Probably depends on how you're reducing poverty...and how long-term your "long-term" is. Something like removing trade restrictions is likely to have very different long-term effects than distributing bednets. Even then I really don't have good answers for you on the nature of these differences.

You might want to check out the persistence studies literature. For example work by Nathan Nunn, who Will MacAskill references in this talk. This may not precisely align to what you're asking for, but Nunn has studies finding for example that:

• Countries that adopted the plough have lower female labour force participation today
• Greater raiding for slaves in Africa led to lower social trust and GDP per capita today
• Medieval trading in Indian towns led to lower levels of Hindu-Muslim conflict today

Persistence studies seems a very interesting field and one I want to delve into more.

• Addressing Global Poverty as a Strategy to Improve the Long-Term Future (havent read yet)
• Flow-through effects (have read)

You may be interested in Superabundance by Marian Tupy and Gale Pooley. I haven't actually finished it, myself, but from what I've read so far they seem to argue that a greater population (which is a likely effect of poverty reduction) will, counterintuitively, increase wealth and prosperity since we'll have more workers, scientists, and inventors. I should mention, though, that it's published by a politically-conservative American think tank, so it may be somewhat biased in favor of limited government and against birth control.

"The graphs that show so much recent progress in the developing world—on poverty, on hunger, on education and infant mortality and life expectancy and gender relations and more—are, practically speaking, the same graphs that trace the dramatic rise in global carbon emissions that has brought the planet to the brink of overall catastrophe." -- The Uninhabitable Earth by David Wallace-Wells