Copenhagen economists put Denmark's cross-border shopping loss at just over a third of the official figure

The two figures measure different things. "The Ministry of Taxation bases its calculations on what Danes buy in Germany. But if we want to understand what Denmark actually loses, we need to look at what happens to consumption in Denmark. That is precisely what we have done," said Magnus Munk Bjerg, a Ph.D. student in the University of Copenhagen's Department of Food and Resource Economics and a co-author of the study ^[6][14]. The team's DKK 415 million is about 36% of the ministry's 2019 figure of DKK 1.16 billion, a number that excludes tobacco ^[3][4][17]. The gap is roughly DKK 745 million ^[18].

Bjerg offered a possible reason why German purchases do not simply reappear at home. "Once people have packed the car or trailer and driven a considerable distance, they are likely to buy a range of additional products to make the trip worthwhile," he said ^[19]. If he is right, part of what Danes buy in Germany is spending that exists only because the trip happens. It is a hypothesis about motive, and the spending data alone cannot confirm it.

The closures handed the researchers something close to a natural experiment. Cross-border shopping was effectively impossible in 2020 and 2021 ^[2], so they could watch what came back instead of modelling it. Their comparison group was households living so far from the border that crossing it had never paid ^[7]. Those households went through the same pandemic, so a country-wide rise in snacking at home would show up in both groups and cancel out. Within 30 km of the border, spending in Danish stores on candy, chocolate, potato chips, soft drinks, beer, wine and spirits rose 109% ^[8]. Beyond 120 km, the team could detect no change ^[10]. The 21% average for all households within 150 km ^[9] includes the 120-to-150 km band where nothing moved, so it sits well below the near-border figure.

The thing this doesn't tell you is how shoppers respond to a price rise. A closed border removes the German option outright. A tax makes buying at home dearer and leaves the option open. The researchers extend the first result to the second, concluding that a tax rise would mainly send people who live near the border across it ^[16]. "Some residents of the border region might travel to Germany even more frequently than they already do, but this is a relatively small group overall. The effect is therefore primarily local rather than national," said Carl-Emil Pless, a postdoctoral researcher and co-author ^[12][15]. Pless went further: "If the policy objective of taxing these products is both to increase government revenue and improve public health, our findings suggest that those effects are likely to be fully realized for the vast majority of Danish households," he said ^[11]. The phys.org account reports spending only, and it does not give a sample size or any health measure.

I think the revenue estimate holds up for the question it asks. The control group makes sense. A response that fades with distance from the border is the pattern a real border effect should produce ^[8][10]. The condition is that shopping during the pandemic closures is close enough to ordinary shopping to stand in for it. Bjerg kept the claim narrow. "We are not saying what the tax rate should be. But our results show that cross-border shopping should carry less weight when policymakers decide how taxes on unhealthy foods ought to be designed," he said ^[13].