Measuring and relating aggregate and subaggregate total factor productivity change without neoclassical assumptions

Abstract

This article considers the relation between total factor productivity measures for individual production units and those for aggregates such as industries, sectors or economies. This topic has been treated in a number of influential publications, such as Hulten (1978), Gollop (1979) and Jorgenson et al. (1987). What distinguishes this article from other publications in this area is that I deliberately avoid the making of all kinds of (neoclassical) structural and behavioural assumptions, such as the existence of production frontiers with certain properties, or optimizing behaviour of the production units. In addition, I also treat dynamic ensembles of production units, characterized by entry and exit. Thus, a greater level of generality is achieved from which the earlier results follow as special cases.

Various Approaches to the Aggregation of Economic Productivity Indices

“…The top‐down approach, pursued by Balk () with respect to empirical productivity indices, is guided by the principle that aggregate productivity should be interpreted as (or, be equal to) productivity of the aggregate. Thus, let us treat as a (super) production unit .…”

“…The relation between aggregate and individual measures of productivity change can be studied from two viewpoints, characterized by the names ‘bottom‐up’ and ‘top‐down’, and reviewed, respectively by Balk () and (). These two articles are confined to so‐called statistical indices.…”

Dissecting aggregate output and labour productivity change

“…When change is measured as ratio the following symmetric decomposition can be used (see Balk 2003 and2009):…”

“…For the derivation of expression (26) the reader is referred to the Appendix. 3 The exponent ξ k R can be interpreted as the (normalized) mean share of nominal revenue of production unit k in aggregate nominal value added; or, again as a Domar weight. Similarly, the exponent ξ k EM S can be interpreted as the (normalized) mean share of nominal intermediate inputs cost of unit k in aggregate nominal value added.…”

“…As a starting point we consider the method of Dufour, Tang and Wang (2006) (DTW) for computing industry contributions to aggregate output and labour productivity change. In this paper I first reconstruct their method by using the notational framework of Balk (2009), (2010a), (2010b). This reconstruction reveals a number of things.…”