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:

  1. "AK" model

  2. Model of research and development (R&D)

  3. 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: Y<em>t=AK</em>tY<em>t = AK</em>t

Capital depreciates at rate δ\delta.

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:

  1. Manufacturing sector: produces manufactured goods using labor and knowledge as inputs.

  2. 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:

  1. Manufacturing sector: produces goods.

  2. 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