The Engel curve for alcohol and the rank of demand systems

This paper shows that the quadratic shape of the Engel curve for alcohol is induced by preference heterogeneity between drinkers and abstainers in a Japanese data set. With controlling the heterogeneity, it is shown that the Engel curve for alcohol slopes monotonically downwards for drinkers, and that the probability of being a drinker is an increasing function of total expenditure. These two relationships generate a quadratic shape for the Engel curve for alcohol. Other goods in this data set appear to have nearly linear Engel curves, so if the alcohol Engel curve for drinkers is also linear, then after controlling for this preference heterogeneity the rank of this demand system would be two.