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«A Theory of Intra-Firm Group Design∗ Semih Tumen † Central Bank of the Republic of Turkey August 6, 2012 Abstract I develop an intra-firm theory ...»

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A Theory of Intra-Firm Group Design∗

Semih Tumen †

Central Bank of the Republic of Turkey

August 6, 2012

Abstract

I develop an intra-firm theory of group design and teamwork in the presence of peer effects. The purpose

is to understand the interlinkages between intra-firm group formation and the extent of wage dispersion

within the firm. Given a set of heterogeneous workers, the manager faces the challenge of allocating workers

into endogenous groups (or teams) to maximize total profits. The optimal allocation features locational proximity between workers with similar productivity levels. I discuss the implications of this allocation on intra-firm wage outcomes. The main idea is that the wage paid to a single worker is determined by the productivity levels of the teammates as well as the worker’s own productivity. This means that team composition is critical to understanding the within-firm productivity and wage differentials. I show that intra-firm wage dispersion is more pronounced when workers are more alike within each team and more different across the teams. I provide numerical exercises designed to illustrate how the model’s predictions change as the key parameters are varied. One striking result is that a rise in the correlation between education and productivity (this can be interpreted as hiring workers with vocational education) leads to a decline in wage inequality within the firm. I also show that changes in the dispersion of worker efficiency lead to nonmonotonic effects on within-firm wage inequality.

JEL codes: J31, L22, L23, M51, M52.

Keywords: Group design; peer effects in the workplace; within-firm pay differences; sorting; selectivity.

∗I thank Iwan Barankay, Yossi Spiegel, and Ayhan Bulent Toptas for useful comments. The views expressed here are of my own and do not necessarily reflect those of the Central Bank of the Republic of Turkey. All errors are mine.

† semih.tumen@tcmb.gov.tr. Central Bank of the Republic of Turkey, Istiklal Cad. No:10, 06100 Ulus, Ankara, Turkey.

Contents 1 Introduction 3 2 Related Literature 6 3 The Model 9 4 Implications for Intra-firm Wage Dispersion 17 5 Concluding Remarks 20 1 Introduction For many production processes, especially in large firms, output per worker is not only a function of the characteristics of a single worker, but also of the characteristics of the peers working close to her.1 This “peer effects” viewpoint in production is of particular importance for jobs requiring teamwork and communication.2 It imposes a major organizational challenge on firms in terms of the optimal assignment of workers to peers (or teams), as a misallocation may result in inefficiencies and severe output loss. For example, Lazear (1998) argues that complementarities in production among co-workers make it economically desirable for a firm to form groups or teams. This viewpoint is also important to understand the role of peer effects on the structure of within-firm wage structure, as the wage payments to a single worker is affected by the productivity levels of her co-workers as well as her own [Ledford, Lawler, and Mohrman (1995)].

The theoretical framework I develop in this paper addresses three related, but distinct, questions. First, how to consider the optimal assignment of heterogeneous workers to endogenously defined peer groups or teams in the workplace? Second, how to assess the role of endogenously formed peer groups on wage differences within the firm? Third, how to uncover the connections between team composition (i.e., the intra-team mix of worker characteristics) and wage outcomes? Existence of strong empirical evidence highlighting the importance of peer effects in the workplace [see, for example, Ichino and Maggi (2000), Hamilton, Nickerson, and Owan (2003), Mas and Moretti (2009), and Bandiera, Barankay, and Rasul (2010)] necessitates the development of a coherent theoretical framework to enhance our understanding of how peer effects shape within-firm resource allocation and the resulting wage outcomes. The fact that peer groups are endogenously formed within the firm makes the problem more interesting.

This paper embeds the idea of endogenous teams into a hedonic pricing model, which makes it possible to study group design in the presence of worker heterogeneity in multiple dimensions.

1 For expositional purposes, the worker is a “she” and the manager is a “he” throughout the paper.

2 Theconcept of positive spillover externalities in the workplace is not new and goes back to Marshall (1890). Lazear and Shaw (2007) provide evidence that the incidence of teamwork has been steadily increasing over time.

The first question is related to within-firm organizational practices. Given a set of heterogeneous workers, the manager faces the challenge of allocating workers into groups to maximize total profits. Empirical evidence suggests strong complementarities between individual- and group-level productivities. In other words, the marginal product of a worker increases with the productivity levels of the peers she works with. The production externalities reflect the benefits to any worker from the existence of other workers nearby. In an optimal allocation, employees with similar productivities should work close to each other. Due to complementarities, locational proximity of highly productive workers leads to greater profits.





Interestingly, this doesn’t imply a perfect segregation story in the sense that workers with superior efficiency levels should work close to each other in isolation and the less efficient ones should not interact with them. The intuition is as follows. Teams are composed of heterogeneous workers. I define productivity as a three-dimesional object: efficiency, education, and luck.3 There is a positive correlation between efficiency of a worker and her education. The manager observes and acts on only efficiency and education, forming expectations on the luck component. He forms groups or teams in production to maximize total profits. In each group, there is a balance of highly efficient but less educated and less educated but more efficient workers. The groups are ranked by the quality of this mix. Accordingly, worker productivity is defined as a combination of efficiency and education. As a result, team composition, which is endogenously determined, is an important element of the analysis.

The second question, which is closely linked to the first one, investigates the impact of group design on the within-firm wage structure in the equilibrium. In particular, I analyze the relationship between the manager’s decisions on group formation and wage inequality within the firm. The key assumption is that the members of a team are paid similarly, but wages differ across teams. I show that team composition is a critical element in explaining withinrm wage differentials. When selectivity is stronger (i.e., when workers within a team are more alike), the degree of sorting goes up and teams become more different from each other.

