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An important EU Digital Single Market policy objective is to achieve an open and integrated market for online e-commerce in the EU, to make it easy for consumers to go outside their domestic market and shop online in other EU Member States. This study applies a standard gravity model of international trade to Google e-commerce data to estimate the prevalence of home bias in online shopping in the EU. It compares how much EU Member States trade domestically and with other Member States, and how much the EU trades with itself and with the rest of the world. The research confirms the findings of the (offline) international trade literature, according to which there is strong home bias. There is no unambiguous evidence about the strengths or weaknesses of the EU Digital Single Market. Strong intra-EU home bias suggests that online consumers have a tendency to stay in their home country market. Equally strong extra-EU home bias suggests that online consumers who do decide to shop abroad have a tendency to stay in the EU however, rather than going to a non-EU country. There are indications that online home bias is lower in a comparable cross-border trade setting in North America. Data and methodological limitations do not allow a more detailed analysis.