科拉多·基尼
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科拉多·基尼(Corrado Gini,1884.5.23-1965.3.13.)，義大利統計學家、經濟學家和社會學家，在1922年提出關於收入分配不平均的一種衡量辦法——基尼繫數(Gini Ratio)。
Gini was born into comfortable circumstances in northeastern Italy. He graduated in law at Bologna in 1905, with a thesis on Gender from a Statistical Point of View (published 1908). His interest in public issues with a mathematical slant, rather than in law in the usual sense, was already evident, and it marked the rest of his career. That career was an energetic and productive one, and extended over fields often thought of as separate. Before it was over, he had collected honorary degrees in four different disciplines.
By 1909 he was teaching statistics in a junior position at Cagliari. The next year, at the age of 26, he succeeded to the Chair of Statistics at that university. In 1912 he occupied himself with the descriptive statistics of situations not related to the normal distribution; in this he patterns with Pareto, who discovered the first significant non-normal distributions.
In 1913 he moved to Padua, and in 1914 published a book on the wealth of nations (Adam Smith's classic treatise of 1776, which established economics as a separate subject of inquiry, had left some things unsaid, and the world had changed). In 1920 he founded the international journal Metron. In 1921, and in another journal, appeared one of his most important contributions, a weighty three pages on the Measurement of Inequality of Incomes. Also in 1921 he collected some papers from 1915-1920 under the title Problemi Sociologici della Guerra.
Gini was continuously occupied with questions of measure, such as extending the concept of the mean to distributions having no obvious mean, as well as the parameters of bivariate distributions. From such seemingly simple matters, he found much of value to contribute to science. His 1921 work on the economic analysis of income and wealth had its context in more general investigations of measures of variability.
Another important contribution to economics, specifically index number theory, appeared in 1924, distinguishing previously confused elements such as "price variation" and "quantity variation." In 1926, Mussolini created an independent Central Institute of Statistics, reporting directly to the Premier and responsible to no government bureau, to serve as the repository and analytical center for information gathered by those bureaus. Gini was made President. In 1927 he moved to the Chair of Statistics at Rome.
Gini was a great collector of data, and directed several scientific expeditions studying the demographic and medical profiles of populations in Fezzan, Palestine, Mexico, Poland, Lithuania, and, within Italy, in Calabria and Sardinia. As President of the Central Institute, he became an organizer and centralizer of statistical information in the tradition of Quetelet. But there was opposition to the Institute's structure from the various bureaus which were intended to be in part subordinate to it. Mussolini intervened in the controversy, which was resolved in favor of the Institute's independence, but with the result of souring the previously good relationship between him and Gini. The growing interference of Fascism in intellectual matters also discouraged continued close involvement with government. Gini resigned from the Institute in 1932. Another enterprise founded under Gini's direction in 1926, the journal La Vita Economica Italiana, was closed by the government in 1943.
Gini's round the clock work scheduled continued after the 1932 break, as did his academic career, his development of publication outlets for statistics, and his participation in learned societies. In 1932 he received an honorary degree (in economics) from the Catholic University of Milan, and in 1933 became Vice President of the International Sociological institute. Italian policy under Mussolini aimed at population increase; the role of women in that policy as breeders (fattrici). Gini followed an independent line. Nora Federici, who later succeeded in establishing demography as a field apart from statistics, took her degree under his direction (in political science) at Rome in 1933.
In 1934 he received another honorary degree (in sociology) from Geneva, and founded the journal Genus as the print medium of the Italian Committee for the Study of Population Problems. In 1936, Harvard's tercentennial year, he received an honorary Doctor of Science degree from that university, and also founded the Faculty of Statistical, Demographic, and Actuarial Sciences at Rome, of which he remained Dean until 1954. Academic honors lull many; Gini, they only further energized.
