Endogenous Persistence at the Effective Lower Bound

We develop a perfect foresight method to solve models with an interest rate lower bound constraint that nests OccBin/DynareOBC and \cite{Eggertsson2010}'s as well as \cite{Mertens2014}'s pen and paper solutions as special cases. Our method generalizes the pen-and-paper solutions by allowing for endogenous persistence while maintaining tractability and interpretability. We prove that our method necessarily gives stable multipliers. We use it to solve a New Keynesian model with habit formation and government spending, which we match to expectations data from the Great Recession. We find an output multiplier of government spending close to 1 for the US and Japan.