The start of Yugoslavia's disintegration: Where borders cut commuting spheres

Enrico Bombieri proved that the ABC Conjecture implies Roth's theorem in 1994. This paper concerns the other direction. In making use of Bombieri's and Van der Poorten's explicit formula for the coefficients of the regular continued fractions of algebraic numbers, we prove that Roth's theorem implies a weakened non-effective version of the ABC Conjecture in certain cases relating to roots. Borders are often associated with low economic activity. A popular explanation for this phenomenon argues that borders cut market access. But as a growing amount of literature demonstrates that border effects persist after the removal of formal barriers, the forces behind low economic activity near borders remain unclear. This paper develops a new methodology to measure the market access of 16,596 settlements in the Socialist Federal Republic of Yugoslavia in 1965, right before the hardening of Yugoslavia's federal borders. Based on elevation, rivers, roads and the Dijkstra algorithm, this methodology identifies 4,682 settlements whose commuting spheres crossed Yugoslavia's federal borders. Using panel data for the 1948-1991 period, a difference-in-differences estimation identifies that the settlements that lost access to their nearest town due to hardened federal borders experienced strong decline in population growth following the reforms. Robustness checks demonstrate that depopulation occurred when settlements lost access to towns of significant size. This effect appears regardless of ethnicity and history. Instead, depopulation occurred in the absence of a nearby alternative town in the same federal unit.