We show analytically that whether incomplete markets resolve New Keynesian “paradoxes” depends primarily on the cyclicality of income risk, rather than marginal propensity to consume (MPC) heterogeneity. Incomplete markets reduce the effectiveness of forward guidance and multipliers in a liquidity trap only with procyclical risk. Countercyclical risk amplifies these “puzzles.” Procyclical risk permits determinacy under a peg; countercyclical risk generates indeterminacy even under the Taylor principle. MPC heterogeneity leaves determinacy and paradoxes qualitatively unaffected, but can change the sensitivity of GDP to interest rates. By affecting the cyclicality of risk, even “passive” fiscal policy influences the effects of monetary policy.