In the Basic New Keynesian model, when there is a liquidity trap, if the central bank promises higher inflation in the future, then

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In a liquidity trap, traditional monetary policy tools become ineffective because nominal interest rates are at or near zero, limiting the central bank's ability to stimulate the economy through rate cuts. By promising higher inflation in the future, the central bank can effectively lower real interest rates (since real interest rate = nominal interest rate - inflation expectation), encouraging spending and investment. This leads to an increase in both output and inflation, as future expectations of inflation stimulate demand in the economy.

In the Basic New Keynesian Model, When There Is a Liquidity