Monopoly power does not seem to be up at the actual market level

Using U.S. NETS data, we present evidence that the positive trend observed in national product-market concentration between 1990 and 2014 becomes a negative trend when we focus on measures of local concentration. We document diverging trends for several geographic definitions of local markets. SIC 8 industries with diverging trends are pervasive across sectors. In these industries, top firms have contributed to the amplification of both trends. When a top firm opens a plant, local concentration declines and remains lower for at least 7 years. Our findings, therefore, reconcile the increasing national role of large firms with falling local concentration, and a likely more competitive local environment.

That is from a new NBER working paper by Esteban Rossi-Hansberg, Pierre-Daniel Sarte, and Nicholas Trachter.