economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...

, total-factor productivity (TFP), also called multi-factor productivity, is usually measured as the ratio of aggregate output (e.g., GDP) to aggregate inputs. Sickles, R., & Zelenyuk, V. (2019). Measurement of Productivity and Efficiency: Theory and Practice. Cambridge: Cambridge University Press. doi:10.1017/9781139565981
/ref> Under some simplifying assumptions about the production technology, growth in TFP becomes the portion of growth in output not explained by growth in traditionally measured inputs of labour and capital used in production. TFP is calculated by dividing output by the weighted geometric average of labour and capital input, with the standard weighting of 0.7 for labour and 0.3 for capital. Total factor productivity is a measure of productive efficiency in that it measures how much output can be produced from a certain amount of inputs. It accounts for part of the differences in cross-country per-capita income. For relatively small percentage changes, the rate of ''TFP'' growth can be estimated by subtracting growth rates of labor and capital inputs from the growth rate of output.

Background

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-rivals which enhance its position as a driver of economic growth. Total factor productivity (TFP) is often considered the primary contributor to GDP growth rate. Other contributing factors include labor inputs, human capital, and physical capital. Total factor productivity measures residual growth in total output of a firm, industry or national economy that cannot be explained by the accumulation of traditional inputs such as labor and capital. Since this cannot be measured directly the process of calculating derives TFP as the residual which accounts for effects on total output not caused by inputs. It has been shown that there is a historical correlation between TFP and energy conversion efficiency. Also, it has been found that integration (among firms for example) has a causal positive impact on total factor productivity.

Calculation

The equation below (in Cobb–Douglas form) is often used to represent total output (Y) as a function of total-factor productivity (A), capital input (K), labour input (L), and the two inputs' respective shares of output (α and β are the share of contribution for K and L respectively). As usual for equations of this form, an increase in either A, K or L will lead to an increase in output.

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

Estimation and refinements

As a residual, TFP is also dependent on estimates of the other components. In 2001,

William Easterly William Russell Easterly (born September 7, 1957) is an American economist, specializing in economic development. He is a professor of economics at New York University, joint with Africa House, and co-director of NYU’s Development Research Inst ...

and

Ross Levine Ross Levine (born April 16, 1960) is an American economist who currently holds the Willis H. Booth Chair in Banking and Finance at the University of California at Berkeley. He is also a senior fellow at the Milken Institute, a member of the Counc ...

estimated that for an average country the TFP accounts for 60 percent of growth of output per worker. 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''.

Critiques

The word "total" suggests all inputs have been measured. Official statisticians tend to use the term "multifactor productivity" (MFP) instead of TFP because some inputs such as energy are usually not included. External costs including attributes of the workforce, public infrastructure such as highways and environmental sustainability costs such as mineral depletion and pollution are not traditionally included.W.E. Diewert and A.O. Nakamura. 2007. The measurement of productivity for nations. Chapter 66 of ''Handbook of Econometrics'', volume 6A, edited by J.J. Heckman, and E.E. Leamer
p. 4514
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Growth accounting Growth accounting is a procedure used in economics to measure the contribution of different factors to economic growth and to indirectly compute the rate of technological progress, measured as a residual, in an economy. Growth accounting decomposes ...

exercises and total factor productivity are open to the Cambridge critique. Therefore, some economists believe that the method and its results are invalid or need to be carefully interpreted and used along with other alternative approaches. On the basis of

dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as mi ...

, TFP has been criticized as lacking meaningful

units of measurement A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multi ...

. The units of the quantities in the Cobb–Douglas equation are: * : widgets/year (wid/yr) * : man-hours/year (manhr/yr) * : capital-hours/year (caphr/yr; this raises issues of heterogeneous capital) * , : pure numbers (non-dimensional), due to being exponents * : , a balancing quantity, which is TFP. In this construction the units of ''A'' would not have a simple economic interpretation, and the concept of TFP appears to be a modeling artifact. Official statistics avoid measuring levels, instead constructing unitless growth rates of output and inputs and thus also for the residual.

References

Bibliography