Unobservable Heterogeneity and the Shape of the Engel Curve: Evidence from the Japanese Household Survey Data

In this paper, I will show that the quadratic shape of the Engel curve for alcohol can be explained by preference heterogeneity between drinkers and abstainers. The main findings here are; i) the shape of the Engel curve of drinkers for alcohol was linear and negatively sloping; ii) the share of drinkers was a positively sloping linear function of the log of total expenditure. Since the two relationships generate the quadratic shape of the alcohol Engel curve, the rank of demand sysytem reduced to two, after controlling heterogeneity. Therefore, the rank-3 demand sysytem is not required.