About 40% of employment in manufacturing is in services functions. This paper develops a measure of narrow outsourcing, matching services functions performed by workers inside manufacturing firms to the same services functions provided by outside suppliers. The measure allows us to analyse the competition that, say, workers at the IT services desk in manufacturing firms face from outside IT suppliers. Narrow outsourcing is entered into labour demand functions where labour is broken down on business functions using OECD data combined with the 2016 releases of the World Input Output Database (WIOD). On average, a one percentage point increase in narrow local outsourcing of services reduces manufacturing employment in the same services function by between 1.5% (R&D) and 3% (transport). The impact of offshoring on manufacturing labour demand is small on average, but depends strongly on the complexity of the value chain, the policy environment and technology. Manufacturing employment is more services intensive the longer the value chain. In-house IT functions complement and support offshored IT functions, while offshored R&D functions tend to replace in-house R&D. Tentatively, technology as measured by IT maturity and the length of the value chain is more important for employment in services functions in manufacturing than is offshoring.