Engel, Ernst

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Engel, Ernst



Ernst Engel (1821-1896) was a German statistician. After his early training at a mining academy in Germany, Éngel went to the ficole des Mines in Paris, where he came under the influence of Frédéric Le Play, a pioneer in the study of family budgets, who was a professor there. During a subsequent stay in Belgium he became acquainted with Adolphe Quetelet, well-known for his faith in the possibility of discovering quantitative social laws. Upon his return to Germany Engel took up statistics as a profession and became director of the statistical bureaus of Saxony, 1850-1858, and Prussia, 1861-1882. As a vigorous administrator and inspiring teacher he did much to establish the modern tradition of official statistics; in particular, he insisted on making statistical data accessible and intelligible to the general public. He was also active in the social reform movement, which he supplied not only with figures but also with various practical proposals. In 1881 he published a pseudonymous attack on Bismarck’s agricultural protectionism and was promptly relieved of his position on grounds of ill-health. Of the great work on “demology” that he then set out to write only a fragment was completed.

His greatest contribution to the social sciences soon became known as “Engel’s law.” It states that the proportion of a consumer’s budget spent on food tends to decline as the consumer’s income goes up, or, in more technical terms, that the income elasticity of demand for food is less than one. Engel derived this generalization from the budgets collected in different countries by his teacher Le Play and from Belgian data compiled by édouard Ducpétiaux; it has since been invariably confirmed in hundreds of more elaborate surveys in all parts of the world.

Engel published his discovery in the context of a study of the economic development of Saxony (1857), in which he demonstrated that a general rise in productivity requires a shift of population from agriculture to manufacturing because of the effect of an increase in income on the pattern of demand. He also advanced his observations as an argument against Malthus’ fears of overpopulation.

From a methodological point of view Engel’s law is important as the first significant quantitative law ever established by empirical economic data. Formulated when economic theory proceeded largely by deduction from a priori assumptions, the law pointed the way to a more reliable approach. It also drew attention to the study of demand, which had been neglected by the classical economists, and suggested that economic development is not merely a matter of capital accumulation. Engel, however, was not much interested in economic theory and considered himself primarily a statistician, as did his numerous followers in the empirical study of family budgets, at least until recently.

Attempts were soon made to find similar generalizations for other categories of expenditure, such as housing and clothing. But here the pattern of demand was not so simple, at least when analyzed in terms of increasing or decreasing budget shares. Thus the “laws” of Schwabe for housing and Schiff for clothing, which state that the share of these categories respectively falls and rises as income increases, are not as universally valid as Engel’s law, although they probably hold in a majority of budget surveys. For these two categories the income elasticity is normally so close to one that in a particular survey it may be on either side of unity. From a review of the evidence accumulated during the century following the enunciation of Engel’s law, Houthakker (1957) concluded that the typical elasticity with respect to total expenditure is 0.6 for food, 0.8 for housing, 1.2 for clothing, and 1.6 for all other expenditures combined.

The relation between the expenditure on a particular item or group of items on the one hand and income or total expenditure on the other is now generally known as an “Engel curve.” Such curves have been extensively studied, especially after the development of regression analysis around the turn of the century. Engel could not avail himself of this technique and had to fit his food-total expenditure relationship by graphical methods. Perhaps the most important instance of an Engel curve is Keynes’s consumption function (1936), which relates total expenditure to income and has become the cornerstone of macroeconomic analysis. There is a clear line of descent from Engel’s law to Keynes’s “fundamental psychological law,” according to which the proportion of total consumption to income falls as income goes up.

Engel refined his analysis of family budgets by taking household composition into account. In his little book Der Kostenwerth des Menschen (“The Cost of Man”), published in 1883, he proposed what has since become known as an equivalent adult scale to give appropriate weights to persons of different ages and sexes; Engel’s unit, however, was not the consumption of an adult male, as in most later scales, but the consumption of an infant under one year. He called this unit “quet” in honor of Quetelet. In this book there are also interesting calculations on some economic aspects of education.

With a little more perseverance Engel could have established another claim to fame, namely, to have initiated not only the cross-section analysis but also the time-series analysis of demand. In a paper of 1861 on the Prussian grain market he derived an empirical demand curve for rye with a price elasticity of about one-half, but he did not consider the results sufficiently trustworthy to pursue the subject, although he did claim to have refuted Gregory King’s “law” on the demand for grain. The lack of suitable curve-fitting techniques may have held back his work in this area, and the estimation of empirical demand curves had to wait until the twentieth century.

