Ranking of Job Applicants, On-the-job Search and Persistent Unemployment*
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, Torsten
When one compares European and US labor markets, several differences are apparent.
Unemployment rates are much higher, turnover is much lower, and the adjustment back to equilibrium after a shock appears to be much slower in Europe. While high
unemployment may plausibly be blamed on unions and labor market rigidities, and low turnover may be due to cultural differences, the last observation is especially intriguing.
In several European countries, temporary cyclical shocks have raised unemployment and then it has remained high for a long time. Adjustment costs may be one explanation for sluggish employment adjustment, but it can hardly be the whole story. Why is
unemployment so persistent in Europe?1 In this paper we take a new look at this question, 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 significant training costs to replace them. Consequently, firms consider the implications for turnover when they set wages.
The second important starting point is that unemployed seem to be at a
disadvantage compared to employed workers when they compete for jobs. This may be because workers lose some of their human capital in unemployment or because
unemployment is taken as a signal of unobserved personal characteristics. If employers perceive unemployed workers to have lower average productivity, they will be reluctant to hire them, and this is especially true if wage structures are rigid, preventing
differentiation of wages according to perceived productivity differentials.
If turnover is important then the firm’s optimal wage should depend on the probability that a worker looking for another job will actually find one; if this probability increases the firm will respond by raising its wage to prevent costly turnover. If, in addition, unemployed workers do not compete for jobs on an equal basis with employed applicants, this must raise the probability for employed workers to get the jobs they apply for and this in turn will tend to raise the wage. In other words, we should expect an interaction 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 alternative approaches. By “persistence” we mean a high serial correlation in unemployment.
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 new job, and the higher is, ceteris paribus, the ”efficiency wage” that is optimal from the firm’s point of view.
To formalize this intuition, we formulate a model where a fraction of all employed workers apply for new jobs while maintaining their current jobs. Whether a person applies for a new job or not depends both on the relative wage offered by the firm and on a stochastic non-pecuniary job satisfaction factor which affects the utility gain from switching jobs. The wage may be set by the firm or in a bargain with a union. In either case, the wage setters take the effect of the wage on turnover into account. We first consider the case when employers chose whom to hire randomly (no ranking). We show that even without ranking unemployment will be persistent. Because of the fear of costly turnover, a permanent negative shock is not fully accommodated in the next wage
contract, 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 to hire employed applicants. Ranking increases the probability that an employed worker gets the job he applies for and this makes it optimal for firms to set higher wages. The result is both lower steady state employment and a slower adjustment following a shock.
Simulations show that the effects of a limited degree of ranking are substantial for reasonable parameter values.
The model is used to interpret the differences between the US and Europe. As noted above, both the level and the persistence of unemployment are much higher in Europe. There are three main factors in our model that might explain these observed differences: lower mobility, stronger unions and, perhaps, more ranking in Europe. We find that the lower turnover in the European economies should, by itself, lead to lower unemployment and approximately the same amount of persistence. Since unemployment is in fact much higher in Europe, this has to be explained either by strong unions or by more prevalent ranking. Our simulations show that, within this model, wage pressure due to strong unions can explain high unemployment, but not the high persistence observed empirically. Instead, our analysis points to ranking of job applicants as a potentially important explanation for the persistence of unemployment observed in most European labor markets.
The notion that unemployed workers - and especially those who have been unemployed for a long time - have difficulty competing for jobs has been around for
some time (see e. g. Phelps (1972), Layard and Nickell (1986)) but there are few microbased models formalizing the idea. The insider bargaining model developed by Blanchard and Summers (1986) and Gottfries and Horn (1987) emphasizes the distinction between employed and unemployed workers, but can hardly generate the extreme
amount of persistence found in the data.2 Other related papers are Huizinga and Schiantarelli (1992) and Gottfries and Westermark (1998), who show that persistence may arise due to the forward looking nature of wage decisions, but without the interaction between 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). They analyze ranking of unemployed workers by duration in a matching model. The wage is determined by Nash bargaining with the expected utility of a recently laid off worker as threat point. Their main question is how the wage is affected if firms rank job applicants according to the length of unemployment. The result is that ranking has small effects on the 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 currently employed - 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 the advantage of employed job searchers relative to the unemployed rather than the
distinction between short-term and long-term unemployed. Second, while Blanchard and Diamond 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 the effects quantitatively. Third, our results differ qualitatively from those of Blanchard and Diamond. In our model, ranking has substantial effects not only on the dynamics, but also on the long run equilibrium level of wages and employment. We believe that our focus 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 for many European countries (see references below). The Blanchard and Summers (1986) version of the insider bargaining model generates hysteresis, which is an extreme form of persistence, but only because they 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. There is no ranking in his model. Instead, firms cannot distinguish long-term and short-term unemployed, so all job seekers have the same chance to get a job. Persistence arises because long term unemployment implies a deterioration of the average quality of unemployed workers which makes it less profitable for firms to hire workers and fewer vacancies are created. Thus the mechanisms are quite different from those considered here.
