Firms’ Market Power, Wage Dispersion and Business Cycle Annaïg Morin∗ European University Institute

September 2012 JOB MARKET PAPER

Abstract This paper investigates a dynamic search and matching model with wage posting in which workers can receive several job offers each period. Firms have full monopsony power in the sense that they unilaterally set wages but wage dispersion arises due to search frictions and inter-firm strategic wage policy differential. I analyze how the business cycle affects workers’ outside options valuation and subsequently workers’ market power over firms. Through this channel, I show that the market power of firms, defined as the extent to which firms exert their monopsony power, is countercyclical. Moreover, I relate the fluctuations over the cycle of the relative market power of workers and firms to the fluctuations of wage dispersion. In good times, a jump in vacancies brings workers to face a higher number of offers, constraining firms in their wage setting decision. The market power of firms erodes which leads to a decrease in wage dispersion and a convergence in wages towards the competitive level. This paper therefore gives a rationale for the observed countercyclicality of the wage dispersion.

Keywords: Monopsony; Wage differentials; Cycles JEL classification: J42; J31; E32 ∗

Max Weber Postdoctoral Programme, European University Institute, Florence, Italy. I am grateful to Tito Boeri, Antonella Trigari and Alain Sand for their precious advice and support. I would like to thank Árpád Ábrahám, Jérôme Adda, Alberto Alesina, Michael Burda, Aurélien Eyquem and Nicola Pavoni who provided valuable comments at different stages of this project. I have also benefited from comments received at Bocconi internal seminars, at the EUI macro seminar, at the EEA 2012 conference and at the IEA 2011 conference.

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1

Introduction

Large observed differentials in wages are not only on account of different levels of skill, qualifications, status, tenure, age or sex. Homogeneous workers in terms of observable characteristics are often paid differently for similar jobs, phenomenon which represents a challenge in terms of theoretical modeling. Deviations from the purely competitive wage reflect the monopsony power of the firms, i.e. their ability to impose the wage to the workers. Observing wage dispersion leads to the conclusion that the firms monopsony power is either differently distributed across firms or strategically partially unexploited. The current paper focuses on the second argument and presents a dynamic model of the labor market where wage dispersion arises even though workers and firms are ex ante perfectly homogeneous.1 I endogenize the market power of firms, formally defined as the extent to which firms choose to exercise their monopsony power, and analyze how the wage setting decision of firms evolves along the cycle by investigating the cyclical properties of the firms’ market power. Relatedly, the impact on the cyclical properties of wage inequality is examined. As of now, the presence of important frictions on the labor market is a consensus view in the literature. Diamond (1971) emphasizes the role of search frictions in rising prices from competitive to monopoly levels. As long as frictions are large enough so that a price increase does not cause the buyer to pay another search cost for getting an alternative price quotation, sellers get full monopoly power. Burdett and Judd (1983) complete this analysis and point out that, in case there is a positive, but not certain as in Diamond, probability that each job searcher knows only one price, firms do not all set their prices at the monopoly level but instead have the incentive to offer differing prices. With a specific focus on the labor market, Manning (2003) argues that the firms behave like monopsonies, not in the sense that they each stand alone in different sub-markets, but because the supply of labor to each individual firm is not infinitely elastic.2 In1

Krueger and Summers (1988) examine the magnitude of wage differentials for equally skilled workers and find that there are important variations in wages which can not be explained by human capital differences. 2 Mortensen (1972) has first shown that search behaviors induce an upward-sloping supply curve to individual firms.

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deed, search frictions are such that both the worker and the firm would be worse off if their employment relationship would come to an end. Therefore, as long as the wage provides a utility which is greater than the value of unemployment, a slight decrease in the wage does not lead to the worker’s resignation. Also, a job seeker might accept a relatively bad wage offer if he only gets that offer during a certain time span. Hence, search frictions give firms some monopsony power, power which is exploited when the wage is set below the competitive level. Furthermore, wage dispersion at equilibrium naturally emerges from this setting. Indeed, the extent to which firms exercise their monopsony power affects their hiring and turnover rates but, as long as the proposed wage remains above the reservation level, each firm eventually do find workers. Therefore, the trade-off between the profit per worker and the easiness to get and retain workers3 leads to differential wage setting strategies across firms. This mechanism is at the core of the model developped by Burdett and Mortensen (1998). As a pioneer, they show how wage dispersion at equilibrium can be generated when search frictions are combined with on-the-job search, in a framework where workers and firms are perfectly homogeneous and have perfect information4 . The present paper proposes a dynamic investigation of the cyclical properties of the wage differential by analyzing how the business cycle affects the firms’ incentive to exercise their monopsony power. Specifically, the paper develops a tractable dynamic stochastic equilibrium model of the labor market which draws together homogeneous monopsonistic firms, which unilaterally set wages and compete for workers, and homogeneous workers getting some market power from this inter-firm competition. In such a setting, wage dispersion results from differing wage setting strategies across firms, i.e. from differing market powers. By studying how the strategical wage setting decision of firms evolves over the business cycle, I make two contributions to our 3

