GSSE/ACT/2/1973
International Labour Organisation
MEETING OP THE ACTUARIAL SUBCOMMITTEE OP
THE COMMITTEE OP SOCIAL SECURITY EXPERTS
Geneva, 1975
A SIMPLE COMPUTER MODEL TO PORECAST INCOME
AND OUTGO OP UNEMPLOYMENT INSURANCE PROGRAMMES
Denis R.J. George
ILO Consultant
Geneva
International Labour Office
73
Sa
y,8/£
*3
43878
TABLE OP CONTENTS
Page
INTRODUCTION
I.
II.
III.
IV.
V.
1
OUTLINE OP REASONS FOR COMMISSIONED STUDIES
1
THE GENERAL APPROACH
1
GENERAL OUTLINE OP TYPE OP COMPUTER PROGRAMME
2
REGRESSION PROGRAMME
„.
Graph A
7
Graph B
8
FINANCIAL FORECAST PROGRAMME
9
FINANCIAL PROJECTIONS - SERIES C
VI.
11
CONCLUSION
12
APPENDIX A
NOTES
3
13
o
14
INTRODUCTION
A number of studies have recently been commissioned by various states and the
Unemployment Insurance Service of the United States Department of labor in connection with long term financial projections of their respective state unemployment
insurance programmes.
This paper is a summary of the basic approach taken in
these studies, some of which have yet to be completed.
It is appreciated that the substance of this paper is no more than a first
step in the direction of more sophisticated approaches to long term financial
forecasting of unemployment insurance.
The process of evolution will ensure
that improvements will be made in the techniques used; in fact, some of the
techniques described in this paper are more sophisticated than those adopted in
the early days of the first study.
Because unemployment insurance plans vary considerably from jurisdiction to
jurisdiction, especially in the area of financing, no attempt has been made to be
overly specific in any area, but rather to give an overview of the approach used.
I.
OUTLINE OF REASONS FOR COMMISSIONED STUDIES
Unemployment insurance benefits in the United States are financed through a
payroll tax levied on the employers of covered employees.
No contributions are
required from employees, except small amounts in three states.
Benefits are
payable for various periods dependent upon labour attachment history, and the
amount of the benefit is a specified percentage of wages up to a stated maximum.
The increase in rates of unemployment experienced from late 1969 resulted in
the serious depletion of the unemployment compensation funds of a number of states.
This was due, in a number of instances, to the rates of payroll tax being reduced
to very low levels during the period of low unemployment encountered during the
latter part of the nineteen-sixties.
Each state has its own unemployment insurance plan, and to reduce employers'
federal taxes to the minimum each plan has to conform to certain federal standards,
one of the most important of which is that almost every employer has to pay a rate
of tax in accordance with his own individual unemployment experience.
The existence of experience rating does, in many instances, inhibit an immediate increase
of taxes in the event of an increase in the rate of unemployment, as the
administrative work involved in gathering the experience of each individual
employer is time consuming.
The unemployment compensation funds in a number of
states have, consequently, experienced considerable financial difficulties before
effective remedial action in the way of tax increases could be taken.
In
recognition of these problems, a number of states are developing, with the help
of actuarial consultants, computer programmes which permit the quick evaluation of
the effect on the unemployment compensation funds of changing levels of unemployment.
II.
THE GENERAL APPROACH
The traditional actuarial approach to making financial forecasts of the
future operations of any benefit plan has been to make one set of calculations
using the best estimates of probable future operations.
This approach was made
necessary because of technical difficulties involved in making lengthy mathematical calculations.
Since the advent of the computer, however, this approach
has changed, as it is now easy to obtain in a matter of hours any number of
financial forecasts based on alternative assumptions.
The great disadvantage of working with one set of assumptions is that the
probability of the assumed occurrences actually taking place is very small, so
that the forecast figures are unlikely to be accurate on a year to year basis,
and can only be used as an indication of the future on an average basis.
- 2 -
The solvency of any unemployment compensation fund depends on the interaction
of taxes received and benefits paid, so that knowledge of the incidence of cash
flow from year to year is more vital than long-term forecasts based on average
levels of unemployment.
Any forecasts based on the analysis of past data must be viewed with care.
However good any curve fitting to past data may be, this mathematical approach will
not necessarily produce viable results as the sociological and economic environments in which the past data were observed are not likely to exist in the future.
