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I study the dynamic consequences of average inflation targeting in a tractable monetary model with sticky prices. I demonstrate that in the case in which the central bank attaches a relatively high weight on the distant past, average inflation targeting not only ensures local determinacy of equilibrium but is also capable of eradicating the liquidity trap problem—differently from standard Taylor rules. Specifically, I show the existence of a saddle connection from the deflationary steady state to the target steady state, along which reflation occurs in equilibrium due to limited and gradual increases in expected nominal interest rates.