We develop an endogenous growth model to simulate the long-term impact of Italy's National Recovery and Resilience Plan (NRRP) on the persistent North-South productivity gap. Our model underscores public investment as a catalyst for sustained economic growth and highlights the reliance of local government quality on the surrounding social capital. In regions with low social capital, local investment management diminishes efficiency due to prevalent misappropriation. In contrast, centralized management enhances the effectiveness of public action in these situations. The NRRP's overall effect therefore relies on the government level to which investment management is assigned. Our quantitative exercises show that compared to centralization, decentralization weakens the NRRP's impact on the relative position of the South. However, even under our our best scenario — centralized management — the NRRP only slightly reduces the North-South productivity gap from 75% to 76.4%. Finally, our research highlights the pivotal role of a reform aimed at maintaining central control over Southern public investments well beyond 2026, when the NRRP's actions and governance are due to stop. This type of reform can potentially yield more substantial, positive, and lasting impacts on the region.