The Engel curve for alcohol and the rank of demand systems
利用日本数据发现，酒精的恩格尔曲线呈二次形状是由饮酒者与不饮酒者的偏好差异造成的；控制该差异后，饮酒者的酒精恩格尔曲线单调下降，而饮酒概率随总支出增加，两者共同导致二次形状。
Abstract 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. Copyright © 2006 John Wiley & Sons, Ltd.