Using danish data, Christensen, Lentz, Mortensen, Neumann, and Werwatz (2005) empirically show that search effort declines with the wage. 4 Parallel to this stream of literature, some authors argue that equilibrium wage differential results from unobservable workers heterogeneity (heterogeneity in preferences over non-wage job characteristics (Bhaskar, Manning, and To (2002)), heterogeneity in unobservable ability (Murphy and Topel (1987), Postel-Vinay and Robin (2002))) or workers incomplete information about the wage distribution (Winter-Ebmer (1998)).

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understanding of wage fluctuations. First, I explicitely differentiate the concept of market power from the one of monopsony power. In so doing, I can fully focus on explaining what drives the incentive of firms to exert their monopsony power and why the intensity with which they exert it evolves with the business cycle. Second, I show that fluctuations of the firms market power constitute the channel through which the business cycle affects the equilibrium wage dispersion. This paper builds on Burdett and Mortensen (1998)’s model (henceforth BM98). I keep the two assumptions of imperfect labor market due to search frictions and of on-the-job search. Unlike BM98, time is discrete and job seekers can receive more than one offer each period. This assumption has valuable advantages. First, I am able to distinguish between the meeting process and the matching one. Firms make take-it-or-leave-it wage offers to workers and matches are formed only when they are accepted by the workers. This gives an interesting active role to the workers and allows me to analyze to which extent the workers’ job acceptance decision constraints the firms’ wage setting decision, in a setting abstracting from any type of explicit bargaining. Second, I am proposing a richer framework where the firms’ wage setting decision is not only constrained by the strategical behavior of employed workers, who can choose to keep or to quit their current job, but also by the strategical behavior of unemployed workers. Indeed, each unemployed workers getting more than one job offer will opt for the best wage contract and the remaining vacancies will be left idle. The crucial feature of the model is the endogeneous nature of the firms market power directly stemming from the endogenous workers’ market power, its counterpart. Workers’ market power indeed emerges from two distinct sources: the possibility that unemployed and employed workers have to refuse wage offers and the possibility employed workers have to quit their job for a better paid one. Both the rejection and the resignation probabilities increase in period of economic growth, when vacancy posting is large and workers are contacted by a relatively high number of firms, rising the market power of workers. Mechanically, it implies that the firms market power erodes in good times. The opposite mechanism takes place in periods of economic slowdown. So to be, I focus on one essential determinant of the rent sharing process between firm and worker, 4

which is the inter-firm competition,5 and analyze the impact of the business cycle on the workers’ outside option valuation and subsequently on the relative market power of workers and firms. Moreover, I seek to relate the fluctuations of their relative market powers to the fluctuations of wage dispersion. At equilibrium, firms strategically choose differing wage policies. When the economy is hit by a favorable shock, the market power of firms weakens which subsequently constraints them to post higher wages. Both the wage distribution and the range of potential wages are affected. I show that this mechanism forces the convergence in wages towards the competitive wage level. In case of an adverse shock, a similar wage convergence process occurs, yet towards the pure monopsonistic wage level. Indeed, the probability for workers to only get one offer increases which gives the incentive to firms to deeper exert their monopsony power. The wage distribution is therefore more dispersed when the economy is around the steady state. The paper proceeds as follows: Section 2 proposes a review of the existing literature on wage dispersion. Section 3 presents the model which embed wage posting into a search and matching model in which job searchers can get several offers per period. I show how wage dispersion arises in such a framework and explain the source of the market power of the firms. Section 4 focuses on the dynamic analysis of the labor market, with an emphasis on the cyclical properties of the firms’ market power and of the wage dispersion. Section 5 concludes.

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Related literature

The main motivation of the paper is to endogenize the firms market power and to investigate its cyclical properties with the final aim of exploring the channels through which the business cycle affects the equilibrium wage differential. In doing so, I seek to contribute to the growing literature on dynamic search and matching with wage dispersion. Following BM98, several authors propose de5

See Cahuc, Postel-Vinay, and Robin (2006) for a study of the determinants of the wage setting process. Using a panel of French administrative data, they find that interfirm competition is an essential determinant of the workers’ market power and results in a large rise of wages above the reservation level.

