Measuring aggregate inflation is subject to two opposing biases: unobserved quality and variety growth, and the use of incorrect weights when new varieties are misclassified. We show that it is possible to measure an aggregate price index free of these biases when we have a subset of products where these two errors average to zero. This procedure does not require us to distinguish new from existing goods, measure quality attributes directly, or classify new varieties into the appropriate category. We implement this approach using BEA data from 1959 to 2019, approximating the official PCE price index with a CES aggregate of BEA prices at the product level. Our estimate of the inflation rate exceeds the CES aggregate of BEA prices by 0.3 to 1.0 percentage points per year on average. The aggregate bias was close to zero prior to the BLS introducing hedonic adjustments, which suggests that only adjusting for quality bias can lead to an underestimation of overall inflation, particularly in quality-adjusted categories.