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As we all know the US has a big debt and increasing deficits. The head of FED J. Powell commented that the US was on an unsustainable path w.r.t some debt to GDP ratio. A few commentators I listen to argue that if the US increases it GDP, then they can "grow out of" this problem that Powell mentioned.

Could someone explain this logic to me?

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If they invest in productivity-enhancing stuff, GDP could grow at a faster pace than the [increase in] debt. Then the debt to GDP would decrease.

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