Exogenous growth model

What Is Exogenous Growth Model?

The exogenous growth model, also known primarily as the Solow-Swan model, is a foundational concept within Economic theory that explains long-run economic growth by attributing it primarily to factors external to the model itself. This model posits that sustained increases in output per worker are driven by forces like technological progress and population growth, which are assumed to occur independently of economic decisions made within the system³³. It is a cornerstone of neoclassical macroeconomics, offering insights into how nations accumulate capital and achieve a steady-state in their economic development.

History and Origin

The exogenous growth model was independently developed in 1956 by American economist Robert Solow and Australian economist Trevor Swan³². This model emerged as a significant advancement over earlier growth theories, such as the Harrod-Domar model, by incorporating diminishing returns to capital and allowing for substitution between capital and labor in the production function³¹. Robert Solow's seminal work on the theory of economic growth, which culminated in the exogenous growth model, earned him the Nobel Memorial Prize in Economic Sciences in 1987³⁰. His contributions fundamentally reshaped how economists understood the drivers of long-term prosperity, emphasizing the crucial role of technological innovation in spurring growth beyond what can be achieved through mere capital accumulation²⁸, ²⁹.

Key Takeaways

• The exogenous growth model attributes long-run economic growth primarily to external factors such as technological progress and population growth.
• It suggests that economies, absent technological advancements, will eventually reach a steady-state where capital per worker and output per worker stop growing.
• The model highlights the importance of savings and investment in raising the level of output per capita, though not its long-run growth rate.
• Technological progress, being exogenous, is considered the ultimate driver of sustained increases in living standards within this framework.
• The model predicts conditional convergence, implying that poorer countries can catch up to richer ones if they have similar savings rates and access to technology.

Formula and Calculation

The core of the exogenous growth model, particularly the Solow-Swan model, revolves around the capital accumulation equation and the aggregate production function. A simplified version of the production function often used is the Cobb-Douglas form:

$Y = A K^{\alpha} L^{1-\alpha}$

Where:

• (Y) = Total output (or Gross Domestic Product (GDP))
• (A) = Total factor productivity (representing the level of technology), which is the exogenous factor²⁷
• (K) = Capital stock
• (L) = Labor force
• (\alpha) = Output elasticity of capital (a constant between 0 and 1)

The change in the capital stock per worker ((\Delta k)) over time is given by:

$\Delta k = s f(k) - (n + \delta) k$

Where:

• (k = K/L) = Capital per worker
• (f(k) = Y/L) = Output per worker (derived from the production function, often written as (A k^{\alpha}))
• (s) = Savings rate (proportion of output saved and invested)
• (n) = Population growth rate
• (\delta) = Capital depreciation rate

In the steady-state, (\Delta k = 0), meaning (s f(k) = (n + \delta) k). This indicates that the amount of saving per worker is exactly enough to cover the capital needed for new workers (due to population growth) and to replace depreciated capital.

Interpreting the Exogenous Growth Model

The exogenous growth model provides a framework for understanding the long-term determinants of a nation's wealth. Its interpretation centers on the idea that while increased savings and investment can raise the level of a country's income, they cannot sustain per capita growth indefinitely due to diminishing returns to capital²⁵, ²⁶. Instead, long-term per capita growth is primarily driven by external technological advancements²⁴. For example, if a country increases its savings rate, it will accumulate more capital per worker and achieve a higher level of output per worker. However, this growth will eventually slow down as additional capital becomes less productive, leading the economy to a new, higher steady-state of capital and output per worker, but not a perpetually increasing growth rate²³. Sustained growth requires an exogenous boost, typically from technological innovations that shift the production function upward, enabling more output from the same inputs²².

Hypothetical Example

Consider two hypothetical countries, Alpha and Beta, that both operate under the assumptions of the exogenous growth model. Initially, both have identical levels of capital per worker, technology, and labor force.

• Year 1: Both countries produce 100 units of output per worker.
• Country Alpha: Implements policies to significantly increase its national savings rate. This leads to higher investment in physical capital, such as machinery and infrastructure.
• Country Beta: Maintains its existing savings rate.

Over the next few decades, Country Alpha experiences faster economic growth than Country Beta as it rapidly accumulates capital. Its output per worker climbs to 150, then 180, and so on. Country Beta's output per worker grows more slowly, perhaps from 100 to 110. However, due to the principle of diminishing returns, Country Alpha's growth rate gradually decelerates. Eventually, both countries, assuming they have access to the same technological frontier (the exogenous factor), will settle into a new steady-state where their capital per worker and output per worker are no longer growing per capita (unless technology advances). The model suggests that without further technological progress, Country Alpha will simply reach a higher level of prosperity than Country Beta, but both will cease to grow their per capita output indefinitely.

