Exogenous growth

What Is Exogenous Growth?

Exogenous growth is an economic concept within the broader field of Economic growth theory that posits that long-term economic expansion is driven by external factors not explained within the economic model itself⁵⁴, ⁵⁵. These "exogenous" factors are typically outside the direct control or influence of economic agents, contrasting with internal, interdependent elements. The most prominent exogenous factor often cited in this theory is technological progress ⁵², ⁵³.

In macroeconomics, exogenous growth models highlight that while factors like capital accumulation and labor supply contribute to economic expansion in the short to medium term, sustained long-run growth primarily depends on these external, unexplained advancements. The concept suggests that economies eventually reach a steady state where per capita income growth ceases without continuous boosts from outside the system⁵¹.

History and Origin

The concept of exogenous growth is predominantly associated with the Solow-Swan model, developed independently by American economist Robert Solow and Australian economist Trevor Swan in 1956⁵⁰. Solow's seminal work, particularly his 1957 paper "Technical Change and the Aggregate Production Function," revolutionized the understanding of economic dynamics by explicitly incorporating technological progress as a key driver of growth⁴⁹.

Prior to Solow's contributions, earlier models, such as the Harrod-Domar model, struggled to explain sustained growth, often predicting instability or a tendency towards zero growth in the long run⁴⁸. Solow's model offered a more robust framework, showing that technological advancement, treated as an external, autonomous force, could continuously offset diminishing returns to capital, thereby enabling ongoing increases in output per capita⁴⁶, ⁴⁷. For his groundbreaking work, Robert Solow was awarded the 1987 Nobel Prize in Economic Sciences⁴⁵.

Key Takeaways

Exogenous growth theory posits that economic growth is primarily driven by external factors, most notably technological progress, which is not explained within the economic model⁴⁴.
The Solow-Swan model is the foundational framework for exogenous growth, illustrating how economies converge to a steady state where long-run per capita growth depends solely on the rate of exogenous technological advancement⁴², ⁴³.
Factors such as capital accumulation and labor force expansion contribute to growth in the short term, but their impact on per capita growth eventually diminishes without external technological improvements⁴¹.
A key implication of exogenous growth theory is that government policy can affect the level of output per capita but cannot permanently influence the rate of long-run growth, as the ultimate driver (technology) is outside the model's scope³⁹, ⁴⁰.
The "Solow residual" is an empirical measure representing the portion of output growth that cannot be explained by changes in capital and labor inputs, often attributed to exogenous technological progress ³⁸.

Formula and Calculation

The core of the exogenous growth model, particularly the Solow-Swan model, is represented by an aggregate production function. This function describes the relationship between inputs and outputs in an economy. A common form, adjusted for technological progress, is:

Y(t) = F(K(t), A(t)L(t))

Where:

( Y(t) ) = Total output (e.g., Gross Domestic Product) at time (t)
( K(t) ) = Total capital stock at time (t)
( L(t) ) = Total labor force at time (t)
( A(t) ) = Level of technology or total factor productivity (TFP) at time (t). This is the "exogenous" component, assumed to grow at a constant rate independent of other economic variables.
( F ) = The production function itself, which typically exhibits constant returns to scale for capital and labor combined, but diminishing returns to each factor individually.

The accumulation of capital is also modeled:

\dot{K}(t) = sY(t) - \delta K(t)

Where:

( \dot{K}(t) ) = Change in capital stock over time
( s ) = Savings rate (proportion of output saved and invested)
( \delta ) = Depreciation rate of capital

In this framework, long-run per capita output growth is driven solely by the growth rate of (A(t)), the exogenous technological progress ³⁶, ³⁷.

Interpreting Exogenous Growth

Interpreting exogenous growth involves understanding that the ultimate driver of sustained increases in living standards comes from sources outside the direct influence of domestic economic policies, aside from those that facilitate the adoption of technology³⁵. For instance, a country can boost its capital accumulation through higher investment or savings rate, leading to short-term economic growth and a higher level of output. However, in the absence of exogenous technological improvements, the economy will eventually hit a steady state where additional capital yields progressively smaller returns, and per capita growth halts³³, ³⁴.

Therefore, interpreting exogenous growth means recognizing that technological advancements, which might arise from global innovation or fundamental scientific breakthroughs, are the primary engine for continuous improvements in productivity and sustained long-run prosperity. It implies that while sound government policy can optimize resource allocation and enable the adoption of new technologies, it does not directly create the technological frontier itself³¹, ³².

Hypothetical Example

Consider a hypothetical country, "Econoville," which initially relies on traditional manufacturing methods. The country experiences modest economic growth through increasing its labor force and accumulating more basic machinery (capital). However, after a period, Econoville's growth rate slows down as the benefits from adding more workers and capital begin to diminish, reaching a form of steady state.

