Assortative Matching With Large Firms

Abstract

Two cornerstones of empirical and policy analysis of firms, in macro, labor and industrial organization, are the determinants of the firm size distribution and the determinants of sorting between workers and firms. We propose a unifying theory of production where management resolves a tradeoff between hiring more versus better workers. The span of control or size is therefore intimately intertwined with the sorting pattern. We provide a condition for sorting that captures this tradeoff between the quantity and quality of workers and that generalizes Becker's sorting condition. A system of differential equations determines the equilibrium allocation, the firm size, and wages, and allows us to characterize the allocation of the quality and quantity of labor to firms of different productivity. We show that our model nests a large number of widely used existing models. We also augment the model to incorporate labor market frictions in the presence of sorting with large firms.

Human Capital, Firm Capabilities, and Innovation

“…Second, we extend an important literature that considers how workers and firms match to the context of innovation. Consistent with recent studies of routine workers that record departures from the standard positive assortative matching framework (Becker 1973), we provide evidence for negative assortative matching between firm-specific innovation capabilities and human capital (see also, Eeckhout 2018, Lindenlaub 2017, Eeckhout and Kircher 2018. We document positive assortative matching among workers-highly talented workers prefer to work at firms with other highly talented workers.…”

Growth, Trade, and Inequality

“…Assumption 1 implies ψ ϕa > 0 for all ϕ and a. As is known from Costinot (2009), Eeckhout andKircher (2016), Sampson (2014), and others, the strict log supermodularity of ψ(·) implies that, for any upward-sloping wage schedule w(a), each manufacturing firm hires the particular type of labor that is most appropriate given its technology ϕ, and there is positive assortative matching (PAM) between firm types and worker types. We denote by m(ϕ) the ability of workers employed by firms that operate a technology ϕ; PAM is reflected in the fact that m (ϕ) > 0.…”

Vacancy Durations and Entry Wages: Evidence from Linked Vacancy-Employer-Employee Data

“…See alsoEeckhout and Kircher (2018) who provide an extension of the model ofKaas and Kircher (2015) with more general production functions, but linear vacancy posting costs.…”