assumed to be identical and therefore solve the same problem.10 Thenwe have from equation (7):

1)1( −−Ω= ttt lasl , (8)

where Ω = -c S’(1/µ). The parameter Ω is a measure of “wage pressure” arising fromthe combined effects of the efficiency wage mechanism and union bargaining power;both factors tend to raise wages in a completely symmetric way in our model.

The final step is to determine ta , the probability to get a job for an employed

searcher. In a symmetric equilibrium, the number of people hired per firm is:

11 )1()1()1( −− −+−−= ttttt laSslslh . (9)

This equation simply says that hiring is equal to the number of workers the firm wishes toemploy this period minus the workers who remain from last period, taking into accountexogenous and endogenous separations. There are many more workers than firms andwe assume that each firm gets at least as many applicants as it has job openings. In thissection we consider the case without ranking where the firm has no preferences betweenemployed and unemployed workers but simply draws the desired number of workersrandomly from the pile of applications. Then the probability to get a job is the same forall searchers and is determined by:

10 We assume that all firms set the wage at the same time so we do not have overlapping contracts.Obviously, overlapping contracts of the Taylor variety may generate persistence, but we want toexamine how much persistence we get in the model without this additional source of persistence.

9

11

11

)1()1()1()1(

−−

−−

−+−−−+−−

=tt

ttttt Slslsn

lSaslsla , (10)

where we simplify notation by writing S(1)=S. This equation says that the probability toget a job for a searcher is the number of hirings (given by (9)) divided by the total numberof searching workers consisting of both unemployed workers, 1)1( −−− tlsn , andemployed workers searching on-the-job 1)1( −− tSls . Solving equation (10) for ta we get

the following expression:

1

1

)1()1(

−

−

−−−−

=t

ttt lsn

lsla , (11)

which is simply hiring divided the number of unemployed job seekers. The chance to geta job does not depend on the number of employed workers looking for jobs. Theintuition is that every worker who changes jobs leaves one job and takes one job, so thenumber of jobs available for the remaining searchers remains the same. Combining (11)with equation (8) gives us:

1

11 )1(

)1()1(

−

−− −−

−−−Ω=

t

tttt lsn

lsllsl . (12)

This equation implicitly determines employment as a function of employment in theprevious period. Evaluation of (12) in an equilibrium with constant employment,

1−= tt ll , allows us to determine the steady state employment rate

)1)(1(1

Ω+−=

ssnl ss

. (13)

The model has the natural rate property; productivity does not affect employment in thelong run. Higher wage pressure Ω due to high turnover costs or strong unions results inlower employment, an increased flow from employment to unemployment (s) has anambiguous effect on the natural rate, but for plausible parameter values it raisesunemployment.

10

Differenting (12) with respect to 1−tl and evaluating in steady state we get an

expression for the monthly persistence of employment which, for later reference, wedenote mρ ;

))(1()21( 2

1ssss

ssss

t

tm slus

lsusll

ssll+−−−

=∂∂

≡

=−

ρ , (14)

where u denotes unemployment. It can be shown that this expression is positive forreasonable values for the parameters.

To understand why employment depends positively on employment in the previousperiod, imagine that we are initially in steady state. Then θ falls unexpectedly andpermanently. This happens after the wage has been fixed, so firms respond by cuttingemployment. Employment stays at this lower level until the end of the period. In the nextperiod firms cut their wages, but not so much that employment immediately returns to itssteady state value. If wages would immediately fall to the new steady state level, there wouldbe a large increase in employment, many vacancies open to workers searching on the job, andfirms would suffer from excessive turnover. Foreseeing this, each individual firm would thenhave an incentive to deviate by raising its wage so as to reduce turnover. Therefore theequilibrium solution must be that firms reduce wages less and employment remains low forsome periods after a negative shock.11

Numerical analysis of the modelWe have just shown that employment will remain low for some time after a negativeshock even without ranking of job applicants. In the next section we will show that thismechanism is reinforced when firms rank job applicants. But before turning to the effectsof ranking, it is informative to put some numbers into the model to see how persistentunemployment will be without ranking.

Effectively, there are three free parameters in the model: the flow fromemployment into unemployment, s, the fraction of employed workers searching on thejob, S, and, the combined "wage pressure" effect resulting from turnover costs and strongunions, Ω. While s can be measured with reasonable precision, there are few estimates of

11 Huizinga and Schiantarelli (1992) and Gottfries and Westermark (1998) make a similar argument, butthose papers did not consider on-the-job search.

11

S available, and no direct measures of Ω. We do, however, have measures of the averagejob-to-job flow, which in our model corresponds to S times a, and the unemploymentrate, u/n. We therefore set S and Ω in such a way that the equilibrium job-to-job flowand unemployment correspond to the values observed empirically. In Table 1 we reportempirical estimates that we use for s, Sa and u/n and the implied values for S and Ω.12

The period is taken to be one month. The last two rows show the implied steady stateprobability to get a job for a job applicant and the resulting yearly persistence ofunemployment generated by the model, defined as 12

mρρ = .

Table 1 Observed stocks and flows and implied parameter values and (yearly)persistence for different economies.

