DLW (2012) became the de facto method to "compute" market power.
This lecture (https://www.nuffield.ox.ac.uk/media/3209/mktpower.pdf) by Steve Bond (future Nobel Prize winner) just destroys the method. I quote:
"In the benchmark case of Cobb Douglas technology and constant elasticity
demand, there is no information about the price-cost markup in the ratio of
an estimated revenue elasticity to the corresponding cost share for a perfectly
flexible input"
"More generally, we should be cautious in inferring anything about markups
or market power from the ratio of an estimated revenue elasticity to the
corresponding cost share"