As far as I can tell, research on the economics of poverty is very empirically driven, and this is probably appropriate. What kind of economic theory has been developed though? I'd also be interested in theory of some influence too. To avoid wholly opinion-based answers, let's measure influence by how the theory directed other research or anti-poverty measures. As an example, I know papers have been written on the theory of poverty traps, but I'm not sure that concept is a contribution from theorists so much as some theorists developed a model for what might have already been an empirical observation. Are there any cases where concepts started in theory?
Links to papers are good, but the question is also about history to some extent, so it would be nice if you can show a trail of this paper influenced that paper or this policy.