Pen's Parade

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Pen's Parade or the Parade of Income is a sensually impressive illustration of income or wealth inequality, in which all people in a country, sorted according to their income and with body measurements according to their income level , march one after the other past a spectator stand into a stadium . The average income people are of average height; likewise the viewer. Those who earn twice as much are twice as big, and so on. The viewer sees a “parade of dwarfs , followed by a few incredible giants ” (Jan Pen).

The Dutch economist Jan Pen described his moving symbol for the first time in 1971 in his book Income distribution : facts, theories and methods (Original: Income distribution: facts, theories and policies ) to illustrate income inequality using the example of Great Britain in the chapter A Parade of Dwarfs (and a Few Giants) . Pen parade is a term that is widespread in the specialist literature for a data set of economic variables sorted in this way , in particular for personal variables such as income and wealth variables . Modifications of the Pen Parade now exist, for example the square Pen Parade , the Augmented Quadratic Pen's Parade , Parsimonious Quadratic Pen's Parade , Polynomial Pen's Parade or the Power Pen's Parade .

Because the train would actually take a long time, Pen sets the duration of the parade from the first to the last person to one hour . The full hour represents 100% of the population and the parade starts at time 0 with 0% people marching by. Pen's Parade is a clear representation of a quantile function .

Observed events

Pen describes how the parade for the spectators in the stands visually and in the time course represents. The viewer would not see a row of people growing evenly. After exactly half an hour half of all people would have already passed the stands and at the same moment the person in the middle of all people and incomes would pass by - the median (see also: Average income ) - but the average-sized people would with the average income does not run in the middle of the train, and do not reach the stands halfway through, but only much later.

  • At first, despite the running parade, the viewer doesn't see anything at all for a while: the indebted people in front run upside down under the surface, because their height is negative.
  • Shortly afterwards, the first upright people with a positive income appear . They are tiny and hard to see.
  • For about five minutes, the viewer looks down at small figures, just a few centimeters tall: predominantly old people and children, people without permanent jobs who get by with odd jobs.
  • After ten minutes, the full-time workers arrive, initially the mostly low-skilled unskilled workers , office staff and shop assistants - waist-high to the audience. This continues for over half an hour.
  • Halfway through the time, the audience might expect to be able to look passers-by in the eye, Pen wrote. Average-sized people should be in the middle, but marchers are still quite small; now the experienced tradespeople , skilled industrial workers and well-trained office workers - many are still less than five feet and more and more of them are arriving.
  • It takes around 45 minutes for the passers-by to be as big as the audience. Only now does the size increase noticeably, albeit slowly.
  • In the last 6 minutes, the top 10% earners are running in. The sizes are now increasing faster and faster. Doctors , lawyers and senior civil servants .
  • Moments later, successful company managers , bankers and stockbrokers stare down from 15 m, 30 m, 150 m.
  • In the last few seconds a glimpse of pop stars , film stars, the most successful entrepreneurs - right down to their knees.
  • At the very end a giant , the soles of his shoes meters thick.

Pen's Parade in Switzerland 1969/70

  • Average height during the first six seconds: 14 cm.
  • After 16 minutes the parade reaches a size of one meter.
  • The average height of 1.75 m is only reached after 41 minutes.
  • The body size continues to increase only slowly, after 46 minutes it reaches 2 m.
  • 55 minutes: height 3 m.
  • 57 minutes: Height 4 m.
  • After 58 minutes and 18 seconds: 5 m.
  • Four seconds before the end of the parade, after 59 minutes and 56 seconds, about 45 m is reached.

Pen parade → Lorenz curve → Gini index

A pen parade in its mathematical representation is the basis for deriving various measures of unequal distribution . For example, the Lorenz curve is a form of evaluation of the pen parade for a quantile function; many unequal measures of distribution, such as the Gini coefficient , are in turn evaluations of the Lorenz curve. The corresponding Lorenz curve becomes clear from Pen's Parade when a large box is set up in the stands and everyone who marches past puts their income or assets into the box. After the parade, the initially empty box contains all the income or assets of the entire marching group. The filling level of the box is therefore a function of the time or the number of people who have passed by. If the box is just big enough to hold all the "gifts", it will be one hundred percent full at the end of the parade, after one hundred percent of the time has elapsed or people. The Lorenz curve is the percentage fill level as a function of the percentage of time elapsed or people who have walked in from zero to one hundred percent. A Lorenz curve of income is a normalized integral function of a pen parade. Plotted in a coordinate system, the result is a continuous graph from point (0,0) to point (100%, 100%). A non-uniform distribution measure is calculated from the curvature of the Lorenz curve by means of statistical mathematics, for example the Gini coefficient mentioned above, often called the Gini index for short .

See also

Web links

Individual evidence

  1. ↑ a b Ambros P. Lüthi: Measurement of economic inequality. In: Lecture Notes in Economics and Mathematical Systems. Volume 189, p. 14, Springer-Verlag, Berlin Heidelberg New York, 1981. ISBN 978-3-540-10700-2 , e- ISBN 978-3-642-95387-3 .
  2. ^ Jan Pen: Income Distribution: Facts, Theories, Policies. Praeger Publishers, New York, USA, 1971.
  3. ↑ Examples: Tomson Ogwang - Additional properties of a linear pen's parade for individual data using the stochastic approach to the Gini index
    Ambros P. Lüthi: Measurement of economic inequality, Figure 2.1. In: Lecture Notes in Economics and Mathematical Systems. Volume 189, p. 15. Springer-Verlag, Berlin Heidelberg New York, 1981, ISBN 978-3-540-10700-2 .
  4. ↑ S. Mussard, JS Kamdem, F. Seyte, M. Terraz: Quadratic Pen's parade and the computation of the Gini index. In: Review of Income and Wealth , Université Montpellier I , France, 2011. (PDF)
  5. ↑ Example: JS Kamdem - Gini Index and Polynomial Pen's Parade. Université Montpellier I, France, 2011. (PDF)
  6. ↑ Example: Jules Sadefo Kamdem - A nice estimation of Gini index and power Pen's parade
  7. ^ Rowan Colbeck: The Income Parade . The Open University , 2010.