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terministic models of wage dispersion.6 The main contribution is the paper by Postel-Vinay and Robin (2002) which distinguishes three sources of wage dispersion: unobserved workers productive heterogeneity, firms productive heterogeneity and search frictions. The importance of search frictions, and hence of the threat of inter-firm competition, for pushing wages up is also taken in consideration by Carrillo-Tudela and Smith (2009). In both papers, the resulting wage dispersion is in keeping with empirical regularities. Only few authors extend the analysis towards stochastic models. Moscarini and Postel-Vinay (2010) perform the first analysis of aggregate stochastic dynamics in the class of search wageposting models originating with BM98. They investigate the conditions under which the positive link between employer size and wages constitutes an equilibrium. They do not focus on the cyclical behavior of the labor market variables, work which is undertaken by Robin (2011). Based on a model with heterogeneous agents and wage bargaining, he analyzes how aggregate productivity shocks affect unemployment dynamics through endogenous separation. This additional channel enhancing unemployment fluctuations, he partially solves the Shimer’s (2005) critic. He also highlights the fact that each decile of the wage distribution reacts differently to productivity shocks. However, his setting faces two restrictions. First, the rates at which workers get job offers is exogeneous. Second, firms are homogeneous hence they all have the same wage upper bound. As a result, no firm can poach any worker from a Bertrand competition and job-to-job movements have to be artificially created. In the present paper, I replace these restrictions by first endogenizing the average number of wage offers that each worker gets, and second by dropping the assumption that firms are fully informed of the alternative offers that their employees get, or at least that they do react to it. This last relaxation also allows me to obtain a full distribution of wages for each state of the world.7 By endogenizing the vacancy posting decision, I endogenize the hiring and quitting rates, and therefore the out-of-unemployment flow and the job-to-job flow. To my knowledge, two papers only (Menzio and Shi (2010a) and 6

See for example Mortensen (1990), Green, Machin, and Manning (1996), Mortensen (1998), Burdett and Mortensen (1998) and Acemoglu (2001). 7 In case of Bertrand competition, each state of the world is characterized by only two wage levels: the reservation wage and the competitive one.

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Menzio and Shi (2010b)) endogenize these two flows. More specifically, Menzio and Shi (2010a) focuses on measuring the effect of productivity shocks on workers’ turnover (out-of-unemployment, job-to-job and out-of-employment). In both papers, the authors replace the standard assumptiom of random search with the one of directed search. This modification is crucial in order to solve the model outside the steady state given that, in such a setting, agents do not need to forecast the evolution of the infinite-dimensional wage distribution in order to solve their individual problems. However, such an assumption faces two main limitations. First, it mechanically reduces frictions on the labor market. Second, it implies that firms only meet candidates having the same reservation wage. This implication is at odd with the observed matching process and considerably narrows the range of interactive strategies beween firms and workers.

3 3.1 3.1.1

The model General set-up Timing

Time is discrete. Each period is characterized by the following sequence of events: exogenous separation, matching, voluntary resignation and production. At the beginning of the period, a proportion λ of the existing matches exogenously splits up. Subsequently, the matching process takes place. Due to search frictions, each searching worker only meets a certain fraction of vacant firms each period. I depart from the standard search and matching model in making two assumptions. First, job seekers can get more than one job offer each period. This realistic assumption gives an interesting active role to the workers and allows me to analyze to which extent the workers’ job acceptance decision constraints the firms’ wage setting decision. Second, I assume on-the-job search. Workers are therefore able to switch to better jobs. Firms make take-it-or-leave-it offers to job candidates. In case of acceptance, matches are created. After the matching process, employed workers who are still in place after the exogenous shock and who did not get poached can decide to leave their current employer if in so doing they reach a 7

higher level of utility. In that case, they accept an interim unemployment spell in hope of getting a better job in the next matching process. At the end of the period, production takes places and salaries and unemployment benefits are paid. 3.1.2

Aggregate productivity shock

The state of the economy is characterized by the level of aggregate productivity denoted by z which follows a AR(1) process. Fluctuations in aggregate productivity lead to fluctuations of the firm surplus from an employment relationship.

3.2

Wage contracts

Firms and workers are homogeneous. Firms post take-it-or-leave-it wage offers. Once a wage contract is accepted by a worker, the wage remains constant during the whole employment relationship duration. Workers can quit at any time in case the lowest bound of the current wage set exceeds the wage which has been accepted at the beginning of the employment spell. These voluntary resignations will occur in good times of the economy when wage expectations, and therefore the reservation wage, are high.

3.3

Workers

Job seekers. A continuum of identical workers of measure 1 participates in the labor market. Each period, unemployed and employed workers are looking for a job. Empirical evidence8 show that the job-to-job rate is much lower than the outof-unemployment rate. Therefore, in order to propose a realistic modelling of the labor market, I assume that all unemployed workers look for a job with probability one but that each employed worker has a certain probability et (w) ∈ (0, 1) with ∂e(w)/∂w < 0 to be searching for a job. I assume the following fonctionnal form for et (w):  1 − w α et (w) = 1 − wt 8

See Nagypal (2008) as well as the discussion about the calibration presented in the next section.

