Endogenous Growth Models Lecture Notes
Endogenous Growth Models
Introduction
The Solow growth model explains long-run growth of output per capita through growth in technological progress. However, the growth rate of technological progress is assumed to be exogenous, meaning the model does not explain how technology grows.
This lecture focuses on models in which technological progress is endogenously determined.
Introduction: Endogenous Growth Models
Endogenous growth models provide implications for economic policy to affect growth and can explain why differences between growth rates in different countries persist over time.
This lecture considers three models:
"AK" model
Model of research and development (R&D)
Model of human capital accumulation
The AK Model
The AK model is similar to the Solow model in that growth happens through capital accumulation.
Difference:
The Solow model assumes decreasing marginal returns to capital, leading to a stable steady state.
The AK model assumes capital exhibits constant marginal returns.
Production function:
Capital depreciates at rate .
The AK Model: Justification
There are different ways to justify the AK production function. One example is "learning by doing."
Workers become more productive while working because they learn. Suppose learning by doing is a function of the capital stock, i.e., more capital makes workers develop skills more quickly.
Example: Workers who spent more time with computers developed proficiency more quickly than workers who spent less time with them. As computer technology improved, all workers became more efficient at using them.
The AK Model: Implications
In the AK model, capital accumulation is the main engine of growth.
All else equal, two countries with different saving rates will grow at different rates, and these differences will persist over time.
There is no convergence between capital-poor and capital-rich countries.
The model predicts that countries with higher investment rates should have a higher growth rate of income per capita.
This prediction seems to be consistent with the data.
Average Growth Rate of GDP per Capita vs. Average Investment Rate (1960-2000)
The data provided show a positive correlation between the average investment rate and the average growth rate of GDP per capita across different countries. Countries with higher average investment rates tend to have higher average growth rates of GDP per capita.
A Model of Research and Development
This model has two productive sectors:
Manufacturing sector: produces manufactured goods using labor and knowledge as inputs.
R&D sector: produces knowledge using labor as input.
A Model of Research and Development: Implications
The model tells us that R&D can be the engine of sustained economic growth.
More and better R&D production increases the growth rate of output per capita.
This is well-recognized nowadays, and many countries have policies in place that support R&D:
Patent laws
Tax incentives to correct positive externalities
Grants to fund basic research at universities
Industrial policy to encourage specific industries that are key for rapid technological progress
A Model with Endogenous Human Capital Formation
It appears that more and better education is positively correlated with high growth rates of income per capita.
To understand the relationship between human capital and growth, we consider a similar model as before, with two sectors:
Manufacturing sector: produces goods.
Education sector: produces human capital (i.e., educated workers).
A Model with Endogenous Human Capital Formation: Graph
The information highlights that more and better education is positively correlated with higher growth rates of income per capita. The graph plots the average growth rate of GDP per capita (1960-2000) against the average years of schooling (1960-2000) across different countries. The upward trend suggests a positive relationship between education and economic growth.
Endogenous Growth Models
The AK Model
Justification for the AK Model
Implications of the AK Model
Average Growth Rate of GDP per Capita vs. Average Investment Rate (1960-2000)
A Model of Research and Development
Implications of the Research and Development Model
A Model with Endogenous Human Capital Formation
Graph of Human Capital Formation vs. Growth Rates