We study heterogeneity in the transmission of monetary shocks across euro-area (EA) countries using a dynamic factor model and high-frequency identification. Deploying a novel methodology to asses the degree of heterogeneity, we find it to be low in financial variables and output but significant in consumption, consumer prices, and variables related to local housing and labour markets. We show that a large proportion of the variation in the responses to monetary shocks can be accounted for by differences in some characteristics of these markets across EA member countries: the share of adjustable mortgage contracts, homeownership rates, shares of hand-to-mouth and wealthy hand-to-mouth consumers, as well as wage rigidity.