If this “first sector” includes the fish workers, the agricultural labor productivity measures are not correct in the regions with sea access.
The authors could enrich the results’ part with reference to the concepts of convergence of Barro and Sala-i-Martin, beta and sigma convergence. The authors wrote about these concepts, for example pg. 6 lines 22-23 and pg. 9 lines 5-6, but they can point out the non existence in the case of Chinese prefectural level.