Heterogeneity in inflation persistence and optimal monetary policy

In ation persistence di ers substantially across sectors. This paper analyzes the relevance of sectoral in ation persistence di erentials for optimal monetary policy using a two-sector sticky price model, which generalizes the models existing in the literature by introducing in ation persistence to both sectors. Heterogeneity in in ation persistence results from introduction of di erent price setting mechanisms across sectors. The literature suggests that in purely forward looking models, when the degree of nominal rigidity is uniform across sectors, it is optimal to target the CPI in ation. In this paper, the degree of nominal rigidity, which is computed according to the approximate measure proposed by Benigno and Lopez-Salido (2006), is uniform across sectors but the same rigidity is produced by di erent combinations of price change frequency and backward looking behavior. Based on a second order approximation to the utility function, rst the fully optimal monetary policy is computed. Then, using the fully optimal policy as a benchmark, the performance of the CPI in ation targeting rule proposed by Benigno and Lopez- Salido and the optimal in ation targeting policy are compared under di erent parameter combinations culminating to the same degree of nominal rigidity but generating di erent degrees of in ation persistence across sectors. Welfare analysis shows that adopting CPI in ation targeting instead of optimal in ation targeting implies a signi cant increase in deadweight loss. This loss is highest when one of the sectors has in ation persistence close to zero.