A more flexible decomposition of productivity growth

Abstract

Conventional productivity growth decompositions, such as those of Baily, Bartelsman and Haltiwanger (2001) and Grilliches and Regev (1995), first aggregate each firm's productivity level into an aggregate productivity index, and then allocate aggregate growth back to the firms forming the aggregate. It is shown that this can produce misleading results, and two more flexible decompositions are proposed that are consistent with the superlative Törnqvist productivity growth index.

Acknowledgements

The author would like to thank Les Oxley, Bert Balk, and Kevin Fox for useful comments.

Notes

¹ See, for example: Bailey et al . (1992); Grilliches and Regev (1995); Bernard and Jones (1996), with a decomposition to industry level; Foster et al . (2001); and Bailey et al . (2001). Balk (2001) and Balk and Hoogenboom-Spijker (2003) discuss a range of conventional productivity decompositions.

² It is usually the case that the researcher uses output shares as weights when analysing total factor productivity (Haltiwanger, 1997), and labour shares when analysing labour productivity (Grilliches and Regev, 1995; Baily et al ., 2001).

³ Equations 9 and 10 are arithmetic averages of two equations following Bennet (1920): one equation uses period 0 levels and shares to weight the changes, and the other uses period 1 levels and shares to weight the changes (see Balk, 2001 for a discussion in the context of productivity change). Diewert (1998) shows that the Bennet (1920) indicator approximates any superlative index (such as Fisher, 1922 or Törnqvist, 1936), under certain conditions.

⁴ These two effects have been isolated in (at least) two different ways in the productivity growth decomposition literature: the first produces a cross-term (as in Haltiwanger, 1997), and the second averages over the initial and the end periods (as in (9) and (10)).

⁵ The resulting index confounds productivity changes with share changes and thus does not satisfy the monotonicity test from index number theory (Diewert, 1992): monotonicity requires that increases in quantities between two periods yields an increase in the index aggregating those quantities.

⁶ Törnqvist indexes are the convention in productivity measurement (see, for example, OECD (2001))

⁷ The effect from the entry and exit of firms can also be viewed as a change in industry shares. To be devoid of the effects of all share changes the last term in (15) must be removed, producing a standard Törnqvist productivity growth index.