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to be clear: 1) are you just talking about QE on treasuries, or also buying other assets? 2) does it have impact on interest rates, even if not *directly* on monetary supply? (If so, this would likely lead to an effectively larger monetary supply b/c of increased lending.)
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1) buying other assets is also an asset swap not just injecting new money in a quantitative sense. you're taking asset risk out of the economy but not necessarily changing overall quantities by much 2) you can have low interest rates and lending contraction and high rates and
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lending expansion. there isn't a mechanical link b/w rates and quantity of credit/investment expended and its certainly not what most people are talking about when they talk about QE increasing the money supply that's about M0 increasing which ignores the asset-swap aspect
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1) its important but not in the "printing money" or "increasing the money supply" sense. It's adjusting the qualitative composition/risk profile of assets in the economy. It may increase asset prices or simply prevent them from falling but its not "money supply=inflation"
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ie you could simply enact a govt guarantee on those instruments, like we do with bank deposits which expand/contract endogenously with private demand and are also part of any 'money supply' reasonably understood), even without the asset swap part and it would have similar effect
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