Probably the best natural experiment is to look at what happened on the introduction of Social Security in the US and the analogous programs in other countries.

We should also realize that we can't just give net $xx,000 each to the entire population. The proposals usually fund BI with taxes on the higher earners. Spending should increase (as we move money from savers to spenders), but most (or much) of the population will be either near-neutral or pay extra taxes more than BI.