Average Inflation Targeting: How far to look into the past and the future?

We analyze the optimal window length in the average inflation targeting rule within a Behavioral THANK model. The central bank faces an occasionally binding effective lower bound (ELB) or persistent supply shocks, and can also use quantitative easing. We show that the optimal averaging period is infinity for a moderate myopia. Finite yet long-lasting windows dominate for stronger cognitive discounting; i.e., the makeup property is shown to be qualitatively resistant to deviation from rational expectations. We point out that the optimal window depends on the speed of return to the target path when myopia plays a bigger role. We quantify the welfare effect of uncertainty due to the ELB (downward inflation bias) and show how it varies across window lengths and cognitive discounting degrees.