In this paper we develop and estimate a behavioral model of inflation dynamics with monopolistic competition, staggered price setting and heterogeneous firms. In our stylized framework there are two groups of price setters, fundamentalists and naive. Fundamentalists are forward-looking in the sense that they believe in a present-value relationship between inflation and real marginal costs, while naive are backward-looking, using the simplest rule of thumb, naive expectations, to forecast future inflation. Agents are allowed to switch between these different forecasting strategies conditional on their recent relative forecasting performance. The estimation results support behavioral heterogeneity and the evolutionary switching mechanism. We show that there is substantial time variation in the weights of forward-looking and backward-looking behavior. Although on average the majority of firms use the simple backward-looking rule, the market has phases in which it is dominated by either the fundamentalists or the naive agents.