  How should central banks optimally aggregate sectoral inflation rates in the
presence of imperfect labor mobility across sectors? We study this issue in a
two-sector New-Keynesian model and show that a lower degree of sectoral labor
mobility, ceteris paribus, increases the optimal weight on inflation in a
sector that would otherwise receive a lower weight. We analytically and
numerically find that, with limited labor mobility, adjustment to asymmetric
shocks cannot fully occur through the reallocation of labor, thus putting more
pressure on wages, causing inefficient movements in relative prices, and
creating scope for central banks intervention. These findings challenge
standard central banks practice of computing sectoral inflation weights based
solely on sector size, and unveil a significant role for the degree of sectoral
labor mobility to play in the optimal computation. In an extended estimated
model of the U.S. economy, featuring customary frictions and shocks, the
estimated inflation weights imply a decrease in welfare up to 10 percent
relative to the case of optimal weights.