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Workers who are employed at the lowest wage wt have a probability one to look for a job. This probability is decreasing and approching 0 for employed workers in the upper tail of the distribution. Meeting process. Due to frictions on the labor market, job seekers get in contact with a limited number of firms. For the sake of simplicity, I assume that frictions are such that each vacant firm only contacts one candidate per period.9 Let denote by st the average number of offers that (employed and unemployed) workers get. I assume random matching. Unemployed and employed workers can therefore be contacted by any firm. The number of offers Ot received by a worker follows a binomial distribution of parameters (vt , vstt ), where vt denotes the level of vacancies, and can be approximated by a Poisson distribution of parameter st for large values of vt . The probability that an employed or unemployed worker receives k offers is therefore: e−st skt P (Ot = k) = k! Offer acceptance decision. BM98 make the restrictive assumption that employers do not respond to offers from other firms received by their employees. Alternatively, Postel-Vinay and Robin (2002) propose to consider that firms are able to make counteroffers in order to prevent their employees from quitting.1011 The current and alternative employers are therefore brought in a Bertrand price competition resulting, in the case firms are homogeneous, in a wage rise up to the competitive level. I choose not to exploit this way as my goal is to analyze how the wage setting decision of firms is constrained by the strategical behavior of workers, induced by inter-firm competition, even in absence of any bargaining interaction between the worker and the firm.12 I therefore assume, as in BM98’s 9

It could easily be extended to more complex cases. An intuitive pattern would be that firms are able to contact a higher number of job applicants during economic slowdown. Such a countercyclical average number of candidates would strengthen the results. 10 This assumption is subsequently used by several authors: Cahuc, Postel-Vinay, and Robin (2006), Robin (2011) and Carrillo-Tudela and Smith (2009) for instance. 11 Another interesting mechanism through with firms can affect the workers’ incentive to quit, explored by Burdett and Coles (2003) and Burdett and Coles (2010), is to propose wage-tenure contracts. In a setting where the wage paid depends upon the worker’s tenure, the expectation of being internally promoted reduces the incentive to change employer. 12 Notwithstanding, I expect such an alternative assumption to strengthen my results. A

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model, that firms do not react when their employees get poached by other firms. If a unemployed worker only gets one offer during the period, he accepts it with probability one, as long as the proposed wage provides a welfare which is greater than the value of unemployment. However, if the unemployed worker receives k offers, he accepts the firm’s offer wo only if the other firms propose a lower wage, which occurs with probability Ft (wo )k−1 . The probability aUt (wo ) that an unemployed worker accepts an offer wo , conditional on getting at least one offer, is therefore: aUt (wo )

∞ X P U (Ot = k) Ft (wo )k−1 = U P (Ot ≥ 1) k=1 o

aUt (wo )

e−st (1−Ft (w )) − e−st = Ft (wo )(1 − e−st )

(1)

(see Appendix A for the derivation details), and the probability of flowing out of unemployment is: pUt = 1 − P U (Ot = 0) pUt = 1 − e−st

(2)

For employed workers who are looking for a job, the wage acceptance rule is as follows. An employed worker accepts the highest wage offer obtained during the period on condition that it is higher than the wage he is earning in his o current job. The conditional probability aE t (w ) that an unemployed worker who currently earns a wage w accepts an offer wo is therefore: o aE t (w )

∞ X P E (Ot = k) F (wo )k−1 = 1wo >w E (O ≥ 1) t P t k=1 o

o aE t (w )

=1

wo >w

e−st (1−Ft (w )) − e−st Ft (wo )(1 − e−st )

(3)

jump in vacancies following a positive shock brings workers to face a higher number of offers. The probability that at least one wage offer exceeds the current wage, and therefore that the current firm enters in a Bertrand competition with another firm, increases. The average effective monopsony power of firms will substantially decrease as each competing firm entirely looses its market power.

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and the probability of quitting the current job paying w (or probability of getting a job offer paying at least w) is: pE t (w)

= et (w)

∞ X

P E (Ot = k)(1 − Ft (w)k )

k=0 −st (1−Ft (w)) pE t (w) = et (w) 1 − e




(4)

As a result, the vacancy filling rate for a firm proposing a wage wo can be expressed as follows: qt (wo ) =

ut e¯t (1 − ut ) o aUt (wo ) + Gt−1 (wo )aE t (w ) ut + e¯t (1 − ut ) ut + e¯t (1 − ut )

(5)

where e¯t is the average job searching probability amon employed workers and Gt (wo ) is the end-of-period fraction of employed workers earning a wage less than wo .

