Research on disaggregate price indices has found that sectoral shocks generate the bulk of sectoral inflation variance, but no persistence. Aggregate shocks, by contrast, are the root of sectoral inflation persistence, but have negligible relative variance. We argue that these findings are largely an artefact of using overly simple factor models to characterize inflation. Sectoral inflation series are subject to particular features such as sales and item substitutions. In factor models, these blow up the variance of sectoral shocks, while reducing their persistence. Controlling for such effects, we find that inflation variance is driven by both aggregate and sectoral shocks. Sectoral shocks, too, generate substantial inflation persistence. Both findings contrast sharply with earlier evidence from factor models. However, these results align well with recent micro evidence. This has implications for the foundations of price stickiness, and provide quantitative inputs for calibrating models with sectoral heterogeneity.