The paper examines a New Keynesian model with product entry and exit and with two types of households. Households consume different product baskets and, therefore, face different inflation rates. The statistical bureau used in the model measures aggregate inflation but observes product entry with a probabilistic delay. Consequently, measured inflation suffers from product replacement bias with respect to aggregate inflation. Measured inflation is less volatile but more persistent than aggregate inflation, and the correlation between aggregate inflation and aggregate output is lower than the correlation between measured inflation and measured output. When monetary policy responds to measured variables, it stabilizes aggregate inflation insufficiently. Nevertheless, under discretionary monetary policy, responding to measured variables improves welfare.