Lowest wage rate. wt denotes the lowest wage rate that an unemployed worker will accept. Given that no worker would accept a wage providing a lower utility than the utility of unemployment, wt is obtained by the following equality: Wt (wt ) = Ut

(6)

where Wt (w) is the worker’ value of working for a wage w and Ut is the value of unemployment. Ut and Wt (w) are defined as: Ut = b +

h

Et βpUt+1

Z

w ¯t+1

Wt+1 (wt+1 )dFt+1 (wt+1 ) + β(1 − pUt+1 )Ut+1

wt+1

11

i

and h Wt (w) = w + Et β(1 − λ)(1 − pE t+1 (w))1w>wt+1 Wt+1 (w) Z w¯t+1 Wt+1 (wt+1 )dFt+1 (wt+1 ) + β(1 − λ)pE t+1 (w) w Z w¯t+1 U + βλpt+1 Wt+1 (wt+1 )dFt+1 (wt+1 ) wt+1

+ β(λ(1 − pUt+1 ) + (1 − λ)(1 − pE t+1 (w))1wwt+1 Jt+1 (w) + β[λ + (1 −

λ)(pE t+1 (w)

+ (1 −

pE t+1 (w))1wwt+1 qt (w) qt+1 (w) 13

(10)

Highest wage rate. w¯t is the upper bound of the range of wage rates for which the zero-value vacancy equilibrium condition is respected. Above this threshold, the value of a filled vacancy Jt (w¯t + ) would lie below κ/qt (w¯t + ) such that either the time t value of the vacancy would be negative or the time t + 1 value of the vacancy would be required to be positive.

3.6

Equilibrium wage differential

The free entry condition also states that each vacancy type is equally valuable, which opens the room to wage dispersion in equilibrium. Indeed, for any wage offer in the bargaining set, the corresponding vacancy filling rate and job-to-job rate ensure the equilibrium condition. To see this, consider equation (10). Wage dispersion arises due to the fact that firms play a mix strategy in the wage posting t −w < 0) in one hand game, trading-off between the current profit per worker ( ∂z∂w ∂pE ∂qt (w) t (w) and the vacancy filling duration ( ∂w > 0) and the quitting rate ( ∂w < 0) in the other hand. As a result, each vacancy type is equally valuable. In particular, we have: Vt (w) = Vt (wt ) = 0 which can be rewritten as follows: qt (w)Jt (w) = qt (wt )Jt (wt )

(11)

The ratio of vacancy durations equals the ratio of expected profits from opening a vacancy. This last equation pins down Ft (w), which is the equilibrium wage offer distribution function. Once Ft (w) is determined, Nature chooses the type of each firm. The equilibrium wage offer distribution must be continuous. In order to understand this condition, lets consider a mass point at the wage level w∗ ∈]wt , w¯t ). Firms proposing such a wage have the incentive to deviate by proposing a slightly lower wage. In so doing, they increase their per period profit and increase the probability to find a worker (given the absence of mass at the wage level w∗ − ). The possibility of a mass point at the reservation wage is also ruled out. A slight increase in the proposed wage would decrease the per period profit but would 14

largely increase the probability to fill the vacancy.

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Countercyclicality of the firms’ monopsony power

4.1

Equilibrium

The equilibrium of the present model is such that: • From the free entry condition, each vacancy type in (wt , w¯t ) has a zerovalue. Outside this range the value of posting a vacancy is negative.13 The job creation curve (10) determines the equilibrium level of overall vacancies (or average number of job offers). • The continuous equilibrium wage offer distribution is pined down by equation (11). • The reservation wage is determined by equation (6). • Unemployed and employed workers accept job offers as described by equations (1) and (3). • The out-of-unemployment flow and the job-to-job flows are framed by equations (2) and (4). • Unemployment and employment stocks evolve according to equations (7) and (8). The dynamics of the model are obtained by taking a log-linear approximation of the aggregate productivity process and of equations (1), (2), (3), (4), (5), (7), (8), (9), (6), (10) and (11) around the steady state.

4.2

Calibration

The calibration of the model is described in Table 1. These values are chosen to match the empirical regularities of the US. 13

A firm proposing wage below wt would pay a cost for posting a vacancy which has a zero probability to be filled. A firm proposing a wage above w ¯t would get a profit equal to zt − w ¯t which is too small to compensate the vacancy cost.

