This paper investigates optimized monetary policy rules in the presence of government intervention to stabilize prices of certain categories of goods and services. The paper estimates a small-scale, structural equilibrium model with a sticky-price sector and a subsidized price sector for a large number of countries using Bayesian methods. The main result of this paper is that strict headline inflation targeting could be outperformed by sectoral inflation targeting, output gap stabilization, or a combination of these. In addition, several country cases exhibit lower performance of both headline and core inflation stabilization, the two most common policies in modern central banks' practices. For practical monetary policy design, we numerically identify country specific thresholds for the degree of government intervention in price setting under which core inflation targeting turns out to be the optimal choice in the context of implementable Taylor rules.