Monetary Policy and Heterogeneity: An Analytical Framework

An analytical (heterogeneous-agent New-Keynesian) HANK model allows a closed-form treatment of a wide range of NK topics: determinacy properties of interest-rate rules, resolving the forward guidance FG puzzle, amplification and fiscal multipliers, liquidity traps, and optimal monetary policy. The key channel shaping all the model's properties is that of cyclical inequality: whether the income of constrained agents moves less or more than proportionally with aggregate income. With countercyclical inequality, good news on aggregate demand gets compounded, making determinacy less likely and aggravating the FG puzzle (the resolution of which requires procyclical inequality)---a Catch-22, because countercyclical inequality is what HANK (and TANK) models need to deliver desirable amplification. The dilemma can be resolved if a distinct, "cyclical-risk" channel is procyclical enough. Even when both channels are countercyclical a Wicksellian rule of price-level targeting ensures determinacy and cures the puzzle. Optimal monetary policy is isomorphic to RANK and TANK but calls for less inflation stabilization. In a liquidity trap, even with countercyclical inequality and FG amplification, optimal policy does not imply larger FG duration because as FG power increases, so does its welfare cost.