This paper tests a geography and growth model using regional data for Europe, the US, and Japan. We set up a standard geography and growth model with a poverty trap and derive a log-linearized growth equation that corresponds directly to a threshold regression technique in econometrics. In particular, we test whether regions with high population density (centers) grow faster and have a permanently higher per capita income than regions with low population density (peripheries). We find geography driven divergence for US states and European regions after 1980. Population density is superior in explaining divergence compared to initial income which the most important official EU eligibility criterium for regional aid is built on. Divergence is stronger on smaller regional units (NUTS3) than on larger ones (NUTS2). Human capital and R&D are likely candidates for transmission channels of divergence processes.