Endogenous Growth Theory Notes

Introduction

• Developed as a response to omissions and deficiencies in the Solow-Swan neoclassical growth model.

• Explains the long-run growth rate of an economy based on endogenous factors.

Critique of Solow-Swan Model

• Attributes long-run growth to exogenous variables: rate of population growth and rate of technological progress.

• The long-run growth rate is considered independent of the saving rate.

• Limited policy implications due to the dependence on exogenous factors.

• Romer's critique: government action doesn't matter in models with exogenous factors.

Extension of Neoclassical Theory

• Extends the neoclassical theory by incorporating endogenous technical progress.

• Key contributors: Arrow, Romer, and Lucas.

Endogenous Growth Models

• Emphasize technical progress resulting from: rate of investment, size of the capital stock, and stock of human capital.

Assumptions

1. Many firms in a market.

2. Knowledge is a non-rival good.

3. Increasing returns to scale.

4. Technological advance comes from the creation of new ideas.

5. Many individuals and firms have market power and earn profits.

Arrow's Learning-by-Doing Model

• Introduced learning-by-doing as endogenous (1962).

• Hypothesis: New capital goods embody available knowledge.

• Model: $Y=A(K) F(Ki, Li)$

  • $Y$: Output of firm i.

  • $K_i$: Stock of capital of firm i.

  • $L_i$: Stock of labor of firm i.

  • $K$: Aggregated stock of capital.

  • $A$: Technology factor.

• Limitation: Growth eventually halts due to insufficient social investment.

Levhari-Sheshinski Model

• Generalized and extended Arrow's model.

• Emphasize spillover effects of increased knowledge.

• Assumption: Each firm's investment is the source of knowledge.

• Firm's knowledge is a public good available to other firms.

• Economy operates under increasing returns to scale.

• Endogenous technical progress is reflected in an upward shift of the production function.

King-Robson Model

• Emphasize learning-by-watching.

• Investment by a firm represents innovation.

• Successful innovations are adapted by other firms.

• Externalities are key to economic growth.

• Innovation in one sector impacts others.

• Multiple steady-state growth paths can exist.

Romer Model (1986)

• Variant on Arrow's model known as learning-by-investment.

• Knowledge creation is a side product of investment.

• Knowledge as an input: $Y = A(R) F(Ri, Ki, Li)$

  • $Y$: Aggregate output.

  • $A$: Public stock of knowledge.

  • $R_i$: Stock of knowledge by firm i.

  • $K<em>i$ and $L</em>i$: Capital stock and labor stock of firm i.

• Function F is homogeneous of degree one.

• $R_i$ is treated as a rival good.

• Key elements: Externalities, increasing returns, and diminishing returns in new knowledge.

• Spillovers from research create new knowledge.

• New knowledge is the determinant of long-run growth.

• Research technology exhibits diminishing returns.

• Firms investing in research won't be the exclusive beneficiaries.

Lucas Model

• Based on investment in human capital.

• Investment in education leads to human capital, crucial for growth.

• Distinction between internal and external effects.

• Investments in human capital increase technology.

• Output for firm i: $Y<em>i = A(K</em>i) . (H_i) . He^e$

  • $A$: Technical coefficient.

  • $K<em>i$ and $H</em>i$: Inputs of physical and human capital.

  • $H_e$: Economy's average level of human capital.

  • $e$: Parameter representing external effects.

• Each firm faces constant returns, but there are increasing returns for the whole economy.

• Learning-by-doing and spillover effects involve human capital.

• Technology is endogenously provided and treated as a public good.

Romer's Model of Technological Change (1990)

• Identifies a research sector specializing in the production of ideas.

• This sector uses human capital and existing knowledge.

• Ideas are more important than natural resources.

• New knowledge enters in three ways:

  1. New design in the intermediate goods sector.

  2. In the final sector, labor, human capital, and producer durables produce the final product.

  3. New design increases the total stock of knowledge.

• Assumptions:

  1. Economic growth comes from technological change.

  2. Technological change is endogenous.

  3. Market incentives play a role.

  4. Invention requires human capital.

  5. Aggregate supply of human capital is fixed.

  6. Knowledge is partially excludable.

  7. Technology is a non-rival input.

  8. Low cost of using an existing design reduces the cost of creating new designs.

  9. Externalities are internalized by private agreements.

• Model: $\triangle A = F(KA, HA, A)$

  • $\triangle A$: Increase in technology.

  • $K_A$: Capital invested in producing the new design.

  • $H_A$: Human capital employed in research and development.

  • $A$: Existing technology of designs.

  • $F$: Production function for technology.

Criticisms of Endogenous Growth Theory

1. Ideas traced to Adam Smith and Marx.

2. Nothing new, increasing returns and endogeneity from neoclassical and Kaldor models.

3. Depends only on the production function and the steady state.

4. Emphasizes human capital and neglects institutions.

5. Unclear difference between physical and human capital.

6. Physical and human capital accumulation cannot lead to perpetual economic growth.

Policy Implications of the Endogenous Growth Theory

1. Convergence of growth rates per capita may not occur.

   • Increasing returns imply rate of return to investment won't fall in developed countries.

   • Capital need not flow from developed to developing countries.

2. Measured contribution of capital to growth may be larger than suggested by the Solow residual model.

   • Investment in education has spillover effects.

3. Economies having increasing returns must not reach a steady state level of income growth.

   • When there are large positive externalities, diminishing returns may not start.

   • Increase in the saving rate can lead to a permanent increase in the growth rate.

4. Countries with greater stocks of human capital and investing more on research will