Engel wrote on many other subjects, including labor and industry, taxation, insurance, banking, and war. His influence extended into many other countries; in the United States, Carroll Wright, founder of the Bureau of Labor Statistics, was his principal follower. Engel was also active in the International Statistical Congresses, the forerunners of the International Statistical Institute of which he was a founder in 1886.

H. S. Houthakker

[For the historical context of Engel’s work, see the biographies ofKING; LE PLAY; MALTHUS; QUETELET. For discussion of the subsequent development of his ideas, seeCONSUMERS, article onCONSUMPTION LEVELS AND STANDARDS; CONSUMPTION FUNCTION; DEMAND AND SUPPLY, article onECONOMETRIC STUDIES.]


(1857) 1895 Die Productions–und Consumtionsverhalt-nisse des Knigreichs Sachsen. International Statistical Institute, Bulletin 9, no. 1, supplement 1. → First published in Volume 3 of Saxony, Statistisches Landesamt, Zeitschrift des statistischen Bureaus des Königlich Sächsischen Ministeriums des Innern.

1861 Die Getreidepreise, die Ernteerträge und der Getreidehandel im preussischen Staate. Prussia, Statistisches Landesamt, Zeitschrift des Königlich Preussischen Statistischen Bureaus 1:249-289.

(1866) 1872 Der Preis der Arbeit: Zwei Vorlesungen. 2d ed. Berlin: Habel.

1872a Beiträge zur Statistik des Krieges von 1870-1871. Prussia, Statistisches Landesamt, Zeitschrift des Königlich Preussischen Statistischen Bureaus 12:1-318.

1872b Die Wohnungsnoth: Bin Vortrag auf der Eisenacher Conferenz. Prussia, Statistisches Landesamt, Zeitschrift des Königlich Preussischen Statistischen Bureaus 12:379-402.

1875 Die Klassen–und klassificirte Einkommensteuer und die Einkommensvertheilung im preussischen Staat in den Jahren 1852 bis 1875. Prussia, Statistisches Landesamt, Zeitschrift des Königlich Preussischen Statistischen Bureaus 15:105-148.

1881 Deutschlands Getreideproduktion, Brodbedarf und Brodbeschaffung. By C. Lorenz [pseud.]. Volkswirthschaftliche Zeitfragen, Vol. 3, Part 6. Berlin: Simion.

1883 Der Kostenwerth des Menschen. Berlin: Simion. → Published as Part 1 of Engel’s Der Werth des Menschen, a projected multivolume edition.

1895 Die Lebenskosten belgischer Arbeiter-familien früher und jetzt. International Statistical Institute, Bulletin 9, no. l:i-vi, 1-124.


Allen, Roy G. D.; and BOWLEY, ARTHUR L. 1935 Family Expenditure: A Study of Its Variation. London School of Economics and Political Science, Studies in Statistics and Scientific Method, No. 2. London: King.

Blenck, E. 1896 Zum Gedächtniss an Ernst Engel: Bin Lebensbild. Prussia, Statistisches Landesamt, Zeitschrift des Königlich Preussischen Statistischen Bureaus 36:231-238. → Contains a partial bibliography.

Feig, J. 1907 Ernst Engel. Allgemeines Statistisches Archiv 7, no. 1:349-359.

FÖldÉs, Bela 1918/1919 Ernst Engel. Allgemeines Statistisches Archiv 11:229-245.

Houthakker, H. S. 1957 An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel’s Law. Econometrica 25:532-551.

Keynes, John Maynard 1936 The General Theory of Employment, Interest and Money. London: Macmil-lan. → A paperback edition was published in 1965 by Harcourt.

Knapp, G. F. 1897 Grundherrschaft und Rittergut. Leipzig: Duncker & Humblot.

Prais, S. J.; and HOUTHAKKER, H. S. 1955 The Analysis of Family Budgets With an Application to Two British Surveys Conducted in 1937-1939 and Their Detailed Results. Cambridge Univ. Press.

Stigler, George J. 1954 The Early History of Empirical Studies of Consumer Behavior. Journal of Political Economy 62:95-113.

Zimmerman, Carle C. 1936 Consumption and Standards of Living. New York: Van Nostrand.