chapter 3 competitive equilibrium and compensating wage di ... · labor economics chapter 3...

Labor Economics

Chapter 3Competitive Equilibrium and

Compensating Wage Differentials

Pierre Cahuc, Stephane Carcillo and Andre Zylberberg

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This chapter will:

I Describe the basic model of the labor market in competitiveequilibrium

I Analyze the interactions between supply and demand givenfiscal incidence issues

I Understand how the hedonic theory (within the perfectsituation) predicts that wage differentials compensate for thelaboriousness or danger of tasks

I Understand how the assortative matching model shows thatthe small difference in capacity leads to huge wage differntials

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Table of contents

The competitive equilibriumPerfect comptition

Compensating wage differentials and the hedonic theory of wagesA simple model of compensating wage differentialsEstimation

Assortative matchingA competitive equilibrium with assignmentWage rule and the superstars phenomenon

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Introduction

I Section 1 describes the basic model of the labour market incompetitive equilibrium.

I Through the model of perfect competition, we shall see theimpact of taxes on employment

I Section 2 presents how the hypothesis of perfect competitionis related to the theory of wage setting.

I The hedonic theroy of wages, sketched by Adam Smith andrecently formalized by Rosen, defines differences that arisefrom hard working conditions.

I We will present how wage earners can choose among differentjobs with different degrees to jobs adapted to the preferencesof workers.

I Section 3 describes the competitive functioning of the labormarket in a context where agents and jobs are heterogeneous.

I In this market, the competitive functioning may lead to steeplyunequal compensation package.

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The competitive equilibrium (1)

Perfect competition with identical workers and jobs of equaldifficulty.

I Supply and demand in a simple model of the labor market:I Production function: F (L)I Utility function: u(R, e, θ) = R − eθ with R income, e

employment dummy variable and θ the disutility of labor forthe individual

I Those with a low θ accept it more easily than those with ahigh θ

I Firm’s profit: F (L)− wL and its FOC: F ′(Ld ) = w

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The competitive equilibrium (2)

Equilibrium of perfect competition yields a collective optimum.The planner’s choice at equilibrium entails:

F ′[(G (w ∗)] = w ∗

I In the competitive equilibrium model, there is no involuntaryunemployment

I It can be shown that a perfectly competitive market yields thesame allocation of resources that an omniscient planner wouldhave chosen

I At the competitive equilibrium, the allocation of individualsbetween employment and non-participation is efficient

I Despite simplifying assumptions, perfect competition is asimple and tractable benchmark to analyze various shocks

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Market equilibrium with perfect competition

Figure: Market equilibrium with perfect competition

I Effects of a reduction of social security contributions, t < 0I Labor demand increases and so at equilibrium both labor and

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The question of tax incidence (1)

I The essential point about tax incidence is knowing who theend payer of the tax or the end recipient of the subsidy is

I The labor demand is F ′(Ld ) = w(1− t), with t the rate ofpayroll tax on the net wage w

I Labor demand: F ′(Ld ) = w(1 + t)I t > 0, t designates a tax paid by the firmI t < 0, t designates a subsidy paid to the firm

LD [w(1 + t)] = LS (w)

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The question of tax incdience (2)

I We also see that the respective amplitudes of these risesdepend on the slopes of the curves of labour supply anddemand

I The elasticity wage-tax is:

ηwt =

ηdw

ηsw − ηd

w

I ηdw < 0 represents labor demand elasticity

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Illustration of the tax incidence (1)

Figure: The effects of a reduction in payroll taxes with inelastic laborsupply

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Illustration of the tax incidence (2)

I In this situation, ηwt =-1, which means any reduction in payroll

taxes is fully passed on Consequently, the level of employmentis unchanged

I Fiscal incidence is the situation in which the agent to whomtax is charged is not the real payer

I Knowledge of the the elasticities of labor supply and demandmakes it possible to calculate the impact of a change inpayroll taxes on wages and employment

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Compensating wage differentials and the hedonic theory ofwages

In the previous section, the labor market was perfectlyhomogeneous.

