3.1. Growth Accounting: Decomposing Growth into its Sources

Growth accounting is an empirical methodology used to decompose observed economic growth into two principal components: the contribution from the accumulation of factors of production (like capital) and the contribution from gains in overall productivity. First developed by Solow (1957), it is a crucial first step in evaluating the empirical relevance of different growth theories by helping us quantify the sources of growth in the real world.

The method distinguishes between labor productivity (y = Y/L), which is simply output per worker, and Total Factor Productivity (TFP).

Total Factor Productivity (TFP): A measure of the overall efficiency with which all factors of production (e.g., capital and labor) are used in an economy. Growth in TFP captures improvements in technology, efficiency, and organization that are not attributable to the mere accumulation of inputs.

Starting with a standard Cobb-Douglas production function for output per worker, y = Bk^α (Equation 5.2), where B is TFP and k is capital per worker, we can derive the core growth accounting equation by taking growth rates:

G = (ΔB/B) + α(Δk/k) (Equation 5.3)

This equation states that the growth rate of labor productivity (G) can be broken down into two parts:

1. TFP Growth (ΔB/B): This term captures improvements in technology, efficiency, and organization.
2. Capital Deepening (α(Δk/k)): This term captures the contribution of growth in the capital-per-worker ratio.

To use this equation, we need to measure TFP growth, which is not directly observable. This is done by calculating the “Solow residual.” The process involves two steps:

1. Estimate the capital share of income, α, using national accounts data on factor payments. This value is typically found to be around 0.3 for most developed economies.
2. Calculate TFP growth as the residual amount of labor productivity growth that is left over after subtracting the contribution from capital deepening: (ΔB/B) = G – α(Δk/k).

Empirical studies using this method for OECD countries generally find that both TFP growth and capital deepening account for substantial shares of overall productivity growth, with each typically contributing between 30 and 70 percent.

However, it is crucial to grasp the distinction between accounting and causation. While an accountant might attribute, say, 30% of growth to TFP and 70% to capital deepening, this is not a causal statement. A neoclassical theorist would argue that 100% of long-run growth is caused by TFP. The reason for this apparent contradiction is that, in the neoclassical model, technological progress is what prevents diminishing returns from halting capital accumulation in the first place. Without TFP growth, the capital-deepening term would eventually fall to zero. Therefore, technology is the ultimate cause of both measured components of growth in the long run.

To understand the true causal drivers of growth, we must move beyond accounting to analyze the deeper determinants of innovation and investment, such as the functioning of financial systems and the quality of institutions.

3.2. Finance, Credit Constraints, and Growth

The financial system plays a strategically vital role in economic growth. While many foundational growth models assume perfect capital markets where funds flow frictionlessly to their most productive uses, reality is far different. Financial frictions and credit constraints are often a primary obstacle to both innovation and capital investment, particularly for new entrepreneurs who lack established collateral or a track record.

To analyze this, we can introduce credit constraints into the Schumpeterian growth framework. In a model where entrepreneurs have some initial wealth but may need to borrow to finance the full cost of R&D, two key scenarios emerge:

1. No Credit Constraint: When entrepreneurs have enough wealth or access to credit, the level of R&D and the resulting growth rate are determined by the profitability of innovation. The growth rate is given by g = (γ-1)(λ^2 * π / 2). In this case, policies that increase the profits from innovation will directly translate into faster growth.
2. Binding Credit Constraint: When entrepreneurs are constrained, they can only invest up to an amount determined by their own wealth and the level of financial development (e.g., how much lenders are willing to leverage their initial capital). The growth rate becomes gh = (γ-1)λ√(νω/γ). The key implication here is that growth is now determined by the entrepreneur’s wealth (ω) and the level of financial development (ν), and is independent of profitability. When credit constraints bind, only improvements in wealth or financial access matter for growth, not the potential rewards of innovation.

