Growth Accounting
What is Growth Accounting?
Growth accounting decomposes the growth of output into contributions from capital, labor, and total factor productivity (the Solow residual).
Starting from the aggregate production function, growth accounting attributes a country's output growth to growth in capital, growth in labor (each weighted by its share of income), and a leftover 'Solow residual' attributed to technological progress and efficiency gains. The residual captures everything not explained by measured inputs and is treated as total factor productivity (TFP) growth. Empirically, much of long-run growth in output per worker comes from TFP rather than sheer input accumulation, highlighting the role of innovation. It is the standard framework for explaining why some economies grow faster than others.
Growth Accounting: a worked example
Country Marisol reports output growth of 4.5 percent, capital stock growth of 5 percent and labor force growth of 2 percent, with capital taking 30 percent of national income so alpha = 0.3. Capital contributes 0.3 x 5 = 1.5 percentage points. Labor contributes 0.7 x 2 = 1.4 percentage points. Measured inputs therefore explain 1.5 + 1.4 = 2.9 of the 4.5 points. The Solow residual is 4.5 - 2.9 = 1.6 percentage points, so total factor productivity grew 1.6 percent and accounted for 1.6 / 4.5 = 36 percent of Marisol's growth.
The mistake students make with growth accounting
The residual gets treated as a measurement of technology, when it is defined as whatever the input data failed to explain. It quietly absorbs mismeasured capital, factories idling below capacity, shifts in workforce skill, and any input left out of the equation. Count labor as headcount rather than hours worked and a rise in average hours shows up as a productivity miracle. Naming it total factor productivity, then glossing that as innovation, hides how much is simply leftover.
Growth Accounting questions
How do you calculate total factor productivity growth?
Total factor productivity growth is calculated as a residual: take output growth and subtract the income-share-weighted growth of each input. With a capital share of 0.3, output growth of 4 percent, capital growth of 6 percent and labor growth of 1 percent, inputs explain 0.3 x 6 + 0.7 x 1 = 2.5 points, so TFP growth is 4 - 2.5 = 1.5 percent.
What is the Solow residual?
The Solow residual is the slice of output growth left over once the contributions of capital and labor have been subtracted, named for the growth model it comes from. It serves as the estimate of total factor productivity growth, covering better technology, better organization and better allocation of resources. Because it is computed by subtraction rather than measured directly, every error in the input data ends up inside it.
Why are the weights in growth accounting equal to the income shares?
The weights are income shares because under constant returns to scale and competitive factor markets each input is paid its marginal product, which makes the elasticity of output with respect to an input equal that input's share of total income. So if capital earns 30 percent of income, a 1 percent rise in capital raises output by 0.3 percent. The weights sum to one, which is what constant returns to scale requires.
Formula / Example
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