Regions of the United States represent a set of economies where the co
nditions often argued as underlying convergence in per-capita income a
re satisfied, Stochastic convergence among regions implies the rejecti
ons of a unit root in relative per-capita income, a hypothesis which i
s not supported by conventional tests. Carlino and Mills (1993) allow
for an exogenous trend break, but can only reject the unit root hypoth
esis in three of the eight U.S. regions. We incorporate endogenously d
etermined break points and significantly strengthen their results, bei
ng able to reject the unit root hypothesis in seven regions.