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The Top-Down Approach 2: Aggregate Total Factor Productivity Index

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Productivity

Part of the book series: Contributions to Economics ((CE))

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Abstract

This chapter considers the relation between total factor productivity (TFP) measures for individual production units and for aggregates such as industries, sectors, or economies. Though this topic has been treated in a number of influential publications in the literature, this chapter’s distinctive feature is that all kinds of (neo-classical) structural and behavioural assumptions are avoided, such as assumptions about the existence of production frontiers with certain properties, or optimizing behaviour of the production units. In addition, the chapter treats dynamic ensembles of production units, characterized by entry and exit. Thus, a greater level of generality is achieved from which the well-known results follow as special cases.

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Notes

  1. 1.

    Recall that the logarithmic mean, for any two strictly positive real numbers a and b, is defined by \(\mathit {LM}(a,b) \equiv (a - b)/\ln (a/b)\) if a ≠ b and LM(a, a) ≡ a.

  2. 2.

    Actually the arguments of the functions P(.) and Q(.) are all the prices and quantities of the commodities involved in the scope of these indices. Thus we are using the shorthand notation introduced earlier.

  3. 3.

    Recall that for index numbers in the neighbourhood of 1 their logarithms approximate percentage changes.

  4. 4.

    See also Tang and Wang (2015) on the importance of the contribution of differential price change to aggregate productivity change.

  5. 5.

    The definition of ‘active’ should of course be made precise in any empirical application on microdata to ascertain that exit of a certain production unit is due to quitting business and not due to e.g. obtaining a new name, merging with an other unit, splitting into two or more units, or falling below the observation threshold; likewise for entry.

  6. 6.

    A typical quote from Jorgenson (2018, 881) reads “A distinctive feature of Domar weights is that they sum to more than one, reflecting the fact that an increase in the growth of the industry’s productivity has two effects: the first is a direct effect on the industry’s output and the second an indirect effect via the output delivered to other industries as intermediate inputs.”

  7. 7.

    See Zheng (2005) for a reproduction of this derivation.

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Authors and Affiliations

  1. Erasmus University, Rotterdam School of Management, Rotterdam, The Netherlands

    Bert M. Balk

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  1. Bert M. Balk
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Balk, B.M. (2021). The Top-Down Approach 2: Aggregate Total Factor Productivity Index. In: Productivity. Contributions to Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-75448-8_7

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