Can Trend Inflation Solve the Delayed Overshooting Puzzle?

We develop an open economy New Keynesian model with heterogeneity in price stickiness and positive trend inflation. The main insight of our analysis is that, in the presence of heterogeneity in price stickiness, there is a strong link between trend inflation and the timing of the peak response of the real exchange rate to a monetary policy shock. Without trend inflation, the real exchange rate peaks almost immediately. With trend inflation set at historical values, the peak occurs at around 2 years. Delayed overshooting is a consequence of the interaction between heterogeneity in price stickiness and trend inflation