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Most macroeconomic models for monetary policy analysis are approximated around a zero-inflation steady state, but most central banks target inflation at a rate of about 2 percent. Many economists have recently proposed even higher inflation targets to reduce the incidence of the zero lower bound (ZLB) constraint on monetary policy. In this survey, we show the importance of appropriately accounting for a low, positive trend inflation rate for the conduct of monetary policy. We first review empirical research on the evolution and dynamics of U.S. trend inflation, as well as some proposed new measures to assess the volatility and persistence of trend-based inflation gaps. Then we construct a generalized New Keynesian model that accounts for a positive trend inflation rate. We find that, in this model, higher trend inflation is associated with a more volatile and unstable economy and tends to destabilize inflation expectations. This analysis offers a note of caution in evaluating recent proposals to address the existing ZLB situation by raising the underlying rate of inflation.