Parameter US 1968-86 Germany 1986-88 France 1986-88

s 0.015 0.004 0.006

Sa 0.012 0.004 0.006

u/n 0.07 0.08 0.106

S 0.07 0.09 0.12

Ω 6.1 22.8 20.9

a 0.17 0.04 0.05ρ 0.09 0.51 0.51

We see that, with parameter values consistent with the stocks and flows observedin the US and European labor markets, unemployment becomes quite persistent inGermany and France but not in the U. S. The persistence found in the model is muchsmaller than empirical estimates, however. Blanchard and Summers (1986) andAlogoskoufis and Manning (1988) estimated simple autoregressive models for unemploymentand found that the coefficient for lagged unemployment is close to unity for most Europeancountries, but only around .4 for the US (with yearly data).13 Our basic model thereforeseems to generate too little persistence.14

12 See Section 5 for further discussion of this approach and Appendix 3 for detailed discussion of thesenumbers.13 High serial correlation in unemployment may be due to two conceptually different mechanisms. One isthat cyclical (aggregate demand) shocks affect unemployment and then the adjustment back to equilibriumtakes a long time. Another possibility is that shocks to the natural rate (e. g. changes in union bargainingpower) themselves are highly persistent (and frequent). The present model is of the first type. Jaeger and

12

3. Ranking of Job Applicants

Having formulated the basic model we are now ready to analyze the effect of ranking.There is evidence that employers prefer to hire already employed workers. Blau andRobins (1990) showed that in the U. S. employed job searchers receive almost twice asmany job offers as unemployed searchers with the same search effort. Winter-Ebmer(1991) found that employment status is used as a screening device for productivity inAustria. Agell and Lundborg (1999), in a survey of Swedish firms, found that employersdo view unemployment as a signal of lower productivity. How will ranking affect thebasic decisions made by the agents in our model? How will ranking affect the steadystate level of employment and the degree of persistence? How big are the effectsquantitatively? These are the questions to which we now turn.

Before we incorporate ranking in the model it is important to be clear about whatwe mean by ranking. In this model, ranking means that employers sometimes, whenchoosing between applicants for a particular job, prefer to employ someone who has a jobto an unemployed worker. Formally, we assume that firms rank applicants in this way fora fraction r of the jobs. Since there are many applicants of each category per job, onlyemployed applicants are hired to those jobs.

This definition of ranking raises an important question. Why do firms chose to ranktheir applicants? Within the context of our formal model we can simply defend ourassumption by pointing out that workers are identical, so firms are indifferent between rankingand not ranking and may as well rank applicants. But the model would be more convincing iffirms had a reason to rank workers.

A natural argument is that the perceived productivity of an employed worker ishigher than that of an unemployed worker. In fact, it is enough that unemployed workersare perceived to be an infinitesimal amount less productive, on average, to justify ranking,provided that the wage is the same. Such an argument could be criticized, however, by Parkinson (1994) use an unobserved components technique to try to distinguish these two sources ofpersistence. They find that effects of cyclical shocks on unemployment are substantially more persistentin Europe than in the US. Similar results with Swedish data are obtained in Assarsson and Jansson (1998)

14 In addition, the obtained values of S and Ω appear implausible. Low turnover in Europe is not at all

explained by a lower willingness to change jobs, but entirely by an extremely low probability to find a new

job.

13

arguing that the firm could offer different wages for the different groups, each wagecorresponding to the productivity of the group. Thus there must be some rigidity of thewage structure that prevents firms from differentiating wages according to perceivedproductivity differences. In the following we assume that there is such a rigidity.

With ranking, the search and wage setting decisions are made as before, butemployed workers are more likely to get hired than unemployed workers are. We assumethat workers do not know for which jobs ranking is applied but send in their applicationsat random. Using ta to denote the probability for an employed searcher to get a job we

have:

11

11

1

11

)1()1()1()1(

)1()1(

)1()1(

−−

−−

−

−−

−+−−−+−−

−+−

−+−−=

tt

tttt

t

ttttt Slslsn

lSaslslr

SlslSaslsl

ra .

(15)

With probability r the worker applies for a job where employed searchers are preferredand in this case the probability to get a job is hiring per firm divided by the number ofemployed searchers per firm. With probability (1-r) the worker applies for a job wherethe employer does not have any preference for a particular type of worker and in this casethe probability to get a job is hiring divided by the total number of searchers per firm.Solving (15) for ta gives us:

11

111

)1()1)()1(())1()1()()1((

−−

−−−

−−−−−+−−−−

=tt

ttttt lrSslsn

Slslsrrnlsla . (16)

Contrary to the case without ranking the fraction of employed workers looking for jobs,S, affects at directly. If more workers search on-the-job, their chance to get a jobdecreases for a given level of employment. Looking back at equation (15) we see that anincrease in S has two counteracting effects on the probability for employed workers to geta job. More on-the-job search means that more workers leave their jobs and this increasesthe number of job openings, but there are also more applicants for jobs, especially forthose jobs which are predestined for employed applicants. Inspecting the right hand sideof (15) we see that the latter effect dominates: the more workers that do on-the-job searchthe smaller is their chance to get a job. Combining (16) with (8), finally, gives us:

14

)1()1)()1(())1()1()()1((

)1(1

111

rSslsnSlslsrrnlsl

slt

ttttt −−−−

−+−−−−−Ω=

−

−−− . (17)

As before, this equation implicitly determines employment as a function of employmentin the previous period. Evaluating (17) in steady state we get

)1()1()1()1()1()1()1(

222 rSsSssrssrssrSs

nl ss

−−+−Ω+−Ω−Ω−−−−

= . (18)

For the steady state level of employment l ss to be positive the following condition mustbe fulfilled:

Ss

rr Ω

>−1 . (19)

Equation (19) can be interpreted as giving a limit to how much ranking our model cantake. If r gets very high we get a situation where equilibrium employment is equal tozero. That r cannot be too large is most evident if we consider the extreme case whenemployers hire almost only employed workers. Then unemployed workers have a verysmall chance to be hired. Since every period a share s leaves employment but very fewunemployed workers get hired employment is only stable at zero. In the following weassume that condition (19) is satisfied.

