Growth Accounting — Decomposing Output Growth (the Solow Residual)

Use growth accounting to decompose a country's output growth over time into the contributions of capital growth, labor growth, and Total Factor Productivity growth (the Solow Residual). Starting from $Y = AF(K,N)$, differentiating and dividing by $Y$ gives

so the Solow Residual is $g_A = g_Y - \varepsilon_{Y,K}\, g_K - \varepsilon_{Y,N}\, g_N$.

1. Collect data on $g_Y$, $g_K$, $g_N$ (with quality adjustments if possible).
2. Estimate the elasticities $\varepsilon_{Y,K}$ and $\varepsilon_{Y,N}$ — for Cobb-Douglas these equal the income shares $\alpha$ and $\beta$, read from national accounts.
3. Calculate the capital and labor contributions ($\alpha g_K$ and $\beta g_N$).
4. Calculate TFP growth as the residual — everything in output growth left unexplained by inputs.

Common pitfalls

• The elasticities equal income shares only under Cobb-Douglas (competitive markets); otherwise estimate them directly.
• TFP is a residual, so it absorbs all measurement error in $g_Y$, $g_K$, $g_N$ — quality-adjust inputs where you can.

Worked example

$g_Y = 0.10$, $g_K = 0.05$, $g_N = 0.02$, $\alpha = 1/3$, $\beta = 2/3$:

so 70% of growth is explained by TFP — capital and labor contributions are much smaller. See Lec_04-Production.