Capital-Skill Complementarity Beyond Firm Boundaries

New machinery has long been argued to raise the relative demand for skilled labor, yet firm-level evidence finds no such shift at investing firms. We resolve this puzzle by looking beyond firm boundaries. Linking Belgian data on capital investments, buyer–supplier transactions, and worker skills, we show that the skill bias of new machinery arises entirely at external suppliers. Following machinery investment spikes, purchases from suppliers raise firms’ total demand for high-STEM workers by 45%, three times the rise for other skill groups, while in-house hiring raises it by less than 5%, evenly across skill groups. This external demand comes first from machine integrators and later from complementary services such as software, and is stronger for smaller firms, lumpier investments, and rapidly advancing capital, consistent with fixed and adjustment costs of hiring high-STEM workers in-house. In a general-equilibrium model estimated on our event studies, the rise in machinery per worker from 2003 to 2021 raises relative demand for high-STEM workers by 8.8 log points and their wage premium by 3.1. Measured on payrolls alone, both would fall.