The Zero Lower Bound on the Interest Rate and a Neo-Classical Phillips Curve

With sticky prices, optimizing agents and money in the utility function, I derive the exact analytical solution for optimal monetary policy given a zero lower bound (ZLB) on the interest rate. The Phillips curve is Neo-Classical, and the ZLB is then not a constraint on optimal policy. Optimal policy is history dependent even without a commitment problem and implements a Friedman rule equilibrium. The role of forward guidance in policy is more limited than under a New-Keynesian Phillips curve. The optimal policy rule intercept term is time varying and depends on the variance of the natural real rate.