Understanding the weak relationship between firm size and productivity

The standard economic framework predicts a positive relationship between size and productivity. If firms can pay a fixed cost to export or enter a new product market, this relationship will be even stronger. Most empirical studies, however, find only a small productivity premium for larger firms. This could be due to misallocation of resources, an active area of research, but other explanations are possible. Either the theory misses an important element, or productivity is measured imperfectly.

First, we study the size-productivity relationship theoretically. Several widely-used models of trade feature discrete jumps in output when firms enter new markets. We derive analytic expressions for the “expected” elasticity of size with respect to productivity. We show this elasticity can be lowered if a 2nd source of heterogeneity is added, firm-specific fixed costs of market entry or demand variation (which can be interpreted as quality).

Our model can accommodate a wide range of size-productivity relationships, which we estimate using data for three countries. Each country's dataset has specific advantages. The Chinese firm sample is particularly large and allows estimation by industry. For Belgium, we observe sourcing of intermediates and R&D services, which we use to control for quality differences. For Slovenia, we observe the occupational structure of each firm's workforce, which we use to measure fixed costs and improve productivity measurement.