I see a problem with Krugman's argument that savings is global. Since the 1980's those outside the US have been doing our saving for us, for their security and marketing reasons. Although savings appears low for US citizens, in the global economy as a whole, there is a savings glut, so no surprise that a global depression results.
A second problem is that rich people in the USA may choose to buy assets such as mansions and yachts, and also corporate stocks, another form of asset therefore not savings, which form a large portion of the wealth of wealthy in the USA. Corporations are themselves international and may have assets and valuable networks in other countries, with their savings, if any, serving more as a defensive buffer.
Dean Baker has emphasized the "wealth effect" that sustained consumer spending even in the presence of falling relative wages and savings. This argument is seconded by Matais Vernengo at TripleCrisis.
Inequality is different. If you look at the world as a whole, the average may show decreasing inequality (often not considering local alternatives) and from an invalid averaging effect and tendency to discount or ignore non-monetary losses. Within each nation or region there is a small group 1% to 0.01% that becomes super wealthy from trading derivatives of capital and labor across countries, but meanwhile their locals may become temporarily richer but ultimately poorer in health, freedom, and access to natural resources such as water and clean air under the crushing weight of the invisible foot of capitalism, ever more unmitigated by the race to the bottom created by free capital mobility and lack of world standards.