A central bank aiming for a stable average inflation rate, rather than focusing on short-term inflation, can benefit the economy when interest rates are stuck at a lower limit. This approach helps by adjusting future inflation based on current shortfalls and by increasing inflation when hitting the lower bound risk. For best results, a long averaging window is ideal, similar to price level targeting. Even with shorter windows, significant welfare improvements can still be achieved. If people's cognitive limitations are strong, a shorter averaging window may be more effective, but the overall welfare gain might be smaller.