Monetary Policy and Heterogeneity: An Analytical Framework

THANK is a tractable heterogeneous-agent New-Keynesian model that captures analytically key micro-heterogeneity channels of quantitative-HANK: cyclical inequality and risk as separate but related channels; idiosyncratic uncertainty and self-insurance, precautionary saving; and realistic intertemporal marginal propensities to consume. I use it for a full-fledged New Keynesian macro analysis: determinacy with interest-rate rules, solving the forward-guidance puzzle, amplification and multipliers, and optimal monetary policy. Amplification requires countercyclical while solving the puzzle requires procyclical inequality: a Catch-22, resolved in theory if the separate "pure" risk channel is procyclical enough. Price-level-targeting ensures determinacy and is puzzle-free, even when both inequality and risk are countercyclical, thus resolving the Catch-22. The same holds for a rule fixing nominal public debt in the model version with liquidity. Optimal policy with heterogeneity features a novel inequality-stabilization motive generating higher inflation volatility---but it is unaffected by risk, insofar as the target equilibrium entails no inequality.