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Growth accounting decomposes output growth into contributions from capital growth, labor growth, and total factor productivity (TFP) growth: ΔY/Y = α(ΔK/K) + (1-α)(ΔL/L) + ΔA/A. The Solow residual (TFP growth) captures technological progress but also mismeasurement and organizational improvements. Growth accounting reveals that in developed economies, most long-run growth comes from productivity rather than factor accumulation.
From your study of the macroeconomic production function, you know that output Y depends on inputs: capital K, labor L, and total factor productivity A, in a relationship like Y = A × F(K, L). This tells us *what* determines output but not *how much* each component explains observed growth. Growth accounting applies this framework to a diagnostic question: when GDP grew by 3% last year, how much came from having more capital, how much from having more workers (or workers putting in more hours), and how much from getting more output from the same inputs?
The decomposition follows from logarithmic differentiation of the production function under two standard assumptions: constant returns to scale, and competitive factor markets where each factor earns its marginal product. Under these conditions, capital's share of national income (α ≈ 0.33 in most rich economies) equals the elasticity of output with respect to capital. This gives the accounting equation: ΔY/Y ≈ α(ΔK/K) + (1-α)(ΔL/L) + ΔA/A. Capital's contribution is α times capital's growth rate; labor's contribution is (1-α) times labor's growth rate. The residual — output growth minus these two calculated contributions — is Total Factor Productivity growth (ΔA/A), often called the Solow residual after Robert Solow who first applied it systematically in 1957.
TFP growth captures everything that makes the economy more productive without simply using more inputs: technological improvement (better machines, new production methods, improved software), organizational and managerial improvements, better resource allocation across firms and sectors, and gains from specialization and trade. Think of it as the efficiency of the economy's production process. A country that doubles its capital and labor and gets exactly twice the output has TFP growth of zero — it just scaled up. A country that doubles its inputs and gets 2.2 times the output has positive TFP growth of roughly 10% — it got smarter about how it uses what it has. The uncomfortable corollary is that TFP is calculated as a residual, meaning it absorbs all measurement error in capital and labor inputs. Solow himself acknowledged this problem, noting that his residual was "a measure of our ignorance."
The empirical results from growth accounting reshape our understanding of development. For today's rich economies, roughly two-thirds of long-run growth per worker comes from TFP, with capital deepening (more capital per worker) contributing the remainder. This ratio has profound implications: because of diminishing returns to capital (from your production function), a country cannot sustain growth indefinitely by simply accumulating more machines. Each additional unit of capital contributes less than the last. Sustained long-run growth *requires* sustained TFP growth — continuous improvements in how inputs are combined. For rapidly industrializing countries like South Korea and Taiwan in the 1960s–80s, factor accumulation mattered more during the catch-up phase (vast amounts of capital were being installed where little existed before), but even there, TFP ultimately drove convergence toward the technology frontier. This is the bridge between growth accounting and growth theory: accounting reveals the proximate sources of growth; theory explains why TFP grows at all.