The global productivity frontier and dark matter

Alex Tabarrok cites a study that says productivity may not be growing overall, but is growing for firms on the "global productivity frontier". It does seem a bit strange to select a subset consisting of the most productive firms and then saying these firms have high productivity growth. While not exactly contradictory (it's a finding that high productivity "stock" has high productivity "flow"), it does seem like they should go a bit farther in figuring out if this partitioning of the data makes sense.

In any case, the result isn't particularly shocking if we go back to the dark matter problem. Selecting the most productive firms is very much like the selection process going into selecting firms for a stock index. You end up over-representing the firms with large information transfer index values.