We show that in a broad class of menu cost models, the first-order dynamics of aggregate inflation in response to arbitrary shocks to aggregate costs are nearly the same as in Calvo models with suitably chosen Calvo adjustment frequencies. We first prove that the canonical menu cost model is first-order equivalent to a mixture of two time-dependent models, which reflect the extensive and intensive margins of price adjustment. We then show numerically that in any plausible parameterization, this mixture is well approximated by a single Calvo model. This close numerical fit carries over to other standard specifications of menu cost models. Thus, for shocks that are not too large, the Phillips curve for a menu cost model looks like the New Keynesian Phillips curve, but with a higher slope.

We generalize the traditional, static Keynesian cross by deriving an intertemporal Keynesian cross for the dynamic output response to government spending and taxes in microfounded general equilibrium models. Intertemporal marginal propensities to consume (iMPCs) are sufficient statistics for this response, with fiscal multipliers depending only on the interaction between iMPCs and public deficits. We provide empirical estimates of iMPCs and argue that they are inconsistent with representative agent or two-agent models but can be matched by certain heterogeneous agent models. Models that match empirical iMPCs imply larger and more persistent output responses to deficit-financed fiscal policy, with cumulative spending multipliers above 1.

Motivated by the effects of the COVID-19 pandemic, we present a theory of Keynesian supply shocks: shocks that reduce potential output in a sector of the economy, but that, by reducing demand in other sectors, ultimately push aggregate activity below potential. A Keynesian supply shock is more likely when the elasticity of substitution between sectors is relatively low, the intertemporal elasticity of substitution is relatively high, and markets are incomplete. Fiscal policy can display a smaller multiplier, but the insurance benefit of fiscal transfers can be enhanced. Firm exits and job destruction can amplify and propagate the shock.

We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous‐agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence‐space Jacobians —the derivatives of perfect‐foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous‐agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood‐based estimation and computation of nonlinear perfect‐foresight transitions. We apply our methods to three canonical heterogeneous‐agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.