We propose a theory of indebted demand, capturing the idea that large debt burdens lower aggregate demand, and thus the natural rate of interest. At the core of the theory is the simple yet underappreciated observation that borrowers and savers differ in their marginal propensities to save out of permanent income. Embedding this insight in a two-agent perpetual-youth model, we find that recent trends in income inequality and financial deregulation lead to indebted household demand, pushing down the natural rate of interest. Moreover, popular expansionary policies—such as accommodative monetary policy—generate a debt-financed short-run boom at the expense of indebted demand in the future. When demand is sufficiently indebted, the economy gets stuck in a debt-driven liquidity trap, or debt trap. Escaping a debt trap requires consideration of less conventional macroeconomic policies, such as those focused on redistribution or those reducing the structural sources of high inequality.

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.