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Table 1: Calibration

Description Stochastic process for labor productivity Autocorrelation Standard deviation Mean labor productivity Other parameters Discount rate Exogenous separation rate Unemployment income Vacancy posting cost Curvature of the searching effort

Parameter

Value

ρ σ z

0.98 0.0086 1

β λ ¯b κ α

0.991/3 0.1/3 set to target b/E(w) ≈ 0.6 0.247 set to target pU = 0.45 set to target M m = 1, 7

Note: Monthly calibration.

I interpret a period as a month. The discount factor is set to 0.991/3 which corresponds to a yearly interest rate of 4% commonly used in the macro-RBC literature. The log productivity level zt is assumed to follow an AR(1) process: log(zt ) = ρ log(zt−1 ) + t where  ∼ N (0, σ 2 ). The persistence of the technology shock is set to ρ = 0.98 and the standard deviation to σ = 0.0086. This standard calibration is used by Rogerson and Shimer (2010) and is based on the estimations of Cooley and Prescott (1995). The mean of z is normalized to one. Each match has a probability to end λ set to 0.1/3. This value is comprised within the broadly accepted range of 8% − 10% proposed by Hall (2005) and is similar to Shimer (2005) who measures this exit probability at 0, 1/3 in average in the US. I target the probability pU that an unemployed worker forms a match within the period to 45%, implying unemployment spells of around two months. This choice is consistent with Hall (2005) who estimates a monthly job finding rate of 0.48% and in line with the measure of this rate presented by Rogerson and Shimer (2010) for the US for the period 1948-2009. I choose to target the Mean/minimum (Mm) ratio instead of the job-to-job 16

rate. The reason is that the present model does not accomodate for any mechanism of wage increase during the employment spell. If such a possibility would be introduced, either by modelling a promotion schedule or by allowing firms to compete with potential poachers by making counteroffers so as to retain the worker, the worker’s value of keeping his job would be higher and the probability of changing jobs lower. In targeting the job-to-job rate, I would mechanically reduce the incentive of workers to accept relatively bad jobs which would translate into a very right-skewed wage distribution. I rather target the Mean/min ratio to be equal to 1.7, which is the measure proposed by Hornstein, Krussel, and Violante (2007) based on the Census data, the PSID data and the OES data. In contrast with the other parameters and targets, there exists a debate about the value of non work activity ¯b = b/E(w), revived by the recent paper by Hagedorn and Manovskii (2008) which proposes a new estimate of this value at 0.95. Indeed, unlike Shimer (2005) who restricts the value of non work activity to the unemployment benefits and sets ¯b equal to 0.4, Hagedorn and Manovskii (2008) additionally integrate the home production and the value of leisure. Delacroix (2006) also distinguishes within the unemployment income set at 0.6 a home production of 0.3 and unemployment benefits of 0.3. In order to keep my results as plausible as possible, I choose an average value of 0.6.

4.3

Dynamics

Job offer acceptance rate Figure (1) shows the response of a specific labor market (w=E(w)=0.85) to a positive productivity shock of one standard deviation. In expansion, the firms’ surplus increases which leads to a jump of the value of posting vacancies and hence to an increase in vacancies and in the average number of job offers unemployed and employed workers get. The labor market becomes tighter. Job seekers become choosier as they get more job offers and of better quality. As a result, firms record a decline in the job offer acceptance rate coming from both categories of workers. The vacancy duration raises which brings back the value of vacancies to zero. 17

Wage offer distribution In order to understand how firms react to a change in productivity, I examine how the firms surplus changes for different levels of wage. Figure (2) shows that, following a positive productivity shock, the firms surplus increases more for high paying firms. This is explained by the following argument. As discussed by Hagedorn and Manovskii (2008), what gives the firms the incentive to post vacancies is the size of the percentage change in profit in response to the change in productivity. Therefore, for high paying firms getting small profits, the change in productivity leads to a large percentage change in the profit. The higher the wage, the larger the percentage change in profit, the bigger the incentive to post vacancies. As a result, firms have a large incentive to post relatively good vacancies following an increase in productivity. The distribution of wages changes accordingly, as can be seen in Figure (3). Following the positive shock, the wage distribution shifts downwards, illustrating the fact that the composition of vacancies leans more towards good vacancies compared to before the shock. Wage dispersion and firms’ market power In expansion, the downward shift of the wage offer distribution, which results from the disproportional jump of high paying vacancies, comes together with a decrease in wage dispersion and a convergence towards the upper bound of the wage range. Figure 4 displays the percentage change in the variance of wages and of the Mean/min ratio for the ten periods following a positive productivity shock. Wage dispersion clearly behaves countercyclically. Moreover, the countercyclical properties of wage dispersion mainly stems from the change in composition of vacancies. The wage range (distance between the highest and the lowest wage) is barely modified as a positive shock increases both the reservation wage and the highest one. I measure the market power of the firms by the distance between the average wage and the competitive one zt . This market power of firms is directly generated by the search frictions which prevent workers to contact all the firms with an open vacancy in order to choose the most generous wage contract. In expansion, as the number and the quality of offers workers get increases, making them choosier, the search frictions faced by workers fade, the labor market becomes more competitive and the firms’ market power lessens. Market power and wage dispersion are 18

