Lecture 3 - Economic Growth

Economic Growth

• The analysis of economic growth is pivotal for understanding how societies improve their living standards over time. It involves examining the factors that contribute to the sustained increase in the production of goods and services.

Key Concepts

• Economic Growth: Refers to the sustained increase in the production of goods and services in an economy over a specific period, usually measured by the percentage increase in real Gross Domestic Product (GDP).

• Key aspects include:

  • Analysis of GDP growth rates: GDP growth rates are critical indicators of economic performance, reflecting the pace at which a country's economy is expanding or contracting.

  • Examination of productivity improvements: Productivity enhancements, driven by technological advancements and efficient resource allocation, are vital for sustainable economic growth.

  • Impact of technological advancements: Technological innovation spurs economic growth by increasing efficiency, creating new products, and transforming production processes.

  • Demographic influences on economic output: Population size, age distribution, and labor force participation rates all influence economic output and growth potential.

Global GDP per Capita Over Time

• The trend of global GDP per capita shows a significant upward trajectory, increasing from minimal levels to approximately $8,000 over two millennia. This increase reflects substantial improvements in average income levels worldwide.

• The x-axis represents years, ranging from 0 to 2000, providing a historical context for evaluating long-term economic development.

• Source: DeLong (1998)

Economic Growth Factors

• Several key factors drive economic growth:

  • Capital Accumulation: Involves investments in physical capital such as machinery, infrastructure, and equipment, enhancing the productive capacity of an economy.

  • Human Capital: Encompasses improvements in the education, skills, health, and overall well-being of the workforce, boosting productivity and innovation.

  • Technological Progress: Includes innovations, research and development, and the adoption of new technologies, which enhance efficiency and productivity.

  • Natural Resources: Refers to the availability and efficient utilization of natural resources, which can significantly contribute to economic output.

  • Institutional Factors: Comprises legal, regulatory, and political frameworks that foster economic activity, property rights, contract enforcement, and the rule of law.

• The mathematical expression y = \frac{Y}{P} defines per capita income y as the ratio of total income Y to population P, serving as a fundamental metric for assessing economic well-being and living standards.

Growth Rate Calculation

• Growth rates are calculated using the formula g = \frac{Y
  {t+1} - Yt}{Yt} = \frac{\triangle Y}{Y_t}. This measures the change in income over time.

• Expressed as a percentage, the growth rate formula is g = \frac{\triangle Y}{Y_t} * 100, quantifying the percentage change in income over a specific period.

Projecting Future Income

• The formula for projecting future income is given by Yt = Y0(1 + g)^t, where Yt is the income at time t, Y0 is the initial income, and g is the growth rate.

• The term (1 + g)^t illustrates how initial income compounds over t periods, assuming a constant growth rate. This is analogous to compound interest in finance.

• For small g, the approximation ln(1 + g) \approx g is used, simplifying calculations when growth rates are relatively low, especially in continuous-time models.

Approximation of Growth Rate

• Logarithmic transformations are employed to approximate growth rates, particularly useful in continuous-time models where instantaneous rates of change are considered.

• If the growth rate is small, ln(1 + g) \approx g, enabling simplified analysis and modeling of economic growth dynamics.

Sample Calculation

• Example 1: If A is 1,000 and B is 10,000, this serves as a basic illustration for understanding magnitudes of income or investment.

Sample Calculation 2

• Example 2: If A is 10,000 and B is 2,000, the difference is 8,000, showing the variance between two economic variables.

• \Y_A,Year = 1000 * 10 = 10,000

• \Y_B,Year = 1,000 * 10 = 10,000

Logarithmic Transformation for Growth Analysis

• Transforming the growth equation into logarithmic form facilitates regression analysis and simplifies calculations:

• Yt = Y0(1 + g)^t

• ln(Yt) = ln(Y0) + t * ln(1 + g)

• Employing the approximation, ln(1 + g) \approx g

• Yields: ln(Yt) = ln(Y0) + g * t

• Which resembles a linear equation: y = b + m * x. This transformation enables the use of linear regression techniques to estimate growth rates and analyze economic trends.

GDP per capita 1870-2010

• Historical trends in GDP per capita for selected countries from 1870 to 2010 highlight diverse growth trajectories and economic development patterns.

• Countries such as the UK, US, Germany, and Japan represent a mix of early and late industrializers, providing insights into the varied experiences of economic modernization.

• Source: Jones and Vollrath (2013)

Analyzing Economic Growth 3

• Further analysis of economic growth with reference to y(t) involves considering logarithmic differentiation to assess growth rates.

• Logarithmic differentiation is used to analyze growth rates: \frac{d}{dt} ln[y(t)] = \frac{1}{y(t)} * \frac{dy(t)}{dt} \approx \frac{\triangle y}{y}, offering a method to approximate and interpret growth dynamics.

Harrod-Domar Model

• The Harrod-Domar model emphasizes the roles of savings and investment in driving economic growth, providing a theoretical framework for understanding capital accumulation and economic expansion.

• Refer to detailed notes on the Harrod-Domar