Semi-Endogenous Growth Theory

Prior to the 1980s, neoclassical growth theory dominated macroeconomic thought about long-run economic growth. The Solow growth model, developed by Robert Solow in 1956, posited that technological progress was the primary driver of sustained per capita output growth, but treated this progress as exogenous to the economic system. This limitation led to the development of endogenous growth theories in the 1980s and 1990s, which sought to explain technological advancement as resulting from purposive economic activities like research and development (R&D) and human capital accumulation.

The Evolution of Growth Theories

The first generation of endogenous growth models developed by Paul Romer (1986, 1990) and others demonstrated how scale effectswhere larger economies could experience faster growth due to their larger knowledge base or more resources devoted to innovationcould generate perpetual growth through market incentives. These models highlighted how policies affecting incentives for innovation, such as intellectual property rights, could influence long-term growth rates.

However, these early endogenous growth models faced significant empirical challenges. The scale effects predicted by these modelsthat countries with larger populations or more R&D inputs should experience faster growthdid not align with observed data. This discrepancy between theory and empirical evidence led to the development of semi-endogenous growth theory.

What is Semi-Endogenous Growth?

The seminal contribution to semi-endogenous growth theory came from Charles I. Jones (1995), whose model eliminated the problematic scale effects of earlier endogenous growth models while retaining the crucial insight that technology results from purposive research efforts. Rather than assuming that a fixed stock of resources devoted to innovation leads to perpetual growth, semi-endogenous models incorporate the idea of diminishing returns to technological knowledge.

Key Components of Semi-Endogenous Growth Models

1. Knowledge Production Function

In semi-endogenous models, the creation of new technological knowledge follows a research production function where the growth rate of knowledge depends on the ratio of research effort to the existing stock of knowledge:

= A * (R/G)^

Where G is the stock of knowledge, R is resources devoted to research, A is a productivity factor, and <1 captures diminishing returns to innovation. This specification ensures that as knowledge accumulates, generating further knowledge becomes more challenging, unless more resources are devoted to research.

2. Endogenous Research Allocation

The model assumes that a growing fraction of resources in the economy are devoted to research activities as the economy grows. This can happen because:

• Rising incomes allow more resources to be allocated to non-subsistence activities
• Larger markets create stronger incentives for innovation
• Division of labor improves research productivity
• Education and human capital accumulates, increasing effective research capacity

3. Long-Run Growth Determination

A crucial feature of semi-endogenous models is that in the steady state, the growth rate of per capita output is determined solely by the population growth rate (n). The equilibrium growth rate can be expressed as:

g = n/(1-)

Where n is the population growth rate and is the degree of diminishing returns in knowledge production. This formulation eliminates the scale effects of earlier models while maintaining that long-run growth depends on fundamental demographic parameters.

Theoretical Contributions

The semi-endogenous approach resolves key theoretical puzzles:

1. Elimination of scale effects: Explains why larger economies don't necessarily grow faster than smaller ones, addressing a major empirical shortcoming of earlier endogenous models.
2. Policy invariance: In the long run, changes in R&D subsidies or tax policies affect the level of output but not the growth rate, aligning with historical experiences where policy changes have typically caused level effects rather than persistent growth effects.
3. Role of population: The model successfully accommodates the empirical relationship between population growth and economic growth observed across countries and time periods.
4. Understanding stagnation: Provides a framework for understanding how declining population growth could lead to lower long-run growth rates, a concern for many developed economies.

Empirical Evidence

Semi-endogenous growth theory has found support in various empirical studies:

Jones (1995) examined U.S. data and found that while R&D employment has increased by a factor of five since the 1950s, productivity growth has not correspondingly increaseda finding inconsistent with strong scale effects but consistent with diminishing returns to innovation.

Ha and Howitt (2007) found evidence that productivity growth depends positively on population growth, as predicted by semi-endogenous models, across a sample of OECD countries.

Madsen (2008) documented that across 21 OECD countries over more than a century, the relationship between R&D employment and productivity growth is weaker than predicted by first-generation endogenous models but more consistent with semi-endogenous specifications.

Limitations and Criticisms

While semi-endogenous growth theory addresses important empirical shortcomings of earlier models, it faces several criticisms:

1. Policy irrelevance: Critics argue that the implication that policies don't affect long-run growth rates contradicts historical examples where specific policy frameworks appear to have accelerated growth (e.g., East Asian development strategies, post-war European recovery).
2. Underestimates innovation opportunities: The model may underestimate the potential for new paradigms or breakthrough technologies to overcome diminishing returns to knowledge accumulation.
3. Demographic focus: The heavy emphasis on population growth as the driver of long-run economic growth seems increasingly problematic in an era of potential population decline in many regions.
4. Globalization context: The framework may not adequately account for how globalization and knowledge diffusion affect the relationship between domestic R&D and growth.
5. Measurement challenges: Difficulties in accurately measuring the stock of knowledge and research productivity make empirical testing challenging.

Policy Implications

Despite its limitations, semi-endogenous growth theory offers important policy insights:

• Demographic policies: Policies affecting population growth rates (those influencing fertility or immigration) could have long-term implications for economic growth.
• Level effects vs. growth effects: The distinction reminds policymakers that R&D subsidies and similar policies primarily affect the level of output rather than permanently increasing growth rates, requiring sustained effort to maintain the gains.
• Research efficiency: Policies that improve the productivity of research efforts (such as education, basic science funding, and research infrastructure) become central to maintaining innovation as knowledge accumulation faces diminishing returns.
• International knowledge flows: In a global context, the model suggests that policies affecting knowledge diffusion across borders can help economies overcome domestic limitations in research capacity.

Extensions and Variations

Researchers have developed several extensions to the basic semi-endogenous growth framework:

• Schumpeterian semi-endogenous models: Howitt (1999) incorporated creative destruction into a semi-endogenous framework, showing how innovation can be gradual rather than episodic.
• Stochastic variants: Some models incorporate uncertainty in research outcomes to better match observed volatility in innovation.
• Skill-biased models: Variants that incorporate differences in research productivity across skill levels help explain wage inequality trends.
• Multi-sector extensions: Models that differentiate between applied and basic research provide a more nuanced view of innovation processes.
• General purpose technologies: Extended frameworks that incorporate occasional paradigm-shifting technologies that temporarily alter growth dynamics.

Conclusion

Semi-endogenous growth theory represents an important evolution in our understanding of long-run economic growth. By bridging neoclassical and endogenous approaches, it provides a framework that better matches empirical observations while preserving crucial insights about the deliberate nature of innovation.

The theory's core messagethat sustained economic growth depends on population growth and the allocation of resources to research in the face of diminishing returnsoffers significant implications for policymakers concerned with long-run prosperity. However, as economies continue to evolve and knowledge creation becomes increasingly complex and globalized, the theory may require further refinement to fully capture the dynamics of modern innovation systems.

Current research continues to explore how semi-endogenous models can be extended to address issues like climate change, digital transformation, and the relationship between inequality and growth, ensuring this framework remains relevant to contemporary economic challenges.