Regarding the global power structure, what matters is probably not overall global levels of convergence, but rather whether some large countries (e.g. China) converge with the US.
Regarding that question, it probably doesn’t matter that much if a country is very poor or somewhat poor—since only relatively rich countries can compete militarily and politically anyway.
But from the perspective of global poverty and welfare, it obviously matters a lot whether a very poor country manages to reduce their level of poverty.
Some parts of the world aren’t closing in much on the US.
Regarding the global power structure, what matters is probably not overall global levels of convergence, but rather whether some large countries (e.g. China) converge with the US.
Regarding that question, it probably doesn’t matter that much if a country is very poor or somewhat poor—since only relatively rich countries can compete militarily and politically anyway.
But from the perspective of global poverty and welfare, it obviously matters a lot whether a very poor country manages to reduce their level of poverty.