The pitfalls of speed-limit interest rate rules at the zero lower bound

We show that interest rate rules that feed back on the growth rates of target variables (such as output or asset prices) may induce recessions in the presence of a zero lower bound, through purely self-fulfilling dynamics. This pathology is illustrated in a small New Keynesian model with interest rates responding to the growth rate of output, and in a version of a model by Matteo Iacoviello where interest rates respond to the growth rate of house prices and credit. Our results provide a cautionary note, contrasting with previous work which has suggested several desirable properties of speed-limit rules, namely that they are devices enabling the policymaker (i) to side-step uncertainty about natural rates, (ii) to counter booms and busts in asset prices or (iii) to implement optimal commitment policies.