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The inverse relationship between food price and energy density: Is it spurious?

17 / 02 / 15

Davies & Carlson investigated the relationship between food price and energy density (i.e. is real or spurious) using a simple statistical test.

They challenge current literature that shows an inverse relationship between the price of food and energy density by questioning if the relationship has been created by a mathematical artefact (a result of the food price equation) and therefore a ‘spurious’ relationship. 

The ‘spurious’ argument is based on the fact that if the price of food is defined as price per energy density, then density appears in both variables but on opposite sides of the divisor (i.e. p/d and d), so one would expect the variables to be inversely related.

The study included 4430 different consumed foods by the non-institutionalised adult population (aged 19+years) from NHANES, these foods were matched with corresponding prices from the Center for Nutrition Policy and Promotion’s Food Prices Database. A simple regression model was used to test if the relationship between food price and energy density.

Of 25 food categories, 16 showed a significant inverse relationship between price and energy density (via the equation currently used in literature). Of these 16 cases, 14 were found to be spurious, leaving only 2 cases (poultry and fish) where the relationship was ‘real’.

The belief that higher energy-dense foods are purchased because they are cheaper is not substantiated. The key point is that the demand and supply for a product will be determined by a collection of attributes and not by a single attribute such as energy density.

The results are particular to USA foods and prices and not universal – other time periods, locations and foods could yield different results. However the method is universal and can be applied to any data set.