Growth Accounting, Diffusion, and the Asian Tigers: Notes from the Lecture

Growth Accounting, Catch-Up, and Diffusion: Hong Kong, Singapore, and Beyond

  • Big-picture themes from the discussion

    • The UK is highlighted as having the lowest growth rate in both panels shown, after being a hegemon for about 150 years until World War I.

    • Postwar dynamics: The US experienced a baby boom after World War II.

    • Labor’s contribution to growth varies by region: Western Europe (e.g., France, Germany, Italy) shows especially low labor contribution due to very low fertility; Latin America and East Asia show stronger growth trajectories.

    • Regions far from the technological frontier tend to grow via catch-up growth and technological diffusion.

    • Technological diffusion = the spread of ideas and technologies from frontier countries (e.g., the US) to other countries; ideas are hard to contain and tend to diffuse, enabling other countries to catch up.

    • The “Asian Tigers” (East Asia) are highlighted as a group that grew rapidly postwar, often cited as 5.6% per year through capital accumulation alone, illustrating a strong role for capital deepening.

    • Growth accounting framework is used to decompose growth into capital, labor, and productivity (the residual).

    • Peru’s experience is used as a counterexample where productivity measured as the residual can be negative, implying productivity contracted or did not keep up with capital and labor growth.

    • Next steps: move beyond event-level growth to explore drivers of productivity (the next layer after growth accounting).

  • Growth accounting framework: how to read the data

    • Core idea: output growth can be decomposed into contributions from capital deepening, labor force growth, and a residual productivity term.

    • The standard accounting identity (for a Cobb-Douglas production function) is often written as:

    gy = \alpha \, gK + (1-\alpha) \, gL + gA

    • Here:

    • $g_y$ = growth rate of output (GDP)

    • $g_K$ = growth rate of capital

    • $g_L$ = growth rate of labor

    • $\alpha$ = capital share of income (a parameter between 0 and 1)

    • $g_A$ = productivity growth (TFP growth, the residual)

    • The residual $g_A$ captures all factors other than capital and labor, including advancements in technology, institutions, and efficiency.

    • In the exercise discussed, the chart/ table for Hong Kong and Singapore covers five-year periods (roughly across the 1970s–1980s) to illustrate the decomposition.

    • Reading the columns:

    • The first few columns show observed growth components from capital and labor.

    • The last column shows the residual productivity gains; this last column is what we use to judge productivity-driven growth.

    • Specific example: what accounted for growth in Hong Kong and Singapore between 1970 and 1990?

    • Hong Kong: large productivity gains (positive $g_A$) relative to Singapore.

    • Singapore: productivity gains are negative in the last column, meaning most of Singapore’s growth came from capital accumulation rather than productivity improvements.

    • Capital share (the parameter $\alpha$) is country- and period-specific; recall the value used for the United States historically was around $\alpha = 0.4$ (the “point four” figure).

    • In the Hong Kong/Singapore table, Singapore’s implied capital share in the 1970s is around $\alpha \approx 0.55$, which is 15 percentage points higher than the US’s 0.40. This implies, in those years, about 15% more of GDP was represented by machinery/capital stock in Singapore than in the US.

    • Hong Kong’s capital share is described as being a little lower than Singapore’s, but still high relative to the US.

    • How to interpret: with $\alpha = 0.55$ for Singapore in the 1970s, a larger portion of output is produced with capital; if the productivity residual is negative or small, growth is driven primarily by capital deepening rather than efficiency improvements.

    • The US, in the same three-decade span, shows growth that is roughly split: almost half from productivity (the residual), implying substantial gains in efficiency or technology adoption, rather than purely capital deepening; labor’s contribution tends to be positive but modest; capital accumulation remains significant as well.

    • In some Western European countries at the time, labor’s contribution can be negative or small due to aging populations and weak employment growth, so capital accumulation and productivity dominate growth.

  • Regional patterns and interpretation

    • Western Europe

    • Labor contribution to growth often weak due to low fertility; reliance on capital deepening and productivity improvements to sustain growth.

    • Latin America

    • Growth is still positive on average, but not as strong as East Asia; productivity dynamics and capital deepening vary by country.

