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:: Typoskript, 28 Seiten

Year of publication:: 1972

Source material date:: August-September 1972

Language:: English

Note:: Mit handschriftlichen Anmerkungen.

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

JEL Classification:: D31 [Personal Income, Wealth, and Their Distributions]

Shelfmark:: S/M.2.1

Access:: Free access

2 There are only two alternative transition for a person in this system: Either a rise of income from one year to the next (note that the income classes are on the log scale) which has probability p; or death of the person, i.e. transition to the zero class, which has probability q (p + q = 1). In addition, there are entries from the zero to class/lreplenish the stock of income receiver^ 1 ^ The essence of this model is described by Feller ' in the following terms; The state Ek represents the age of the system. When the system reaches age K, it either continues to age or it rejuvenates and starts afresh from age zero.’ The successive passages through the zero state represent a recurrent event. The probability that the recurrence time equals K. is p q. We are interested in the question; How many years have passed, i.e. how many income steps have been mounted, since the last rejuvenation? This is the "spent waiting time" of the renewal process. Choosing an arbitrary starting point we can say that in the year n the system will be in state En- if and only if the last rejuvenation occured in year n-K. Letting n-K increase we obtain in the limit the steady state probability of the 'fepent waiting time" 2 \ It is proportionate Vol. I. XV,3, p. 382. ^ Chapter V.

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