His flow of publications (during his career there were more than 800 of them) continued through these years, a notable one being a 1939 address to the first meeting of the Società Italiana di Statistica. This was The Dangers of Statistics, an attack on Fisher's fiduciary methods and the Neyman-Pearson theory of hypothesis testing. In this he took a somewhat Bayesian line, arguing for the importance of prior probabilities in judging the measures of a sample. He was generally impatient of the tendency toward purely mathemetical elaboration (a trait that others besides himself criticized in Fisher and Neyman), and preferred a more concrete approach. Applications were his forte.
His most widely known contribution, the Gini Coefficient, is his 1921 measure of the inequality of distribution of wealth (or any other variable). Imagine a graph of cumulative population, summed from the poorest upward, and plotted against cumulative wealth. If all in that population are equally wealthy, the cumulative curve will rise steadily; it will in fact be the diagonal (the "45 degree line") of the chart. This represents perfect equality of wealth; no rearrangement can improve it. We may assign it the inequality value 0. If only one person has wealth, the extreme inequality situation, the cumulative wealth curve will instead follow the bottom or zero line of the chart until the last moment, when it will suddenly leap upward to 100%. That is, it will follow the edges of the chart, and between it and the equality diagonal will lie half the area of the entire chart. We can assign this situation the value of 1, or perfect inequality.
Lorenz Curve (after William King)
Now imagine an empirical curve drawn on that chart, representing an actual cumulative wealth distribution. This is the Lorenz curve. It will lie somewhere between the above extremes. How shall we measure the degree of departure of the Lorenz curve from the 45 degree diagonal equality line? If we take the area between the curve and the equality diagonal (the pink area in the chart above, representing the actual departure from equality), and divide that area by the area of half the chart (representing the maximum departure from equality), we will have a measure of the degree of inequality in that population. This ratio is called (miscalled, since it is not actually a coefficient) the Gini Coefficient. It is simple when you think of it, but it took a Gini to think of it. It is widely used today by governments and supervisory bodies as an index of wealth inequality and other variables.
For comparison purposes, the G number for the USA in 1996 was G = 0.456; the figure for Canada hovered around a less unequal 0.300 for that decade. It was considered an advance in social justice that the Gini Coefficient for the Philippines went from 0.4881 in 1997 to 0.4814 in 2000, a decline of 1.4% in four years.
The end of WW2 registered with Gini as an increase in the flow of major publications. He wrote on the effect of migrations in 1946, on statistical relations and their inversions in 1947, on measures of fecundity in 1949 and 1950, on the measurement of differences between two populations in 1953, and on the wealth of nations in 1956. All these were further contributions to topics which had engaged him throughout his career. His criticisms too did not end with his 1939 attack on Fisher and Neyman; he challenged another field with a 1956 paper on Delusions in Econometrics. In it, he faulted the econometrists for exaggerating formal aspects, "because of the well-known difficulties of getting down to empirical brass tacks in economics." No one who has chafed at the number-flinging of the economists, and their remoteness from economic reality, will fail to give Gini their salute, across the decades. He had long sought to include more reality in economic computations.
The concept of human capital was his. He distinguished stages in the growth of societies, and also distinguished normal from abnormal processes in societies, making thinkable a rational process of restoration for unbalanced societies.
His last major works, in 1959, were on transvariation and on the transition from forced to free labor and to spontaneous labor. His early work on the wealth of nations was reissued in a 2nd edition in 1962. Gini's recognitions also continued; he received an honorary degree (in social sciences) from the University of Cordoba (Argentina) in 1963. To the end, he remained the cold and single-minded organizer, who lived only for his work. His wife and two daughters, though they arguably existed, impinged not at all on his professional persona. That singleness was undoubtedly his mechanism of continuity, in a career spanning, but continuing steadily through, two world wars and their aftermaths.
Gini and Toscanini, contemporaries, contributed to Italy's stature from opposite sides of the WW2 line, but they were cognate personalities. Toscanini once scolded an orchestra which did not know the Beethoven Septet, recalling how in his early days he had gone without lunch in order to buy that score. Gini in similar fashion discouraged unprepared students who wanted to do a PhD with him. He scorned the modern youth who bought a car, where Gini himself, at that age, "had bought a calculator."
