Sectoral heterogeneity matters for monetary policy. Using CPI microdata, we estimate for 227 products a time-varying menu-cost model to investigate the quantitative relevance of this heterogeneity. We find a substantial degree of cross-sectoral heterogeneity in all structural parameters. Heterogeneity in the Calvo component of the pricing friction is, however, the main source of heterogeneity in price rigidity. Cross-sectoral heterogeneity amplifies the output effect of a monetary shock by a factor of about 2.5, compared to a single-sector model estimated with mean moments. Heterogeneity in the Calvo parameter plays a key role in this amplification.