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A theory of intra-firm group design

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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 non-monotonic effects on within-firm wage inequality.

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Notes

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

  2. The concept 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.

  3. The luck component can be interpreted as an independent idiosyncratic shock that affects the worker’s output.

  4. Formally speaking, the terms “sorting” and “selectivity” can be best understood by comparing the population and within-team distributions of productivity. Specifically, the gap between within-team versus population-level average productivities describes the degree of sorting. Similarly, the gap between within-team versus population level variance of productivity describes the degree of selectivity. These two terms jointly define the structure of teamwork within the firm. See the relevant section for a much more detailed description of these two terms.

  5. Section 4 presents the details of this result as well as further results from additional comparative statics exercises.

  6. A 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.

  7. See Tinbergen (1956), Rosen (1974), and Ekeland et al. (2002, 2004).

  8. 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].

  9. This is tangentially related to the “homophily principle.” In other words, the similarities between individuals make them more likely to form social groups within each other. See McPherson et al. (2001), Marmaros and Sacerdote (2006), and Currarini et al. (2009) for further reading.

  10. Heckman selection-correction procedure develops a framework to deal with non-randomly selected samples from the population and removes the associated biases [see Heckman 1979]. The theoretical model developed in this paper embeds a Heckman selection argument, because the problem of non-random sorting of more productive workers into more productive teams is a clear case of self-selection. Thus, the tools developed by Heckman can be used to analyze the patterns of sorting and selectivity within the firm.

  11. Lazear (1989), Drago and Garvey (1998), and Carpenter et al. (2010) argue that increased team-level pay differences might reduce cooperation within teams. But I abstract from such strategic complexities.

  12. See also Milgrom (1988) and Milgrom and Roberts (1990).

  13. Lallemand et al. (2009) provide an excellent review of the related literature. See also Gibbons and Waldman (1999).

  14. See, e.g., Camerer (2003), Fehr and Schmidt (2006), Bartling and von Siemens (2010), and Bose et al. (2010).

  15. The manager plays the role of a social planner aiming to optimally allocate workers across teams within the firm. Other than this role, there is not a formal managerial body or a CEO in the model that decides on operational issues within the firm.

  16. See Ross and Yinger (1999) for an extensive review of the related literature.

  17. This resembles the selectivity (or the control functions) idea due to Heckman (1979).

  18. This will be linked to higher and more unequally distributed wages in Section 3.

  19. Notice that the group-level variances are compressed when \(\delta\) goes up. But this compression does not produce a mean-preserving spread. The fact that it raises the differences in means across groups is due to the correlation imposed by the decision rule.

  20. The log-normality assumption is not critical for the qualitative nature of the results presented in this paper. However, the log-normality assumption is required to obtain analytically tractable formulas for equilibrium objects such as wages and group-level productivity levels. In particular, this assumption is extremely helpful to derive the formulas for sorting and selectivity, since the regression interpretation given in Eq. (3.12) critically relies on the normality assumption. The log-normal distribution is also used very often in economics, since various critical variables—such as income, earnings, firm size, firm productivity, human capital, and consumption—are empirically shown to be log-normally distributed. Log-normality fits to reality well in general, because it reflects the fact that “high-quality is rare.” This is also relevant within the context of the current paper. I conjecture that relaxing the log-normality assumption should not change any of the results as long as the alternative distribution comes from the exponential family—such as exponential, gamma, Pareto, Dirichlet, etc. The only requirement is that there should be a clearly right-skewed distribution with a long right-tail for the results to hold. Without log-normality, however, analytical tractability will be much harder to obtain.

  21. The idea is simple. As one moves away from the left tail, incremental improvements in x comes with increased densities of better quality worker groups. Once the mean point is past behind, the incremental improvements in x bring decreasingly smaller contributions to the group quality.

  22. For the sake of analytical tractability, I limit the dimension of the characteristics vector to be two (efficiency and education). In a more elaborate version (or in a version designed for the purpose of empirical applicability), the characteristics vector may be allowed to consist of three or more worker traits.

  23. It is also noteworthy that the effect of increasing \(\sigma _{ee}\) on wage inequality over the x horizon is irregular, i.e., a higher \(\sigma _{ee}\) raises inequality in the lower tail while it increases inequality in the upper tail in a certain interval, whereas in another interval this effect may be reversed.

  24. See Table 2 for the values of these fixed parameters.

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Acknowledgements

I thank Iwan Barankay, Jesper Sorensen, Yossi Spiegel, Peter Thompson, seminar participants at the Central Bank of the Republic of Turkey, and the participants of the 2012 Turkish Economic Association conference in Izmir for useful comments. I am particularly grateful to William Greene (the editor), an Associate Editor, and an anonymous referee for extremely helpful suggestions. 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.

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  1. Research and Monetary Policy Department, Central Bank of the Republic of Turkey, Istiklal Cad. No:10, 06100, Ulus, Ankara, Turkey

    Semih Tumen

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Tumen, S. A theory of intra-firm group design. J Prod Anal 45, 89–102 (2016). https://doi.org/10.1007/s11123-015-0452-0

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