4. σ-CONVERGENCE
This section deals with the notion of convergence in terms of levels. Do cross-country
differences in energy- and labour-productivity levels decrease over time? Are patterns of
energy-productivity convergence similar to those of labour-productivity convergence? And to
what extent do the results depend on the level of aggregation? To answer these questions we
calculated for each sector the unweighted cross-country standard deviation ( σ) of the log of
energy- and labour productivity, among the 14 OECD countries (insofar as data are
available).9 Figure 1 presents the degree of variation in ‘macroeconomic’ energy- and labour-
productivity levels, being the sum of aggregate Manufacturing, Transport, Services and
Agriculture.10 The figure shows that cross-country differences in energy-productivity levels
are substantially larger than cross-country differences of labour-productivity levels.
Moreover, it can be seen that over time the standard deviation of the log of energy-
productivity performance is increasing, indicating σ-divergence, while the opposite is true for
cross-country labour-productivity performance, displaying a pattern of σ-convergence.
( Figure 1, Page 23)
As we noted in the introduction, a convergence analysis at aggregate levels may mask
considerable variation in sectoral productivity developments (cf. Bernard and Jones, 1996a,b,
Dollar and Wolff 1988, 1993). Therefore, we continue by examining the development of
cross-country productivity differentials within different sectors.
In Figures 2a and 2b we present the standard deviation of the log of, respectively,
energy- and labour productivity for aggregate Manufacturing, Transport, Services and
11
Agriculture.
9 In the literature on convergence analysis, two measures for σ-convergence are used interchangeably: (1) the
standard deviation of the log of per capita income or productivity (y) and (2) the coefficient of variation which
equals the standard deviation of per capita income or productivity divided by the sample average. Dalgaard and
Vastrup (2001) show that these measures lead to different conclusions when applied to the Penn World Table
caused by the fact that the measures assign different weights to individual countries’ performance. We have
therefore used both measures in our convergence analysis, finding both measures to yield an identical pattern of
convergence, although with small differences in the size of cross-country variance. Details are available upon
request. Here, we only present the result of the SD log-measure (1).
10 Due to limited data availability the calculation of cross-country dispersion, as shown in Figure 1, excludes
Canada, Japan, the Netherlands and Sweden.
11 Due to limited data availability, the following countries are not included in the calculation of cross-country
dispersion, shown in Figure 3. Manufacturing: Japan, the Netherlands; Agriculture: Japan, the Netherlands;
Services: the Netherlands, Sweden; Transport: Canada, the Netherlands.