Kind of: as price level falls *relative to the national average*, UBI would fall, but of course I also used caps and floors so UBI can’t get *too* small/large this way. And as unemployment rises *relative to the national average*, UBI would fall, but, again, caps and floors.
So generally speaking, a recession wouldn’t lower UBI. It would lower it in the areas hardest-hit by a recession (after a few years lag), but raise it in less-hard-hit areas. The idea being to encourage people to move. If people do in fact move at high rates, then we’d expect unemployment and/or prices to converge a bit more than they presently do, and UBI would end up evening out a bit.