Solving the milk addiction paradox

The milk addiction paradox refers to an empirical finding in which commodities that are typically considered to be non addictive, such as milk, appear instead to be addictive. This result seems more likely when there is persistence in consumption and when using aggregate data, and it suggests that the AR(2) model typically used in the addiction literature is prone to produce spurious result in favor of rational addiction. Using both simulated and real data, we show that the milk addiction paradox disappears when estimating the data using an AR(1) linear specification that describes the saddle-path solution of the rational addiction model. The AR(1) specification is able to correctly discriminate between rational addiction and simple persistence in the data, to test for the main features of rational addiction, and to produce unbiased estimates of the short and long-run elasticity of demand. These results hold both with individual and aggregated data, and they suggest that, for testing rational addiction, the AR(1) model is a better empirical alternative than the canonical AR(2) model.