Consequently, any regression technique must be viewed only as a tool to "put one's
feet on the ground", and any future values thus obtained should be examined
subjectively with a view to changing some or all of them to allow for possible
changing future conditions.
•
Finally, any approach utilising a computer must be one that permits a quick
evaluation of the future by measuring what the financial effects on the fund would
be if certain rates of unemployment and other economic conditions were experienced
in the future.
Furthermore, if such an approach is to be used frequently, it
must be easy to understand by. the user, applicable to data that is immediately
available, and capable "of simple modification to reflect changing conditions and
increasing refinement in available statistics.
III. GENERAL OUTLINE OF TYPE OF COMPUTER PROGRAMME
Many organisations view the development of computer programmes with some
scepticism.
Frequently, such programmes are expensive to produce and require a
great deal of developmental time.
Furthermore, they are very often so complicated
as to require a great deal of input data not immediately available, so that the
production of results is further delayed while the required input data is gathered.
In the studies under review it was felt that it was essential to develop a very
straightforward and reasonably simple computer programme.
It was recognised that
in concentrating on the simpli»ity of the programme some degree of accuracy m the
forecast results might be forfeited.
At the same time, it was also recognised
that, as any future .forecast is based on assumptions, the important factor is the
ability to compare the relative levels of benefit outgo and tax income according
to various economic condtions.
The development of a simple computer programme written by the state staff,
under the guidance of a consultant, was felt to be the best approach, as this
ensured the ongoing interest of the state staff.
Furthermore, as time went by
and more refined statistics could be developed, the programme could evolve in such
a way as to reflect more closely the needs of the particular state.
Two basic approaches to financial forecasting were studied. ' The first was
a system which would simulate the underlying economic forces of the state, thus
resulting in the forecasting of future unemployment rates and benefit costs based
on various assumptions of the values of the factors affecting the economic
activity of the state.
This approach would, in effect, result in the building
of an analog system.
The second approach was to consider only the financial effects on the income
and outgo of the unemployment compensation fund if certain rates of unemployment,
rates of inflation and changes in the labour force were experienced in the future.
This is, in essence, a "what if?", approach enabling a quick evaluation of the
financial effects of any series of assumptions that one might like to make.
As stated earlier, any forecasts based on past experience cannot be used
without adjustment, as the economic, sociological and political environment of
the future will be different from that in the past when the data was gathered.
Because of this, and in view of the complexities of building an analog model, it
was decided to use two sequential mathematical programmes.
In these particular studies the changes to the respective state unemployment
insurance programmes over the past few years had been sufficiently minor that,
through regression techniques, relationships could be established between the
various factors underlying the cost of benefits and the levels of taxation.
-3 The first mathematical programme was written on an iterative basis such that
the relationships so developed from past experience could be used to forecast the
corresponding relationships in future years.
The output from this regression
programme was scrutinised by economists and other skilled observers and subjective
changes made to reflect their expert opinion on changing future conditions.
These adjusted values were used as input to a second mathematical programme
which converted them into financial terms of benefit outgo and tax income.
Where a new unemployment insurance plan is being introduced, or where the
modifications to a previous plan are very substantial, a regression approach may
not be valid, as previously established relationships may no longer apply.
In
this event other techniques would have to be used to determine the various future
relationships.
It was felt that this paper was not the proper place to consider
such other techniques, as these would depend very greatly on available statistics
in each case; however, the principles of the approach outlined in this paper
would still apply.
IV.
REGRESSION PROGRAMME
It was recognised early in the studies that cause and effect relationships in
unemployment insurance should be studied over successive short intervals, and it
was finally decided to utilise data gathered at three monthly intervals.
Under an unemployment insurance plan which pays benefits for up to twentysix weeks, the payments in any particular quarter are being made to beneficiaries
who became unemployed in the current quarter as well as in each of the two
preceding quarters.
It was obvious, therefore,, that unemployment experience in
previous quarters had some bearing on the benefit payments in a particular
quarter.
In fact, it might be considered that a three month period could be too
long an interval when rates of unemployment are changing rapidly.
As mentioned earlier, it was decided, in the interests of simplicity, to have
three basic input variables, namely:
(a)
rates of total unemployment}.
(b)
rates of change in labour forcej
(c)
rates cf increase in wage levels.
