HIERARCHICAL ORGANIZATION AND PERFORMANCE INEQUALITY: EVIDENCE FROM PROFESSIONAL CYCLING

• Author: Bertrand Candelon,Arnaud Dupuy
• Published date: 01 November 2015
• DOI: http://doi.org/10.1111/iere.12135
• Date: 01 November 2015

INTERNATIONAL ECONOMIC REVIEW

Vol. 56, No. 4, November 2015

HIERARCHICAL ORGANIZATION AND PERFORMANCE INEQUALITY:

EVIDENCE FROM PROFESSIONAL CYCLING∗

BYBERTRAND CANDELON AND ARNAUD DUPUY1

IPAG Business School, France; LISER, Maastricht School of Management, and IZA,

Luxembourg

This article proposes an equilibrium theory of the organization of work in an economy with an implicit market for

productive time. In this market, agents buy or sell productive time. This implicit market gives rise to the formation

of teams, organized in hierarchies with one leader (buyer) at the top and helpers (sellers) below. Relative to autarky,

hierarchical organization leads to higher within and between team payoffs/productivity inequality. This prediction is

tested empirically in the context of professional road cycling. We show that 46% of performance inequality in the Tour

de France is due to hierarchical organization within team whereas team composition only accounts for 6%.

1. INTRODUCTION

Many economies have witnessed rising wage inequality in the last five decades (Acemoglu,

2003; Acemoglu and Autor, 2010) alongside large changes in many firms’ organizational struc-

ture (see, e.g., Rajan and Wulf, 2006). Early theoretical models developed by Lucas (1978) and

Rosen (1982) show that earnings inequality rises with span of control. This result has recently

been tested empirically in a few studies. Fox (2009) shows that earnings inequality increases

with job responsibility in Swedish and U.S. firms, and Gabaix and Landier (2008), Garicano and

Hubbard (2009), and Tervio (2008) conclude that the recent increase in earnings inequality in

large U.S. firms and in law firms is largely due to the rise in span of control in these firms.

This article proposes an alternative channel through which hierarchical organization and

earnings inequality might be related, namely, the exchange of productive time. This article

studies an economy with an implicit market for productive time. The scarce resource in this

market is the time each agent can dedicate to production. Agents can dedicate their productive

time to their own production (autarky), buy (part of the) productive time from helpers and

herewith increase their own production, or sell (part of) their productive time to a leader, hence

giving up own production. There exists an implicit market for productive time where transactions

transform productive time of the seller into productive time for the buyer. This implicit market

for productive time gives rise to the formation of teams, which have a hierarchical organization

with a leader at the top producing output, assisted by helpers below. Since the time of better

helpers is more productive, the hedonic equilibrium price for productive time compensates (i)

forgone own production and (ii) helping ability.

There are many examples of goods and services produced with teams organized in this

manner. We may think, for instance, of a lawsuit: The defense of a case is performed by a lead

lawyer who receives full credit for the outcome of the trial. The lead lawyer, however, might

∗Manuscript received October 2012; revised June 2014.

1We thank three anonymous referees, an anonymous associate editor, and the editor (Hanming Fang) as well as

Yin-Wong Cheung, Xavier Gabaix, Jules Leichter, Michael Sattinger, Jesper van Thor, and especially Alfred Galichon,

Luis Garicano, Bertrand Verheyden, and Michael Waldman for their valuable comments on earlier drafts of this

article. We also acknowledge the comments of seminar participants at Ecole polytechnique, Maastricht University,

University of Alicante, LISER and BETA, and the University of Lorraine as well as the data assistance of Sander

Dijksman. Please address correspondence to: Arnaud Dupuy, LISER, 3, avenue de la Fonte L-4364 Esch-sur-Alzette,

Luxembourg. E-mail: Arnaud.dupuy@liser.lu.

