Source is Mazzucato’s The Value of Everything. Actually, I recommend it, to everyone but to you, Matt, in particular. And of course it is an arbitrary agreement, when you think about it. Humans (who are different) need to agree on what is important, what has value. The book has a historical section: the physiocrats in 17th century France believed that only agriculture was “production”; an ironsmith would be an unproductive worker, a kind of service provider, whose living was underwritten by the farming class. In this sense, the ironsmith would be as useless to society as a duke’s valet (or the duke himself). Smith disagreed, and pointed out that manufacture is also productive, but disdained services, and so on.
So, the agreement on what has value and what does not has been evolving – which makes sense to me. It’s politics, and ethics, not science. It is also fitting that it should be encoded in a U.N. standard, since that makes the nature of GDP as a convention more transparent.
That said, a hardline marginalist economist would tell you that there is an element of science encoded in the current concept of GDP. This: under certain (highly restrictive) conditions, individuals are led by their preferences to transact on the market until they achieve their optimal mix of goods/services/leisure. In the process, prices form to carry information about the marginal social value of all goods and services. This is proven as the first fundamental theorem of welfare economics. It means that each transaction increases someone’s well-being. GDP, at its heart, is the sum of all transactions, net of double counting (intermediate goods are incorporated into final goods rather than counted, like in VAT calculation).
Other economists (including non-hardline marginalists like Stiglitz) are aware that, even if the math checks out, the first theorem requires certain conditions to hold, and these are not met in reality. So, the theorem itself is irrelevant to real life.