The analysis of this paper demonstrates that when the Phillips curve has forward-looking components, a goal for average inflation - i.e. targeting a j-period average of one-period inflation rates - will cause inflation expectations to change in a way that improves the short-run trade-off faced by the monetary policymaker. Average inflation targeting is thus an example of a 'modified' loss function, which when implemented ina discretionary fashion results in more efficient outcomes from the standpoint of the true social objective (inflation targeting under commitment), than the discretionary pursuit of the true objective itself. In purely forward-looking models, average inflation targeting is dominated by price level targeting. But we also demonstrate that in models where the Phillips curve has both forward- and backward-looking components, there are cases when the average inflation target provides more efficient outcomes than both 'ordinary' one-period inflation targeting and price level targeting.