What it means
The core idea is that output grows for only a few reasons: you add machines and buildings, you add people and hours, or you get better at using what you already have. Growth accounting assigns a share of measured growth to each of those causes.
Each input is weighted by its share of total income. If capital earns 30% of the income generated and labour earns 70%, then a 1% increase in capital contributes 0.3% to output growth while a 1% increase in labour contributes 0.7%.
Whatever growth remains after those contributions are subtracted is total factor productivity, often called the residual or the Solow residual. It is measured rather than observed directly, which means it also absorbs measurement error and anything the model failed to capture.
In a company setting the same arithmetic explains where revenue growth came from. A business that grew 20% by hiring 20% more salespeople has produced no productivity gain, while one that grew 20% with the same headcount has improved something real about how it operates.
The practical value is that it separates growth you have to keep paying for from growth that compounds. Adding inputs has a direct cost and eventually runs into diminishing returns, whereas productivity gains raise output without a matching increase in spend.
In practice
Real-world examples.
Example
A logistics operator reports 15% revenue growth and celebrates. A growth accounting breakdown shows fleet capacity up 12% and driver hours up 10%, so almost all the growth was bought rather than earned, and margin per delivery is flat.
Example
A national statistics office decomposes 4% annual output growth into 1.2% from capital investment, 0.8% from a larger workforce and 2.0% from productivity. Policymakers use the split to argue that education and technology adoption, not just investment incentives, drive the country's long-run growth.
Example
A software business grows revenue 30% while headcount rises only 5% and infrastructure spend rises 8%. The residual is large and positive, and the board treats it as evidence that the product is genuinely scaling rather than simply being sold harder.
Formula
Calculation
Output growth = (capital share x capital growth) + (labour share x labour growth) + total factor productivity growth
An economy or business grows output by 6% over a year. Capital input grew 5%, labour input grew 2%, and capital's share of income is 30%, leaving labour's share at 70%.
Contribution from capital = 0.30 x 5% = 1.5%
Contribution from labour = 0.70 x 2% = 1.4%
Combined input contribution = 1.5% + 1.4% = 2.9%
Total factor productivity growth = 6% - 2.9% = 3.1%
So roughly half the growth came from adding inputs and slightly more than half came from using those inputs better. If the same business had grown 6% while capital grew 10% and labour grew 6%, the input contribution would have been (0.30 x 10%) + (0.70 x 6%) = 3.0% + 4.2% = 7.2%, implying productivity growth of 6% - 7.2% = -1.2%, meaning efficiency actually fell.Case study
Seen in the real world.
The following is an illustrative and fictional case. Vantry Components grew revenue 6% in a year the board considered disappointing, and the initial explanation from the operations team was that the market had softened. The chief financial officer instead applied a simple growth accounting decomposition to the business itself.
Capital employed had grown 5% through new machinery, and labour hours had grown 2% through overtime. Weighting those at 30% and 70% gave contributions of 1.5% and 1.4%, a combined 2.9%, leaving 3.1% of growth attributable to productivity. In other words the plant had genuinely become more efficient, and more than half the year's growth had come from that rather than from spending.
The board's conclusion in this fictional illustration was the opposite of its starting assumption. Rather than a weak year, Vantry had produced the best productivity performance in its history while investing modestly, and the next capital budget was redirected towards the specific process changes that had generated the residual.
Watch out
Common mistakes.
- Treating total factor productivity as a directly measured quantity, when it is a residual that also absorbs data errors and anything the model left out.
- Using headcount instead of hours worked as the labour input, which distorts the result whenever overtime or part-time patterns change.
- Assuming a positive residual always means better management, when it can also reflect a temporary price effect or a one-off change in the product mix.
Questions
People also ask.
Why are capital and labour weighted by income shares?
Because under competitive conditions each input is paid roughly its marginal contribution, so its share of income approximates its share of the output it produces.
Can growth accounting be applied to a single company?
Yes, using revenue or gross profit as output, capital employed as the capital input and hours worked as the labour input, though the weights need judgement.
What does a negative residual mean?
It means output grew more slowly than the growth in inputs would predict, so efficiency declined even if the headline growth figure looked positive.
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