Heterogeneity in inflation persistence and optimal monetary policy

Inflation persistence differs substantially across sectors. This paper analyzes the relevance of sectoral inflation persistence differentials for optimal monetary policy using a two-sector sticky price model, which generalizes the models existing in the literature by introducing inflation persistence to both sectors. Heterogeneity in inflation persistence results from introduction of different 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 inflation. 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 different combinations of price change frequency and backward looking behavior. Based on a second order approximation to the utility function, first the fully optimal monetary policy is computed. Then, using the fully optimal policy as a benchmark, the performance of the CPI inflation targeting rule proposed by Benigno and Lopez- Salido and the optimal inflation targeting policy are compared under different parameter combinations culminating to the same degree of nominal rigidity but generating different degrees of inflation persistence across sectors. Welfare analysis shows that adopting CPI inflation targeting instead of optimal inflation targeting implies a significant increase in deadweight loss. This loss is highest when one of the sectors has inflation persistence close to zero.