The greatest inequality of wealth holdings is among the elderly and the primary reason for that inequality is the different saving rates of people when they are young. Here is Noah Smith:
If you do the math, you discover that in the long run, income levels and initial wealth…are not the main determinants of wealth. They are dwarfed by…savings rates and rates of return. The most potent way to get more wealth to the poor and middle-class is to get these people to save more of their income, and to invest in assets with higher average rates of return.
Pointer from Arnold Kling.