In Section 2 we formulate the basic model without ranking, solve it for steady state employment and show that unemployment is persistent even without ranking. In Section 3 we introduce ranking and show that this increases unemployment and persistence. Section 4 extends the model to allow for wage contracts spanning several periods. In Section 5 we use numerical simulations to examine whether the observed differences in turnover, unemployment and persistence between Europe and the US can be 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 turnover considerations are important for firms when they set wages. The importance of voluntary turnover is well documented. Holmlund (1984), Akerlof, Rose and Yellen (1988) report quit rates around two percent for the U. S., Sweden and Japan and Boeri (1999) finds that quits from one job to another constitute around 50 per cent of all hiring in several European economies. According to Holmlund (1984), about 8 percent of employed workers 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 a new job. Lane, Stevens and Burgess (1996) show that worker reallocation is two to three times as great as job reallocation. Another indication of the importance of quits is the fact that total worker turnover is procyclical – reflecting the procyclicality of quits (Anderson and Meyer (1994)). Also, survey evidence shows that firms care about turnover. Fear of training/ hiring cost as a result of quits, as well as fears that the most productive workers would 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 and non-pecuniary factors seem to influence quit decisions.
We first consider a case when there is no ranking of job applicants. There are a large number of workers and a large number of identical firms, but the number of firms is much smaller than the number of workers. Events take place in discrete time and the sequence of events in each period is the following. Near the end of every period a fraction s of the workers leaves employment and enters the pool of unemployed. This fraction is exogenously given and represents workers quitting or being laid off for exogenous reasons. Then wages
are set – either by the firm or in a bargain - and the remaining workers decide whether to look for a new job or not, considering the wage offered by the firm, the wage offered elsewhere and a non-pecuniary “job satisfaction” factor. All unemployed workers also search and every searcher submits one application to a randomly chosen firm.4 Firms receiving the applications then make their choices of whom to hire.
We have three distinct decisions: firms set wages, workers decide whether to search and firms decide whom to hire. We now proceed by first analyzing search and turnover in a specific firm for a given wage, then analyzing the firm’s optimal decision about the wage, and then we consider the case when the wage is set in a bargain between the firm and the workers. Finally we turn to employment dynamics in a symmetric general equilibrium and calculate long-run unemployment and persistence.
Every worker who remains employed when a new period begins has to decide whether to look for a new job or not. We assume that every employed worker draws a number ν that determines his job satisfaction from continuing to work at his present job. The number ν is drawn from a random distribution with cdf G(ν). Given ν, his expected utility from the current job is wti/ν ; the expected utility from a randomly chosen new job is wt . 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 and have a mean smaller than unity, so if the wage is the same most workers prefer the job they have.
The employed workers decide whether to search or not given the wage offered by the firm,wti, the wage expected elsewhere in the economy wt and the parameter ν . On- the-job search is costless, so a worker will start searching if wt >wti/νi. 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 that search 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 job satisfaction. Also, the workers would have to consider effects on utility in future periods when they consider switching jobs.
) / ( 1 ) /
(wit wt G wti wt
S = − , (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 is then (1−s)S(wti/wt)at, where atis the probability that an employed searcher finds a job (to be determined later).
