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In this paper, I propose an optimal interest rate rule under heterogeneous expectations derived from
a welfare criterion that is a second-order approximation of heterogeneous household utility following
Di Bartolomeo et al. (2016). Additionally, I explore the agent level of the Branch and McGough
(2009) framework in a more detailed fashion which is important as the central bank's welfare criterion
depends on consumption inequality. I find that the consumption decision of "rational" agents in
Di Bartolomeo et al. (2016) is inconsistent with the higher-order beliefs assumption of Branch and
McGough (2009). Hence, consumption rules are derived that are consistent with the micro-foundations
of Branch and McGough (2009) including a possible specication of agent's long-run beliefs. Further,
the welfare analysis shows that the optimal interest rate rule yields welfare gains that range between
0.1 and 7.1 percent under the considered parameter values relative to a rule that is optimized under
a conventional inflation-targeting objective as in Gasteiger (2014). Welfare gains are high when the
underlying economy features a high degree of heterogeneity.