The state was requested to supply historical data on a quarterly basis for a
number of past years as shown in the following table..
The period for which data
was requested was dependent on the changes that had occurred in the particular
unemployment insurance programme in the recent past..
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Total Labour Force (TLF)
Insured Labour Force (EI)
Total Unemployed (UT)
Insured Unemployed (Ul)
Total Unemployment Rate (QT)
Insured Unemployment Rate (QI)
Total Weeks Compensated (TWO)
First Payments (FP)
Average Duration of Benefits (AD)
Average Weekly Wage (AVW)
Average Weekly Benefits (AWB) •
Total Wages (TOW)
Taxable Wages (TAW)
Year 19
Quarter
Year 19
Quarter
1 2 3 4
1 2 3 4
..... Year 1972
Quarter
1 2 3 4
- 4There can, in many states, be a considerable difference between total
unemployed and the insured unemployed.
A considerable proportion of the labour
force is not insured under the regular payroll tax programme, for example, state
employees, teachers, agricultural and domestic workers etc. Furthermore, an
insured employee who exhausts his benefits and remains unemployed is included in
the total unemployed figure but not the insured unemployed.
Using regression techniques, and the facilities of computer stored statistical
packages, the various combinations of dependent and independent variables were
examined on both linear and non-linear bases.
Formulae expressing relationships
between the variables were then developed such that from the three input variables
(1, 5 and 10) the remaining variables could be estimated for future years.
Bearing in mind the requirement for simplicity and ease of understanding by nontechnical state staff, it was decided to use linear relationships wherever possible.
The relationships actually developed from the historical data are set out in the
following paragraphs;
(a)
QT
u!f f , l QT c> + .),
QT
Cx+o/QTa.o)/QTa.()),QTa)]
where\t+l)ref ers to calendar year(x+i)and ~kL
to calendar quarter t
(b)
QiM-fl
[Q!EU+0|
<°>
QI
(d )
TLP ^ TLF , X HI '^
U+i)
<*+0
QiCx)
t
QT ( x)]
( t f f3 l Q I (mi, w c o , fa u+o\fau+ •>)*,QI °° 3
where EI
is the ratio of total labour
force for quarter t to total labour force
for full year.
(e)
EI = TLP *• B.2
'a**)
<"*•+<)
Cx-n)
where R2c,t+,;is the proportion of the
total labour force in yearfr+'Jwho are
insured employees of employers paying
a payroll tax for unemployment insurance.
(f)
COV
C-0
=E
1 QI
W
C" - ~ ut,))
where COV^^iis the number of insured
employees actively
at work in quarter t
of year C *+ 0
(g)
AVW
=AVWu)<(l-hR3,t+0)
where E3fX+1;is the rate of increase in
wage levels for yearU)to year (x. + \)
(h)
TOW
^COV,,.
,,
x
AVW ,-
,-> X S A
pit
where COV
ty
= l|)cOV .
^J
- 5
(i)
TOW^Pr**
TOW a + i >
where Pr ^ i s t h e p r o p o r t i o n of t o t a l
wages f o r q u a r t e r t t o t o t a l wages f o r
full, year
(3)
IAP V * =
f,
PAT
QI,
J
where T A P ^ ^ i s t h e p r o p o r t i o n of t a x a b l e
wages f o r q u a r t e r t t o t o t a l wages f o r
q u a r t e r t. i n y e a r Cv. + i)
. 1Tajr Wage Base f o r y e a r (*-+t)
and PAT
AVW C% + i)
+
(k)
Af
yt,
-t/c,
lAW^.^TAP,
*TOW.
(1)
TAW,
-t/u
TWO
=f
f
(m)
r
(n)
t/t
HP,
= T TAW.
- 1.
4
-t=L
Ult
VH.
EI,
%
UI
Vtf
x QI
(o)
A D / \ - TWO -^ P P ,
.
Cm?
Cx-n)
C* + iJ
(p)
AWB
= f,
IATO
N
QI,
t±- 7
TWO , ** ^
-vv
EI %
MAX B -
•+-*
QI"^
"%
"*- £
EI.
* QI ^
>v
EI,
7
.
•* ]
where MAX B
is maximum weekly benefit
in year (IL-M)/*"*')'
<*>
A W I B ^ - ^ A W B ^ * TWO ^ J ~
TWC^
where TWC,,,^ x -
> TWO ,
.