In this section we assume that the wage can be changed every period.6 When setting the wage, the firm takes account of the fact that labor turnover is costly. For every worker the firm hires, it incurs a hiring cost equal to c times the average wage wt. The
production function is θtF(lti), where θ may be interpreted as productivity, price, ort product demand. If wages are set in nominal terms, θt will be a composite variable including both real and monetary factors.7
To simplify, we assume that voluntary quits are sufficiently large that all employment adjustment can be made by variations in hiring,8 and subjective certainty; the firm optimizes as if the future was known with certainty.9 The firm solves the following maximization
6 In Section 4 we generalize this to the case when the wage is set for N periods
7 If, for example, each firm faces a demand curve of the form qi =(pi/ p)−ηm/ p, where pi is the
firm’s price, p is the price level and m is money supply, and produces under constant returns to scale with productivity θ, revenue of the firm can be written
( ) η( ) η
θ1−1/η m/p 1/ li 1−1/ .
With predetermined prices, an unexpected monetary shock clearly affects employment. With
predetermined nominal wages but fully flexible prices, the situation is more complicated. Prices are set with a fixed markup on marginal cost, which is w plus the hiring cost minus the hiring cost that is saved next period, all divided by θ. Still, fixed nominal wages imply that prices adjust less than fully to monetary shocks. 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 optimality of 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 changing the macroeconomic analysis.
9 Hence the dynamic analysis below refers to the adjustment of employment after an unexpected once and for all shock to θ.
( ( ) ( (1 (1 ) ( / ) ) ))
max ti j 1
i j t j t j t i
j t i
j t j t i
j t i
j t j
l t w
l a w w S s s
l cw l
j t i
− + + + + +
= − − − − − −
(2) The first order conditions are
' − 1 =
− t t ti−
i t i
t cS w w s al
/ ( ) 1 ( )
' − − + +1 − +1 t+1 t+1 =
i t t
t i t i t
tF l w cw βcw s S w w a
θ . (4)
Equation (4) defines the labor demand function = ( , , , +1 , +1 , t+1)
i t t t t i t i
t l w w a w w
l θ . Inserting
this into (3) we get the following equation, which implicitly determines the firm’s optimal wage, the “efficiency wage”, wte:
i t t t e t t
e t t t t e
t w a w w scS w w al
l( , ,θ , +1 , +1 , )=−(1− ) ' ( / ) −1. (5)
The optimal wage is such that the direct cost of a marginal wage increase equals the reduction in turnover costs associated with a wage increase. The optimal wage depends positively on the average wage level, the hiring cost, and the probability that a searcher gets a job.
Unions and Bargaining
In most European labor markets, and some parts of the US labor market, the wage is set in negotiations between employers and a union. Even if there is no formal union organization, workers may have bargaining power because they could potentially take collective action against the firm. The negotiation process is modeled as in Gottfries and Westermark (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, wte, defined above. Otherwise, bargaining continues until one party accepts a bid made by the other party. This wage setting mechanism generates a wage that is approximately equal to a “union markup factor” µ times the wage that the firm would set if it was free to set the wage:
e t i
w =µ . (6)
The size of the markup depends on the workers’ ability to last a conflict, the impatience of the parties etc. (see Appendix 1). Substituting into (5) we get the following equation which determines the wage when workers have bargaining power:
i t t t i t t
i t t t t i
t w a w w c s S w w al
l( /µ, ,θ , +1 , +1/µ , )=− (1− ) ' ( /µ ) −1. (7)
The Level and Persistence of Unemployment
Since we are interested in aggregate employment, we consider a symmetric general equilibrium where all firms set the same wage. This is the natural situation since all firms and workers are assumed to be identical and therefore solve the same problem.10 Then we have from equation (7):
( − −
= t t
t s al
l , (8)
where Ω = -c S’(1/µ). The parameter Ω is a measure of “wage pressure” arising from the 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 at, the probability to get a job for an employed searcher. In a symmetric equilibrium, the number of people hired per firm is:
1 1 (1 ) (1) )
( − − + − −
= t t t t
t l s l s S al
h . (9)
This equation simply says that hiring is equal to the number of workers the firm wishes to employ this period minus the workers who remain from last period, taking into account exogenous and endogenous separations. There are many more workers than firms and we assume that each firm gets at least as many applicants as it has job openings. In this section we consider the case without ranking where the firm has no preferences between employed and unemployed workers but simply draws the desired number of workers randomly from the pile of applications. Then the probability to get a job is the same for all 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 to examine how much persistence we get in the model without this additional source of persistence.
