Understanding HANK: Insights from a PRANK

Does market incompleteness radically transform the properties of monetary economies? Using an analytically tractable heterogeneous agent New Keynesian (HANK) model, we show that whether incomplete markets resolve "policy paradoxes" in the representative agent New Keynesian model (RANK) depends primarily on the cyclicality of income risk, rather than incomplete markets per se. Incomplete markets reduce the effectiveness of forward guidance and multipliers in a liquidity trap only if risk is procyclical. Acyclical or countercyclical risk amplifies these puzzles relative to RANK. Cyclicality of risk also affects determinacy: procyclical risk permits determinacy even under an interest rate peg, while countercyclical income risk generates indeterminacy even if the Taylor principle holds. Finally, we uncover a new dimension of monetary-fiscal interaction. Since fiscal policy affects the cyclicality of income risk, it influences the effects of monetary policy even when "passive".