Determinacy under inflation targeting interest rate policy in a sticky price model with investment (and labor bargaining)

In a sticky price model with investment spending, recent research shows that inflation-forecast targeting interest rate policy makes determinacy of equilibrium essentially impossible. We examine a necessary and sufficient condition for determinacy under interest rate policy that responds to a weighted average of an inflation forecast and current inflation. This condition demonstrates that the average-inflation targeting policy ensures determinacy as long as both the response to average inflation and the relative weight of current inflation are large enough. We also find that interest rate policy which responds solely to past inflation guarantees determinacy when its response satisfies the Taylor principle and is not large. These results still hold even when wages and hours worked are determined by Nash bargaining.