One of the "most enduring relationships in economics", discovered around 1857 by Ernst Engel, a German economist. It states that as their income increases, people devote a smaller share of it to food. The regularity can be used to predict food spending, but also in reverse, to infer incomes: other things being equal, the share of outlays devoted to food is "the best measure of the material standard of living of a population", as Engel declared.
Engel discovered his measure in data painstakingly collected by others. Edouard Ducpetiaux, a Belgian jurist, tabulated the budgets of 199 households across all nine provinces of Belgium in the 1850s. Frederic Le Play, a pioneering sociologist, gleaned similar figures from 36 families across Europe, gaining their confidence through praise, small gifts and "interesting conversation". Ducpetiaux and Le Play had "delivered the pearls", Engel admitted, "but not the string"—what tied the data together was the consistent relationship between income and food spending.
Richard Anker of the University of Massachusetts, Amherst, reviewed the law 150 years after its discovery and found the link still easy to discern across over 200 countries. China's National Bureau of Statistics considers the "Engel coefficient" an "important indicator for measuring the standard of living of residents".
In 2014 Emi Nakamura and Jon Steinsson of the University of California, Berkeley, and Miao Liu of Boston College used Engel's finding to cast doubt on China's growth and inflation statistics. They compared households in 2006 with those that reached a similar income two years later and discovered that the later households were still devoting substantially more of their budgets to food—suggesting they were not as prosperous as official figures claimed.
Restaurant meals complicate Engel's law. When people eat out, they pay not just for food but for cooking, washing-up and ambience. Anker conducted fieldwork buying noodles and steamed buns in street markets in Xi'an, China, and patronising McDonald's and Outback Steakhouse in Massachusetts. He calculated that Chinese street food cost up to 30% more than a similar meal at home, McDonald's cost 150% more, and steak at a restaurant cost 233% extra. If dining out is included, food spending may be overstated; excluding it poses the opposite danger.
China's official Engel coefficient (which includes cigarettes, alcohol and dining out) stopped falling around 2017, remaining at 29.3% in 2025—the same as eight years before—despite reported economic growth. Adam Wolfe of Absolute Strategy Research argues this "violation" suggests China has suffered a "severe development setback". However, data from Wind, a financial-data platform, show that restaurants and other catering services rose from 5% of consumption in 2017 to 7.4% in 2024. Subtracting dining out, food's weight in Chinese consumption fell from about 20.7% in 2017 to 17.2% in 2025 (the latter figure revealed for the first time by the NBS in a revision of the consumer-price index). China has not broken Engel's law after all.
Smoking is one of the leading causes of statistics.