Economic convergence

What Is Economic Convergence?

Economic convergence refers to the theory and observation that poorer economies tend to grow faster than richer ones, eventually catching up in terms of per capita income or Gross Domestic Product (GDP) per capita. This concept falls under the broader field of macroeconomics, specifically within the realm of economic growth theory. The idea is rooted in the principle of diminishing returns to capital: developing economies with less capital per worker can achieve higher returns on investment and thus faster growth rates than developed economies that are already rich in capital. Economic convergence suggests a natural tendency for the gap in living standards between countries to narrow over time, leading to a more equitable global distribution of wealth and improved standard of living globally.

History and Origin

The concept of economic convergence gained significant theoretical traction with the development of the neoclassical growth models, most notably the Solow-Swan model (often simply called the Solow model), pioneered by Robert Solow and Trevor Swan in the mid-1950s. This model provided a framework where, given similar savings rates, population growth, and technological progress, economies would converge to their own unique steady-state levels of capital and output per worker. The Solow model's prediction of conditional convergence—that economies converge only after controlling for differences in their structural characteristics—became a cornerstone of modern economic growth theory.

Empirical studies in the late 20th century, particularly those examining data from OECD countries, often found evidence supporting this conditional convergence. By the early 1990s, a "new age of convergence" was observed, as the pace of per capita income growth in emerging and developing economies began to significantly outpace that in advanced economies, marking a substantial shift in global economic dynamics.

##⁸ Key Takeaways

• Economic convergence posits that poorer countries grow faster than richer countries, closing the income gap.
• The theory is largely based on the principle of diminishing returns to capital, suggesting higher marginal returns in capital-scarce economies.
• Different types of convergence exist, including beta-convergence (poorer economies growing faster) and sigma-convergence (reduction in income dispersion).
• Factors such as technological diffusion, human capital accumulation, and institutional quality play crucial roles in facilitating or hindering economic convergence.
• Recent global shocks, such as the COVID-19 pandemic, have at times reversed the trend of global income convergence, particularly for the most vulnerable nations.

##⁷ Formula and Calculation

While economic convergence is a broad concept, specific types of convergence, such as beta-convergence ((\beta)-convergence) and sigma-convergence ((\sigma)-convergence), involve formulas for empirical testing.

Beta-Convergence ((\beta)-convergence)
(\beta)-convergence occurs if poorer economies tend to grow faster than richer ones. It is often tested using a regression of the average growth rate of per capita income over a period on the initial level of per capita income.

The formula for absolute (\beta)-convergence (assuming all economies have the same steady state) can be expressed as:
$\frac{1}{T} \ln\left(\frac{y_{i,t+T}}{y_{i,t}}\right) = \alpha - \beta \ln(y_{i,t}) + \epsilon_{i,t}$
Where:

• ( y_{i,t} ) = Per capita income of country (i) at time (t)
• ( T ) = Length of the time period
• ( \frac{1}{T} \ln\left(\frac{y_{i,t+T}}{y_{i,t}}\right) ) = Average annual growth rate of per capita income for country (i)
• ( \alpha ) = Constant term
• ( \beta ) = Convergence coefficient (expected to be positive for convergence)
• ( \epsilon_{i,t} ) = Error term

A positive and statistically significant (\beta) indicates that countries with lower initial per capita income tend to have higher subsequent growth rates, thus converging.

⁶Sigma-Convergence ((\sigma)-convergence)
(\sigma)-convergence occurs if the dispersion of per capita income levels across a group of economies tends to decrease over time. It is measured by the evolution of the standard deviation or coefficient of variation of per capita income across economies.

$\sigma_t = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (\ln y_{i,t} - \overline{\ln y_t})^2}$
Where:

• ( \sigma_t ) = Standard deviation of the logarithm of per capita income at time (t)
• ( N ) = Number of economies
• ( \ln y_{i,t} ) = Natural logarithm of per capita income for economy (i) at time (t)
• ( \overline{\ln y_t} ) = Average of the natural logarithm of per capita income across all economies at time (t)

A decrease in (\sigma_t) over time indicates (\sigma)-convergence.

Interpreting Economic Convergence

Interpreting economic convergence involves understanding whether the income gap between countries is shrinking and why. When economies demonstrate economic convergence, it implies that policy interventions in less developed nations—such as promoting capital accumulation, fostering technological innovation, and improving institutional quality—can lead to faster rates of economic growth.

A finding of conditional convergence, for example, suggests that while poorer countries may not automatically catch up to richer ones, they will converge to their own steady states, which are determined by their specific characteristics like savings rates, population growth, and human capital. This nuanced interpretation highlights that convergence is not a guaranteed outcome for all nations but rather depends on a country's internal policies and external environment. Empirical research often examines various factors that influence the speed and extent of this convergence, including trade openness, education, and political stability.

Hypothetical Example

Consider two hypothetical countries: Econland (a developing economy) and Prosperland (a developed economy). In 2000, Econland has a GDP per capita of $5,000, while Prosperland has a GDP per capita of $50,000.