1207

C

(2015) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1208 CANDELON AND DUPUY

receive help from other lawyers at her firm to prepare the trial. The opportunity cost of spending

productive time helping the lead lawyer requires a compensating wage. Other examples can be

found in architect offices, maisons de Haute Couture, and music bands, to name a few. These

structures can also be found in certain sports, in particular, professional road cycling, but have

the interesting characteristic that the size of teams is fixed exogenously. These economies allow

us to abstract from the extensive margin and focus on the core: the relation between exchange

of productive time and performance inequality.

The existence of an implicit market for productive time raises many interesting questions

about the structure of such an economy. For instance, who becomes a leader and who becomes

a helper? Are abler helpers assigned to abler leaders? Are all leaders systematically abler

than any helpers? What does the distribution of payoffs/performance look like? Is there more

inequality in payoffs/performance with hierarchical organization than with autarky?

In this article, we elaborate a core theoretical model using stylized features of professional

road cycling. In this core model, the distribution of roles (leaders, helpers, and individual

riders), the assignment of leaders to helpers, and the distribution of payoffs (the hedonic price

for productive time) are endogenously determined. We show that under mild conditions, a

competitive equilibrium in this economy exists and is Pareto optimal. Moreover, the equilibrium

assignment should be such that (i) within teams the better rider becomes the leader, (ii) better

helpers are matched with better leaders, and (iii) some form of stratification arises: Abler agents

either become leaders or helpers and less able agents either become helpers or ride individually.

The stratification implied by (iii) is richer than the strict stratification arising in existing models

(Lucas, 1978; Rosen, 1982;2Waldman, 1984; Garicano and Rossi-Hansberg, 2006) where no

production workers (helpers) can be of higher ability than the least able manager (leader). The

equilibrium stratification in our model can indeed be such that some helpers are abler than

some leaders (of different helpers). For example, in a four-agent economy, ranking agents by

decreasing ability, standard models would generate teams such as (1,3) and (2,4) where the

first rider is the leader and the second the helper of the team, but preclude the existence of

teams (1,2) and (3,4). In contrast, our framework is general enough to allow for the occurrence

of both situations. This unique feature of our model is of crucial importance in our empirical

exercise for two reasons. First, the prediction that some leaders are less able than some helpers is

corroborated by empirical evidence. Second, this original feature allows us to test the existence

of an implicit market for productive time by testing in the data for whether the performance of

helpers (leaders) is lower (respectively, higher) than in autarky. Intuitively, since the equilibrium

stratification implied by our model is such that there are some helpers of higher ability than some

leaders and since leaders’ performance is enhanced while helpers’ performance is lessened by the

exchange of productive time within a team, one should expect that some of these leaders exhibit

higher performances than those abler helpers. This test is only feasible because stratification is

as predicted by our model; it would be meaningless in a model exhibiting strict stratification of

leaders and helpers.

The core model developed in this article is most closely related to the one-sided assignment3

models studied by Lucas (1978), Rosen (1982), Waldman (1984), Garicano and Rossi-Hansberg

(2004, 2006), and Garicano and Hubbard (2005). However, unlike our model where the leader

produces the largest share of the output, in these models, output is produced by agents at the

bottom of the hierarchy helped by managers at the top of the hierarchy. In the economy studied

by Garicano and Rossi-Hansberg (2006), for instance, hierarchical organization arises as an

2Rosen (1982) recognizes that if the rents function is sufficiently convex, then the model predicts that both the least

and most able agents become managers, a result also obtained in Waldman (1984). Rosen (1982) classifies this case as

a ‘pathology’ of the model since it implies that some managers are less able than their workers.

3This contrasts with two-sided assignment models studied in Tinbergen (1956), Becker (1973), Rosen (1974), and

Sattinger (1993), among others, where agents on one side of the market (workers, women, sellers) meet agents on the

other side of the market (firms, men, buyers). These models have been used in the recent literature on CEO pay by,

e.g., Gabaix and Landier (2008) and Tervio (2008). More recently, Edmans et al. (2009) embedded a moral hazard

problem into a talent two-sided assignment model to study CEO-pay incentives.