Income Distribution: Line of Reasoning (Fassung 1)
Josef
Steindl
AL00659437
Income distribution: Line of Reasoning
Eliminate all reference to demand and supply
The basic dichotomy is that of grade £ a Stock) and payment per gradey
urade is
wealth, rank in a hierarchy of offieials(seniority),
degree of skill or specialisation, place in educational hierarchy,
sometimes place in a hierarchy of gifts and talents.
\ The age may better be seen as a separate dimension, or as an
^influence on the grade.
The grade should be mesasurable wihj^in each field, either
directly or indirectly ( scope of operations; with managers it
would be siye of company or organisation and rank in the organisation ),
It might be connected with a historical element - years of training
or education, seniority); the whole development may have a
historical element - technological and organisational development.
Between various fields,however,there is no direct
comparison ( although the cost of education etc would offer
such a possibility, this is not always fully relevant in practice
and in the gase of gifts it does not apply ). The comparison
is in effect based on considerations oprestige of the calling fr^
traditional standards^ etc, factors irrational from the economists
point of view.It is acts of_economic policy on the side of employers
which decide finally these standards. It follows that the
grading remains undefined as between professions^ callings, fields,
and the comparison is affected only on the plane of payments.
We can therefore get distributions with respect to grade only in
the various separate fields - managers, footballers, ski as or
filmstars etc. From this are derived distributions with respect ^t£?
I
payment; they have then to be mixecpith distributions of the
41 the JpK/vVw? ' ifT" £*>1^
Obtained - in practice the Pareto coefficient - in tjie
parameters
whole population of income earners in order to obtain the
distribution of income for tthis population.
Reconciliation of the pattern of distribution for the w^hole
and for the constituent parts: The miaing has to explain that
( that presupposes large numbers of professions etc )♦
Perhaps the result obtained for the wealth distribution - that
XMX#XP&MXXX&XXXMXpMS^/i s independent of the distxxfex
distribution ».r.t.payment)
payment per grade (return on wealthVcan he generalised, but that
does not seem to contribute to/che question of standards of various
professions. /
A
W,
e accept a§ the general pattern of explanation the interplay of
the two systems": grades, and payment*for grade differentials,
the pattern which was outlined at the start in connection with
Champernownes theory. his duality of grades and differentials
is preferable to that of demand and supply which is too static
and is bound to lead us astray.
-*-n the case of earned income the grade would be wealth,
and the differential payments would be the return rates on different
amounts of wealth. (
The grade here depends indirectly on time; in other cases -~tfu
burocratiw pattern - the grade depends directly on time (promotion);
in still other cases, the grade depends on the qquisition of knowledge
or skill, aand therefore again on time. In many cases, however,
fit
the grades are provided by natural gifts , as with the film star,
the sportsman, and probably also the manager;in all these cases
learning^ does play a very important role,too, but we could hardly
expect a close correlation between the time of learning and the grade here.
Rather, it would seem thq,t there is a natural distribution of gifts
( not merely genetically , but also ±fe*x due to the influence of the
milieu and*^childhood influences). This distribution would, most plausibly,
A
be rather skew, and that of the grades would therefore be also skew.
We might asume that it would be exponential or geometrical § theoretical
reasons might be found in ConngePalm^4^ghtxe theory f)~. "f £
W f 1
t*sf‘'
^hile in the case of'^eSFEF the whole weight of the u<
explanation was put on the distribution of wealth, which moreover
had alreddy all the required qualities which needed only to be shown
to reproduce themselves in the iy&come distribution, the weight of
the eyplanatory procedure in these other cases is shifted entirely to
the distribution of the payment. This is very largely dependent ,
indi^rectly, on processes of economic development evolving in time.
The information space accessible to the®w£ners of high grades gets
larger and larger, and with it grows the payment received by that grade.
We must now argue from the distribution of payments conditional
on grade, via the distribution of grades, to the distribution of
payments among persons.
f/C^ &?.(* ■> rr~ 3 0-1 ATT
h
It is required by the above that the grades or rather the
difference bitween the grades should be measurable.
This measure would be provieded by the scale of operations
which again, in my interpretation, has something tquo with
the information spg.ce of the individual.
The relative income differentials - income per grade times so
many percent gives the income of the higher grade,—
are determined by a kind of random walk governed by technical
developmen^ind organisational development - making for a
diffusion process; this will be counteracted by competition
through the appearance of new supply - training and eduction
of people. Teh distribution of grades will thek.determine the
frequency of income receivers in varions classes.
The diffusion of managers and stars earnings may be regarded
as a change in thecapitalist system - a shift of incomes from
wealth to these"new men". It remains to be decided, however,
whether the excess incomes of these people are an "additional
exploitation", in other words whether they are paid by the
workers, or whether they are derived incomes, representing
a share in the surplus of capitalist which the latter are
gracing to the new men for one reason or another ( Baran-Sweezy
would say for the purpose of expanding effective demand , in
other wonds as a counter to underconsumption. )
The old classics' ideas about derived income may still
prove quite useful in the event.
The manager may be likendd to the oa.ior domus who ultimately
replaces the letigimate owner who has become decadent.
What is the basis for the position of the manager since it
is not wealth? One might say it is the distribution of power,
but that is not very revealing. I should say it is the scope of
his information over which he rules ( he is like the spider in
the center of a net ). This is of course the snjae as the
scale of operations concept used by T.Mayer, ^he distribution of
ability and earnings, fi.E.&S-t.i960.