Over the next 20 years, Econland, due to lower initial capital stock and higher marginal returns on investment, implements policies that encourage foreign direct investment, improves its educational system, and adopts new technologies. As a result, Econland experiences an average annual real economic growth rate of 7%. Prosperland, already at a high level of development, experiences a more modest average annual growth rate of 2%.

• Econland (2000): $5,000 GDP per capita
• Prosperland (2000): $50,000 GDP per capita

After 20 years:

• Econland (2020): ( $5,000 \times (1 + 0.07)^{20} \approx $19,348 )
• Prosperland (2020): ( $50,000 \times (1 + 0.02)^{20} \approx $74,297 )

While Econland has not fully caught up to Prosperland, its GDP per capita has quadrupled, and the gap between the two countries' income levels has narrowed significantly. This demonstrates economic convergence in action, where the poorer country grows at a faster rate, reducing the relative income disparity.

Practical Applications

Economic convergence is a central theme in global economic policy and development.

• International Development Policy: Organizations like the International Monetary Fund (IMF) and the World Bank consider economic convergence when designing aid programs and policy recommendations for developing economies. Policies promoting trade liberalization, infrastructure development, and education are often aimed at fostering conditions conducive to faster growth and catch-up.
• I⁵nvestment Decisions: Investors looking for high-growth opportunities often target economies exhibiting strong convergence trends, as these regions may offer higher potential returns due to their rapid catch-up growth. Understanding the drivers of economic convergence helps in identifying markets with strong future prospects.
• Regional Integration: In regions like the European Union, economic convergence is a key objective, aiming to reduce disparities in per capita income and standard of living among member states. Policies often involve structural funds and cohesion initiatives to support less prosperous areas.
• Forecasting and Analysis: Economists and financial analysts use convergence models to forecast future global income distribution and identify potential shifts in economic power. For example, research indicates that various global crises can disrupt and delay the process of income convergence, leading to a persistence of low relative income in some nations.

Lim⁴itations and Criticisms

While the theory of economic convergence offers a compelling vision of global income equalization, it faces several limitations and criticisms. One significant critique is that absolute convergence—where all economies converge to a single steady state—has not been universally observed. Instead, empirical evidence often points to "conditional convergence," meaning economies converge only if they share similar structural characteristics such as savings rates, population growth, and technological innovation. Countries with poor institutions, political instability, or insufficient human capital may struggle to converge, even if they start from a lower income base.

Furthermore, recent global events have highlighted the fragility of convergence trends. For instance, the COVID-19 pandemic led to a reversal in global income convergence, with the gap between richer and poorer countries widening as developing nations were disproportionately affected. This sugges³ts that external shocks can significantly disrupt the convergence process. Some research also indicates that while overall convergence may occur, income inequality within countries can simultaneously increase, meaning the benefits of growth may not be evenly distributed. The "middle²-income trap," where developing economies grow rapidly but then stagnate before reaching high-income status, also presents a challenge to the idea of inevitable convergence.

Economic Convergence vs. Economic Divergence

Economic convergence describes the phenomenon where the income and productivity levels of poorer countries tend to catch up with those of richer countries over time. This process is driven by factors such as diminishing returns to capital, allowing less developed economies to achieve higher growth rates.

In contrast, economic divergence refers to a situation where the gap in income and productivity between countries, or regions, widens rather than narrows. This can occur if factors like technological advancements, institutional quality, or access to global markets disproportionately benefit already wealthy economies, or if poorer countries face persistent challenges such as conflict, weak governance, or lack of investment that hinder their growth.

The confusion between the two often arises from selective observation periods or specific groups of countries. While some periods have shown widespread global convergence, others have seen significant divergence, particularly for the poorest countries that struggle to integrate into the global economy. The simulta¹neous existence of convergence among certain groups (e.g., OECD nations) and divergence among others (e.g., fragile states) underscores the complex dynamics of global economic development.

FAQs

What are the main types of economic convergence?

The two main types are beta-convergence and sigma-convergence. Beta-convergence refers to poorer economies growing faster than richer ones. Sigma-convergence describes a reduction in the dispersion of income levels across economies over time.

Does economic convergence mean all countries will have the same income?

No, not necessarily. The theory of conditional convergence suggests that economies converge to their own steady states, which are influenced by their unique characteristics such as savings rates, population growth, and technological innovation. Therefore, income levels may not become identical, but the relative differences can decrease.

What factors drive economic convergence?

Key drivers include the principle of diminishing returns to capital (leading to higher productivity in capital-scarce economies), technological innovation diffusion, human capital accumulation through education, and sound economic policies that encourage investment and market efficiency.

Why might economic convergence fail to occur?

Economic convergence can fail due to various factors, including persistent institutional weaknesses, political instability, inadequate capital accumulation, lack of access to technology or global markets, and the impact of severe external shocks or crises that disproportionately affect developing nations.

How is economic convergence measured?

Economic convergence is typically measured using statistical methods, such as cross-country regressions to test for beta-convergence or by tracking changes in the standard deviation or coefficient of variation of Gross Domestic Product per capita over time to assess sigma-convergence.