Positive Assortative Matching: Evidence from Sports Data

• Author: Antonio Filippin,Jan C. Ours
• Date: 01 July 2015
• Published date: 01 July 2015
• DOI: http://doi.org/10.1111/irel.12096

Positive Assortative Matching: Evidence from

Sports Data

*

ANTONIO FILIPPIN and JAN C. VAN OURS

It is difficult to establish empirically whether or not there is positive assortative

matching in the labor market. We use longitudinal data from a 24-hour relay mara-

thon in Belluno, Italy, in which participants are affiliated with teams, to study group

dynamics in a manner that closely resembles workers’accessions to and separations

from firms. In our dataset the productivity of the individual agents is measured and

we exploit this by investigating the determinants of accessions, separations, and

assortative matching. We find support for the existence of positive assortative

matching; i.e., better runners moving to better teams in subsequent years.

Introduction

Firms can use hiring and separations as tools to increase productivity and

profits. Firms may hire young, inexperienced workers who have just entered

the labor market or more experienced workers who have quit or been let go

from another job. Separations may occur through layoffs, quits, or retirement.

That there is positive assortative matching, i.e., better workers tend to move to

better firms, looks like a natural consequence. However, this fact is not well

established in the literature. The way firms and workers form a match is the

topic of both theoretical and empirical research. If there are complementarities

in the production function, it is optimal when the best firms match with the

best workers. Then, a random allocation of workers across firms would imply

a loss of output. Similarly, if characteristics of firms and workers are substi-

tutes in production a random allocation is not optimal either.

It is not easy to establish whether or not there is assortative matching and if so

whether it is positive or negative. Originally, studies used wage data to investigate

*The authors’affiliations are, respectively, Department of Economics, University of Milan, Italy, and IZA

(Bonn). Email: antonio.filippin@unimi.it; Department of Economics, CentER, Tilburg University, the Neth-

erlands; Department of Economics, University of Melbourne, Parkville, Australia; CEPR (London); CESifo

(Munich); IZA (Bonn); Email: vanours@uvt.nl.

JEL: J14, J24, J31.

The authors thank the organizers of the San Martino Marathon for making the data available, and Lorenzo

Cappellari and Giovanni Pica as well as participants to the XXXVI SAEe conference (Malaga) for helpful

suggestions. The usual disclaimers apply.

INDUSTRIAL RELATIONS, Vol. 54, No. 3 (July 2015). ©2015 Regents of the University of California

Published by Wiley Periodicals, Inc., 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington

Road, Oxford, OX4 2DQ, UK.

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the matching between workers and firms. Worker fixed effects and firm fixed

effects are derived from wage equations estimated on matched worker–firm data.

The correlation between the two types of fixed effects is interpreted as being infor-

mative about the existence and the nature of assortative matching. Abowd,

Kramarz, and Margolis (1999) initially used this idea to analyze French worker–

firm data and found that the correlation between the two types of fixed effects is

small or negative. Abowd et al. (2009), applying a similar method to U.S.earnings

data, found that the correlation between worker and firm effects is close to zero.

Andrews et al. (2008) argued that estimation errors can cause a downward

bias in the estimated correlation between worker and firm fixed effects. An over-

estimate of a worker effect on average leads to an underestimate of a firm fixed

effect. This bias is bigger the fewer workers move between firms. Using German

matched worker–firm data they found that this bias can be considerable but not

sufficiently large to remove the negative correlation between worker and firm

fixed effects. Andrews et al. (2012), also using German data, addressed the

“limited mobility bias”by focusing on firms for which the number of movers is

large and found that there is significant positive assortative matching.

Eeckhout and Kircher (2011) and Lopes de Melo (2013) argued that the

method of Abowd, Kramarz, and Margolis (1999) did not properly measure sort-

ing because wages are not monotone in the firm type. Wages of a given worker

have an inverted U-shape around the optimal allocation. Wages can be lower

not only when the worker matches with a bad firm, but also, more surprisingly,

with a very good firm. The reason is that in the case of complementarities higher

productivity firms pay a very high cost if they match with a bad worker, because

it destroys their opportunity to match with a better one. Hence, they need to be

compensated for a suboptimal match via a lower wage. This implies that the

compensation is the highest when a worker meets the right firm and that the

wage schedule is not monotonically increasing in the firm type. Consequently,

standard firm fixed effects are not correlated with the true type of the firm.

Lopes de Melo (2013) suggested that the correlation between the fixed

effects of workers and the average fixed effects of his/her coworkers should be

used as an indicator for assortative matching. Applying this idea to Brazilian

matched worker–firm data Lopes de Melo (2008) found evidence of sorting.

However, this procedure and the use of wage data in general can only be

informative about the intensity of assortative matching, but not about its sign.

More recently, Bartolucci and Devicienti (2013) exploited the movers in a

matched worker–firm dataset, showing that there is positive assortative match-

ing. They used firms’profit and workers’wage to build a ranking of their

respective types. Relying upon such proxies they found that the direction of

assortative matching is positive, while the opposite would emerge estimating

the fixed effects of a wage equation.

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