Adam Bede

    D1 - East Asian 🐅

    • Gemini
    • GPT

    Every economy produces output (GDP). Over time, output grows.

    The natural question: why?

    There are three possible reasons output goes up:

    1. More labor (L): hiring more workers or more hours worked.
    2. More capital (K): building more machines, buildings, or technology.
    3. More productivity (A): getting more output from the same inputs (smarter management, better technology, educated workers, stable institutions).

    Growth accounting is a way of dividing observed GDP growth into these three parts.

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    Elasticity

    What “elasticity” means here

    In the growth accounting framework, elasticity of output with respect to an input = how sensitive output is to changes in that input.

    • If αK = 0.3, it means: a 1% increase in capital, holding everything else constant, raises output by 0.3%.
    • If αL = 0.7, it means: a 1% increase in labor raises output by 0.7%.

    Because αK + αL ≈ 1, we can think of them as weights: the share of output growth that can be “explained” by each input, leaving the residual as productivity.

    Why these numbers are what they are

    • In practice, αK and αL are usually estimated from national accounts:
      • αK ≈ capital’s share of income (profits, rents).
      • αL ≈ labor’s share of income (wages, salaries).
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    Not quite, and this is a crucial distinction that gets to the heart of growth accounting.

    A 68% increase in the participation rate doesn't mean the number of workers grew by 68%. It means the share of the population that works grew by 68%. The actual increase in the number of workers is much larger because it's the result of two effects happening at once: a growing population and a larger percentage of that population working.

    Let's Break It Down with an Example 💡

    Let's imagine a simplified Singapore in 1966.

    The "Before" Picture (1966)

    • Let's say the Population (N) was 1,000,000 people.
    • Let's assume the

      • Participation Rate (E) was 30%1. (The actual starting rate was 27% in 1966, but 30% is a round number for our example).

    • The Number of Workers (L) would be 30% of 1,000,000 = 300,000 workers.

    The "After" Picture (1991)

    Two things happened over those 25 years:

    1. The Participation Rate Grew by 68%: The new participation rate isn't 68%, but the old rate increased by 68%.
      • New Rate = 30% × (1 + 0.68) = 30% × 1.68 = 50.4%.
      • This reflects the massive social change of more people entering the workforce.
    2. The Population Also Grew: The population wasn't static. It grew at an average of 1.91% per year2. Over 25 years, that's a total increase of about 60%.
      • New Population ≈ 1,000,000 × (1.0191)²⁵ ≈ 1,600,000 people.

    Now, let's find the new number of workers by applying the new, higher participation rate to the new, larger population:

    • New Number of Workers (L) = 50.4% of 1,600,000 = 806,400 workers.

    Why This Matters

    Your initial thought was that 100 workers would become roughly 168. If we applied that to our example, the number of workers would have grown from 300,000 to about 300,000×1.68=504,000.

    However, the actual number of workers grew from 300,000 to 806,400. This is a total increase of about 169%!

    The growth in the number of workers was so massive because it was a powerful combination of two factors:

    • A 60% bigger population.
    • A 68% higher share of that bigger population being in the workforce.