One may suspect employment to be lower the more ranking there is since rankingimplies a less well functioning labor market. In Appendix 2 we differentiate (18) andshow that this is in fact the case:

0)/(

<∂

rnl ss

∂ . (20)

This result can be explained as follows. In our model the flow from employment tounemployment is a constant fraction of employment. The flow from unemployment toemployment on the other hand is depends on the probability for an unemployed worker toget a job. If more firms rank by employment status this probability is reduced, ceterisparibus, and the only way this can be reconciled with the steady state condition thatinflow equals outflow is that the level of unemployment is higher.

15

Another interesting question is how ranking affects the persistence ofunemployment. Differentiating (17) with respect to 1−tl and evaluating in steady state we

get an expression for ρ and differentiating once more with respect to r we can show thatranking increases persistence (see Appendix 2):

.0/ 1 >∂∂∂

=∂

∂

=

−

ssllrll

rttmρ

(21)

The intuition behind equation (21) can be understood by extending the discussion in thenon-ranking case. After a negative shock to productivity, the wage will not fallimmediately to the new steady state level because, if it did, employment would recoververy rapidly and there would be many vacancies and excessive turnover. Thus wagesadjust slowly although the level of unemployment is high. This mechanism is reinforcedby ranking, since when employed workers have priority for some jobs, their chance to geta new job depends less on the stock of unemployment and more on the number ofvacancies.

Quantitative Effects of RankingHaving showed analytically that ranking reduces the level of employment and raises thepersistence of unemployment we now ask whether these effects are quantitativelyimportant. To answer this question we take the values for the US economy in Table 1and examine what happens to steady state employment and persistence as we increase thefraction of jobs for which workers are ranked from zero to 40 percent

The numbers in Table 2 are calculated keeping s, S and Ω constant at the valuesfrom Table 1. Our purpose here is not to describe any real world economy but toexamine the potential quantitative effects of ranking, keeping the other fundamentalparameters constant at some reasonable values.

16

Table 2 Equilibrium values with different degrees of ranking.

u/n ρ

r=0.0 0.07 0.09

r=0.1 0.09 0.21

r=0.2 0.13 0.42

r=0.3 0.22 0.70

r=0.4 0.54 0.96

From Table 2 we can conclude that ranking has large effects on both the level and thepersistence of unemployment. If ranking is applied for one fifth of the new jobs,unemployment almost doubles and becomes much more persistent.

Comparing our results to those of Blanchard and Diamond (1994) who foundsubstantial effects on wage dynamics, but only small effects on the steady state, one mightwonder why we also get long run effects. Our interpretation is the following. In Blanchard andDiamond the wage is set according to the Nash bargaining solution and the state of the labormarket affects wage setting via the ”threat point”, which they take to be the situation if theemployed worker was to become unemployed.15 This means that ranking has two competingeffects on the wage. If an employed worker were to become unemployed, his chance to finda new job soon would be much better since he would be “first in line” for new jobs. But onthe other hand he does run a small risk of becoming long-term unemployed himself. As itturns out in the simulations made by Blanchard and Diamond, the net effect on the wage issmall unless he totally ignores the future, i.e. has a very high discount rate.

In our model the worker can continue to work at his old job if he does not get the onehe applies for. Since employed job-searchers do not risk becoming long-term unemployedthe second effect does not appear. Therefore, ranking has an unambiguous and strong effecton wages and employment in the long run.

15 See Gottfries and Westermark (1998) for a criticism of this way of modeling wage bargaining.

17

4 Wage Contracts

So far, we have abstracted from medium term wage contracts. We assumed that wagescould be changed as often as workers decide whether to search or not. But there is ampleevidence that wages are changed infrequently. Union contracts typically specify wagesfor one to three years, and less formal “implicit” wage contracts in non-union sectorsprobably also extend for some time. Since medium or long-term wage contractsthemselves contribute to persistence, it is important to allow for such contracts innumerical simulations.16 We now assume that wages are fixed for N periods; to beconcrete, think of the case when the period is one month and wages are changed inJanuary each year (N=12).

To avoid some technical complications in this case, we assume that the firm has tochoose one employment level for the whole year after it has observed the wage.Turnover still occurs throughout the year. This implies that (unless there is a shock)employment will only change in January; in the other months, only replacement hiringtakes place. The efficiency wage condition corresponding to (5) is therefore:

)])1()[/(' )1( 211iTT

iTTT

eT

iT laNlawwcSsNl −+−−= − , (22)

where T is a time index for years, a1T is the probability to get a job in the first period of thewage contract (in January) and a2T is the (constant) probability in the remaining periods(February-December).17 Considering a symmetric general equilibrium, defining Ω asbefore and using (16) we now get:

16 Also, the importance of unexpected shocks is much greater when wages are fixed for substantialperiods.17 If the wage is set for a year, but the firm is allowed to change employment every month, there will becomplicated within-year employment dynamics. When hiring, firms take account of the probability that ahired worker quits in the next period, in which case they do not save hiring costs in that period. Suchwithin-year dynamics appear peripheral relative to our purpose and we avoid it by assuming thatemployment changes once each year.

18

)1()1)()1(())1()1((

)1(

)1()1)()1(())1()1(()1(

)1( 1

111

rSslsnSlslsrrns

N

lrSslsnSlslsrrnlsl

sN

T

TT

TT

TTTT

−−−−−+−−

−

+−−−−

−+−−−−=

−Ω −

−−−

. (23)

As before, this equation implicitly determines employment as a function of employmentin the previous period. Long run equilibrium employment is the same as before –independent of the length of wage contracts – but persistence increases (for more detailssee Appendix 2). This is illustrated in Table 3 where we again set s, S and Ω as in Table1 and show values of ρ for wage contracts of different length and different levels ofranking.

