This study examines the impact of education, which has the characteristics of a quasi-public good, on local economic performance, specifically in Gümüşhane Province. The aim of the study is to identify the direct and indirect effects of education, infrastructure, health, and population variables on economic growth within the framework of both short and long term dynamics. The dataset used in the analysis was obtained from the Turkish Statistical Institute (TSI) database and consists of annual observations from the 2000–2024 period. The multidimensional variables of education (EDU), infrastructure (INFRA), and health (HEALTH) were transformed into composite indices using Principal Component Analysis (PCA). Due to the varying degrees of stationarity among the series, the Autoregressive Distributed Lags (ARDL) method was chosen. Additionally, mediation analysis was applied to identify indirect effect mechanisms among the variables, and the statistical significance of the mediation effect was verified using the Sobel test. Boundary test results indicate the presence of a strong long-run cointegration relationship among the variables. Long-run estimation results show that a one-standard-deviation increase in the education index boosts economic growth by approximately 0.95%, while a similar increase in the health indicator increases it by approximately 1.87%. The error correction term is negative and statistically significant. Approximately 26% of the imbalances emerging in the short term are resolved in each period, and the system converges toward equilibrium in approximately four periods. The findings of the mediation analysis indicate that the effect of the infrastructure variable on economic growth occurs indirectly through the education channel rather than directly, and the Sobel test statistically confirms this indirect effect.