When more is not better: heterogeneous dose–response effects of R&D subsidies by firm size

Abstract

This paper examines how the level of public R&D subsidies and firm size jointly influence firms’ net R&D investment. Using data on Spanish manufacturing firms from 2008 to 2018, we estimate parametric and non-parametric dose–response functions after applying entropy weighting to balance covariate distributions across treatment levels. The results reveal an inverted U-shaped relationship between subsidy intensity and net R&D expenditure for small, medium-sized, and large firms, but not for very large firms, which display a negative linear pattern. We also find substantial heterogeneity in subsidy effects within both the SME and large-firm categories, and show that the public funding share of R&D expenditure at which the positive impact of subsidies peaks declines markedly with firm size. These findings suggest that support schemes should implement progressively lower maximum subsidy rates, rather than relying on only two distinct caps for SMEs and larger firms. Overall, the results underscore firm size as a critical determinant of innovation policy effectiveness and provide practical guidance for optimizing subsidy design.