What is "personal savings"?

No, personal saving is not the difference between income and spending plus investments. Personal saving is the difference between disposable income and outlays. Income is not a synonym for disposable income. Spending is not a synonym for outlays, unless you choose to define spending in precisely the same manner as personal outlay is defined. You’re trying to substitute common words, or the common, everyday definitions of words, for words that are being used in a specific economic context with their specific economic definitions.

Spending personal cash to purchase a stock is an expediture, yes. You lose personal cash and gain personal ownership of the shares of stock. Spending personal cash to purchase a stock is not an outlay, because the BEA chooses to define outlay in a specific manner. You cannot equate “spending” with “outlay”. The word “spending” appears only once in this month’s Personal Incomes and Outlays News Release, and it is used as synonym for Personal Consumption Expenditures, not Outlays.

Personal Income, Personal Outlays, and Personal Saving are metrics used to measure activity by individuals, and are not applied to businesses by definition. As the BEA mentions in its definition, persons, business proprietors, and business partnerships are all lumped into the category of individuals for BEA purposes. No, this does not conform to the common, everyday, definition of the word “individual”. The BEA is specifically choosing to define the word “individual” in a certain manner for its purposes.

So again, when the BEA is reporting a Personal Saving Rate in its monthly report, it is:

  1. Estimating Personal Income for individuals over the past month
  2. Estimating Personal Taxes paid by individuals over the past month, and subtracting that from Personal Income to determine Personal Disposable Income
  3. Estimating Personal Outlays (not all Personal Expenditures, Personal Outlays only!) by individuals over the past month, and subtracting Outlays from Personal Disposable Income to determine Personal Saving.
  4. Dividing Personal Saving by Personal Disposable Income to determine the Personal Saving Rate.

Yes, defining “personal savings” in common, everyday-language fashion is not that complicated. But it seems to me the OP is not asking about the common, everyday definition of personal saving; he is asking about the BEA-specific definition of personal saving, which is a different beast.