We analyze differences in consumption and wealth in an estimated New Keynesian model with rational and boundedly rational households. Shocks are shown to cause consumption and wealth heterogeneity due to the `rationality bias’ of boundedly rational households. This bias can be decomposed into three components which, for certain specifications of monetary policy, can exactly offset each other. Moreover, a more hawkish response to inflation leads to more volatility in consumption and wealth heterogeneity, which makes it optimal for the central bank to set lower coefficients in the Taylor rule than would have been the case under homogeneous rational expectations.