Simple Analytics of the Government Investment Multiplier

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.