AN INDEX OF THE POOR AND RICH OF SCOTLAND, 1861–1961
| Published date | 01 February 1971 |
| Date | 01 February 1971 |
| Author | Lee Soltow |
| DOI | http://doi.org/10.1111/j.1467-9485.1971.tb00973.x |
AN INDEX
OF
THE
POOR
AND RICH
OF
SCOTLAND,
1861-1961
LEE
SOLTOW
The extent of poverty and affluence in a country are relative to time and
place. Over a period of time a!; long as a century changes in the degree
of
inequality are especially intriguing because they may give
strong
clues about
future changes. Has the industrial revolution continually made the poor
relatively poorer or richer? Has there been a long cycle in inequality in
developed countries, with greater inequality in the middle stages of econo-
mic growth?
There are formidable statistical problems which arise in trying to
con-
struct a long-run inequality ind.ex. Almost
no
country
known
to the author
has ever
obtained
income or wealth figures from a sampling or complete
enumeration of its total labour Eorce except in the last generation'. Certainly
no continuous time series exists for different wealth or income groupsa. This
leads us to look for some proxy for income or wealth of different groups.
The housing index of inequality to be presented in
this
paper may represent
very adequately change in income inequality. This proxy derives from the
exciting Scottish figures pertaining to the number of rooms occupied by each
family in Scotland for each of the census years from
1861
to
1961.
On
this
basis, a long-run inequality index will be constructed which may be the
best representation of inequality change of economic well-being that exists
in the world. It will
be
shown
from some estimated income distributions of
1867
and
1959-60.
that the chmge in the inequality
of
the distribution
of
rooms
has
been about the same as the change in the inequality of the distri.
bution of income for the century.
I
THE
1861
DISTRIBUTION
Suppose a population had three families living in houses with
2,
3. and
7
rooms. The distribution of the use of the aggregate wealth of the
12
rooms
among the three families would yield an arithmetic mean,
xm/,,
of
4
and
a
Gini
coefficient of relative inequality of
R=A/(2@=(2.2)/(2 X4)=*28
where
A
is the average of the paired differences in number of rooms
between
families. At least two questions arise immediately. Might not the family with
*
Dramatic exceptions were the censuses of
1850-70
in the United
States,
when
each individual was asked the value of his wealth.
2The
experience in Great Britain is described in Soltow
(1968).
Explanations
of
decreased inequality are offered
using
a
framework
of
economic
growth.
4
49
50
LEE
SOLTOW
7
rooms have lodgers or boarders while the others do not? Might not the
family with
7
rooms have more family members such that adjustment to a
room-per-person level would show little or
no
inequality? It is found that the
lodger problem has very little significance
in
the aggregate resultss. Adjust-
ment of rooms per family to rooms per person does temper results, but
it
probably
is
misleading as a measure of economic power. It is not common to
adjust income or wealth per family to income or wealth per person before
computing the level of inequality.
Allied ramifications
occur
over time as the distribution of the sizes of
families alters. Division of families into smaller units occurs with economic
freedom; each of these in turn may limit the number of children it has.
Changes in distributions of rooms over time will be standardized for family
size. It
will
be
found that standardization for family size has little effect
except for
an
anomaly for families of
size
one.
It
is
freely admitted
that
the
quality of rooms
in
a nation changes over time and aat our index for
change in number of rooms will not adequately reflect the change
in
the
real value of rooms.
The distribution of rooms among families in
1861
is given
in
Table
I.
Harsh weather dictates that one have at least a roof over his head
so
there
is
no
class
with
a value of zero. But
one
of every three families had
only
one
room to live in. It might
be
supposed that part of this startling figure could
be explained by large numbers of single men or women.
If
one examined
the size of the relatively poor families, he would iind that few were families
of
size
1;
the average size
of
3.5
accounted for
829,000
or more
than
a quarter
of Scotland's population. Thus there were sizeable numbers living
in
very
cramped housing conditions. This was true not only in large cities but in
rural districts. About one of each
30
of the one-room dwellings had
no
windows at
all.
The proportion of families living in one-room houses may not be a very
adequate index of general inequality of rooms among families. The correla-
tion coefficient between the proportion and Gini coefficient for
33
counties
in Scotland in
1861
was but
.05.
It
is
quite possible that mansions are as
likely to
be
in rural districts as in urban areas. in poor
as
in rich districts.
Inequality is very often depicted
in
the form of a Lorenz curve as are
our
figures for
1861
in
Chart
1.
It is
seen
that inequality was relatively large by
3The
census
authorities published tables of room
numbers
for families having
lodgers in Glasgow, Edinburgh, and Linlithgow
County
in 1871. It was possible
to
test the effect of lodger families on
Rm/fm.
It is found that eliminating lodger families
had almost
no
effect
on
the value of
R
for Scotland and decreased
R
by
3
or
4
per
cent. in Glasgow and Edinburgh.
'
The text deals with the problem of family size by examining inequality for
groups
of
families classified by size of family. Transforming rooms per family into
rooms per person necessitates the assumption of perfect equality of
rooms
within
the family in the absence of other information.
It
is
assumed that each person in the
has
Xro,per=Xro/fnm'Nper,fam.
When
all
men, women, and children are assigned
an
'ro/per*
'ro/per
is
,413
for 1861 and
~304
for
1961.
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