There's no evidence that spending or investment decisions by the rich hurt US output.
Sometimes, the flip side of a fallacy is also a fallacy. For example, import tariffs are often defended with the argument that the producers (or "jobs") are more important than consumers. Other times however, trade is restricted in the form of exports ban (like Russia's recent ban on exports of wheat) on the view that consumers are more important than producers.
Just because the "producers are more important than consumers" argument is false doesn't mean that the "consumers are more important than producers" view is correct. Both "producers" and consumers are equally important as all producers are consumers and as all consumers are either producers or dependent on producers.
Now we see the flip side of the mercantilist "trade deficits are necessarily bad" view in the form of the argument that "capital outflows are necessarily bad" (Note the emphasis on "necessarily". Just as trade deficits can be symptoms of bad policies, so can capital outflows. The below reasoning assumes that it reflects voluntary preferences as Reich's argument is based on that).
In an op-ed at the New York Times, Robert Reich argues for income redistribution on the basis of how it will stop supposedly harmful capital outflows:
"The rich spend a much smaller proportion of their incomes than the rest of us. So when they get a disproportionate share of total income, the economy is robbed of the demand it needs to keep growing and creating jobs.
What’s more, the rich don’t necessarily invest their earnings and savings in the American economy; they send them anywhere around the globe where they’ll summon the highest returns — sometimes that’s here, but often it’s the Cayman Islands, China or elsewhere."
The first statement about the "thrifty rich" has been proven false. There is no evidence (at least, I haven't seen any evidence) for the second claim that they invest their savings abroad to a higher extent than others, but it really wouldn't matter even if it was true.
The reason for that is that capital outflows equal a trade surplus (or a reduction in the trade deficit in the case of America) given the balance of payments accounting identity. From that it follows that capital outflow from American will either be cancelled out by capital inflows from foreigners, in which case it won't make any difference in terms of availability of capital for entrepreneurs, or it will result in a reduction of the trade deficit, something which will cancel out the reduction in domestic demand caused by their savings. Either way, this capital outflow will not result in reduced output.
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