Lecture 4 - Models of Economic Growth (part 2)

The Solow Model

• Comprehensive lecture notes are available on Moodle. These notes cover all aspects of the Solow Model, providing key insights and detailed explanations. The Solow Model is crucial for understanding economic growth, capital accumulation, and technological progress. Additional resources such as practice problems and supplementary readings may also be available.

Empirics of Growth

• A comparison of the Harrod-Domar (H-D) and Solow models with empirical evidence:

  • Both models aim to predict long-term economic growth and provide frameworks for understanding the factors that influence a country's economic trajectory.

  • The Solow model suggests that, under similar conditions, poorer countries should experience faster growth rates due to the principle of diminishing returns to capital. This implies a process of economic convergence.

  • The Harrod-Domar model does not inherently support the idea of economic convergence among countries. It focuses more on the relationship between savings, investment, and growth, without necessarily predicting that poorer countries will catch up to richer ones.

Empirical Prediction: Convergence

• Unconditional Convergence: The theory that poorer economies will naturally grow at a quicker pace, irrespective of other influencing variables such as government policies, institutions, or geographical factors. This is based on the assumption of diminishing returns to capital.

• Conditional Convergence: The hypothesis that poorer countries will exhibit higher growth rates, contingent on factors such as savings rates, population growth rates, education levels, and institutional quality. These conditions must be met for convergence to occur.

• Equation for convergence: g*i = \beta * ln(initial GDPpc*i) + \varepsilon_i

  • Where:

    • g_i represents the growth rate of country i.

    • \beta is the coefficient indicating the rate of convergence. It quantifies how quickly poorer countries are catching up to richer ones.

    • ln(initial GDPpc_i) is the natural logarithm of the initial GDP per capita for country i. This is used to normalize the data and to account for the non-linear relationship between GDP and growth rates.

    • \&varepsilon_i is the error term for country i, which accounts for unexplained variations and idiosyncratic factors affecting growth.

Unconditional Convergence

• Long Run (1870-1979): Convergence was observed among a specific group of industrialized nations including Japan, Finland, Sweden, Norway, Germany, Italy, Austria, France, Canada, Denmark, USA, Netherlands, Switzerland, Belgium, UK, and Australia. These countries had similar institutions, levels of development, and access to technology.

  • Reference: Baumol, 1986. Baumol's study highlighted that these industrialized nations showed a tendency to converge in terms of economic output.

• Short Run (1960-1985): Analysis across a wider array of countries reveals less consistent evidence of unconditional convergence. This suggests that other factors, such as policy differences and institutional quality, play a significant role in determining economic growth.

  • Data from: Barro, 1991. Barro's research indicated that when a more diverse set of countries is considered, the evidence for unconditional convergence weakens.

Conditional Convergence

• The absence of consistent unconditional convergence has led to a focus on conditional convergence, which provides a more nuanced and realistic view of economic growth.

• The theory suggests that poorer countries are expected to grow faster when conditioned on variables such as savings rates and population growth, as well as factors like education, health, and institutional quality. These conditions help control for differences that affect a country's growth potential.

• Research by Mankiw, Romer, and Weil (1992) supports this concept. Their augmented Solow model incorporates human capital as a key factor in explaining economic growth and convergence.

• This model assumes that knowledge flows freely and that technological advancements are universally accessible across nations. However, in reality, technology diffusion may be limited by factors such as intellectual property rights, infrastructure, and absorptive capacity.

Conditional Convergence: MRW (Mankiw, Romer, Weil)

• A. Unconditional: Analysis of growth rate between 1960-1985 vs. the log of output per working-age adult in 1960. This analysis examines the basic premise of unconditional convergence without controlling for other factors.

• B. Conditional on Saving and Population Growth: Examination of growth rate between 1960-1985 relative to the log of output per working-age adult in 1960, considering saving and population growth rates. This step assesses how saving and population growth influence the convergence process.

• C. Conditional on Saving, Population Growth, and Human Capital: Assessment of growth rate between 1960-1985 in relation to the log of output per working-age adult in 1960, factoring in saving, population growth, and human capital. This comprehensive analysis provides a more complete picture of the factors driving economic convergence.

Unconditional Convergence: Latest Results

• Examination of the β-coefficient of unconditional convergence through regression analysis of real per capita GDP growth on the log of initial per capita GDP. This coefficient indicates the speed at which poorer countries are catching up to richer ones, without controlling for other variables.

• Data is sourced from:

  • Maddison datasets, which provide historical data on GDP and population.

  • Penn World Table (PWT), which offers data on national accounts, productivity, and relative prices.

  • World Development Indicators (WDI), which includes a wide range of economic and social indicators.

• Each data point represents a coefficient derived from an individual bivariate regression. These coefficients are used to assess the overall trend of convergence.

