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I think it’s well established in economic circles that unemployment goes up as inflation falls. We are seeing signs of this in the UK at the moment.

Letting it run away causes its own problems though. Take a look at South America to see what happens if you can’t manage inflation.

Inflation and unemployment are seen as results of demand. They're both regarded as effects. One isn't the cause of the other.

At least in most economic theory... Which is possibly not the best theory to put much weight in, considering how changeable and unproven it is.

No but they are inversely correlated. As you bring inflation down you expect unemployment to rise.