Resolving the milk addiction paradox

The milk addiction paradox refers to an empirical finding in which consumption of non-addictive commodities such as milk appears to be consistent with the theory of rational addiction. This paradoxical result seems more likely when consumption is persistent and with aggregate data. 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, instead of the canonical AR(2) 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 imply that the AR(1) model is a better empirical alternative for testing rational addiction than the canonical AR(2) model.