  What are the effects of investing in public infrastructure? We answer this
question with a New Keynesian model. We recast the model as a Markov chain and
develop a general solution method that nests existing ones inside/outside the
zero lower bound as special cases. Our framework delivers a simple expression
for the contribution of public infrastructure. We show that it provides a
unified framework to study the effects of public investment in three scenarios:
$(i)$ normal times $(ii)$ short-lived liquidity trap $(iii)$ long-lived
liquidity trap. We find that calibrations commonly used lead to multipliers
that diverge with the duration of the trap.