Suddenly, a global breakthrough in artificial intelligence and automation emerges, originating from advanced research hubs outside Econoville. This "exogenous" technological progress allows Econoville's existing factories to produce significantly more output with the same amount of labor and capital. For example, robots perform tasks faster and more accurately, and AI optimizes production lines. Even without Econoville making new, internal decisions to invest heavily in R&D, its productivity jumps due to this external technological shock. This externally driven increase in productivity, leading to higher per capita output and living standards, is a clear illustration of exogenous growth in action.

Practical Applications

While primarily a theoretical construct in Economic growth theory, exogenous growth has significant practical implications for policymakers and economists. Its emphasis on technological progress underscores the importance of a favorable environment for innovation and technology adoption. Policymakers recognize that while they cannot directly "create" the next wave of disruptive technology, they can implement government policy to facilitate its absorption and diffusion.

This includes investments in public goods like education and infrastructure, fostering an open economy that welcomes foreign direct investment and technology transfer, and ensuring stable institutions and property rights²⁹, ³⁰. International organizations like the International Monetary Fund often analyze factors influencing national productivity, which aligns with the exogenous view of technology as a critical, albeit external, driver of prosperity²⁸. The concept also informs growth accounting methodologies, which attempt to decompose output growth into contributions from capital accumulation, labor force growth, and a "residual" factor (often attributed to exogenous technological change)²⁷. The Federal Reserve, for instance, examines productivity trends which are heavily influenced by such technological shifts.

Limitations and Criticisms

Despite its foundational role in Economic growth theory, exogenous growth theory, particularly the Solow-Swan model, faces several limitations and criticisms. A primary critique is its treatment of technological progress as "exogenous," or outside the model²⁴, ²⁵, ²⁶. This means the model does not explain the origins of technology or how it advances, effectively treating it as a "black box"²³. Critics argue that technology is not a given but rather a result of deliberate investment, research and development (R&D), and the accumulation of human capital within the economic system²¹, ²².

Furthermore, the model provides limited guidance for government policy aimed at directly stimulating long-run growth rates, as the main driver is external¹⁸, ¹⁹, ²⁰. While policies can affect the level of output, they cannot permanently alter the rate of growth if technology is truly exogenous. Another criticism is that the assumption of diminishing returns to capital, while mathematically convenient, may not fully capture the complexities of real-world economies, especially those with increasing returns to scale in knowledge production¹⁶, ¹⁷. The Federal Reserve Bank of San Francisco has discussed the importance of endogenous factors in growth, reflecting this shift in economic thought. Additionally, some argue that the model oversimplifies the role of institutions, resource allocation, and income distribution in affecting technological diffusion and overall growth¹⁴, ¹⁵.

Exogenous Growth vs. Endogenous Growth

The fundamental distinction between exogenous growth and endogenous growth lies in the source and nature of the drivers of sustained economic growth.

Exogenous growth theory, as embodied by the Solow-Swan model, posits that the long-run rate of growth in per capita output is determined by factors external to the model, primarily technological progress that is assumed to grow at a given, constant rate¹³. This means that while policies can influence the level of prosperity, they cannot perpetually increase the rate at which an economy grows in the long run, as the ultimate growth engine is an outside force¹².

In contrast, endogenous growth theory, developed in response to the limitations of the exogenous models, argues that the factors driving long-run growth are internal to the economic system and can be influenced by economic policy and individual decisions¹⁰, ¹¹. These internal factors often include human capital accumulation, research and development (R&D), innovation, and institutional quality. Endogenous growth models suggest that economies can generate sustained growth through these internal processes, potentially leading to increasing returns to scale and ongoing productivity improvements⁸, ⁹. The primary difference is whether the driver of sustained long-run growth is a "black box" external force (exogenous) or a mechanism that can be influenced by economic choices and policies (endogenous)⁶, ⁷.

FAQs

What is the primary driver of growth in exogenous growth models?

The primary driver of long-run growth in exogenous growth models is technological progress, which is assumed to occur independently of the economic system itself⁴, ⁵.

How does exogenous growth relate to the Solow Model?

Exogenous growth is the central concept of the Solow-Swan model. The model uses exogenous technological advancement to explain how economies can achieve sustained growth in per capita output even when facing diminishing returns to capital accumulation ³.

Can government policy influence exogenous growth?

In pure exogenous growth models, government policy can affect the level of output and the transition path to a steady state, but it cannot permanently alter the underlying rate of long-run growth, as this rate is determined by the external rate of technological progress ¹, ². However, policies that foster an environment conducive to adopting new technologies can be impactful.