Total factor productivity

In economics, total-factor productivity (TFP), also called multi-factor productivity, is a variable which accounts for effects in total output not caused by traditionally measured inputs of labor and capital. If all inputs are accounted for, then total factor productivity (TFP) can be taken as a measure of an economy’s long-term technological change or technological dynamism.

TFP cannot be measured directly. Instead it is a residual, often called the Solow residual, which accounts for effects in total output not caused by inputs.

The equation below (in Cobb–Douglas form) represents total output (Y) as a function of total-factor productivity (A), capital input (K), labor input (L), and the two inputs' respective shares of output (α and β are the capital input share of contribution for K and L respectively). An increase in either A, K or L will lead to an increase in output. While capital and labor input are tangible, total-factor productivity appears to be more intangible as it can range from technology to knowledge of worker (human capital).

$Y = A \times K^\alpha \times L^\beta$

Technology growth and efficiency are regarded as two of the biggest sub-sections of Total Factor Productivity, the former possessing "special" inherent features such as positive externalities and non-rivalness which enhance its position as a driver of economic growth.

Total Factor Productivity is often seen as the real driver of growth within an economy and studies reveal that whilst labour and investment are important contributors, Total Factor Productivity may account for up to 60% of growth within economies.

TFP is more accurately measured in long term, since TFP can vary substantially from one year to another.

It has been shown that there is a historical correlation between TFP and energy conversion efficiency.

Criticism

Growth accounting exercises and Total Factor Productivity are open to the Cambridge Critique. Therefore, some economists believe that the method and its results are invalid.

On the basis of dimensional analysis, TFP is criticized as not having meaningful units of measurement. The units of the quantities in the Cobb–Douglas equation are:

• Y: widgets/year (wid/yr)
• L: man-hours/year (manhr/yr)
• K: capital-hours/year (caphr/yr; this raises issues of heterogeneous capital)
• α, β: pure numbers (non-dimensional), due to being exponents
• A: (widgets * year^{α + β – 1})/(caphr^α * manhr^β), a balancing quantity, which is TFP.

The units of A do not admit a simple economic interpretation, and the concept of TFP is accordingly criticized as a modeling artifact.

Estimation

As a residual, TFP is also dependent on estimates of the other components. A 2005 study on human capital attempted to correct for weaknesses in estimations of the labour component of the equation, by refining estimates of the quality of labour. Specifically, years of schooling is often taken as a proxy for the quality of labour (and stock of human capital), which does not account for differences in schooling between countries. Using these re-estimations, the contribution of TFP was substantially lower.

Robert Ayres and Benjamin Warr have found that the model can be improved by using the efficiency of energy conversion, which roughly tracks technological progress.

See also

• Solow residual
• Multifactor productivity
• Productivity model

References

• Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
• Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, vol. 50(6), pages 1393-1414, November.
• Alexandra Daskovska & Léopold Simar & Sébastien Bellegem, 2010. "Forecasting the Malmquist productivity index," Journal of Productivity Analysis, Springer, vol. 33(2), pages 97-107, April.
• Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. 1994. Productivity growth, technical progress, and efficiency change in industrialized countries. The American Economic Review 84, pages 66–83.
• Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June. ]
• Mayer, A. and Zelenyuk, V. 2014. "Aggregation of Malmquist productivity indexes allowing for reallocation of resources," European Journal of Operational Research, Elsevier, vol. 238(3), pages 774-785.
• Zelenyuk, V. 2006. "Aggregation of Malmquist productivity indexes," European Journal of Operational Research, vol. 174(2), pages 1076-1086.