In reality, there is an extremely wide range of working conditionsacross all jobs. Within the hedonic theory of wages, perfectcompetition would ensure that such differences were compensatedby wage differentials.

I Workers who expect to be recalled by their previous employerssearch substantially less than the average unemployed workers

I Across the 50 US states, the time spent looking for a job isinversely correlated to the level of unemployment benefits,with an elasticity between -1.6 and -2.2

I Job seekers who likely have less access to financial resources(e.g. because they do not have a working spouse) tend torespond more to UI benefits than do those with greaterfinancial wherewithal

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Compensating Wage differentials (1)

I In the previous section, labor services were all perfectlyhomogeneous and so did difficulties in a task

I Perfect competition in the labor market ought to lead to awage heterogeneity

I The essence of the hedonic theory of wages: job differenceswere compensated for by wage differentials

I Wages and the difficulty of jobsI The effort variable e allows to measure the difficulty of jobsI The productivity, which is the production net of any costs

except wages, of every sort of job is an increasing and concavefunction of effort

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Compensating Wage differentials (2)

I In this section, let us assume that there is a market for eachof the kinds of jobs that coresponds to each of these degreesof effort

I If w(e) denotes the equilibrium wage that applies to jobs thatdemand effort e, then we have,

w(e) = f (e)

I The problem for a worker of type θ consists of selecting avalue of effort that maximizes her satisfaction, f ′(e) = θ

I As f ′(e) < 0, e ′(θ) diminishes with θ. As a consequence, theequilibrium wage received by a worker of type θ amounts tow [e(θ)] = f [e(θ)], the counterpart of tough jobs is a”compensating” wage differential, since wages increase witheffort

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The hedonic theory of wages

Figure: The hedonic theory of wages

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Estimation (1)

I The main prediction of the hedonic theory of wages is thatwage differentials compensate for the conditions in which ajob is performed

I The method used to test the predictions of the hedonic theoryof wages consists of estimating the wage w received by anindividual as a function of his personal characteristics,represented by a vector x , and the non-wage characteristics ofthe job, represented by a vector e

lnw = xβ + eα + ε

I α and β are vectors of parameters to be estimated and ε is adisturbance term with zero mean (normally distributed).

I But, this model will surely have a problem of unobservedcharacteristics.

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Estimation (2)

I All jobs have same productivity if the work performance isidentical

I Hence, considering the efficiency of workers and jobs constant,wage differences reflect differences in working conditions

I If talent is unobservable and if it influences the choice ofworking conditions, the model is biased, for the nonwagecharacteristics of the job

I For instance, good working conditions are likely to be normalgoods, the consumption of which increases as income rises. Ifthe income effect is sufficiently strong, then the most efficientindividuals choose the less laborious jobs, which entails anegative relation between wages and the laboriousness of jobs

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Estimation (3)

I The other dedicated issue is the heterogeneity of individualpreference

I There is not necessarily unanimous agreement that certaincharacteristics of jobs are disagreeable

I Without these disagreements, the predictions of the hedonictheory of wages can only focus on certain elements that areclearly identifiable as drawbacks or advantages for all worker

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Assortative matching (1)

I The models examined so far assumed the existence of a largepotential number of suppliers and demanders for every type ofservices

I In the hedonic wage model of the previous sectionis, there aremany markets where are a multitude of suppliers anddemanders who are price takers

I We resort to assortative matching models to analyze how thecharacteristics of each workers are associated with their jobs

I We will study the functioning of a market of this type on thebasis of an assortative matching model that associates chiefexecutive officers (CEOs) who have different talents withfirms of varying size

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I A simple modelI F (·) the CDF of talents and G (·) the CDF of firm’s size

I The equilibrium assignment functionI profit π(a, s) = Y (a, s)− w(a)

I The wage rule and the superstars phenomenonI The compensation function w(a) shows that the wage is

increasing with talentI The remuneration function of a CEO is given by:

w(a) = w0 +∫ a

0Y1[x , σ(x)]dx

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Assortative matching (2) - Equlibrium assignment function

I The assortative matching model assumes that the mobility ofCEOs occurs without friction and without cost, and thatinformation is perfect for all agents.