Table 3. Persistence (ρ) with one-month, one-year and two-year wage contracts.

N=1 N=12 N=24

r=0.0 0.09 0.27 0.40

r=0.1 0.21 0.37 0.48

r=0.2 0.42 0.52 0.59

r=0.3 0.70 0.73 0.76

r=0.4 0.957 0.958 0.959

As expected, long term wage contracts contribute to persistence but the effect is fairlymodest compared to the effect of ranking. For example increasing the length of the wagecontracts from one to twelve months leads increases ρ to .27 while increasing the fractionof jobs with ranking to 30 % raises persistence to .7. Note also that with much ranking,the speed of adjustment of employment is so low in any case that medium term wagecontracts add very little to persistence.18

18 We consider wage contracts that fix one wage for the whole contract period. In practice, unioncontracts that extend beyond one year typically specify one wage for each year and hence they are lessrigid than the 24 month wage contract considered here. The one-year wage contract seems most relevant.

19

5. Understanding the Difference between Europe and the US.

Compared to the US, unemployment is higher in Europe, turnover is lower, and fluctuations inunemployment are much more persistent. An interesting question is whether the mechanismsdiscussed above could potentially explain this dramatic difference. Can plausible differencesin the fundamental parameters generate the substantial differences in labor marketoutcomes that we observe empirically?19

There are four fundamental parameters in the model: the fraction of the employedworkers leaving to unemployment in each period, s, the fraction of employed workersthat apply for a new job each period, S, wage pressure, Ω, and the fraction of jobs forwhich firms rank applicants, r. While s can be measured reasonably well we lack directmeasures of the other parameters. However, we do have estimates of the following threeempirical magnitudes: the flow from employment to employment, S times a, the fractionsof the workforce that is unemployed, u/n, and the persistence of unemployment, ρ . We

may thus ask the following question: Are there plausible values of the fundamentalparameters S, Ω, and r such that Sa, u/n and ρ take values consistent with empiricalestimates?20

Since we have three free parameters and three observable magnitudes, theparameters are “just identified”, meaning that we can deduce the values of thefundamental parameters using the steady state equations in our model - provided that asolution exists. But a priori, it is not obvious that a solution exists, and even if a solutionexists, the resulting parameter values may be implausible.

The empirical estimates of s, Sa, u/n and ρ for the US, Germany and France arereported in the first four rows of Table 4.21 These estimates have been collected from varioussources and the measurement of the different flows and stocks is discussed in Appendix 3.We note that turnover rates are much lower in the European countries; both quits intounemployment and turnover between jobs are between one quarter and half the rates 19 Our purpose is not to test the model, but to ask whether the mechanisms discussed here might explainthe observed differences between labor markets20 In principle, one could examine how well the model explains other observations. With comparable timeseries data on labor market flows one could examine whether the model is consistent with cyclicalfluctuations of these flows in different countries. Also, one could examine the relation betweenemployment and wages, but this requires a more explicit modeling of the shocks (real and nominal). Thesetopics are left for future research.21 We think of Germany and France as examples of European economies with high and persistentunemployment. We chose not to look at the Scandinavian countries since centralized wage setting differsin fundamental ways.

20

observed for the US. Unemployment is higher in Europe but the difference with respect topersistence is even more striking.

Can we find plausible values of the unobserved parameters that “explain” thesedifferences? As it turns out, a solution exists and the implied values for S, Ω and r arepresented in Table 4. We also report the implied values for employed and unemployedjob-searchers to get a job in steady state.

Table 4 Observable magnitudes and implied values for the parameters.

Parameter US 1968-86 Germany 1986-88 France 1986-88

s 0.015 0.004 0.006

Sa 0.012 0.004 0.006

u/n 0.07 0.08 0.106

ρ 0.36 0.90 0.90

S 0.042 0.010 0.012

Ω 3.540 2.417 1.936

r 0.185 0.446 0.452

a 0.29 0.41 0.52

au 0.17 0.044 0.049

How should we interpret these results? It seems that in order to explain the observedsmaller worker flows, higher unemployment rates and much higher persistence in Europewithin this model, we must assume that there is much less on-the-job search, a bit lowerwage pressure and much more ranking in Europe than in the US.22 In the following wefirst try to explain why we get these results in the model and how robust the results are.Then we turn to the question whether they are plausible.

Effects of individual parametersTo understand why we get these results it is instructive to examine the effect of eachindividual parameter on unemployment and persistence. In Table 5 we report the effecton unemployment and persistence as we vary one parameter at the time, starting from a

22 The result that there is lower wage pressure in Europe does not appear to be very robust to changes ininput data but the other results are quite robust (see below).

21

baseline case constructed by taking the averages of the parameter values for the US andFrance.

Table 5 Effects of changes in individual parameters on unemployment and persistence.

s S Ω r Unemployment(u/n)

Persistence (ρ)

Baseline case 0.0105 0.027 2.738 0.319 0.068 0.53

s increases 0.0128 0.027 2.738 0.319 0.105 0.65

S increases 0.0105 0.035 2.738 0.319 0.054 0.42

Ω increases 0.0105 0.027 3.139 0.319 0.092 0.64

r increases 0.0105 0.027 2.738 0.386 0.115 0.74

In order to explain these results intuitively, note that firms are always on their labordemand curves, so if employment falls, wages must increase and conversely. Thus wecan infer what happens to employment by examining how wages are affected by theparameter change for a given level of employment. Note also that wages adjust slowlyafter a shock and persistence depends on how quickly wages adjust after a shock toemployment.

