The argument that poor countries will tend to catch up with rich ones is based on the idea that another unit of capital will increase output more in a country that has little capital than one that has much capital. So$,$ for a given share of GDP devoted to investment, a poor country will grow faster than a rich one. This argument assumes that other things are the same, but a share of GDP invested may be lower in a poor country, and the productivity of investment may be less. A politically unstable environment where property rights are unprotected or not secure tends to discourage investment.