Rich man, poor man...the math

Thanks to Daniel Gros, we can see, algebraically, why capital flows from poorer countries to richer;

For advanced economies (as defined by the IMF) the investment rate is at present approximately 20% of GDP (and is expected to remain at that level) and real trend growth about 2%. This implies a steady state capital-to-output ratio of around 2.5 if, following the literature, it is assumed that the depreciation rate is 6%; the steady state calculation is that 2.5= 0.2/(0.02+0.06).

For emerging economies (emerging and developed economies in the IMF classification) the investment rate is at present about 30% and the trend growth rate about 6% (average to 2018). This also leads to a steady state capital-to-output ratio of 2.5 since 2.5=0.30/(0.06+0.06).

....given today’s growth rate and investment rates the capital-to-GDP ratio should be lower in advance nations, so capital should continue to flow from emerging economies to developed ones. 

The returns should be higher in developed economies. But;

When [Robert] Lucas wrote his seminal paper in 1990 the investment rate in emerging economies was much lower than today and they were running consistent current-account deficits – i.e. their investment rates exceeded their savings rates.

At the time puzzle was why there was not more investment in the capital-poor countries. Today the investment rate is more than 10 percentage points of GDP higher in emerging economies than in advanced economies. If their savings rate had remained unchanged emerging countries would be running very large current-account deficits and would thus be importing a lot of capital. However, their savings rates have increased even more than their investment rates and the real puzzle has become: “Why do poor countries save so much?”

Possibly because their governments can't afford to put policies into place that discourage investment and encourage consumption?