Total Factor Productivity (TFP)

Total factor productivity (TFP) is a measure of how efficiently an economy, industry or firm combines all of its inputs, chiefly labor and capital, to produce output. In practice it is calculated as a residual: the growth in output that is left over after subtracting the contributions of growth in hours worked and in the stock of capital goods. Because it captures improvements in technology, organization and know-how, TFP is widely treated in macroeconomics as the core long-run driver of productivity and living standards.

TFP is also called multifactor productivity; the US Bureau of Labor Statistics (BLS) switched from that name to "total factor productivity" in 2021 without changing its data. It is distinct from labor productivity, which is output per hour and rises both when TFP improves and when workers get more capital to work with. The method behind it, growth accounting, was set out by Robert Solow in 1957, which is why TFP growth is often called the Solow residual. It is one input into estimates of potential output and therefore of the output gap.

Imagine a bakery that hires one more baker and buys one more oven, and its output of bread goes up. Part of that increase is simply more people and more equipment. But suppose output rises by more than the extra baker and oven can explain, because the owner rearranged the kitchen, adopted a better recipe and scheduled deliveries more cleverly. That extra part, the gain that comes from working smarter rather than adding more, is what total factor productivity tries to measure.

For a whole economy, TFP growth reflects new technologies, better management, smoother markets and the spread of good ideas. It is the part of growth that does not need more hours or more machines.

Growth accounting usually assumes a Cobb-Douglas production function, $Y = A K^{\alpha} L^{1-\alpha}$, where $A$ is TFP. In growth rates, TFP growth is:

• $g_A$ is the growth rate of total factor productivity.
• $g_Y$ is the growth rate of real output, such as real GDP.
• $g_K$ is the growth rate of the capital stock (or of capital services).
• $g_L$ is the growth rate of labor input, such as hours worked.
• $\alpha$ is capital's share of income, often around 0.3 to 0.4 in advanced economies.

Suppose output grows 3 percent, capital 4 percent and hours 1 percent, with $\alpha = 0.3$. Then $g_A = 3 - 0.3 \times 4 - 0.7 \times 1 = 3 - 1.2 - 0.7 = 1.1$ percent. Of the 3 percent growth, 1.2 points come from capital, 0.7 from labor and 1.1 from TFP.

Because TFP is a residual, anything that raises output without more measured inputs shows up in it:

• Technology. Technological progress and innovation, often driven by research and development.
• Management and organization. Better business practices, logistics and use of data.
• Reallocation. Shifting labor and capital to more productive firms and sectors, helped by competition and creative destruction.
• Institutions. Rule of law, property rights, openness to trade and foreign direct investment, and efficient finance.
• Unmeasured inputs. Gains in worker skills or human capital that the labor measure does not capture also land in TFP unless they are adjusted for, as the BLS does with labor composition.

Solow's 1957 study of the US economy found that most of the growth in output per hour from 1909 to 1949 came from the residual rather than from more capital, a result that helped earn him the 1987 Nobel prize. In his model, technology was external and unexplained. Endogenous growth theory, developed from the 1980s by Paul Romer and others, tried to explain TFP growth through investment in ideas, and the 2025 Nobel prize to Philippe Aghion and Peter Howitt recognized their model of growth through creative destruction. Cross-country research suggests that differences in TFP account for a large share of income gaps between rich and poor countries. Main data sources include the BLS, the Federal Reserve Bank of San Francisco's quarterly US series, the Penn World Table and the OECD.

The economist Moses Abramovitz called the residual "a measure of our ignorance", and the criticism still applies. TFP absorbs measurement errors in output and inputs, so mismeasured software, intangible assets or quality changes can distort it. It moves with the business cycle, because firms use labor and machines less intensively in downturns, so short-run swings should not be read as changes in technology. Results also depend on the assumed production function and on capital's share. TFP is therefore best used for long-run comparisons and in combination with industry and firm-level evidence, not as a precise measure of technical change.

• U.S. Bureau of Labor Statistics: Productivity
• Federal Reserve Bank of San Francisco: Total Factor Productivity