A Firm Link: Overall, Between- and Within-Firm Inequality Through the Lens of a Sorting Model

This paper provides a new theory of the observed co-movement between overall wage inequality and its between-firm component. We develop and solve analytically a frictionless sorting model with two-sided heterogeneity, in which firms consist of distributions of tasks, choose how many workers to employ and reward their workers both through wages and amenities. We show that, for empirically-relevant parameter ranges, overall and between-firm inequality are firmly linked: A change in any of the models' primitives increases overall wage inequality if and only if it also increases the ratio of between-firm to overall inequality. Subsequently, we calibrate the model to match the Norwegian economy and find that the increase in wage inequality from 1995 to 2014 had a different primary cause (raising span-of-control cost) than the accompanying rise in welfare inequality (increased skill variance), and that the apparent decrease in wage inequality after 2015 masked a continued increase in welfare inequality.