therefore the two faces of the same coin. On the contrary, in recession, the labor market tends to behave more like a monopsony. Indeed, in bad times, the workers’ probability of getting more than one offer (and therefore of being able to compare job offers) dampens, search frictions grow and generate more market power for firms. Wage dispersion increase as more firms have the incentive to propose low paid offers. Job-to-job rate and composition of hires Figure (5) shows the immediate percentage change of the job-to-job rate for different levels of wage in response to a positive productivity shock. What can be noticed is the disproportional jump of this rate for high levels of wage. The rationale behind this result is grounded on the change in the quality of vacancies. For an unchanged probability of looking for a job, the probability that the offered wage exceeds the current one increases more the higher the wage. Two results are obtained. First, the job-to-job rate behaves procyclically, a result which is consistent with empirical evidence14 . Second, given that the procyclicality of the job-to-job rate exceeds the one of out-ofunemployment, the composition of hires is modified towards employed workers in good times.

5

Conclusion

In the present paper, I first probe the cyclical properties of the firms’ market power. I find that the extent to which firms choose to exert their monopsony power is lower in good times. The core mechanism is the following. Even in absence of any explicit bargaining process, workers gain some implicit bargaining power as they receive more job offers. The risk for the firms to face an offer rejection decreases their power to dictate wages, which leads to wages getting closer to the competitive level in good times. Moreover, I relate the fluctuations of the firms’ market power to the fluctuations of wage dispersion. The results show that, in peaks, wage dispersion decrease as wages converge towards the competitive wage level. In troughs, wage 14

See for example Sherk (2008).

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dispersion decrease as wages converge towards the monopsonistic wage level. In intermediate states of the economy, dispersion is large. Wage distribution therefore displays a U-shape.

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References Acemoglu, D. (2001): “Good Jobs versus Bad Jobs,” Journal of Labor Economics, 19(1), 1–21. Bhaskar, V., A. Manning, and T. To (2002): “Oligopsony and Monopsonistic Competition in Labor Markets,” Journal of Economic Perspectives, 16(2), 155– 174. Burdett, K., and M. Coles (2003): “Equilibrium Wage-Tenure Contracts,” Econometrica, 71(5), 1377–1404. (2010): “Wage/tenure contracts with heterogeneous firms,” Journal of Economic Theory, 145(4), 1408–1435. Burdett, K., and K. L. Judd (1983): “Equilibrium Price Dispersion,” Econometrica, 51(4), 955–69. Burdett, K., and D. T. Mortensen (1998): “Wage Differentials, Employer Size, and Unemployment,” International Economic Review, 39(2), 257–73. Cahuc, P., F. Postel-Vinay, and J.-M. Robin (2006): “Wage Bargaining with On-the-Job Search: Theory and Evidence,” Econometrica, 74(2), 323–364. Carrillo-Tudela, C., and E. Smith (2009): “Wage Dispersion and Wage Dynamics Within and Across Firms,” IZA Discussion Papers 4031, Institute for the Study of Labor (IZA). Christensen, B. J., R. Lentz, D. T. Mortensen, G. R. Neumann, and A. Werwatz (2005): “On-the-Job Search and the Wage Distribution,” Journal of Labor Economics, 23(1), 31–58. Cooley, T. F., and E. C. Prescott (1995): “Economic Growth and Business Cycles,” in Frontiers of Business Cycle Research, ed. by T. F. Cooley, pp. 1–38. Princeton University Press. Delacroix, A. (2006): “A multisectorial matching model of unions,” Journal of Monetary Economics, 53, 573–596. 21

