An aggregate welfare optimizing interest rate rule under heterogeneous expectations

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 specification 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.