Retrospectives: Engel Curves

Engel curves describe how household expenditure on particular goods or services depends on household income. German statistician Ernst Engel (1821–1896) was the first to investigate this relationship systematically in an article published about 150 years ago. The best-known single result from the article is “Engel's law,” which states that the poorer a family is, the larger the budget share it spends on nourishment. We revisit Engel's article, including its context and the mechanics of the argument. Because the article was completed a few decades before linear regression techniques were established and income effects were incorporated into standard consumer theory, Engel was forced to develop his own approach to analyzing household expenditure patterns. We find his work contains some interesting features in juxtaposition to both the modern and classical literature. For example, Engel's way of estimating the expenditure–income relationship resembles a data-fitting technique called the “regressogram” that is nonparametric—in that no functional form is specified before the estimation. Moreover, Engel introduced a way of categorizing household expenditures in which expenditures on commodities that served the same purpose by satisfying the same underlying “want” were grouped together. This procedure enabled Engel to discuss the welfare implications of his results in terms of the Smithian notion that individual welfare is related to the satisfaction of wants. At the same time, he avoided making a priori assumptions about which specific goods were necessities, assumptions which were made by many classical economists like Adam Smith. Finally, we offer a few thoughts about some modern literature that builds on Engel's research.