The history of cross-country income is marked by mixed patterns. Over the very long run, the world has seen a “great divergence” between the richest and poorest nations. More recent evidence, however, suggests a more complex picture where some countries are converging toward the leaders’ growth path while others continue to fall further behind. This sorting of nations into distinct growth clubs is a central puzzle that simpler models fail to explain. This section formalizes a Schumpeterian model that explains this phenomenon of “club convergence.”

The Mechanics of Catch-Up Growth

In a Schumpeterian world, a country’s aggregate growth rate can be understood as the product of two key factors: the frequency of innovation and the average size of innovations.

1. Innovation Size and Technology Transfer: For a country operating behind the world technological frontier, the primary source of productivity growth is successfully adopting or imitating technologies that already exist at the frontier. A successful “innovation” in this context involves implementing a frontier technology, representing a significant quality jump. The size of this jump—and thus the size of the average innovation—is larger the further a country is from the frontier (represented by the ratio Ā_t / A_t-1, where Ā_t is frontier productivity and A_t is the country’s productivity). This mechanism is the formal expression of the “advantage of backwardness.”
2. Innovation Frequency and Institutional Quality: While the potential size of innovations is determined by a country’s technological gap, the frequency with which these innovations occur is determined by domestic economic incentives. These incentives are shaped by a country’s policies and institutions, which affect both the costs and the prospective profits of innovation. The model formalizes this with an institutional quality threshold, p > h, where p represents the profitability of innovation (shaped by factors like property rights) and h represents the initial fixed cost. If p ≤ h, the expected returns do not justify the costs, and innovation ceases.

The Emergence of Two Clubs

This framework naturally gives rise to a world with two distinct clubs, determined by the quality of a country’s institutions.

The Convergence Club

Countries with institutions that are “good enough” to surpass the innovation threshold (p > h) will have a positive rate of innovation. Entrepreneurs in these countries are incentivized to invest in adopting frontier technologies. Because these countries benefit from technology transfer, their growth rates will be higher the further they are from the frontier. This effect ensures that all countries within this club will, in the long run, converge to the same steady-state growth rate as the world frontier. While their income levels may differ based on the specific quality of their institutions (which determines their long-run proximity to the frontier), their growth rates will converge.

The Stagnation and Divergence Club

In contrast, countries with poor institutions that fail to meet the innovation threshold (p ≤ h) will see no innovative activity. Firms in these countries are not incentivized to invest in adopting new technologies. As a result, they cannot benefit from technology transfer and the advantage of backwardness. Their productivity stagnates while the world technology frontier continues to advance, causing them to fall further and further behind. These nations become trapped in a state of stagnation or, more accurately, divergence.

Credit Constraints: A Mechanism for Divergence

One specific institutional failure that can trap a country in the stagnation club is the lack of financial development. Innovation is a costly and risky endeavor that often requires external financing. If a country’s credit markets are poorly developed, even firms with profitable innovation projects may be unable to secure the necessary funding. These credit constraints act as a powerful barrier to innovation, effectively preventing a country from capitalizing on technology transfer.

Empirical work by Aghion, Howitt, and Mayer-Foulkes (2005) provides strong evidence for this channel. Their cross-country analysis shows that the likelihood of a country converging to the frontier growth path increases significantly with its level of financial development. Poor financial institutions can single-handedly relegate a nation to the divergence club, even if other policies are favorable.

Having established a model where a baseline level of institutional quality determines whether a country joins the convergence club, the next section explores the more subtle argument that it is not just the absolute quality of institutions that matters, but whether those institutions are “appropriate” for a country’s particular stage of development.