Should we use linearised models to calculate fiscal multipliers?

We calculate the magnitude of the fiscal spending multiplier in linearised 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 re-optimisation. We show that the nonlinear solution is associated with a much smaller multiplier than the linearised 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 linearised models to calculate fiscal multipliers in long-lived liquidity traps.