3
The new men also ±hx tend to have wealth - simply because their
large in come enable them to save a lot. However, their wealth is
not the source of their income and ist will in genral be
small as comparedwith the wealth they would have to have in
order to get from it alsone the income they actually have.
In order to take account of these relations we should have
to work out a process in wealth and income, with allthe
feed-backs between the two.
One might- purely formally- calculate a ficticious capital
resulting from the application of the return rate on real wealth
to the income of the manager. Then formally all income would
be shown as a return o/waalth. The proportion of real wealth in
the total would be the lower the newer the men would be.
H.Simon gives an explanation of the earnings of managers
which is based on the hierarchy , measured by scale of
operations, and on the relation between the grade and the
payment; there are again two exponential ( on the face of it
geometri®al)distributions involved. The theory might be
generalised to apply to stars, specialists. There is one
fault iiy^t: It is not a model of a ^Process, ressembliig in this
the theories of Roy etc. To be satisfactory, the hierarchy
of payments would have to be shown to evolve from a historical
process which continues.
See H.Simon, The compensation of Executives. Sociometry 1957*
based on empirical investigations by ^.R. Roberts,
A general theory of executive compensation based on
statistically tested propositions. Qu.J.E.1956
Bases of a historic#®^- explanation would be that the
scale of operations increases in time, or rather that there is
a diffusion of the schale of operations in the course of time.
Diffusion over the space of income payments.
Reason for the diff ustbon is simply the grov/ing complexity of
the economic system.
Before the modern developments we have already basiclally the
same pattern in the classical division of labur which
increased the market of the producer (craftsmen) and created
income differentials.
ThB payments hierarchy is full of irrational factors
and to be explained by sociological factors, as Simon rightly argues.
(Think of the engineers in Austria !
<')
<*-)
0*1
t\
Simon on executives
-'JV
L
First assumption: A constant span of control at all levels of
the hierarchy, ^THis ought really to he a random variable.}
This leads to: jj^S) size ( number of executives^according to
Simon, but a reasonalle measure would bi
capital or sales)^(L) level of the hierarchy^]
In S = L In n + constant,
Second assumption: & constant ratio between a man's salary and that
of his subordinate.^b^ (also that ought tojbe a random variable )-
That is used to determine the salary of the top executive in
('fafrd j !
terms of those at other levels:
In C = L In b + eonstant^
By elimination of the level L we obtain
n _ In b tv
In C = , , , , In b
—---- In S + cpnstant - constant —
the salary of the top(official »')Manager is a function of size of
company^ ^
that is the xsxizx relation empirically observed by Roberts.
It might be hoped that Roberts relation also holds more
generally for all organisations like hospitals, city administrations
etc. although the measure of size becomes again more prob/elematic
(employment? which would however not fit automatized corporations).
Simon now passes to another empirical observation, made by Bavis,
The frequency distribution or density of executive's salaries
at General Motors in 1936 Wfas a -^arato distribution:
f°':
C' = m N~0*^ f C': salary , N;number of executives receiving (P '
O/
The number of markers at level L' from the top is
N ( L' ) = nL'"1
Simon now writes from assumption 2
C'(L') = M b1 L'
1 . AJi
but his M must be logically equal to the to^/salary C, although he
does hot say so.
The equation obtained by eliminating L' is therefore
inc'"4H- lnK
________U W■ , ^ V
jfa. N =\L,-l)fa**'
■fa, £* ~ fa~ M
6m, &
'tv
Note that the two empirical relations are of an entirely
different kind. One determines the top salary in
various companies. The other determines the salary
corresponding to the frequency with which it is paid in
a certain company ( the more natural way of putting it
would be N = m' C-5 tL*
Simonas point(howefer( is that with his explanation the
parameter is the same in thejtwo very different equations
which squares with the empirical isx result.
Simon's theory follows the pattern of the usual Pareto
explanation - the two exponential distributions -
but it is unsatisfactory because, like Roys esplanation of t
lognormal distribution , it does not contain the time element.
We must get history iito it. v
A way by which it can enter: the size of organisations grows
with time.
Incidentally the siye distribution of companies is already
pareto distributed, therefore the-top salurj would bo so ‘
rH-a^ri bo ted, s-inde—irt^-drs—a—linear —function of the s i z W7~7 ^
Elaboration of the algebra:
Substituting from 3 in 7•
('LOln b . _T
In ^ --n’T""1 "r- In N
In n
lnb
In n
( In ^ _ constanti ) + constant
P
In "b
In C' =“ t---- ( In N ^ In S -l-constant.) + constant,, j
-*-^1 n I i0l0^r
The results of Simon imply that th e same parameter In b/ In n
occurs in both relations and the fact that the parame&er is
empirically the same serves him as confirmation.
He has implicitly assumed that the parameter is the same for
all companies, that is implied in his argument.
We stuck to this assumption in deriving the gneral distribution 9
which can be more conventionally put as follows:
In N § In C 1 In S ^constanti j xX chnstant2
In b
N = C '
(ET
exp(constanti -constant2 )
If we now mix the above distribution of N with the frequency function
of S, the size distribution^we ought to get the frequency of
salaries for the whole industry. The distribution of S is Pareto.