I A CEO of talent a obtains a wage w(a) and the firm of size s,that employs this CEO, obtains π(a, s) = Y (a, s)− w(a)

I The composite of functions {w(a), α(s)} is an equilibrium ifthere is no CEO-firm pair that could do better by matchingamongst themselves than they are doing with their currentpartners.

I FOC: Y1(a, s) = w ′(a)

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I At the competitive equilibrium, the assignment function is:

Y1[α(s), s ] = w ′[α(s)]

I Given the SOC, we have α′(s) S 0⇔ Y12[α(s), s ] ≶ 0

I This last inequality links the direction of variation of theassignment function with the cross derivative of theproduction function

I The increasing assignment function means that the mosttalented CEO is assigned to the largest firm and so on downto the least talented CEO

I This kind of allocation is called positive assortative matching

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Assortative matching (4) - Wage rule and superstarphenomenon

Wage is increasing with talent. Thus, greater talent is alwayscompensated by more wage.

w(a) = w0 +∫ a

0Y1 [x , σ(x)] dx

where w0 is a constant representing the remuneration of the CEOof least talent.

This equation shows that the remuneration of each CEO dependson his own marginal productivity, as well as on the marginalproductivity of all the CEOs of least talent.

The equilibrium wage function of the assignment model entailsthat some small differences in talent may give rise to largedifferences in wage.

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An illustration: The upswing in CEO remuneration (1)

Figure: Median compensation of CEOs and other top officers from 1936to 2005

The CEO is identified as the president of the company in firms where the CEO title isnot used. ”Other top executives” include any executives among the three highest paidwho are not the CEO. Source: Frydman and Saks (2010)

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An illustration: The upswing in CEO remuneration (1bis)

I The previous figure shows the median level of totalcompensation, composed of salary, bonuses, long-term bonuspayment and stock option grants

I Gabaix and Landier (2008) explained this upswing in theremuneration of CEO utilizing explicit functions for thedistributions of talent and firm size

I The growth of their remunerations comes from the fact thatthe elasticity of average CEOs’ compensation to average firmsize is equal to 1

I Indeed, CEO’s productivity increases by 500% and equilibriumCEO’s pay incresases by 500%

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An illustration: The upswing in CEO remuneration (2)

Figure: Total compensation and the Standard and Poor’s indexTotal compensation is composed of salary, bonuses, long-term bonus payments, andstock option grants. Based on three highest-paid officers in the largest 50 firms in1940, 1960, and 1990 (a total of 101 firms)Source: Frydman and Saks (2010)

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An illustration: The upswing in CEO remuneration (2bis)

I In the previous figure, we can clearly see that the 1950s and1960s were marked by a substantial increase in the size offirms without a simultaneous increase in CEO remuneration

I Hence, in other complementary or competing theories likemanagerial rent extraction, greater power in the manageriallabor market, or increased incentive-based compensation,partly explains the formation of CEO remuneration, dependingon the epoch in question

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Summary conclusion

I A perfectly competitive equilibrium on the labor market ischaracterized by wages that match supply and demand. If alljobs have equal laboriousness, labor supply is principallydetermined by the disutility of work

I The hedonic theory of wages shows that the mechanisms ofperfect competition allow agents to choose different workingconditions, and that wage differentials compensate thelaboriousness or the danger of tasks

I The assortative matching model explains how far firms andworkers with different characteristics match each other in thesame market. This model shows that the process of matchingmay provoke very steep inequalities of remuneration amongworkers of closely similar characteristics

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