A higher exogenous flow from employment to unemployment (s) implies that fora given level of employment there will be more job openings, it will be easier forsearchers to get a job and firms therefore have an incentive to raise wages, soemployment must go down (compare (7)). Also, there is an increase in persistence.

An increase in on-the-job search (S) implies that there are more people applyingfor jobs, less chance to get a job and hence firms will reduce wages. Thus employmentincreases and there is less persistence.

An increase in wage pressure (Ω) obviously raises wages and leads to higherunemployment and it also slows down wage adjustment after a shock so we get morepersistence. As discussed in the previous section, ranking (r) has the same qualitativeeffect, but from Table 5 we see that ranking has a relatively stronger effect onpersistence.

Having clarified the effect of each of the fundamental parameters on employmentand persistence, consider what happens to employment and persistence if we let the

22

turnover parameters, s and S, go from the higher US values to the lower French values,keeping Ω and r at the US values. This is done in Table 6.

Table 6 Unemployment and persistence when moving from the US values towards theFrench values ¼ of the distance at a time (remember that these approximations get lessand less accurate when we move far away from the calibrated values).

s S u (ss) ρ

0.01500 0.042 0.07 0.36

0.01275 0.035 0.061 0.37

0.01050 0.027 0.052 0.39

0.00825 0.020 0.043 0.40

0.00600 0.012 0.036 0.46

When we decrease the turnover rates, starting from values fitted to the US economy, weget lower unemployment and higher persistence. From this it is clear that the reduction inunemployment coming from lower s dominates the effect in the opposite direction fromlower S. When it comes to persistence the opposite is true; the effect from lower Sdominates. From this exercise we can conclude that the lower turnover ratescharacterizing European labor markets by themselves should give somewhat higherpersistence but also lower unemployment compared to the US economy. We have to findthe explanation for the high and persistent unemployment in Europe among the other twofactors.

Wage pressure and ranking have similar effects in the model: both tend to raise theequilibrium rate of unemployment and make the effects of shocks to employment morepersistent. Thus, the higher level of unemployment and higher persistence in Europecould potentially be explained either by higher wage pressure due to strong unions or bymore prevalent ranking, or by some combination of these factors. But as we have seenabove, ranking has a relatively stronger effect on persistence.23 This is why thesimulation points to more prevalent ranking as a potential explanation of the much highdegree of persistence observed in Europe.

23 Put differently, if we increase wage pressure only until unemployment reaches the level observed forFrance, we get less persistence than what we observe empirically.

23

RobustnessAs discussed above, there is some uncertainty concerning several of the numbers used todescribe the different economies. How sensitive are our conclusions? To check this, wechange the input data one at a time holding the other parameters constant. As can be seenfrom Table 7, our conclusion that ranking is more prevalent in Europe seems to be quiterobust to changes in input data. We can increase or decrease every flow parameter by atleast around 50 per cent without changing our qualitative conclusions.

Table 7 The intervals for which our result that European economies have a higherdegree of ranking than the US holds when one input is changed at a time.

Input France Germany

s 009.0006.00015.0 ≤≤ 007.0004.0001.0 ≤≤

Sa 018.0006.0002.0 ≤≤ 016.0004.00015.0 ≤≤ρ 94.090.070.0 ≤≤ 95.090.070.0 ≤≤

Are the Results Plausible?The result that there is less on-the-job search in Europe is hardly surprising given the lowerturnover rates. European workers appear to be less mobile and this may be due to culturaldifferences, poorly functioning housing markets etc.

The simulations suggest that ranking could potentially be an important cause of highunemployment and, especially, high persistence in Europe. In our view, this is also in line withwhat we would expect a priori. As discussed in Section 3, firms will rationally prefer to hirealready employed workers if two conditions are fulfilled: i) they expect unemployed workersto have lower average productivity and ii) wages cannot be adjusted to make up for thedifference in productivity. If wages were completely flexible, the loss of human capital due tounemployment would affect the future wage, but it would not necessarily affect thereemployment prospects of the unemployed worker.

The loss of human capital in unemployment should be similar in differenteconomies, but there are strong indications that wages are more rigid in Europe. Unionstypically tend to compress wage distributions, especially within groups with similar jobsand qualifications and insist on wage differentials being based on objective and verifiablecriteria – “equal pay for equal work”. Thus it seems likely that employers in Europe find

24

it much more difficult to differentiate wages according to perceived productivitydifferentials compared to the US where unions are nonexistent in most sectors.24

Consistent with this view, there is evidence that workers who are laid off in Europe get asmaller wage reduction compared to the previous job than in the US - if they get a newjob.25 Of course, their chance to get a new job is much smaller.

Wage pressure is found to be of the same order of magnitude in our threeeconomies and in fact is found to somewhat lower in the European economies than in theUS.26 At first sight, this result appears counterintuitive given the strength of Europeanlabor unions. Recall, however, that wage pressure in our model has two differentsources: efficiency wage/turnover considerations and unions with strong bargainingpower. The dramatically higher mobility of the US workforce suggests that the firstfactor should be more important in the US while the latter is clearly more important forEuropean labor markets. In terms of the model, if US workers search on the job moreoften (higher S) we would also expect their job search to be more responsive to wagechanges (higher S’(x) for a given value of x).27 On the other hand, union bargaining power(µ) is surely stronger in Europe, so the net effect on wage pressure (- c S’(1/µ)) is notobvious a priori.