Practical Applications

The exogenous growth model, particularly the Solow-Swan model, has significant practical applications in economic analysis and policymaking, despite its limitations. It provides a foundational framework for understanding the mechanisms behind long-run economic growth and the role of various factors.

For instance, the model underscores that while increasing the savings rate and capital accumulation can boost a country's income level, sustained long-term growth in per capita income hinges on technological progress. This insight has historically influenced government policies aimed at fostering research and development (R&D) and promoting innovation, recognizing these as crucial for shifting the production possibilities frontier outward²¹. International organizations, such as the International Monetary Fund (IMF), utilize various economic models to analyze and forecast global economic growth and provide policy recommendations to member countries¹⁹, ²⁰. While not exclusively relying on the exogenous growth model, its core principles about capital, labor, and technology inform these broader analyses.

Limitations and Criticisms

Despite its foundational role in economic theory, the exogenous growth model faces several significant limitations and criticisms. A primary critique is its assumption that technological progress—the main driver of sustained growth—is an external, unexplained force. Cr¹⁷, ¹⁸itics argue that innovation and technological advancements are not truly "exogenous" but are instead the result of deliberate economic activities, such as investments in human capital, research, and development.

F¹⁵, ¹⁶urthermore, the model's aggregate nature, using a single production function to represent an entire economy, is seen as an oversimplification that may not capture the complexities of different forms of output and investments. It¹⁴ also struggles to fully explain persistent disparities in wealth and growth rates between nations, as its "conditional convergence" prediction suggests that poorer economies should eventually catch up to richer ones if they share similar underlying characteristics. So¹², ¹³me post-Keynesian criticisms also point out that the Solow model may not adequately account for the role of prices in adjusting output to changes in demand, and assumes full employment of labor and capital.

#¹⁰, ¹¹# Exogenous Growth Model vs. Endogenous Growth Model

The exogenous growth model and the endogenous growth model represent two distinct perspectives on the fundamental drivers of long-term economic growth. The key difference lies in how they treat technological progress.

The exogenous growth model, epitomized by the Solow-Swan model, assumes that technological advancement occurs independently of economic activity. It is an "external" factor that simply falls from the sky, leading to sustained increases in output per worker over the long run, while other factors like capital accumulation face diminishing returns and eventually lead to a steady-state.

In contrast, the endogenous growth model argues that technological progress, innovation, and knowledge creation are internal to the economic system and are influenced by economic decisions and policy measures. Developed by economists like Paul Romer and Robert Lucas in the 1980s, endogenous growth theory suggests that investments in human capital, research and development (R&D), and public infrastructure can lead to increasing returns to scale, fostering sustained growth without relying on external shocks. Es⁸, ⁹sentially, while the exogenous model sees technology as a given, the endogenous model views it as a product of intentional economic actions.

FAQs

What is the primary assumption of the exogenous growth model regarding technology?

The primary assumption of the exogenous growth model is that technological progress is an "exogenous" factor, meaning it comes from outside the economic system and is not explained by the model itself. It⁷'s assumed to grow at a constant rate independent of economic decisions.

Can an economy achieve sustained per capita growth indefinitely under the exogenous growth model?

Without continued technological progress, an economy operating under the exogenous growth model will eventually reach a steady-state where per capita output and capital cease to grow. Sustained per capita growth is only possible if this exogenous technological factor continually improves.

#⁵, ⁶## What is the "Solow residual"?
The "Solow residual" refers to the portion of economic growth that cannot be explained by increases in measurable inputs like capital and labor. Robert Solow attributed this unexplained portion to technological innovation and improvements in productivity.

#³, ⁴## How does the savings rate affect economic growth in this model?
In the exogenous growth model, an increase in the savings rate leads to higher investment and a temporary boost in the economic growth rate as the economy transitions to a higher steady-state level of capital and output per worker. However, it does not affect the long-run growth rate of output per capita.

#²## Does the exogenous growth model predict convergence among countries?
Yes, the exogenous growth model predicts "conditional convergence." This means that poorer countries, given similar parameters like savings rates, population growth rates, and access to technology, should grow faster and eventually converge to the same steady-state level of income per capita as richer countries.¹