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Is it reasonable to expect that the US govt's financing of the growing budget deficit and US debt by issuing long term treasury bonds will push long term interest rates higher in the future? Shouldn't that potentially lead to easing or elimination of the current yield curve inversion?

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Inversion hasn't been a permanent phenomenon anyway so it likely won't persist regardless of whether your hypothesis was the reason it ended.

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If it ends people can debate about the cause. If short term yields decrease and the economy avoids a recession, inversion may end for reasons other than a high volume of bond issuance. This is a good economics question but hard to answer because financial markets exist for the assets involved. People know about the possibility of more bond issuance and they could have already shorted long bonds (raise the associated rate) and bought the shorter maturity bond, and yet we have inversions from time to time. There is the matter of the time when longer yields increase. Coupon interest must be paid when a bond has been shorted so this limits willingness to do so. If deflation, recessions, non-recession low growth, and risk aversion are the forces prevailaing then long bond yields can be low even while there is a high volume of bond issuance.

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