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>earned income = income of those who participate directly in production.
“Of those” implies a defined class or category of economic actors. I’d define it differently, just categorizing (household/personal) income.
Income received in recompense for human effort.
This is the kind of categorization and labeling that accountants do constantly, in innumerable realms and situations. In practice the huge bulk of personal/HH income (even including what I call comprehensive [Haig-Simons] income) is straightforwardly measured and categorized by that criterion.
There’s 1. earned labor compensation, and 2. all the rest (unearned), which we can categorize as A. (net) gov transfer income, or B. property income received in recompense for owning stuff. Most of this is easily assembled from the national accounts.
There are remaining judgment calls, for sure, comprising maybe 15% (?) of HH income. But again, even with fairly extreme accounting choices there, the labor/transfer/ownership split only shifts by a few percentage points.
We can certainly interrogate the concepts, methods, and measures used in the national accounts. But I don’t think we can reasonably say that earned/unearned income are unmeasurable.