) 1 ( ) 1 (
) 1 ( ) 1 (
− + −
t t t
t n s l s Sl
l Sa s l
a l , (10)
where we simplify notation by writing S(1)=S. This equation says that the probability to get a job for a searcher is the number of hirings (given by (9)) divided by the total number of searching workers consisting of both unemployed workers, n−(1−s)lt−1, and
employed workers searching on-the-job (1−s)Slt−1. Solving equation (10) for atwe get the following expression:
) 1 (
) 1 (
t t t
t n s l
a l , (11)
which is simply hiring divided the number of unemployed job seekers. The chance to get a job does not depend on the number of employed workers looking for jobs. The
intuition is that every worker who changes jobs leaves one job and takes one job, so the number of jobs available for the remaining searchers remains the same. Combining (11) with equation (8) gives us:
1 (1 )
) 1 ) (
− − − −
− − Ω
t t t
t n s l
l s l l
l . (12)
This equation implicitly determines employment as a function of employment in the previous period. Evaluation of (12) in an equilibrium with constant employment,
l , allows us to determine the steady state employment rate
) 1 )(
1 Ω +
s s n
The model has the natural rate property; productivity does not affect employment in the long run. Higher wage pressure Ω due to high turnover costs or strong unions results in lower employment, an increased flow from employment to unemployment (s) has an ambiguous effect on the natural rate, but for plausible parameter values it raises unemployment.
Differenting (12) with respect to lt−1 and evaluating in steady state we get an expression for the monthly persistence of employment which, for later reference, we denote ρ ;m
) 2 1
m s u sl
l s u s l
l − +
ρ , (14)
where u denotes unemployment. It can be shown that this expression is positive for reasonable values for the parameters.
To understand why employment depends positively on employment in the previous period, imagine that we are initially in steady state. Then θ falls unexpectedly and
permanently. This happens after the wage has been fixed, so firms respond by cutting employment. Employment stays at this lower level until the end of the period. In the next period firms cut their wages, but not so much that employment immediately returns to its steady state value. If wages would immediately fall to the new steady state level, there would be a large increase in employment, many vacancies open to workers searching on the job, and firms would suffer from excessive turnover. Foreseeing this, each individual firm would then have an incentive to deviate by raising its wage so as to reduce turnover. Therefore the equilibrium solution must be that firms reduce wages less and employment remains low for some periods after a negative shock.11
Numerical analysis of the model
We have just shown that employment will remain low for some time after a negative shock even without ranking of job applicants. In the next section we will show that this mechanism is reinforced when firms rank job applicants. But before turning to the effects of ranking, it is informative to put some numbers into the model to see how persistent unemployment will be without ranking.
Effectively, there are three free parameters in the model: the flow from
employment into unemployment, s, the fraction of employed workers searching on the job, S, and, the combined "wage pressure" effect resulting from turnover costs and strong unions, 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, but those papers did not consider on-the-job search.
S available, and no direct measures of Ω. We do, however, have measures of the average job-to-job flow, which in our model corresponds to S times a, and the unemployment rate, u/n. We therefore set S and Ω in such a way that the equilibrium job-to-job flow and unemployment correspond to the values observed empirically. In Table 1 we report empirical 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 state probability to get a job for a job applicant and the resulting yearly persistence of unemployment generated by the model, defined as ρ= ρ12m .
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 0.05
ρ 0.09 0.51 0.51
We see that, with parameter values consistent with the stocks and flows observed in the US and European labor markets, unemployment becomes quite persistent in Germany and France but not in the U. S. The persistence found in the model is much smaller than empirical estimates, however. Blanchard and Summers (1986) and
Alogoskoufis and Manning (1988) estimated simple autoregressive models for unemployment and found that the coefficient for lagged unemployment is close to unity for most European countries, but only around .4 for the US (with yearly data).13 Our basic model therefore seems to generate too little persistence.14
