- Email: [email protected]
Forecasting unemployment insurance trust funds: The case of Tennessee
International North-Holland
Journal
of Forecasting
381
5 (1989) 381-397
Forecasting Unemployment Insurance Trust Funds: The case of Tennessee David M. MANDY * The University of Tennessee Knoxville,
TN 37996-4170,
USA
Abstract: Many state unemployment insurance (UI) trust funds have reached levels inadequate to fund UI programs, resulting in renewed efforts to forecast UI variables. This paper describes efforts in Tennessee to formulate a UI forecasting model that overcomes the weaknesses of existing models. The intent is to help forecasters in other states cope with the problems of UI forecasting and to provide a framework to build upon. The two major goals of the model are to provide accurate forecasts and to facilitate strategic planning. Forecasting errors illuminate some important inaccuracies in the model. However, the model captures the variables most frequently subject to legislative change. Keywords: Forecasting
accuracy,
Model selection,
.A deteriorating solvency position in many state unemployment insurance (UI) trust funds has recently prompted renewed efforts to forecast UI variables. The major goal of these forecasting efforts is to anticipate low trust fund balances so that appropriate changes can be made to avoid insolvencies. For example, states may limit benefits, expand the tax base, and/or increase tax rates in response to an inadequate trust fund balance. Ladin (1986) describes efforts in Maryland to anticipate the effects of a recession on the trust fund. Barnow and Vroman (1986) develop the annual simulation model (ASM), which is easy to use but does not capture the institutional structure of the UI system as well as some other models. The most comprehensive UI forecasting model was developed by Mercer Associates (1977) for the U.S. Department of Labor. Much of the institutional structure of the UI system is captured * Research
assistance from Timothy Ferguson and Martha Miles of the Tennessee Department of Employment Security and Melissa Wood of the Center for Business and Economic Research, the University of Tennessee-Knoxville is gratefully acknowledged. This work was partially funded by the Tennessee Department of Employment Security. Opinions expressed are exclusively the author’s, Any errors or omissions are the author’s.
0169-2070/89/$3.50
0 1989, Elsevier Science Publishers
Strategic
planning,
Unemployment
insurance.
by this model, making it possible for states to simulate the effects of various policy changes. One application of the Mercer model is described by Hultman and Renfro (1979). States using these models must make assumptions regarding future unemployment rates, wages, and the labor force. Depending on the methods used by a particular state, these assumptions may or may not be well-founded and based on sound econometric forecasts of the state. This limitation caused the Tennessee Department of Employment Security to take an alternative approach to UI forecasting. The sensitivity of trust fund activity to economic performance and the simultaneity of many UI variables suggested that an econometric model is the appropriate forecasting tool. However, a UI forecasting model should provide support for strategic planning through the simulation of policy changes. Hence, the Tennessee Employment Security Insurance Forecasting Model (TESIM) is primarily a simultaneous equation econometric model, but policy variables are explicitly incorporated into the model to provide simulation capabilities. This behavioral approach to UI forecasting contrasts with the deterministic approaches used by most UI models. The economic forecasts that drive TESIM are derived
B.V. (North-Holland)
382
D.M. Mandy / Unemployment msurance trust funds
from the quarterly Tennessee Econometric Model (TEM) (Fox and Hake, 1984). This arrangement reflects the environment in which the UI system operates and makes the exogenous assumptions underlying TESIM forecasts more broadly based than the assumptions that underlie a typical use of the Mercer or ASM models. In the sections that follow we provide a general overview of UI systems, describe TESIM, and evaluate its performance. The intent is to help forecasters in other states cope with the problems of UI simulation and forecasting, and to provide a framework to build upon.
1. Overview
of UI systems
Changes in the balance of an UT trust fund can be divided into two basic parts: flows into and flows out of the fund. The flows into the fund are further separated into four revenue categories: premiums, reimbursements, interest, and interstate transfers. Flows out of the fund consist of two expenditure categories: regular and extended benefits. The following paragraphs describe each of these components. Premiums contribute most of the trust fund revenues. These payments come from a tax rate applied to the ‘taxable wages’ of covered employers. Taxable wages are the wages paid to each employee in a calendar year up to a prescribed ceiling, currently $7,000 in Tennessee. Tax rates are determined by the unemployment history of a firm and the solvency of the trust fund. States devise an ‘experience rating’ rule that compares the premium and benefit histories of each firm. Rarnow and Vroman (1986, p. 3) discuss several alternative experience rating formulas. In Tennessee and most other states, the premiums paid by a firm and the benefits received by its employees are aggregated over the entire UI history of the firm. The difference between aggregate premiums and benefits is divided by the average taxable wages of the firm over the most recent three years. This quantity is called the reserve ratio. Firms with low reserve ratios are charged at higher tax rates. However, the rates imperfectly reflect the reserve ratios of the firms so that firms with low average unemployment rates subsidize those with high average unemployment rates.