In such a case, being a part of a better group will contribute more, on average, to an individual 3 The luck component can be interpreted as an independent idiosyncratic shock that affects the worker’s output.

worker’s output. As a result, the wage equation will tend to be a convex function of team quality and the degree of within-firm wage inequality will go up.

The answer to the third question is immediate. Stronger sorting and selectivity leads to greater pay differentials within a firm. Specifically, stronger selectivity is implied by smaller withinthe-team productivity differentials, whereas stronger sorting is implied by larger productivity differentials across teams. I conclude that managers will be more willing to pay for teamwork when team membership complements the individual worker’s effort significantly. In other words, stronger peer effects raise the manager’s valuation of teamwork.

In a nutshell, the main contribution of the paper can be summarized as follows. I consider each worker’s output in the production process as a combination of her own characteristics and the characteristics of her co-workers. Worker characteristics are heterogeneous and the heteroegeneity is multi-dimensional. The manager optimally allocates workers into (endogenous) teams based on these characteristics. Wages are determined based on each group’s productivity, which is a combination of the characteristics of the workers selected in the group. In other words, wages are determined consistent with the hedonic pricing logic. So, the paper contributes the literature by providing a hedonic pricing interpretation to intra-firm group design. Another contribution is that the paper shows that team composition is an important determinant of wage dispersion within the firm. In particular, I show that intra-firm wage dispersion is more pronounced when workers are more alike within each team and more different across the teams.

That worker heterogeneity is multi-dimensional provides a rich basis for comparative statics exercises and, therefore, for policy. Everything else constant, increased dispersion of the years of school education within the firm leads to increased wage inequality. If the manager wants to reduce wage differentials across teams, he has to hire workers with similar education levels. A larger correlation between education and productive efficiency of workers (i.e., if the worker’s are hired on the basis of their vocational education) within the firm leads to decreased wage inequality, since selectivity and sorting will be weaker. When this is the case, efficiency and education become more substitutable, which reduces the incentives for bunching workers with respect to their efficiency levels.4 The analysis builds on the framework developed by Nesheim (2001), and extended by Ioannides (2008, 2011) and Tumen (2011, 2012). The starting point is a simple social interactions story, which falls into the category of endogenous contextual effects.5 The key element is the demand for an intra-firm amenity variable: group-level productivity. The manager’s willingness to pay for each worker is a function of the group that the worker is assigned. Notice that a selection process operates in the background: more efficient workers are assigned to better groups and are paid higher wages. I provide exact selection formulations that resemble the Heckman’s selfselection equations. These selection equations rationalize the sorting of workers into teams.

I show how one can go from the demand equation for the amenity variable to the associated selection and sorting equations.

The plan of the paper is as follows. The next section provides explicit links between the model and the relevant literatures. Section 3 presents the model and outlines a solution strategy that results in analytical solutions for the equilibrium objects featured by the model.

Section 4 discusses the implications of this equilibrium for intra-firm wage outcomes. Section 5 concludes.

2 Related Literature

The backbone of the model is the classical hedonic pricing idea: worker heterogeneity is multi-dimensional and these multiple characteristics are priced jointly in determining wage outcomes. Because of this joint pricing idea, the model can be classified within a particular class of hedonic models, called the Tinbergen-Rosen framework.6 The manager places a worker into a group based on a certain decision-making rationale, which rests on the characteristics of the workers in the group. More specifically, the manager brings together workers with similar 4 Section 4 presents the details of this result as well as further results from additional comparative statics exercises.

5A contextual effect means that the social influence comes from the group-level characteristics. It is endogenous because the group formation is determined within the model. See Manski (1993, 2000) for a more precise definition of the related concepts.

6 See Tinbergen (1956), Rosen (1974), and Ekeland, Heckman, and Nesheim (2002, 2004).

characteristics in each group, but the groups are different from each other. There is a natural hierarchy between the groups in the sense that more productive workers are sorted into better groups. Such an allocation maximizes the firm’s profits. The main idea is the existence of production externalities. This force increases worker productivity if similar workers are close by.7 The key result in the paper is that workers with similar productivities are brought together in teams by the manager in the optimal allocation. The whole idea behind the sorting and selectivity results in the model is based on this positive correlation between worker-level and group-level characteristics. There is new and compelling empirical evidence supporting the validity of this result. Bandiera, Barankay, and Rasul (2010) find that a worker’s productivity is considerably higher when she works close to peers who are more productive than her, and considerably lower when she works with less productive peers. This suggests that within group heterogeneity may be beneficial in increasing the output that low-productivity workers produce, but it is detrimental to highly productive ones. As a result, the existence of large within-group heterogeneity (in productivity) contradicts the whole idea behind production externalities. They present suggestive evidence that group formation within the firm follows the principle of positively assortative matching in the sense that workers with similar abilities tend to be selected into similar groups in the optimal allocation.8 I embed an analytically tractable Heckman selection argument into the model, which governs sorting and determines the pricing of teamwork.

This idea is also closely related to the literature on the effect of team composition on productivity. The main focus in this literature is to investigate whether a team is more productive when it consists of more heterogeneous workers or more homogeneous ones. The results are rather mixed in this literature. For example, Hamilton, Nickerson, and Owan (2003) find that more heterogeneous teams are more productive and the members of those teams receive 7 Similar ideas can be found in the urban economics literature under the topic of “agglomeration economies”. See, for example, Fujita (1989). This idea is also prevalent in residential sorting models [see Ioannides (2011) for a review].



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