The opportunity to present some of these ideas at the Druid Summer conference in Copenhagen in June, 2005 and at the Argentine Economic Association Annual conference in November, 2005 in Buenos Aires are gratefully acknowledged, as are comments from Esben Andersen, Thorbjern Knudsen, Omar Chisari, Dick Nelson and an anonymous referee. The stimulus provided by a reading of Baldwin and Gu (2005) is also acknowledged although we are entirely responsible for the interpretation provided here. A second draft of the ideas was developed at the University of Queensland in summer 2005. JSM is grateful to John Foster for the opportunity to work in this stimulating environment, and to Kurt Dopfer, Jason Potts and John Foster for extended discussion of the evolutionary background to the problem dissected here.
See the more recent discussion in Harberger (1998) on micro diversity and aggregate productivity growth, pointing to the very uneven cross sector incidence of productivity change in the US economy.
Empirically minded scholars such as Massell (1960) clearly understood this point but the pursuit of macro fundamentalism soon buried the implications. Interestingly, careful theorists such as Hicks (1932) who did so much to promote a production function approach, were at pains to point out that the ‘production’ elasticities did reflect the composition of output and thus the composition of demand.
If we take long enough periods of time it is perfectly sensible to think of the entry and exit of entire industries, electric light and gas mantles or mobile phones and telegrams for example.
It could equally be a population of plants within a single firm or set of firms.
On the different accounting methods see Bartelsman and Doms (2000) and Balk (2003).
Similar results are reported in Hazeldine (1985) and Foster et al. (2001).
A more recent study of productivity growth in Germany, pre and post unification, also finds good evidence for ‘between’ effects and notes that they vary considerably across different industries (Cantner and Kruger, 2004, 2005).
In his survey of industry dynamics processes in LDCs, Tybout (2000) discusses some limited empirical evidence in favour of relatively high rates of turnover in plants and employment, the finding that efficiency, compared to survivors, is lower in exiting plants and in entrant plants, and that these categories rarely account for more than 5% of total output in any year. Carlin et al., 2001 discuss productivity growth decompositions for the transition economies of Eastern Europe. This empirical literature provides striking empirical verification of the dynamic nature of competition and of the importance of distinguishing selection of activities in plants from selection of firms.
This is scarcely a comforting conclusion, given our ‘ignorance’ about the determinants of plant and firm level productivity performance. Harberger (1998) captures the essence of the point with his reference to “real cost reductions stemming from 1001 different causes” (p. 5).
ci(t) is the share of each continuing firm in the total output of such firms at date t. Similarly, di(t) is the share of each exiting firm in the total output of those firms at t. We are following the convention of indexing the period by the date at the end of the period.
ni(t) is the share of entrants in the output of all entrants at t + Δt and ci(t + Δt) is the corresponding output share of the continuing firms at this date.
(1) is written in special forms in many different ways in the literature. Baldwin and Gu (2005) for example assume, because the Canadian evidence supports this view, that ‘n’ = ’d’, the displacement hypothesis. Then the only empirical issue is whether entrants on average have higher productivity than exits, which they do.
This formula makes use of the fact that (1 + gc)Δci = ci(gi – gc). The symbol ‘g’ refers to the growth rate of output between the dates defining the interval.
In principle, the between effects can also arise in multi plant firms when new plants are built or existing ones closed or the relative contribution of different plants to total firm output is changed. The firm turns out to be a slippery concept in productivity accounting and we shall short circuit this by assuming our firms are single plant, single process, and single product entities.
We use a caret over a variable to indicate proportional rates of change and a dot to indicate time differentiation. Continuous time differentials allow the suppression of interaction effects.
Carlin et al. (2001) point out that the 90th decile of the UK manufacturing productivity ranking is almost five times more productive in labour productivity terms than the 10th decile.
In calculating the latter we have two alternatives: the first is to calculate the shares in nominal terms, the second is to infer the shares in terms of real output by using (4) and data on real productivity in each sector derived by deflating nominal shipments (output) by the sectoral price deflators. It turns out that nominal and real output shares covary very closely apart from the last two years when large changes in the deflators for the electronic computers (SIC 3571) and the semi conductor (SIC 3674) sub-sectors cause the two measures to diverge very sharply. Our doubts about the validity of their deflators lead us to exclude these two sectors in the following calculations. The correlation coefficient between real and nominal output shares for all 459 industries over the whole period is 0.954. Excluding the two sectors it is 0.970.
See Mazzucato (2000) for discussion of these measures.
Over the sample period the average of the output instability index is 6.26 and of the employment index 5.12.
To avoid undue complication we also set entry and exit rates at zero, the generalisation does not change the substance of the argument.