We study how the level of government debt affects the effectiveness of monetary policy, that is, the elasticity of economic aggregates to interest rate changes. We build a New Keynesian model where fiscal policy is non-Ricardian and government debt is risk-free. Wealth effects generated by government bonds weaken the transmission of monetary policy to output. Using data on private ownership of U.S. public debt, we find that when the debt-to-GDP ratio is one standard deviation above its mean, the response of industrial production and unemployment to a monetary shock decreases by 0.75pp and 0.1pp, respectively, out to a 3-year horizon.