Abstract
<title>Abstract</title> <p>Will the countries that lead global science today still lead mid-century? And will quality leadership prove more or less durable than volume leadership? These questions have become urgent as a wave of emerging economies has expanded their research output dramatically, while established G8 science powers face slower growth in the inputs that drive science production. We estimate Knowledge Production Functions for 181 countries over 2003–2022, using heterogeneous-panel estimators that account for cross-sectional dependence from the global science frontier. Three structural findings emerge. First, knowledge-stock compounding is the dominant engine of academic science output: ˆ ϕ ∈ [0.65, 0.76] across estimators, placing the panel firmly in the semi-endogenous growth regime and substantially above patent-based estimates. We confirm long-run coefficient homogeneity across countries, so that crosscountry differences in knowledge production shares reflect input accumulation histories, not heterogeneous production technologies. Second, volume and quality of scientific output follow structurally distinct production processes. The knowledge-stock elasticity for citation impact is two orders of magnitude below its quantity counterpart (ˆ ϕ q ≈ 0.015 vsˆϕvsˆ vsˆϕ ≈ 0.65): knowledge-stock compounding accrues to volume but not to citation quality. Human capital quality is the principal driver of citation impact (ˆ σ q = 2.19). A complementary decomposition finds that time-invariant institutional characteristics explain 65% of crosscountry citation-quality variation; the near-exact inverse of the quantity specification , where measured inputs dominate. Third, conditional projections to 2047 reveal dramatic G8 quantity-share compression. Quality projections are more nuanced: G8 quality attenuation is substantially arrested when driven by quality factor inputs alone, but approaches the quantity decline when volume compounding is incorporated. The gap between the two warns that volume decline may eventually transmit into quality leadership loss. JEL Classification: O30, O31, O33, O47, C23</p>