Optimal Monetary Policy in a Two Sector with Different Degree of Price and Wage Stickiness

We study optimal monetary policy in a two-sector model. The conventional wisdom in the literature is that the monetary authority should optimally stabilize inflation in the sticky-price sector. We reassess this issue in a two sector economy with capital accumulation subject to adjustment costs. Our main point of departure is whether the presence of different degrees of wage stickiness across sector makes a difference. Factor inputs cannot perfectly move from one sector to the other: aggregate measures of consumption, labor output and investment are obtained according to CES aggregator. The government collects lump sum taxes by targeting the value of government bonds to preserve aggregate price stability under a wide configuration of monetary policy parameter. Monetary policy is of the Taylor type, including a target for a broad inflation measure - as an aggregate of the sectorial inflation rate - or, alternatively, the direct target of each sector's inflation rate. As welfare measure we use a conditional second-order Taylor expansion of the utility function, whereby the model is entirely solved up to second order. The model is calibrated on the US economy, by considering several parametrization in order to detect optimal monetary policy for different configuration of rigidities: different price stickiness across sector and flexible wages; different price stickiness and equal wage rigidities across sectors; different price stickiness and different wage stickiness. We show that targeting the inflation rate of the sticky price sector (or the sector with higher degree of price stickiness) is optimal with respect to a broad inflation rate target if and only if the degree of rigidity across sector is substantial, i.e. if one sector is perfectly flexible and the other is characterized by sticky prices. The presence of sticky nominal wages enlarges the set of results in the following sense: targeting a measure of wage inflation ensures a monetary policy configuration Pareto superior to any other kind of price measure