Scale Economies and Aggregate Productivity

We develop a theoretical framework to investigate the link between rising scale economies and stagnating productivity. Our model features heterogeneous firms, imperfect competition, and firm selection. We demonstrate that scale economies generated by fixed costs have distinct impacts on aggregate productivity compared to those driven by returns to scale (slope of marginal cost). Using UK data, we estimate long-run increases in both fixed costs and returns to scale. Our model implies that this should increase aggregate productivity through improved firm selection and resource allocation. However, increasing markups can offset the productivity gain. Higher markups cushion low-productivity firms’ revenues, allowing them to survive, and constrain firm output, which limits exploitation of scale economies.

💡 Research Summary

The paper tackles the puzzling coexistence of rising scale economies and stagnant aggregate productivity observed in advanced economies, using the United Kingdom as a case study. It builds a tractable heterogeneous‑firm model that incorporates monopolistic competition, endogenous entry and exit, and two distinct sources of scale economies: (i) higher fixed costs and (ii) higher returns to scale in variable inputs (i.e., a flatter marginal‑cost curve). The authors show analytically that both sources increase aggregate productivity through stronger firm selection and a more efficient allocation of resources, but they operate via different channels. Higher fixed costs reduce profits for all firms, shrinking the mass of active firms and thereby intensifying selection; this raises the average productivity of surviving firms regardless of markup levels. In contrast, higher returns to scale improve productivity only if firms can expand output. When markups are low, demand is elastic enough for firms to grow, so the selection effect is strong. However, rising markups—observed empirically in the UK—relax the zero‑profit constraint, allowing low‑productivity firms to survive and limiting the size of high‑productivity firms. Consequently, higher markups increase the number of active firms, raise the share of labour devoted to overhead activities, and dampen the productivity gains that would otherwise arise from scale economies.

Empirically, the authors estimate firm‑level production functions on the Annual Respondents Database (ARDx) covering 1997‑2021. Using the Gandhi‑Navarro‑Rivers (2020) methodology, they obtain time‑varying elasticities for capital, labour and intermediate inputs, and compute a sales‑weighted returns‑to‑scale measure (the sum of the three elasticities). They also construct two proxies for fixed‑cost intensity: the share of administrative expenses in revenue and the share of employment in administrative and support services. Both series display a clear upward trend over the sample period, indicating that UK firms have experienced rising fixed‑cost burdens and increasing returns to scale simultaneously.

The quantitative exercise calibrates the model to the estimated trends in fixed costs, returns to scale, and markups. Holding markups constant at their early‑sample levels, the model predicts that the observed rise in scale economies would have lifted aggregate TFP by roughly 20 % over the study horizon. When the contemporaneous increase in markups is introduced, however, the productivity boost is largely erased, reproducing the observed stagnation in UK TFP after the mid‑2000s. The authors therefore conclude that the interaction between supply‑side technological change (which creates scale economies) and demand‑side market power (which raises markups) is crucial for understanding macro‑productivity dynamics.

The paper contributes to three strands of literature. First, it extends the micro‑foundations of aggregate productivity by distinguishing the distinct aggregate effects of fixed‑cost versus marginal‑cost scale economies. Second, it provides a quantitative bridge between recent empirical findings on rising markups and the “productivity puzzle.” Third, it offers a policy‑relevant insight: fostering competition and containing markup growth are essential complements to technological innovation if the latter is to translate into higher aggregate productivity.