THREE SUMMARY MEASURES OF THE DURATION OF UNEMPLOYMENT
| DOI | http://doi.org/10.1111/j.1467-9485.1982.tb00439.x |
| Published date | 01 February 1982 |
| Date | 01 February 1982 |
| Author | Brian G. M. Main |
Scottish
Journalof
Political
Economy,
Vol.
29,
No.
1,
February,
1982
0
1982
Scottish Economic Society
~3&9292/X2/wO70000 $02.00
Notes and Communications
THREE SUMMARY MEASURES
OF
THE
DURATION
OF
UNEMPLOYMENT
BRIAN
G.
M.
MAIN*
University
of
Edinburgh
There are two common motivations for employing summary measures to
describe an observed frequency distribution. On the one hand, it is often
possible
to
find parameters which completely describe the distribution, e.g. the
mean and variance in the case of the normal distribution. On the other hand,
some measures afford an intuitive interpretation of the phenomenon under
study, e.g. life expectancy at birth in the case of mortality data.
My recent discussion of unemployment and employment durations in Main
(1981) and Layard’s (1981) subsequent comment on that paper, arise very
much from the second of these two motivations. Neither work claims to be
describing the observed distribution of unemployment spells with any
completeness. Rather, the emphasis is on choosing a summary measure
of
the
observed data which will describe the observations in a manner that is readily
understood. There is no possibility of any one such measure being superior to
another in any scientific manner. The familiar statistical concepts
of
“uni-
formly most powerful” or “sufficient” are not relevant.
Thus, although it is always possible to employ a descriptive statistic in an
inappropriate manner, Layard does seem to be overstating any case he might
have when he claims to “reject” two of the three measures discussed in my
paper in favour of the third.
To
make this point clear it is, perhaps, worthwhile
recalling the three measures in question. The terminations-weighted spell
length,
S,,,
reports the average length of a spell of unemployment occurring in
a given period of time. Introduced by Fowler (1968), this measure is akin to the
expected life at birth in demography. The experience-weighted spell length,
S,,,
weights each spell of unemployment in progress by its length at
completion. This may be viewed as the average length of unemployment spell
in which a typical week
of
unemployment
is
spent. The third measure-that
favoured by Layard, is the interrupted spell length,
T,
which measures the
length of unemployment experienced to date by the currently unemployed.
As
the currently unemployed are, by definition, not yet finished their unemploy-
ment spells, each enters this measure with an underestimate
of
his final spell
length.
None of these measures is without its uses. The terminations-weighted
*I
am grateful
to
George Akerlof for helpful discussions. Remaining errors are
my
own.
Date
of
receipt
of
final manuscript:
2
June
1981.
99
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