Stabilizing Inflation under Heterogeneity: a welfare-based measure on what to target

What measure of inflation a Central Bank should respond to? This paper characterizes the optimal targeting index in a multisectorial economy with Calvo-pricing, defined as a composition of sectorial inflations that maximizes a selected welfare criterion. This is a purely quadratic approximation to the representative agent's utility in an environment of distorted steady state and sectorial heterogeneity of price stickiness. The Central Bank is modeled as following a historical Taylor Rule. For most parameter values, weights of sectorial inflations are increasing functions of the degrees of nominal rigidity and productivity volatility and decreasing functions of sectorial wage markup volatilities, resembling most of the conclusions from related literature. Bayesian estimation for the structural model using sectorial quantum and price indexes for Personal Consumption Expenditure (PCE) provides the parameter values that allow constructing the optimal index for the US economy. The result points out towards a price index with similar properties than the PCE, with more weight on services and less weight of inflation from durable goods. I find no evidence that a core index based on the exclusion of food and energy goods is welfare improving