•y*.
y*
The constants such as El
and Pr were
derived from past experience; the variations
in their values from year to year were so
slight that they could be considered constant
for each year.-
Taxable Wage Base is currently $4,200.00 p.a. but has changed in the past
and will change in the future.
- 6 -
In each, formula, consideration was given not only to the co-efficient of
correlation, but also to the size of individual deviations between the calculated
and observed data.
The lowest co-efficient of correlation for variables used in
the financial forecast programme' was 98$.
In developing a forecast programme where the values of variables for any
period are dependent upon the values estimated for prior periods, it is essential
to ensure that, as far as possible, deviations are not compounded.
For example,
estimates of future total unemployment rates were made on an annual basis, and
corresponding quarterly rates were derived therefrom by a regression technique
(Formula (a)}.
In forecasting rates of insured unemployment, these were derived
first on an annual basis (Formula (b)) and then converted to quarterly rates to
reflect the seasonal pattern (Formula (c)). This approach ensured that any
errors in the estimate of a particular quarter would be contained, as it would not
affect the forecast 'of the rate 'in a specific quarter in the following calendar
year.
QTf X+v ) and Ql^x+Owere introduced into Formulae (a) and (c) to reflect the
shape of the •curves -of- QT and QI.
The fact that the rate of unemployment is
increasing or decreasing in a particular period affects the number of claimants
during that period and the average duration of their claims, so that if in a
particular quarter the rate of unemployment was say 5$» the cost of benefits in
that quarter would depend on the rates in the previous and subsequent quarters.
In addition to the development of non-monetary relationships, it was also
necessary to consider the effects on levels of benefit and tax income of lengthy
periods of unemployment and increases in wage levels.
Generally speaking, if rates of unemployment begin to increase, the
employees first laid off are those in-the lower earnings categories.
If rates
of unemployment continue to increase, employees at higher earnings levels will
become unemployed, and, coincident-ally, the benefits of the lower paid employees
will become.exhausted.
Therefore, even without any changes in general wage
levels, the average earnings of claimants will increase as rates of unemployment
increase or persist at higher levels.
Consequently, relationships were sought
between the average amount of benefit, the maximum benefit, and rates of unemployment (Formula (p)j«
In. the US, benefits are based on an employee's total earnings, subject to a
maximum benefit which is frequently dependent upon the average earnings of all
workers in the state.
On the other hand, the taxes are levied on wages up to a
maximum amount which for almost all states is $4,200.00 per annum.
This amount
is substantially less than the average wages of all workers, and in many states
is less than 50$ of such average.
The rate of increase of average wages on
which taxes are levied will increase, therefore, at a slower rate than total wages.
The payroll tax is levied on the first $4,200 of earnings in a calendar year,
so that if an employee is earning say, $10,000.00 per annum, taxes will cease
during the second quarter with nothing being paid in the third and fourth quarters.
Consequently, the proportion of total earnings subject to taxation is very
high during the.first quarter .of the calendar year, with the proportions decreasing
for each subsequent quarter..
Relationships between the proportion of total wages that are taxable in each
of the four quarters and the rate of unemployment were consequently developed
(Formulae (j) and (k)).
Formula (j) also permits the evaluation of the effect of
a change in the taxable wage base.
Graph A which follows shows the quarterly rates of total and insured
unemployment as actually experienced in a small state since I960.
The fluctuations from quarter to quarter are due to there being a small labour force with a
large segment of seasonal unemployment.
Graph B is the unadjusted output from the regression programme arising out of
an input of annual rates of total unemployment.
Appendix "A" is typical of the output of the regression programme for a given
set of values for the input variables.
•
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- 9.V.
FINANCIAL FORECAST PROGRAMME
The .basic formula for the .calculation of benefits is total weeks compensated,
multiplied by average' weekly benefit - TWCV^x AWB^.A .
The computer programme to
make this calculation is therefore extremely simple.
The problem in regard to financial forecasting of state unemployment insurance
programmes lies mainly in the es.tima.te of future taxes, as these are dependent upon
the individual experience rating of each employer,.
There are.five major experience
rating systems in effect in the United States, with each state having its own. variation on one or more of these'basic systems. ' Because' of .the great divergence in
the various experience rating formulae, a programme for each state has to be .
developed individually.
