Negative income tax is an alternative to UBI, but it's discussed less often. Does anyone know why? I feel it should be easier to implement (plugs right into the existing tax system), should be cheaper (the more you earn, the less you get), and feels more in line with the progressive tax system, whereas UBI feels like an extremely coarse first approximation.

Essentially, the tax curve starts at 0 and goes up. Why not shift it down? There's nothing special about 0.