Long-term growth is not a simple transition along the path of equilibrium growth, but a process of the interplay of technological, economic, institutional, and social factors. Social capability is an important prerequisite for late-developing countries to catch up with leading countries, and the combination of social capability and the technology gap co-determine the potential of a country to improve productivity through catching up. This paper clarifies the theoretical mechanism of social capability to promote economic growth, and reveals that accountability quality may become capability gap which impedes the convergence of economic growth of the low-income countries by analyzing the panel data from 166 countries over the period 1996-2019. This paper believes that with the rising income level, it is the general path of sustained economic growth to promote the modernization of economic structure while ensuring the supply of goods and effective social incentives. (c) 2023 Economic Society of Australia, Queensland. Published by Elsevier B.V. All rights reserved.