Optimal Monetary Policy in a Multi-Sector Small Open Economy Model∗

In an influential paper, Aoki (2001) used a closed-economy setup with two sectors – with flexible and sticky prices, respectively – to conclude that it is optimal for inflationtargeting central banks to react only to the inflation rate of the sector with the highest degree of price rigidity. Aoki’s paper also implies that targeting aggregate “average” indices such as the Consumer Price Index (CPI) is suboptimal. Nevertheless, the bulk of inflation targeting central banks focus on such aggregate indices. In this paper, we challenge Aoki’s conventional result and rationalize the preference of most central banks for targeting the CPI. We develop and estimate a multi-sector New-Keynesian small open economy model for Canada with four sectors (tradable, non-tradable, commodity, and imported goods) that are heterogeneous with respect to (i) their degree of price and wage rigidity and (ii) their adjustment cost of capital. Sector-specific nominal rigidities are modelled à la Calvo-Yun and labour is assumed to be imperfectly mobile across sectors. Our estimations using Bayesian techniques show support for the existence of significant heterogeneity across sectors. We next solve the model's equilibrium conditions to a second-order approximation around a deterministic steady-state and compare the welfare implications of five alternative monetary policy rules. These options differ with respect to the price index or inflation rate targeted by the monetary authority. Our main finding is that maximal welfare is achieved by targeting CPI inflation rather than the inflation rate of the sector with the highest degree of nominal rigidity. This is fully explained by the cross-sector heterogeneity and factor mobility costs, and is in direct contradiction with Aoki (2001). When we shut down these features of our model, we obtain Aoki’s result.