RDP 9806: Policy Rules for Open Economies Appendix A: Domestic Goods and Imports

Here I derive the Phillips curve, Equation (2), from assumptions about inflation in the prices of domestic goods and imports. Domestic-goods inflation is given by:

This equation is similar to a closed-economy Phillips curve: π^d is determined by lagged inflation and lagged output.

To determine import-price inflation, I assume that foreign firms desire constant real prices in their home currencies. This implies that their desired real prices in local currency are −e. However, they adjust their prices to changes in e with a one-period lag. Like domestic firms, they also adjust their prices based on lagged inflation. Thus import inflation is:

Finally, aggregate inflation is the average of Equations (A.1) and (A.2) weighted by the shares of imports and domestic goods in the price index. If the import share is γ, this yields Equation (2) with α = (1 − γ)α′ and η = (1 − γ)η′.