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 infinitely long given a conventional degree of myopia. Finite yet long-lasting windows dominate for higher 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 may depend on the speed of return to the target path. We solve the model both locally and globally to disentangle the effects of uncertainty due to the ELB. The welfare loss difference between solution techniques is considerably decreasing in the degree of history dependence.