To illustrate this point, consider the case when the distribution G(ν) isexponential:

νλνˆ

)G( −− 1 = e ; ν≥0. (24)

Suppose further that workers face a moving cost which reduces the utility from a new jobby a fraction 1-φ. Then the fraction doing on-the-job search is

24 Furthermore, employment protection is typically more stringent in European countries. If productivityof individual workers is imperfectly observed, an employer has to use signals such as employment statusto infer the productivity of an individual worker. In such a situation, laws that make it hard and/orexpensive to fire a worker that turns out to have low productivity will make firms reluctant to hire workerswho may turn out to have low productivity. If, in addition the wage cannot be differentiated according tothese signals this “lemons problem” may lead to strict discrimination of groups where there are manylemons.

25 Gibbons and Katz (1991), Jacobson, Lalonde, and Sullivan (1993). Burda and Mertens (1999) review the

evidence and report evidence for Germany. See also Grund (1999).26 This conclusion is not very robust with respect to changes in input data.27 This is not a necessary connection. It could be that higher microeconomic volatility and larger wagedispersion in the US raise turnover, but still the effect of the wage on turnover is the same as in France.

25

ww i

ew /ii )/G(w -1 /w)S(w λφ − = = (25)

where ./ˆ φλλ = Thus λ-e S(1) = , i. e. -ln(S(1))=λ . Using the data on S(1) in Table 4

we find that λ equals 3.17 for the US, 4.61 for Germany and 4.42 for France. Highervalues of λ indicate higher moving costs for European workers. To find out theimplications for the union markup, let us compare the US and France. Using the factsthat Ω = - c S´(1/µ) and µλµ /1)1()/1(' SS −= we can write

US

FR

USUS

FRFR

US

FR

SS

µ

µ

λλ

/1

/1

)1()1(

=ΩΩ

. (26)

Using the numbers from Table 4 we find that the union markup must be higher in Francethan in the US. The equation does not allow us to determine the level of the markup, butto get some idea of the magnitude of the difference, suppose that there is no markup (µ =1) in the US. Then the union markup factor for France must be equal to 1.08. Putdifferently, the negotiated wage in a particular firm/sector in France is 8 percent higherdue to unions for given labor market conditions. Although this example builds on veryspecific assumptions it shows that our simulations are fully consistent with theobservation that unions are stronger in Europe.

6. Concluding Discussion

When an economy recovers from a recession there are many job openings. To avoidexcessive turnover, firms raise wages and, as a result, the return to equilibrium is sloweddown. This mechanism can, by itself, lead to a significant amount of persistence, but itcannot alone explain all the persistence (serial correlation) of unemployment found in thedata. If some employers rank applicants by employment status when they hire, this raisesboth the equilibrium level of unemployment and its serial correlation (persistence). Withranking, employed workers who look for new jobs have a higher probability, ceterisparibus, to get the jobs they apply for. Firms therefore offer higher wages to preventturnover and equilibrium unemployment increases. Persistence also increases since, afteran increase in unemployment, there is less incentive to cut wages because unemployedworkers compete less efficiently for the jobs. We show quantitatively that these effects

26

are substantial for reasonable parameter values. We also show that more frequent rankingof job applicants in Europe compared to the US could potentially explain the extremepersistence of European unemployment.

An interesting aspect of our model is that unemployment benefits do not matter.Unemployment benefits do not affect employed workers considering a change of job and quitsinto unemployment are taken as exogenous in the model. Implicitly, we assume that workerswho want to look for another job need not quit their current job to do so, and that those whoquit into unemployment do this for other reasons. This assumption is in line with evidence thatunemployed workers spend a rather small fraction of their time on job search, so in mostcases it is possible – often even advantageous - to remain employed while searching for a newjob.28 If some workers have to quit their job in order to look for a new job, this implies a rolefor unemployment benefits (provided that quitters can potentially become eligible forunemployment benefit) and makes quits more procyclical, but it also complicates the dynamicanalysis considerably.29

Our model is a variation of the “demand side” explanations of unemployment, containingelements from insider-outsider, bargaining and efficiency-wage theories of unemployment.Parallel to these demand oriented theories there is the supply side explanation: unemploymentarises because high unemployment benefits make unemployed workers search less intensely,unwilling to take the jobs they could get, etc. Ljungqvist and Sargent (1998) have recentlydeveloped a model along those lines. While their main purpose is to explain the secularincrease in European unemployment – something we do not attempt to explain – they alsoshow that their model can generate persistence. But although they assume that workers loseon average 40 percent of their human capital when they become unemployed, and that thereplacement ratio is as high as 70 percent, they get a very modest amount of persistence:about 1/8 of the shock remains after two years.30

These simulations illustrate a point made by Pissarides (1992) and also discussed by Bean(1994). While it is true that unemployment persists if some of those laid off due to a negativeshock are slow to return to employment, this type of effect becomes progressively lessimportant as those who were unemployed at the time of the shock find jobs. It stops tooperate entirely once they have left the unemployment pool, so this type of model cannot

28 For a review of such evidence, see Chapter 8 in Layard, Nickell and Jackman (1991).29 A person quitting into unemployment has to consider the possibility that he remains unemployed for along time, so dynamic programming methods must be employed to solve the model. Ljungqvist andSargent (1995) consider a model with endogenous quits.30 See Table 4 and Figure 8 in Ljungqvist and Sargent (1998).

27

explain a persistence of unemployment that is much larger than the average duration ofunemployment for individual workers. Pissarides’ solution to this problem was to construct amodel where there is an interaction between loss of human capital of the unemployed and jobcreation by firms. Our solution is similar but we focus on the interaction between loss of“competitiveness” of the unemployed, turnover, and wage formation.

