How to Do Growth Accounting
Growth accounting splits output growth into three parts: capital growth weighted by capital's income share, labor growth weighted by labor's share, and the leftover, which is productivity growth.
The Growth Accounting formula
Calculator
Enter output, capital and labor growth plus capital's income share to split growth into inputs and productivity.
Percent change in real GDP over the period.
Percent change in the stock of machines, buildings and equipment.
Percent change in hours worked, or in the number of workers.
The fraction of national income paid to capital. Labor's share is the rest, 1 − α.
Output grew 1.8% faster than the measured inputs can account for, and that leftover is the Solow residual.
- Contribution of capital
- 1.5%
- Contribution of labor
- 0.7%
- TFP share of output growth
- 45%
- Growth in output per worker
- 3%
- Main source of growth
- Total factor productivity
Capital growth weighted by its income share explains 1.5% of output growth.
Labor growth weighted by labor's income share accounts for 0.7% of output growth.
45% of the growth came from getting more out of the same inputs rather than from adding inputs.
Output per worker changed by about 3%, since output growth minus labor growth is what each worker's output did.
The largest of the three contributions. A dominant residual is the usual finding for a rich economy, where capital per worker is already high.
How to calculate Growth Accounting, step by step
- 1Collect the four numbers. You need output growth, capital stock growth, labor growth, and capital's share of income (α). Labor's share is whatever is left, 1 − α.
- 2Weight capital growth by α. Multiply the growth rate of the capital stock by capital's income share. The answer is the percentage points of output growth that extra capital explains.
- 3Weight labor growth by 1 − α. Multiply labor growth by labor's income share for the percentage points that come from more workers or more hours.
- 4Subtract both from output growth. What is left is total factor productivity growth, the Solow residual, the part of growth that measured inputs cannot account for.
- 5Read the residual with care. The residual carries technology and efficiency, but it also absorbs measurement error in capital and labor, so treat it as a leftover rather than a direct reading of technology.
Worked example: Growth Accounting
Real output grows 4% while the capital stock grows 5% and labor grows 1%, with capital's share of income at 0.3. Capital contributes 0.3 × 5 = 1.5 percentage points and labor contributes 0.7 × 1 = 0.7 percentage points, so measured inputs explain 1.5 + 0.7 = 2.2 points. Total factor productivity is the leftover: 4 − 1.5 − 0.7 = 1.8 percentage points, which is 1.8 ÷ 4 = 45% of all the growth. Output per worker grew roughly 4 − 1 = 3%.
Growth Accounting questions
What is the Solow residual?
It is the part of output growth left over after the weighted contributions of capital and labor are subtracted. It is credited to technology and efficiency, and it is always measured as a leftover rather than observed directly.
Why is capital's income share used as the weight?
Under competitive factor markets each input is paid its marginal product, so the share of income a factor earns equals the elasticity of output with respect to that input. That share is exactly the right weight to put on its growth rate.
Can total factor productivity growth be negative?
Yes. If output grows more slowly than the weighted growth of capital and labor, the residual comes out negative, which points to falling efficiency or to inputs that were mismeasured.
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated