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These findings have important implications for understanding the effects of both monetary and macroprudential policy. Consumption inequality is countercyclical in this setting and a high degree of leverage amplifies the redistribution channel.

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Monetary policy therefore becomes more effective compared to models with homogeneous MPC rates. In particular, the effects of a monetary policy shock are amplified as resources are redistributed from high-MPC households to low-MPC households. I show that monetary policy transmission takes place through a redistribution channel, as emphasised by Auclert (2019). Compared to a full-scale HANK model, this model is easier to compute while reproducing many of the same monetary policy shock transmission channels. Abstract In this paper I develop a New Keynesian dynamic stochastic general equilibrium model which features three different types of representative agents (THRANK): the poor hand-to-mouth, the wealthy hand-to-mouth and the non-hand-to mouth households.