This framework also illuminates the complex relationship between credit constraints, wealth inequality, and growth. Two contrasting models highlight the ambiguity:

• Model 1 (Banerjee and Newman, 1993): In a model with diminishing returns to investment, credit constraints are detrimental because they trap capital in the hands of less productive individuals and prevent it from flowing to more productive entrepreneurs who lack collateral. In this context, wealth redistribution that reduces inequality can enhance growth by enabling a larger number of entrepreneurs to overcome the investment threshold.
• Model 2 (Kunieda, 2008): In a model without diminishing returns but with heterogeneous entrepreneurial talent, credit constraints are harmful because they prevent the most talented individuals from leveraging their superior skills. In this scenario, wealth concentration in the hands of the most talented entrepreneurs can actually increase growth.

The empirical evidence, synthesized in Levine’s (2005) survey, strongly supports the importance of finance. A consistent positive correlation between financial development and economic growth has been found across a wide range of studies, including cross-country, cross-industry, and firm-level analyses. To establish a causal link from finance to growth, researchers have used instrumental variables, such as a country’s “legal origins” (e.g., whether its legal system is based on English common law or French civil law), which are thought to influence financial development without being directly caused by recent economic growth.

The interaction between technology, finance, and institutions is another critical determinant of whether countries are able to catch up to the economic frontier or fall further behind.

3.3. Institutions, Technology Transfer, and Convergence Clubs

Institutions—the formal and informal “rules of the game” that structure economic, social, and political interactions—are a fundamental determinant of long-run economic performance by shaping incentives for investment, innovation, and trade. This section explores how the quality of institutions can determine whether countries converge toward the technological frontier or become trapped in stagnation, a phenomenon known as “club convergence.”

Two major lines of empirical research have provided powerful evidence that institutions matter for long-run development:

1. Legal Origins (La Porta et al., 1998, 1999): This research argues that historical differences in legal traditions are a deep determinant of modern institutions. For instance, countries with common law traditions inherited from Great Britain tend to have stronger investor protections than countries with civil law traditions inherited from continental Europe. These institutional differences, in turn, are shown to be strongly correlated with financial development and economic outcomes.
2. Colonial Origins (Acemoglu, Johnson, and Robinson, 2001): This influential theory posits that the type of institutions established by European colonizers depended on the feasibility of settlement. In places with high settler mortality rates (e.g., due to tropical diseases), colonizers established “extractive” institutions designed to transfer resources back to the metropole. In places with low mortality rates, they established “settlement” institutions focused on protecting private property and fostering long-term development. These institutions have shown remarkable persistence and continue to shape economic outcomes today.

Building on this, the work of Gerschenkron (1962) introduced the concept of “appropriate institutions.” The core idea is that the set of institutions that best promotes growth may differ depending on a country’s stage of development. Institutions that are effective for a country far from the technological frontier (e.g., state-led investment, protectionism to foster imitation) may become obstacles to growth for a country nearing the frontier, where frontier innovation and competition become more important.

A formal model of this idea shows that a country’s productivity growth depends on both imitation of frontier technologies (η(1/a_t-1 – 1)) and frontier innovation (γ), where a is the country’s proximity to the frontier. The model generates a growth-maximizing strategy:

• Countries far from the frontier (a < â) should adopt imitation-enhancing institutions.
• Countries that have caught up (a > â) should switch to innovation-enhancing institutions.

This framework can explain the existence of a “nonconvergence trap.” As depicted in Figure 11.6 of the source material, a country can become stuck with imitation-focused institutions that were successful in its early stages of development. Vested interests or political inertia may prevent the necessary switch to more competitive, innovation-enhancing institutions as the country develops. The outcome is that growth slows dramatically as the benefits of imitation are exhausted, and the country’s productivity level stagnates, permanently bounded away from the frontier.

In summary, long-run growth is not a monolithic process. It is shaped by the complex and dynamic interplay between finance, institutions, and a country’s evolving stage of development. This understanding sets the stage for our final module on the concrete design of growth policy.