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Most macroeconomic models for monetary policy analysis are approximated around a zero inflation steady state, but most central banks target an inflation rate of about 2 percent. Many economists have recently proposed even higher inflation targets to reduce the incidence of the zero lower bound constraint on monetary policy. In this survey, we show that the conduct of monetary policy should be analyzed by appropriately accounting for the positive trend inflation targeted by policymakers. We first review empirical research on the evolution and dynamics of U.S. trend inflation and some proposed new measures to assess the volatility and persistence of trend-based inflation gaps. We then construct a Generalized New Keynesian model that accounts for a positive trend inflation. In this model an increase in trend inflation is associated with a more volatile and unstable economy and tends to destabilize inflation expectations. This analysis offers a note of caution regarding recent proposals to address the existing zero lower bound problem by raising the long-run inflation target.