    • East Asia

    • Growth miracles postwar driven by catch-up growth and rapid capital accumulation; ideas and technologies diffuse from the frontier (the US) to East Asian economies, enabling rapid convergence.

    • The Asian Tigers

    • Noted for very high growth rates (around 5.6% per year) through capital accumulation; highlight of catch-up growth and high investment rates.

  • Key takeaways about productivity, diffusion, and the frontier

    • Catch-up growth is most plausible for countries far from the technological frontier; they can grow rapidly by adopting existing technologies and organizational knowledge from frontier countries.

    • Technological diffusion is a central mechanism: ideas are hard to keep contained; once widespread, other countries can implement them to close the gap.

    • The frontier country (historically the US) plays a pivotal role in diffusion; frontier innovations can be adopted and adapted by others, spurring growth elsewhere.

    • A country can experience rapid growth through capital deepening even if productivity improvements are modest or negative (as in the Singapore case for some periods), though sustained growth usually benefits from positive productivity growth as well.

  • Peru as a cautionary example

    • In one period, Peru showed a negative residual in productivity despite capital and labor growth; this highlights that output growth can be explained away by little to no improvement in efficiency or technology, or even deterioration in productivity, which would impede long-run growth.

    • This motivates the study of what drives productivity: institutions, education, infrastructure, governance, investment in R&D, and the organization of production.

  • Implications for forecasting and research strategy

    • Data and decomposition can be used to predict future directions: if a country relies heavily on capital deepening with weak productivity gains, future growth may slow unless efficiency or technology adoption accelerates.

    • An inductive approach (learning from patterns in data) can help identify where growth is coming from and what levers might lift productivity in the future.

  • Next steps mentioned in the lecture

    • Move beyond event-level observations to understand what drives productivity: its causes, mechanisms, and policies.

    • Explore how institutions, innovation, human capital, infrastructure, and governance influence the residual component $g_A$ and long-run growth prospects.

  • Quick recap of key numbers and concepts (for exam-ready recall)

    • Growth accounting identity (Cobb-Douglas form):
      gy = \alpha \, gK + (1-\alpha) \, gL + gA

    • Typical US capital share: $\alpha \approx 0.4$ (point four)

    • Singapore capital share in the 1970s: $\alpha \approx 0.55$ (about 15 percentage points higher than US)

    • Interpretation of a higher $\alpha$ in a country: more of GDP is produced with capital; growth can be more sensitive to investment in physical capital.

    • East Asia’s long-run story: rapid growth via catch-up and capital deepening, aided by technological diffusion from frontier economies.

    • Hong Kong vs Singapore in the 1970s–1980s: Hong Kong showed large positive productivity gains; Singapore showed substantial capital accumulation with relatively small or negative productivity gains in some periods.

    • The Asian Tigers’ growth rate: often cited around $5.6\%$ per year through capital accumulation alone.

  • Conceptual links to broader topics

    • Growth accounting connects to the idea of convergence: poorer economies can grow faster by catching up to richer economies if they implement efficient technologies and institutions.

    • The role of technology diffusion underscores that knowledge is non-rivalrous and can be shared, lowering barriers to growth for developing economies.

    • The residual term $g_A$ encapsulates the impact of innovation, efficiency, and institutional improvements, which are central to long-run growth trajectories.

  • Practical implications for policy and research

    • Policies that boost investment in capital (infrastructure, machinery, and human capital) can accelerate growth via capital deepening, but sustainable long-run growth requires improvements in productivity.

    • Policies that promote education, research and development, governance, and ease of doing business can enhance $g_A$ and lead to more durable growth advantages.

    • Understanding country-specific capital shares helps researchers interpret growth decompositions and tailor policy recommendations accordingly.

  • Philosophical and ethical considerations

    • Growth measurements depend on the chosen production function and parameters (like $\alpha$), which can influence policy emphasis (capital deepening vs. productivity). Transparency about assumptions is crucial.

    • The diffusion of ideas benefits global welfare but requires support for openness, collaboration, and investment in human capital across borders.

  • Final reflection from the discussion

    • Data-driven, inductive analysis of growth components can guide future research and policy.

    • The interplay between capital deepening and productivity improvement shapes long-run growth trajectories and country development narratives.