Does Lumy Investment Matter for Business Cycles?

We present an analytically tractable general equilibrium business cycle model that features micro-level investment lumpiness. We prove an exact irrelevance proposition which provides sufficient conditions on preferences, technology, and the fixed cost distribution such that any positive upper support of the fixed cost distribution yields identical equilibrium dynamics of the aggregate quantities normalized by their deterministic steady state values. We also give two conditions for the fixed cost distribution, under which lumpy investment can be important to a first-order approximation: (i) The steady-state elasticity of the adjustment rate is large so that the extensive margin effect is large. (ii) More mass is on low fixed costs so that the general equilibrium price feedback effect is small. Our theoretical results may reconcile some debate and some numerical findings in the literature.