12 See Section 5 for further discussion of this approach and Appendix 3 for detailed discussion of these numbers.
13 High serial correlation in unemployment may be due to two conceptually different mechanisms. One is that cyclical (aggregate demand) shocks affect unemployment and then the adjustment back to equilibrium takes a long time. Another possibility is that shocks to the natural rate (e. g. changes in union bargaining power) themselves are highly persistent (and frequent). The present model is of the first type. Jaeger and
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 and Robins (1990) showed that in the U. S. employed job searchers receive almost twice as many 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 in Austria. Agell and Lundborg (1999), in a survey of Swedish firms, found that employers do view unemployment as a signal of lower productivity. How will ranking affect the basic decisions made by the agents in our model? How will ranking affect the steady state level of employment and the degree of persistence? How big are the effects quantitatively? These are the questions to which we now turn.
Before we incorporate ranking in the model it is important to be clear about what we mean by ranking. In this model, ranking means that employers sometimes, when choosing between applicants for a particular job, prefer to employ someone who has a job to an unemployed worker. Formally, we assume that firms rank applicants in this way for a fraction r of the jobs. Since there are many applicants of each category per job, only employed applicants are hired to those jobs.
This definition of ranking raises an important question. Why do firms chose to rank their applicants? Within the context of our formal model we can simply defend our
assumption by pointing out that workers are identical, so firms are indifferent between ranking and not ranking and may as well rank applicants. But the model would be more convincing if firms had a reason to rank workers.
A natural argument is that the perceived productivity of an employed worker is higher than that of an unemployed worker. In fact, it is enough that unemployed workers are 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 of persistence. They find that effects of cyclical shocks on unemployment are substantially more persistent in 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.
arguing that the firm could offer different wages for the different groups, each wage corresponding to the productivity of the group. Thus there must be some rigidity of the wage structure that prevents firms from differentiating wages according to perceived productivity differences. In the following we assume that there is such a rigidity.
With ranking, the search and wage setting decisions are made as before, but employed workers are more likely to get hired than unemployed workers are. We assume that workers do not know for which jobs ranking is applied but send in their applications at random. Using at to denote the probability for an employed searcher to get a job we have:
) 1 ( ) 1 (
) 1 ( ) 1 ) ( 1 ) (
) 1 ( ) 1 (
− − − + −
t t t
t t t
t n s l s Sl
l Sa s l
s r l
l Sa s l
With probability r the worker applies for a job where employed searchers are preferred and in this case the probability to get a job is hiring per firm divided by the number of employed searchers per firm. With probability (1-r) the worker applies for a job where the employer does not have any preference for a particular type of worker and in this case the probability to get a job is hiring divided by the total number of searchers per firm.
Solving (15) for at gives us:
) 1 ( ) 1 )(
) 1 ( (
) ) 1 ( ) 1 ( )(
) 1 ( (
t n s l s S r l
Sl s l
s r rn l s
a l . (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 job
decreases for a given level of employment. Looking back at equation (15) we see that an increase in S has two counteracting effects on the probability for employed workers to get a job. More on-the-job search means that more workers leave their jobs and this increases the number of job openings, but there are also more applicants for jobs, especially for those jobs which are predestined for employed applicants. Inspecting the right hand side of (15) we see that the latter effect dominates: the more workers that do on-the-job search the smaller is their chance to get a job. Combining (16) with (8), finally, gives us:
) 1 ( ) 1 )(
) 1 ( (
) ) 1 ( ) 1 ( )(
) 1 ( )( 1 (
r S s l
Sl s l
s r rn l s s l
t − − − −
− − Ω
− . (17)
As before, this equation implicitly determines employment as a function of employment in the previous period. Evaluating (17) in steady state we get
) 1 ( ) 1 ( ) 1 ( )
) 1 ( ) 1 ( ) 1 (
2r s s S s S r
r s s r S s n
− Ω +
= − . (18)
For the steady state level of employment lss to be positive the following condition must be fulfilled:
S s r
r > Ω
1 . (19)
Equation (19) can be interpreted as giving a limit to how much ranking our model can take. If r gets very high we get a situation where equilibrium employment is equal to zero. That r cannot be too large is most evident if we consider the extreme case when employers hire almost only employed workers. Then unemployed workers have a very small chance to be hired. Since every period a share s leaves employment but very few unemployed workers get hired employment is only stable at zero. In the following we assume that condition (19) is satisfied.