• The dependent variable is defined as the annual real per capita growth rate from the specified year up to the most recent data available. This measures how much the economy has grown on average each year during the period under consideration.

• The independent variable is the logarithm of real per capita GDP in the base year. This variable captures the initial level of development and is used to predict future growth.

• This analysis EXCLUDES:

  • Oil-rich countries (identified by 'Export Earnings: Fuel' in IMF DOTS). These countries often experience unique growth patterns due to their natural resource endowments.

  • Countries with populations under 1 million. Small countries may exhibit volatile growth rates due to their size and specific circumstances.

• Source: Patel, Sandefur, and Subramanian, 2018. Their research provides an updated assessment of convergence trends using the latest available data.

Final Thoughts on Solow & Growth Empirics

• Strengths:

  • Strong evidence supporting conditional convergence. This highlights the importance of factors such as savings, population growth, and human capital in promoting economic growth.

  • Highlights the significance of Solow parameters, including the savings rate, population growth rate, and technological progress, in determining long-term economic outcomes.

  • Provides an effective framework for organizing concepts related to economic growth and development, making it easier to understand the key drivers of prosperity.

• Weaknesses:

  • Does not fully explain the fundamental origins of income disparities. The model treats certain parameters as exogenous, without explaining why they differ across countries.

    • What causes differences in the exogenous parameters? This question remains a key challenge for growth economists.

  • Does not adequately explain long-run growth, as it assumes technical progress and does not model the innovation process.

  • Diminishing Returns to Scale (DRS) imply r{poor} > r{rich}, yet capital tends to flow from poorer to richer countries. This contradicts the model's prediction and is known as the Lucas paradox.

• Other issues:

  • Cross-country regressions can be problematic due to variations and complexities in data quality, institutional differences, and policy environments.

  • Economic growth often occurs in irregular patterns, featuring periods of rapid growth and plateaus. This makes it difficult to predict future growth based on past trends.

Capital Flows: MRW

• Analysis of total equity inflows per capita to both rich and poor countries from 1970-2000. This examines the patterns of international investment and their impact on economic growth.

• Figure 1 illustrates inflows of direct and portfolio equity, providing a visual representation of capital flows.

• Source: Alfaro et al, 2008. Their research explores the relationship between foreign investment and economic growth.

Growth Accounting

• Utilizes the Cobb-Douglas production function: Y = AK^\alpha L^{1-\alpha}

  • Where:

    • Y = output, representing the total value of goods and services produced in an economy.

    • A = total factor productivity, which measures how efficiently inputs are used to produce output.

    • K = capital, including physical capital such as machinery, equipment, and buildings.

    • L = labor, representing the number of workers or the total hours worked.

    • \alpha = output elasticity of capital, indicating the percentage change in output resulting from a one percent change in capital.

• Aims to decompose the components of economic growth to understand their individual impacts. This helps policymakers identify the most effective strategies for promoting growth.

• The method involves using growth rates derived from calculus:

  • Given a variable x(t), logarithmic transformation and differentiation over time are applied. This technique is used to convert levels into growth rates.

    • x(t) -> ln(x(t)) -> \frac{d}{dt} ln(x(t))

    • \frac{d}{dt} ln(x(t)) = \frac{1}{x(t)} * \frac{dx(t)}{dt} -> \frac{\Delta x}{x}

    • \frac{\Delta x}{x} * 100

Growth Accounting

• Applying the specified method to the Cobb-Douglas production function: Yt = At Kt^\alpha Lt^{1-\alpha}

  • ln(Yt) = ln(At) + \alpha ln(Kt) + (1 - \alpha) ln(Lt)

• Taking the derivative with respect to time (t):

  • \%%\Delta y = \%%\Delta A + \alpha(\%%\Delta K) + (1 - \alpha)\%\Delta L

    • Where:

      • \%\Delta y = growth rate of output.

      • \%\Delta A = growth rate of total factor productivity (Solow residual), representing technological progress and efficiency gains.

      • \%\Delta K = growth rate of capital.

      • \%\Delta L = growth rate of labor.

• \%\Delta A is known as the Solow residual and represents the portion of growth not explained by capital and labor. It is often interpreted as a measure of technological progress.

• Assuming perfect competition:

  • Factors are remunerated according to their marginal products:

    • MPK = r and MPL = w

    • \frac{\partial Y}{\partial K} = \alpha A K^{\alpha-1} L^{1-\alpha} = r and \frac{\partial Y}{\partial L} = (1 - \alpha) A K^\alpha L^{-\alpha} = w

    • \Rightarrow \alpha = \frac{rK}{Y} and 1 - \alpha = \frac{wL}{Y}

• With the exception of \%%\Delta A, all components of the equation are directly