A strength of this study is that it looked at actual food purchases:

The Effects Of The Danish Saturated Fat Tax On Food And Nutrient Intake And Modelled Health Outcomes: An Econometric And Comparative Risk Assessment Evaluation, European Journal of Clinical Nutrition, online 13 April 2016

This paper uses data from a representative panel of over 2500 Danish households during the period before and after the introduction of the Danish saturated fat tax to estimate the impact of the tax on consumption of saturated fat and other non-targeted dietary measures (e.g. salt intake, fruit and vegetable consumption)

The tax was introduced in October 2010:

… If the level of saturated fat exceeded 2.3 g/100 g, the following foods would be taxed: meat, dairy products, animal fats that were rendered or extracted in other ways, edible oils and fats, margarine and spreads.

The tax resulted in:

• 4.0% reduction in saturated fat intake
• 4.0% reduction in total fat intake
• 7.9% increase in vegetable consumption (10.1% to 14.3% for women under 60)
• 3.7% increase in fiber consumption

The researchers estimated that these changes could save 123 lives a year. The changes were also expected to reduce morbidity (disease and disability) associated with heart disease, vascular disease, diabetes, and several cancers.

I don’t support taxes on food. They are regressive and place a greater burden on the poor than the rich. But, if your goal is public health (and not raising revenue for pet projects), maybe taxing saturated fat should be an option. But you should subsidize fruits and vegetables at the same time.

By the way, this Danish tax was abolished a couple years after it was enacted because people “were travelling to Germany and Sweden to buy butter and other high-saturated fat products at reduced prices” and because the meat and dairy industries complained, e.g “the tax-induced increase in consumer prices might have [an effect] on competitiveness due to wage pressure.”