Questions: Growth Accounting and Sources of Economic Growth

Question 1

An economy has capital share α = 1/3. Capital grows 6%, labor grows 3%, and GDP grows 6% that year. What is TFP (Solow residual) growth?

• A. –3%: TFP is output growth minus total input growth (6% – 6% – 3%)
• B. 2%: capital contributes 2% (= 1/3 × 6%), labor contributes 2% (= 2/3 × 3%), leaving a 2% residual
• C. 6%: TFP equals output growth since factor accumulation is the baseline
• D. 3%: TFP is the unweighted average of capital and labor growth rates

Answer: (B)

Growth accounting weights each input by its income share: capital contributes α × ΔK/K = 1/3 × 6% = 2%, and labor contributes (1–α) × ΔL/L = 2/3 × 3% = 2%. Total factor contribution = 4%. With GDP growing 6%, TFP = 6% – 4% = 2%. The most common error (option A) forgets the income-share weights and subtracts raw growth rates — but raw input growth of 9% exceeding output growth of 6% doesn't mean TFP is negative; the weights are what matter.

Question 2

Empirical growth accounting shows roughly two-thirds of long-run growth per worker in rich economies comes from TFP. What does this imply for strategies that attempt to sustain growth purely through capital investment?

• A. Capital investment is the more reliable lever because it is directly controllable, unlike TFP
• B. Capital accumulation faces diminishing returns; each additional unit contributes less than the last, so capital investment alone cannot sustain long-run growth
• C. Rich economies should shift investment from capital to labor to balance the growth contributions
• D. The 2/3 figure likely reflects measurement error in TFP, so capital's true contribution is larger

Answer: (B)

From the production function, capital exhibits diminishing marginal returns — as K/L rises, each additional unit of capital adds less to output. A country doubling its capital grows output by less than double, so the capital contribution to growth shrinks over time. Sustained long-run growth therefore requires ongoing TFP growth — improvements in how inputs are used. This is one of the core insights of growth accounting: factor accumulation explains catch-up growth but not sustained long-run prosperity.

Question 3

If a country doubles most its factor inputs — capital and labor — and GDP exactly doubles, then TFP growth over that period is positive.

• T. True
• F. False

Answer: False

Under constant returns to scale, doubling all inputs produces exactly double the output with zero TFP growth. Growth accounting assigns TFP growth = ΔY/Y – α(ΔK/K) – (1–α)(ΔL/L). If Y doubles (100% growth) and K and L both double, then the formula gives: 100% – α×100% – (1–α)×100% = 100% – 100% = 0%. TFP growth measures how much more output the economy extracts from a given bundle of inputs — not just whether output grew.

Question 4

Because TFP is computed as a residual — output growth not explained by capital and labor — it absorbs all measurement errors in those inputs.

• T. True
• F. False

Answer: True

This is Solow's own acknowledged limitation — he called the residual 'a measure of our ignorance.' TFP captures genuine technological progress, organizational improvements, and better resource allocation, but it also absorbs any mismeasurement of capital quality, hours worked, or human capital. If capital services are mismeasured (e.g., computing capital depreciation incorrectly), the error flows into TFP. This is why growth accounting reveals the proximate sources of growth without fully identifying their underlying causes.

Question 5

What is the Solow residual, and why does its dominance in long-run growth data matter for understanding economic development?

Model answer: The Solow residual is TFP growth — the portion of output growth not explained by capital and labor input growth, computed as ΔA/A = ΔY/Y – α(ΔK/K) – (1–α)(ΔL/L). Its dominance matters because sustained long-run prosperity cannot come from simply accumulating more factors (which face diminishing returns) but requires ongoing improvements in the efficiency of production — better technology, organization, and resource allocation.

Growth accounting separates proximate accounting from deeper explanation. Countries can grow quickly during catch-up phases by building factories and expanding their workforce, but once factor accumulation slows (as returns diminish), only TFP growth can sustain income levels. This shifts the policy question from 'how do we accumulate more?' to 'how do we innovate and improve efficiency?' — the right question for understanding long-run development.