Elizabeth T. Simpson

H. Robert Bartell

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National Bureau
of Economic Research
Volume Title: Pension Funds of Multiemployer Industrial Groups, Unions,
and Nonprofit Organizations
Volume Author/Editor: H. Robert Bartell and Elizabeth T. Simpson
Volume Publisher: UMI
Volume ISBN: 0-87014-491-X
Volume URL: http://www.nber.org/books/bart68-1
Publication Date: 1968
Chapter Title: APPENDIX I: ESTIMATING PROCEDURES
Chapter Author: H. Robert Bartell, Elizabeth T. Simpson
Chapter URL: http://www.nber.org/chapters/c1112
Chapter pages in book: (p. 18 - 19)18 Pension Funds
APPENDIX I: ESTIMATING PROCEDURES
Data on assetsofmultiemployer and union funds for 1959 are cle-
rivedfrom the survey described above. Of the 715 mult.ieinployer and
eight union funds surveyed, 85 were insured and 577 self-insured;
information was not available on the remaining 61. The total asset
figure used in the study represents an estimate for all self-insured
funds, and the aggregate portfolio composition is that of all self-
insured funds where asset breakdowns were available (561 funds).
The proportion of insured plails in this survey is approximately the
same as that found by the Bureau of Labor Statistics.16
Data on assets and portfolio composition for years were
derived from a stratified random sample of the funds, 'included in the
1959 survey. Information on all of the funds that had more than $5
million in total assets at the end of 1959 was obtained. These 36 funds
represented over 60 percen.t •of the assets in all rnultiemployer and
union funds in the 1959 survey. In addition a sample of 64 funds in the
size classes below $5 million was drawn. (See table 1—4fordata on the
concentration of assets.) The sample' size and the number of sampling
units in each size stratumwere based on a. system of optimum alloça-
tion which takes into account not only the number of funds in each
stratum of the population (N;1) hut also the. stan(lard deviation of each
stratum .Theallocationofsanipi ing uiiits to each stratum was
proportional to the product of the, number of funds in each stratum
amid the standard deviation of the stratum A sample size of
BureauofLaborStatistics.Bulletin 1320. v.17.
'7Whenoptimum allocationIsused,thesample size. (a) for estinrnthig a total, e.g.,total,assets, for all
funds,is given by theformula:
no
i
where
or the sample size. uncorrected for a finite population, and V is the desired in the sample estimate
and Is determined by the formula V= (dX T)', where d is the acceptable margin of error or the. half-width
of the confidence interval (In this casO .025) mmd T is the' universe total (in this case the total assets of all
funds with less than $& million in 1959).
Thus
V= (.025X$478,240)'= 142,945,936.
(114872)'
92.3
+142945936
or a sample size of 64.
Aflocatedaccordingtotheratioineach stratum of the samplesize in each'stratum was:
Tofai Assets Sample Size
(thousandsofdollars) (flA)
1 0-99 1
2 100-249 ,3
3 250-499 ' 4
4 6
5 14
6' 2,000-4,999 36
64'
Source; WillIam 0: Cochran, SarmylingTechniques,ANewYork, 1953, pp. 73—74,87—90I. Multiemployer and Union Pension Funds 19
64 for the funds with less than $5 million in total assets will give an
estimate of the aggregate assets in these funds, with a maximum error
of 2.5 percent. Since each of the funds with assets over $5 million was
surveyed, the resulting estimate for all multiernployer and union
funds for years subsequent to 1959 would be in error by substa.ntially
less than plus Or minus 2.5 percent.
The portfolio composition of rnultiernploye.r and union funds was
by weighting the sample portfolio distribution for each
stratum by the amount ofasset.s in t.hat stratum in 1959. The results
of this calculation are show in table 1—7.
Since the sample used to estimate aggregate assets and portfolio
distribution was drawn from the universe existing in 1959, funds
formed since that year are not included. No attempt was made to derive
an independent estimate of the assets added by newly formed funds
in the years 160—64. This means that the aggregate assets figures
may be too low, and the size of the error may tend to increase as the
sample year moves farther from 1959.
However, there are two factors that may keep the error within
reasonable bounds. First, the growth of funds in the sample is some-
times augmented by the merger of an existing fund not. in the sample.
This lends an offsetting upward bias, but probably not a very large
ones to the estimate of aggregate assets. Secoiicl, new funds are likely
to be relatively small in terms of for several years after their
inception, evemi if they cover sizable numbers of persons, because past
service liabilities are funded slowly.
On balance., it appears that the sample estimates are better for the
earlier years. However, the figures for later years are not likely to be
greatly in

Pension Funds of Multiemployer Industrial Groups, Unions, and Nonprofit Organizations

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