Diamond, P. A. (1971): “A model of price adjustment,” Journal of Economic Theory, 3(2), 156–168. Green, F., S. Machin, and A. Manning (1996): “The Employer Size-Wage Effect: Can Dynamic Monopsony Provide an Explanation?,” Oxford Economic Papers, 48(3), 433–55. Hagedorn, M., and I. Manovskii (2008): “The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited,” American Economic Review, 98(4), 1692–1706. Hall, R. E. (2005): “Employment Fluctuations with Equilibrium Wage Stickiness,” American Economic Review, 95(1), 50–64. Hornstein, A., P. Krussel, and G. Violante (2007): “Frictionnal wage dispersion in search models: a quantitative assessment,” Working paper. Krueger, A. B., and L. H. Summers (1988): “Efficiency Wages and the Interindustry Wage Structure,” Econometrica, 56(2), 259–93. Manning, A. (2003): Monopsony in motion: imperfect competition in labor markets. Princeton University Press. Menzio, G., and S. Shi (2010a): “Block recursive equilibria for stochastic models of search on the job,” Journal of Economic Theory, 145(4), 1453–1494. (2010b): “Directed Search on the Job, Heterogeneity, and Aggregate Fluctuations,” American Economic Review, 100(2), 327–32. Mortensen, D. (1998): “Equilibrium Unemployment with Wage Posting: Burdett-Mortensen Meet Pissarides,” Discussion paper. Mortensen, D. T. (1972): “A theory of wage and employment dynamics,” in Microeconomic Foundations of Employment and Inflation Theory, ed. by E. P. et al. Norton, ISBN 978-0-393-09326-1. 22

(1990): “Equilibrium Wage Distributions: A Synthesis,” in Panel Data and Labor Market Studies, ed. by G. R. J. Hartog, and e. J. Theeuwes. Amsterdam: North Holland. Moscarini, G., and F. Postel-Vinay (2010): “Stochastic Search Equilibrium,” Cowles Foundation Discussion Papers 1754, Cowles Foundation for Research in Economics, Yale University. Murphy, M. K., and H. R. Topel (1987): “Unemployment, Risk, and Earnings: Testing for Equalizing Wage Differences in the Labor Market,” in Unemployment and the Structure of Labor Markets, ed. by K. Lang, p. 103. New York and Oxford: Blackwell. Nagypal, E. (2008): “Worker Reallocation Over the Business Cycle: The Importance of Job-to-Job Transitions,” mimeo, Northwestern University. Postel-Vinay, F., and J.-M. Robin (2002): “Equilibrium Wage Dispersion with Worker and Employer Heterogeneity,” CEPR Discussion Papers 3548, C.E.P.R. Discussion Papers. Robin, J.-M. (2011): “ON THE DYNAMICS OF UNEMPLOYMENT AND WAGE DISTRIBUTIONS,” Working paper. Rogerson, R., and R. Shimer (2010): “Search in Macroeconomic Models of the Labor Market,” NBER Working Papers 15901, National Bureau of Economic Research, Inc. Sherk, J. (2008): “Job-to-job transitions: more mobility and security in the work force,” Report 08-06, The Heritage Foundation, Center for Data Analysis. Shimer, R. (2005): “The Cyclical Behavior of Equilibrium Unemployment, Vacancies and Wages: Evidence and Theory,” American Economic Review, 95(1), 25–49. Winter-Ebmer, R. (1998): “Unknown wage offer distribution and job search duration,” Economics Letters, 60(2), 237–242.

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A

Job offer acceptance rate and labor market tightness aUt (wo )

∞ X P (Ot = k) Ft (wo )k−1 = P (Ot ≥ 1) k=1 ∞

aUt (wo )

X 1 = P (Ot = k)Ft (wo )k−1 1 − P (Ot = 0) k=1 ∞

aUt (wo ) aUt (wo )

∞ X  1 o k P (Ot = k)Ft (w ) − P (Ot = 0) = (1 − P (Ot = 0))Ft (wo ) k=0

aUt (wo ) aUt (wo )

X 1 = P (Ot = k)Ft (wo )k o (1 − P (Ot = 0))Ft (w ) k=1

=

=

∞ X e−st s k

1

t

(1 − e−st )Ft (wo ) 1



(1 − e−st )Ft (wo )

−st (1−Ft (wo ))

e

k!

k=0

Ft (w ) − e

k=0

e−st (1−Ft (w )) − e−st = (1 − e−st )Ft (wo )

which is similar to equation (1).

24

−st



o ∞ X e−st Ft (w ) st Ft (wo )k

o

aUt (wo )

o k

k!

−e

−st



Figure 1: Impulse responses to a positive productivity shock

Note: Percentage deviation from the steady state following a positive productivity shock of one standard deviation. I set w=E(w)=0.85 in this illustration.

25

Figure 2: Job-to-job rate: impulse response to a positive productivity shock

Note: Immediate (t=1) percentage change in the firms’ surplus J in response to a positive shock of one standard deviation for each wage level.

26

Figure 3: Distribution function: impulse response to a positive productivity shock

Note: Distribution function in t=0 (steady state), t=1 (shock), t=2 (one period after the shock).

27

Figure 4: Wage dispersion: impulse response to a positive productivity shock

28

Figure 5: Job-to-job rate: impulse response to a positive productivity shock

Note: Immediate (t=1) percentage change in the job-to-job rate in response to a positive shock of one standard deviation for each wage level.

29