It is possible to reinterpret our model in a more supply-oriented vein, however. Considerthe following setup. All available jobs are announced in the newspaper and observed by allworkers. Each individual job is associated with a non-pecuniary setup cost which is randomlydrawn by each worker. This setup cost, which is a stand-in for location, requiredqualifications etc., makes most jobs irrelevant for a particular worker, so he only applies to ahandful of jobs. In this situation, the fastidiousness of an unemployed worker will depend onhis unemployment benefit. With high benefits he will apply for only a few of the open jobs.Such a model would have similar dynamics as our model. In this interpretation, our model iscloser to Ljungqvist and Sargent (1998), but differs from theirs because the interactionbetween the fastidiousness of the unemployed workers and wage formation magnifiespersistence. Such a model combines supply-side and demand-side explanations ofunemployment. Much careful research is needed in order to discriminate between the variousmechanisms and measure their relative importance.31

31 Available empirical evidence shows clear statistical effects of benefits on exit rates fromunemployment, but most studies find a rather small effect. For reviews, see Layard, Nickell and Jackman(1991) and Holmlund (1998).

28

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31

Appendix 1: Collective Wage Bargaining

In the main text we assume that the firm sets the wage. Consider now a situation whereworkers have bargaining power as a group because they can strike. Following Gottfriesand Westermark (1998) we assume that the firm and the workers make alternating bidsand that after each bid there is a chance that workers turn out to be unable to continue theconflict. In the latter case, the firm can dictate the wage and then the firm sets the”efficiency wage” we, defined by equation (5) in the text. The firm and the workers areassumed to have log utility functions. Denote by Π(wi) the maximized value of the log ofprofits, i. e. when employment is chosen optimally. We leave out other factors that affectprofits since they are exogenous to the firm. We assume that if an agreement w isreached after j bargaining rounds the payoff of the worker is

ln w - j ∆rw

and the payoff of the firm is

( )Π ∆w ri f− .

In order to get an explicit solution we log-linearize the profit function:

( )Π Π Πw wi i≈ +0 1 ln

where Π1<0. The probability that workers turn out to be unable to strike is denoted φ.

The optimal bid for the workers, ww, is such that the firm is indifferent between taking thebid and rejecting it. In the latter case one bargaining round passes and then either theconflict continues and the firm makes a bid, wf, which is accepted, or (with probability φ)the workers turn out to be unable to strike so the firm can set the wage. Thus we have:

Π Π Π Π Π Π ∆0 1 0 1 0 11+ = − + + + −ln ( )( ln ) ( ln )w w w rw f efφ φ .

Similarly, the firm’s bid is such that the workers are indifferent between accepting andrejecting the offer:

32

ln ( ) ln lnw w w rf w ew= − + −1 φ φ ∆ .

Assuming that the workers make the first bid, solving for w and letting ∆ go to zero weget:

ln lnw wr

re fw= − +

12 1φ Π

.

Provided that rf/Π1 is larger in absolute value than rw the wage is set with a fixedpercentage ”union markup” on the ”efficiency wage”.

Appendix 2: The Effect of Ranking on Employment and Persistence

To show that employment is lower with more ranking, differentiate (18) with respect to r:

2

22

][]][)1()1([]][)1()1([)/(

DNSsssDssSs

rnl ss −−Ω−−−Ω−−−−

=∂

∂.

Here D denotes the denominator and N the numerator in (18). To show that thisexpression is negative we have to show that the numerator is negative. The numeratorcan be written as:

[ ][ ] [ ]

[ ] . )1()1()1(

)1()1()1()1()1()1()1()1( 22222

rSsrss

ssSsrSsSssrssssSs

−−+−Ω−

Ω−−−−−−−+−Ω+−Ω−Ω−−−−

Factoring out the expression in the first bracket from both terms gives us:

[ ] [ ]

Ω−−−−

−−+−Ω−−−−+−Ω+−Ω−

)1()1(

)1()1()1()1()1()1()1( 22222

ssSs

rSsrssrSsSssrss

or, after some manipulation:

33

[ ][ ]Ω−+−−Ω− )1()1()1( 2 ssSsSss ,

which is clearly negative.

To find out how ranking affects the persistence of employment we differentiate theemployment equation. The results are derived for the general N period wage setting casebut the proof in the special case with one period wage setting is of course identical with Nset equal to one. We therefore differentiate equation (23) (the N period case equivalent of(17)) with respect to 1−Tl and evaluate in steady state:

))1()1()(1()1())1(())1()1()(1())1((

))1()1(()1())1()()1()1()(1())1()1(())1()()1()1()(1(

0

ssssssss

ssssssss

ssssssss

ssssssss

ll

SlslsrrnsslNlsnSlslsrrnssllsn

SssrslNlsnSlslsrrnsSssrsllsnSlslsrrns

ll

ss

−+−−−−+−−−+−−−−−−

−+−−−+−−−+−−−−+−−−−−−+−−−

=∂∂

==

ρ

where ssl is given by equation (18). This is not a very informative equation, but our maininterest is to see how persistence is affected by ranking. Therefore, we differentiate theexpression with respect to r and show that the resulting expression is indeed positive.

.0/ 1 >∂∂∂

=∂∂

=

−

ssllrll

rTρ

Letting N denote the numerator and D the denominator. We can show this fact asfollows. We know that the derivative can be calculated as:

2

*/*/N

NrDDrN ∂∂−∂∂.

By looking at the equation above we clearly see that D>N since the expressions in thenumerator and denominator is the same except for the presence of N times two termswhich can be written as:

34

0 )1( >− SnsNsl .

