Should we use linearized models to calculate fiscal multipliers?

We calculate the magnitude of the government consumption multiplier in linearized and nonlinear solutions of a New Keynesian model at the zero lower bound. Importantly, the model is amended with real rigidities to simultaneously account for the macroeconomic evidence of a low Phillips curve slope and the microeconomic evidence of frequent price changes. We show that the nonlinear solution is associated with a much smaller multiplier than the linearized solution in long-lived liquidity traps, and pin down the key features in the model which account for the difference. Our results caution against the common practice of using linearized models to calculate fiscal multipliers in long-lived liquidity traps.