The Personal Distribution of Income

Steindl, Josef

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Document type:: Works

Collection:: Josef Steindl Collection

Title:: The Personal Distribution of Income

Author:: Steindl, Josef

Scope:: Kopie eines Typoskripts mit handschriftlichen Anmerkungen, insgesamt 27 Seiten mit originalen handschriftlichen Anmerkungen auf Seite 23 (nummeriert als Seite 18)

Year of publication:: 1972

Source material date:: August-September 1972

Language:: English

Related work:: Steindl, Josef: The Personal Distribution of Income. In: Steindl, Josef: Economic Papers 1941-88. London: Macmillan, 1990, S. 356-371

Topic:: Stochastic processes and size distribution

Shelfmark:: S/M.52.9

Access:: Free access

T.S showing disproportionately increasing output with any increase in input ( cost, or employment ). In fact, however, we often find that it is not so and. that hoth. regression coefficients are smaller than one, decreasing cost and decreasing returns / A ' apparently coexisting. How is this possible? It can only occur with wide dispersion round the regression line. The exceptionally effieient plant will tend to be counted as small plant in the input dimension whi?e the unusually inefficient ones will be counted as large. In consequence there will be a bias in favour of decreasing returns as measured in the input dimension ( regression of output on cost or employment ). The inversion sf the regression corresponds to the fact that the ration of the two standard deviations is reciprocal in the two regression coefficients. If it is 9/10 in the regression of input on output, it is 1o/9 in the other regression. Sut-, mnless the correlation coeffieient is sufficiently high, the regression coefficients will both have values■below unity. The same mechanism must also be at work in - '• the wealth-income distribution: Those with high return for a given wealth will be classified nong large incomes, those with low returns with the same wealth among small incomes, which tends to counteract the natural tendency of wealth to increase with income. This may have contributed to the flatness of the wealth-income regression in the lower income range, although the chief reason for that is no doubt the truncation of the wealth distribution. The preceding example of plant size, in which only one underlying theoretical relamion is presumed to exist, shows that while it is logical to expect in this case, if one regression reflects the underlying relation, that the other should as it were represent the inverse of it, yet in reality this will not be true because the second regression will be more or less distorted by the dispersion of values round the first regression line. If we have two underlying relations then each of the regression lines will be influenced by both of them, either directly or indirectly, because each will be to some

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