If the WEF's notion of competitiveness has similar relevance to growth, then we should be able to use it to divide countries into convergence clubs. In each convergence club, per capita income should be negatively correlated with economic growth.
To check this, I compared the WEF's 2011-12 competitiveness scores for 139 countries and regions to the International Monetary Fund's 2011 estimates of economic growth (adjusted for changes in prices) and per capita income (adjusted for differences in purchasing power). The IMF doesn't keep figures for Puerto Rico, so I dropped it.
Going down the rankings in order, there were 35 groups of 10 countries that differed by at most 0.1 points on the WEF's overall metric for competitiveness, which ranged from 2.87 for Chad to 5.74 for Switzerland. Among these groups of 10, some of which overlapped, the average correlation between growth and per capita income was -0.46. That was a pretty good sign for convergence, considering that the correlation among all the countries in the sample was just -0.13.
For a more refined selection of convergence clubs, I looked at the WEF's three main subindexes: basic requirements, efficiency enhancers, and innovation and sophistication factors. This time I chose groups where no country differed from another by more than 0.5 points in any of the subindexes. I managed to find three groups of eight countries. In each group, the countries were also within 0.16 points of each other in the overall metric.
In the group containing Armenia, Egypt, El Salvador, Georgia, Greece, Lebanon, Moldova, and Serbia, the correlation between growth and per capita incomes was -0.92. This was driven to a great degree by Greece's extraordinary downturn; even if Greece had grown by a couple of percentage points, though, the correlation still would have been about -0.55. In a group of wealthier countries -- Australia, Austria, Belgium France, Malaysia, Norway, Qatar, and Saudi Arabia -- the correlation was strongly positive at 0.58, a sign of divergence rather than convergence. The poorer group of East Timor, Ivory Coast, Lesotho, Madagascar, Mali, Mozambique, Swaziland, and Zimbabwe showed a correlation of 0.22, positive and divergent again.
Taken as a whole, this rudimentary evidence neither supports nor negates a central role for the WEF's concept of competitiveness in convergence. The fact that convergence is not present at a more granular level suggests that the results for the overall metric may be partly due to chance. To be sure, the metric is highly correlated with living standards, and economists have indeed found causal relationships between some of its components and living standards. Yet the metric itself seems to have a connection that is, well, nebulous. That may be exactly what the WEF intended, but it may also give pause to those leaders who would use the report as a reference.