One may suspect employment to be lower the more ranking there is since ranking implies a less well functioning labor market. In Appendix 2 we differentiate (18) and show that this is in fact the case:
) 0 / ( <
∂ . (20)
This result can be explained as follows. In our model the flow from employment to unemployment is a constant fraction of employment. The flow from unemployment to employment on the other hand is depends on the probability for an unemployed worker to get a job. If more firms rank by employment status this probability is reduced, ceteris paribus, and the only way this can be reconciled with the steady state condition that inflow equals outflow is that the level of unemployment is higher.
Another interesting question is how ranking affects the persistence of
unemployment. Differentiating (17) with respect to lt−1 and evaluating in steady state we get an expression for ρ and differentiating once more with respect to r we can show that ranking increases persistence (see Appendix 2):
. / 1 0
l l r
(21) The intuition behind equation (21) can be understood by extending the discussion in the non-ranking case. After a negative shock to productivity, the wage will not fall
immediately to the new steady state level because, if it did, employment would recover very rapidly and there would be many vacancies and excessive turnover. Thus wages adjust slowly although the level of unemployment is high. This mechanism is reinforced by ranking, since when employed workers have priority for some jobs, their chance to get a new job depends less on the stock of unemployment and more on the number of
Quantitative Effects of Ranking
Having showed analytically that ranking reduces the level of employment and raises the persistence of unemployment we now ask whether these effects are quantitatively important. To answer this question we take the values for the US economy in Table 1 and examine what happens to steady state employment and persistence as we increase the fraction 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 values from Table 1. Our purpose here is not to describe any real world economy but to examine the potential quantitative effects of ranking, keeping the other fundamental parameters constant at some reasonable values.
Table 2 Equilibrium values with different degrees of ranking.
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 the persistence 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 found substantial effects on wage dynamics, but only small effects on the steady state, one might wonder why we also get long run effects. Our interpretation is the following. In Blanchard and Diamond the wage is set according to the Nash bargaining solution and the state of the labor market affects wage setting via the ”threat point”, which they take to be the situation if the employed worker was to become unemployed.15 This means that ranking has two competing effects on the wage. If an employed worker were to become unemployed, his chance to find a new job soon would be much better since he would be “first in line” for new jobs. But on the other hand he does run a small risk of becoming long-term unemployed himself. As it turns out in the simulations made by Blanchard and Diamond, the net effect on the wage is small 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 one he applies for. Since employed job-searchers do not risk becoming long-term unemployed the second effect does not appear. Therefore, ranking has an unambiguous and strong effect on wages and employment in the long run.
15 See Gottfries and Westermark (1998) for a criticism of this way of modeling wage bargaining.
4 Wage Contracts
So far, we have abstracted from medium term wage contracts. We assumed that wages could be changed as often as workers decide whether to search or not. But there is ample evidence that wages are changed infrequently. Union contracts typically specify wages for one to three years, and less formal “implicit” wage contracts in non-union sectors probably also extend for some time. Since medium or long-term wage contracts themselves contribute to persistence, it is important to allow for such contracts in numerical simulations.16 We now assume that wages are fixed for N periods; to be concrete, think of the case when the period is one month and wages are changed in January each year (N=12).
To avoid some technical complications in this case, we assume that the firm has to choose 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 hiring takes place. The efficiency wage condition corresponding to (5) is therefore:
) 1 ( )[
/ ( ' ) 1
( Te T 1T Ti 1 2T Ti
T scS w w a l N a l
Nl =− − − + − , (22)
where T is a time index for years, a1T is the probability to get a job in the first period of the wage contract (in January) and a2T is the (constant) probability in the remaining periods (February-December).17 Considering a symmetric general equilibrium, defining Ω as before and using (16) we now get:
16 Also, the importance of unexpected shocks is much greater when wages are fixed for substantial periods.
17 If the wage is set for a year, but the firm is allowed to change employment every month, there will be complicated within-year employment dynamics. When hiring, firms take account of the probability that a hired worker quits in the next period, in which case they do not save hiring costs in that period. Such within-year dynamics appear peripheral relative to our purpose and we avoid it by assuming that employment changes once each year.