The Many Decompositions of Total Factor Productivity Change

Abstract

Total factor productivity change, here defined as output quantity change divided by input quantity change, is the combined result of (technical) efficiency change, technological change, a scale effect, and input and output mix effects. Sometimes allocative efficiency change is supposed to also play a role. Given a certain functional form for the productivity index, the problem is how to decompose such an index into factors corresponding to these five or six components. A basic insight offered in the present paper is that meaningful decompositions of productivity indices can only be obtained for indices which are transitive in the main variables. Using a unified approach, we obtain decompositions for Malmquist, Moorsteen-Bjurek, price-weighted, and share-weighted productivity indices. A unique feature of this paper is that all the decompositions are applied to the same dataset of a real-life panel of decision-making units so that the extent of the differences between the various decompositions can be judged.

Total factor productivity and the factors of green industry in Shanxi Province, China

“…Some new methods have also been introduced in measuring TFP. Balk and Zofio (2018) proposed a multi-direction decomposition idea for TFP. Sato, Tanaka, and Managi (2018) proposed a new method to measure TFP based on both human and natural capital, the results of which demonstrated that consumption had no significant impact on TFP.…”

The Decompositions of Cost Variation

“…A similar decomposition was employed by Brea-Solís et al (2015). 4 Their technical efficiency effect was the same as above, but the remainder…”

“…Grifell-Tatjé and Lovell (2000) called the inner product of expression (4) and 1 2 (w 0 + w 1 ) the technological change effect, and the inner product of expression (5) and 1 2 (w 0 + w 1 ) the activity effect. However, it is immediately clear from the functional structure that expression (4) in fact combines the effect of technological change (as represented by the difference between the cost-minimizing input quantity vectors under the two technologies, x 1 (w, y) and x 0 (w, y)) and the effect of differing input price structures between the periods 0 and 1. 3 Moreover, the combined effect is asymmetric in the sense that it conditions only on the period 0 output quantity vector y 0 .…”

“…A complete discussion of the statistical sources, variable specifications, and summary statistics can be found in Juo et al (2015). 12 The same data set has been used to illustrate the decompositions of total factor productivity change using quantities-only and price-based indices by Balk and Zofío (2018). Regarding the technology and interrelations between inputs and outputs, the variables reflect the intermediation approach suggested by Sealey and Lindley (1977), whereby financial institutions, through labour and capital, collect deposits from savers to produce loans and other earning assets for borrowers.…”

“…To overcome the combination, Grifell-Tatjé and Lovell (2015, 289) decomposed expression(4) as (x 1 (w 1 , y 0 ) − x 1 (w 0 , y 0 )) + (x 1 (w 0 , y 0 ) − x 0 (w 0 , y 0 )), measuring the input substitution effect and the technological change effect, respectively 4. These authors actually considered profit variation (p1 • y 1 − w 1 • x 1 ) − (p 0 • y 0 − w 0 • x 0 ), where p t (t = 0, 1) are output prices.…”