Testing Zipf’s and Gibrat’s laws in the Spanish university system: evidence from a decade of institutional transformation

Abstract

This paper examines the empirical validity of Zipf’s and Gibrat’s Laws in the Spanish higher education system using disaggregated program-level data across institutional types, study modalities, and academic fields over the period 2015–2024. The study contributes by using these laws as diagnostic benchmarks to identify structured deviations and to characterize heterogeneity in growth dynamics and size distributions within higher education systems. Results show consistent rejection of both laws. Growth patterns are statistically associated with initial size, and program size distributions do not follow Zipfian expectations. These patterns are persistent over time and display substantial heterogeneity across institutional types, modalities, and academic fields, with more pronounced departures observed in private and online universities and in fields such as Engineering and Health Sciences. Importantly, the analysis is descriptive in nature and does not identify the causal mechanisms underlying these patterns. Instead, the results are interpreted as empirical regularities that constrain the range of plausible explanations of system dynamics. While the observed patterns are discussed in relation to recent regulatory developments, including Royal Decree 905/2025, no causal claims are made regarding their effects. Several regulatory elements—such as transparency, research standards, and faculty qualifications—are broadly consistent with the observed patterns, others, such as annual limits on new degree offerings, may reduce the system’s responsiveness to emerging academic and societal needs. Overall, the paper provides a structured empirical characterization of growth and concentration patterns in higher education and highlights the relevance of benchmark-based approaches for analyzing system-level heterogeneity.