Furthermore, it can easily be verified that the derivative of the numerator is bigger thanthe derivative of the denominator. The only thing that differs is the term;

rl

SnsNsss

∂∂

− )1(

in the denominator and this expression is clearly negative so the derivative of thenumerator is bigger than the derivative of the numerator. Combining these two factsconcludes the proof.

Appendix 3: Data

We take the period to be one month.

The flow into unemployment (s).We generally have fairly good estimates of this parameter. Before discussing the datasources, however, there are two things worth noting. First, since we are interested insteady state situations the flows in and out of employment/unemployment have to beequal. Second, in our model a worker is always either employed or unemployed and wedo not formally model movements in and out of the labor force. These two factors add abit of complication because empirical studies often present results where the flows are notperfectly equal and where out-of-the labor force is included with flows to and from it. Ina complete model the flows in and out of the labor force should be included but forsimplicity we choose to ignore such flows and take the steady state flows betweenemployment and unemployment as the average of the in and out flows.

The exclusion of labor force dynamics can partially be justified by arguing thatthese flows merely represent the exchange of workers between in and out of the laborforce; i.e. workers retiring and being replaced by workers directly out of school, parentstaking child leave etc. Furthermore, as is shown in Blanchard and Diamond (1990) themost important dynamics in a recession is the increase in the net flow from employment

35

to unemployment while the net flows to and from the labor force vary much lessdramatically.32

For the US economy we use values from Blanchard and Diamond (1990). Thedata are Abowd-Zellner adjusted gross flow series, which are seasonally adjusted datafrom CPS studies. The data set covers the period January 1968 to May 1986 and givesus monthly figures. The flow to/from unemployment averages 1.4 million per month. Toget this in fractional form we divide it with the average stock of employment taken fromthe CPS, which is 93.2 million. The result is a flow from employment to unemploymentequal to 1.5 percent of employment.

For the continental European economies we use data from Layard, Nickell andJackman (1991) based on OECD sources. These data measure the total inflow intounemployment so it includes flows from out-of-the labor force into unemployment but italso excludes workers who flow in and out of unemployment very quickly. ForGermany they report an inflow rate into unemployment of 0.4 per cent monthly for theperiod 1986-88. For France the corresponding flow is 0.6 per cent.

The flow from job-to-job ((1-G)a).Data on this flow is generally of lower quality compared to data for the flows discussedabove. Since there do not exist any direct studies of this flow we instead have to rely onapproximations from other data. This is often done by using series of separations andnew hires. The result is obviously less precision in the estimates than ideally but for ourcalibrations these data are sufficient.

For the US economy we continue to use Blanchard and Diamond (1990) as ourdata source. They conclude that job-to-job movements represent 60 per cent of quits inthe manufacturing sector from 1968-88. Furthermore, they approximate quits to 0.401million out of 19.739 million employed workers for the period 1968-81. This figure isconfirmed by Akerlof, Rose and Yellen (1988) who report a monthly quit rate from1948-81 of around 2 per cent. This implies a fraction of job-to-job movements ofSa=(0.401 / 19.739) * 0.6 = 0.012.

For the continental European economies we have had some problems obtainingaccurate data. We have found two principal data sources; Burda and Wyplosz (1994)

32 Alternatively, we may think of some of the people out of the labor force as “semi-unemployed”. Intheory, we may define unemployment to include this stock, but it implies that our measure underestimatesthe true amount of unemployment.

36

report data for 1987 from national statistics and Boeri (1999) who report data from theyear 1992. Boeri gets his data by taking the annual hiring rate and subtracting all annualinflows into employment from unemployment and inactivity to obtain an employment toemployment flow. For Germany, Burda and Wyplosz report a job-to-job flow of 0.0797million per month implying a fraction of 0.0797 / 27.070 = 0.003. For France thecorresponding figures are 0.0358 million and 0.0358 / 15.685= 0.002. These areextremely small numbers compared to the US. Boeri, on the other hand, reportscorresponding flow rates of 0.0095 for Germany and 0.0073 for France. This means thataround 60 per cent of all hiring in Germany as well as 50 per cent of hiring in France arejob-to-job flows. Although the figures cover different time periods it is puzzling that theydiverge so markedly. In the simulation we assume that 50 percent of hiring in bothGermany and France is job-to-job flows and thus we assign the same numerical value tothe job-to-job flow as to the flow from unemployment to employment, i.e. 0.004 forGermany and 0.006 for France.

Unemployment rate (u/n):For the US we use the above mentioned average stocks from the CPS for the time period1968-86 of 93.2 million employed and 6.5 million unemployed workers. This gives usan unemployment rate of 0.07.

For the European economies OECD (1999) reports an average unemploymentrate between 1986-96 of 8 per cent for Germany and 10.6 per cent for France.

Persistence (ρ ).

Different authors use very different techniques to estimate persistence and this means thatit is difficult to compare different studies. Some studies estimate persistence in simpleautoregressive models while some newer studies use the unobserved components (UC)technique. All studies conclude that persistence is higher in the European labor markets.

Two similar studies using standard econometrics are Blanchard and Summers(1986) and Alogokoufis and Manning (1988). The former estimate the persistence ofunemployment with yearly data for a number of countries including a time trend and theirestimates of ρ are 0.36 for the US, 0.94 for Germany and 1.04 for France. The secondstudy, also with a time trend included, report estimates for the US 0.48, Germany 0.94and France 1.04.

37

In our calibration below we use the following estimates; 0.36 for the US and 0.90for Germany and France. This means that we follow Blanchard and Summers but adjustthe European values downwards a bit.

Obviously, the exact numbers can be questioned, but our simulations are meant toillustrate the importance of various mechanisms and, as we show in the text, ourqualitative conclusions are quite robust.