Second, there may be (read: there is) an association between price and unemployment. When unemployment rises or falls significantly, local prices tend to respond inversely. Ergo, one reason the price graph is messy is because price is associated with our other UBI determinant, unemployment.
Should a Universal Basic Income Be Adjusted for Local Prices?
Lyman Stone

If I understand your methodology correctly, then as unemployment goes up, nominal UBI goes down. And as price level goes down (correlated with a decrease in unemployment), then nominal UBI goes down. So in the correlated situations (unemployment up and price level down), UBI goes in the same direction, not different directions. This should make the plot less noisy, correct?

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