An example, of one such experience rating system arrayed benefit ratio - is given in the following paragraphs.
Each employer is ranked according to a benefit ratio which is obtained by
dividing the benefits chargeable to his account over the past three years by the
aggregate of his taxable wages during the same period.
The employers are then
arrayed according to their benefit ratios starting with .the lowest .benefit ratio,
with those employers with no benefit payments being placed in the first Rate Class
(Rate Class 0 ) .
The remaining arrayed employers are divided into twenty rate classes, each
with its own rate of tax, such that each rate class contains approximately 5$ of
the balance of the total taxable wages of the state after deducting the taxable
wages of those employers with zero benefit charges.
If a particular employer's
taxable wages falls into two or more rate classes he is charged a weighted rate
of tax.
An example of the format of such a table would be as follows:
Class
Taxable Wages
0
1
2
$ 71
14
14
14
14
3
4
19
20
Rate of Tax
Levied on Taxable
Payroll
051 000
895 000
895 000
895 000
895 000
0.4/o
0.5*
0.6*
0.7*
0.8*
14 895 000
14 895 000
2.9*
3.2*
$368 951 000
In practice, the rates of tax applied to each rate class would be dependent
on the financial status of the fund.
If the fund were low, higher rates of tax
would be levied, and vice versa.
The amount of taxable earnings in Rate Class 0, in any particular year, is
dependent on the current rates of unemployment, so that a formula was developed
whereby the proportion of the total state taxable wages that would fall into this
Rate Class in a particular year could be determined.
- 10 -
The amount of taxable wages.falling into the remaining rate classes could then
easily be calculated and the consequent amount of tax income.
The financial forecast programme is again an iterative programme whereby
there is added to and substracted from the fund balance at the beginning of the
period, the tax income during the period, the interest'earned and the benefits
paid, thus producing the fund balance at the end of the period.
The following table is the result of the projections on certain assumptions
for a particular state.
In this case the amounts of tax collected (contributions)
were dependent on a "size of fund index".
Furthermore, emergency contributions
were payable in certain circumstances, as well as deficiency contributions by those
employers with a history of benefit payments exceeding contributions.
The
extended benefits are payable to claimants when rates of unemployment are high and
increasing.
Each year, each state has to supply to the Federal Government in Washington
certain basic statistics concerning the operation of its plan.
This information
is, of course, accumulated-throughout the year.
The financial forecast programme
used these statistics as input, thus "meeting the stated objective of utilising
readily available data, rather than gathering special statistics with a consequent
time elapse.
- 11 -
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VI.
CONCLUSION
As stated earlier, the methods of financing unemployment insurance programmes
vary very considerably from jurisdiction to jurisdiction, so that it was felt
unnecessary to outline the specific formulae which were used to calculate tax
receipts in the various studies, as for these to be meaningful a voluminous amount
of information would have to be given concerning the actual experience rating
formulae in use, and the criteria for measuring the adequacy of the fund.
It was stated at the beginning of this paper that certain of the studies
commissioned by various states are not yet complete.
As each study is completed,
more refinements will be made to the various computer programmes, and more
techniques will be developed to be used in circumstances where regression formulae
are not appropriate.
Already, however, use is being made of the already developed programmes to
evaluate such matters as changes in:
(i)
(ii)
(iii)
(iv)
the trigger mechanism for emergency taxes,
tax tables,
the taxable wage base,
experience rating formulas, etc., etc.
As each state staff becomes more familiar with its programme and less
dependent on its actuarial consultants, a greater variety of uses will undoubtedly
be forthcoming.
Grateful acknowledgement is made to C.G. Lonergan, F.S.A., P.O.I.A. and
L.G. Simard, A.S.A., for their invaluable help in developing the regression
formulae and their conversion into the respective—computer programmes.
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NOTES:
(1) Items marked O w e r e the input variables. All other values were calculated
by the regression programme.
These values are before subjective examination
and possible modification for use in the financial forecast programme.
(2) This particular State is a small one with considerable seasonal unemployment,
thus leading to substantial variations in the quarterly values of such items
as average weekly wage.
(3) The method of calculating certain items on a quarterly basis is such that the
annual total is not always the exact aggregate of the quarterly figures.