The reserve ratio calculation is not sensitive to the balance in the trust fund, but tax rates for all firms increase automatically as the trust fund balance decreases. This is a safety factor designed to maintain solvency, but makes the UI tax procyclical during a sustained recession since tax rates may increase before the recession trough occurs. It also shifts the relative burden of the UI tax to low-risk firms. Hence, trust fund insolvencies have undesirable consequences due to the structure of the UI system, in addition to the interest on funds that must be borrowed to pay unemployment benefits during an insolvency. Some employers may be subject to special rates if their history is too short to determine an experience rating or if they are in an industry with unusual unemployment experience. Reimbursements are made by government and nonprofit institutions that choose not to pay the premiums tax. These employers simply reimburse the trust fund for any benefits paid to their employees. Reimbursements are usually repaid one quarter after the benefits are dispersed. Interest accumulates from investment of the trust fund balance and is credited to the trust fund in the next period. The significance of this revenue source declines during recessions as the trust fund balance decreases. Higher interest rates can bolster these revenues, however. In general, interest revenues depend on the portfolio of assets that is purchased with the trust fund balance, but since all state UI trust funds are deposited with the U.S. Treasury, the interest return is not controlled at the state level. The last revenue category is interstate transfers. Interstate transfers are payments between states to compensate for claims made in one state when the associated premiums were paid in a different state. This occurs when an employee crosses state lines between home and work, or when an employee has earnings in more than one state. Only the net transfers are relevant in determining the trust fund balance. These transfers depend on the net migration of benefit recipients, which varies greatly with no clear pattern. The largest expenditure component is regular benefits, which are paid to an unemployed claimant according to a benefit formula. To receive UI benefits, the claimant must be eligible, and the requirements vary among states. Meeting the eligibility requirements entitles the claimant to a
D.M.
Mandy
/
Unemployment
specific number of weeks of UI benefits. The amount of the weekly benefit is based on the claimant’s previous earnings, subject to some maximum and minimum amounts. Weekly benefit amounts are also influenced by part-time work and, to varying degrees across states, by the number of claimant’s dependents. Extended benefits are paid during cyclical downturns when the duration of unemployment increases. In practice, extended benefit periods are determined by a rule that compares current and past unemployment rates. During an extended benefit period, eligible claimants who have exhausted their regular benefits can receive UI payments for additional weeks. The cost of extended benefits is shared between the federal government and the states. Hence, the sum of regular and extended benefits overstates the flows out of a state UI trust fund.
2. The estimated model In order to forecast the trust fund balance, each of the components described in the previous section must be forecast. This is reflected by equation 1 of table 1, which is the identity that aggregates the components into the trust fund balance. Table 1 also shows the revenue equations, while the benefit equations are given in table 2. The system of equations given in tables 1 and 2 cannot be simultaneously estimated, primarily due to the lack of observations on the independent variable in equation 3. The source for this variable is discussed below, but the implication for estimation is that with only 17 observations there are more predetermined variables than observations. Hence, the equations discussed below are estimated individually, although forecasts are produced with the entire simultaneous system. On the revenue side, premiums are the most important component, and there are two important policy variables involved in the premium forecast. Hence, a substantial portion of the discussion of this section centers on the premium equations. The first step in developing a premium forecast is to forecast the taxable wages that underlie premiums. The pattern of taxable wages is dependent on the taxable wage ceiling. The ceiling becomes binding on many employees in the first quarter and on the average employee in the second quarter
insurance
383
trust funds
of the year; this introduces strong seasonality into the taxable wage data (see fig. 1). Since the ceiling causes taxable wages for each quarter to be generated by a different set of circumstances, slope and intercept dummy variables were used to fit the taxable wage equation. Equation 2 captures the way in which the per-employee ceiling affects taxable wages, on average, by using the minimum of the ceiling and the average wage. In the first quarter average wages are usually higher than the ceiling, so a change in the per-employee ceiling probably would not affect the predicted value for taxable wages. However, the ceiling is undoubtedly binding on some employees in the first quarter. For this reason the ceiling is explicitly included as an additional independent variable in the first quarter. The integration of the ceiling into this equation provides an important policy variable since the effects of legislative changes in this variable can be easily simulated by changing the exogenous assumption. Ideally, the components of equation 2 that are relevant in the second quarter should consist of two terms. The first is any wages below the ceiling paid to employees that were employed in the first quarter. The second is wages below the ceiling paid to new employees. This structure cannot be captured because the net change in employment cannot be empirically disaggregated into additions to and subtractions from employment. Equation 2 approximates the correct structure by treating the net change in employment as if it were all new employment in the second quarter. This overstates taxable wages due to continuing employment and understates taxable wages due to new employment; the magnitude of these inaccuracies depends upon gross employment growth relative to
0 F
ZSOO..
oJ: 01 1070
: 01 1972
01
1974
01
197E
01 ma
Fig. 1. Taxable
ot
01
19110 1902
wages
01
01
ls4
19s
384
Table 1 Tesim revenue equations BAL,
=BAL,_,+(PREM,+REIM,+TRAN,-BN_TN,)xl,OOO+I,_,
1
TW,
=
2
-89.7 + 0.586(D1xMl1,~ECOV)+0.218(D1~B,)+0.430(D2xM12,xECOV,)+ (- 1.60 “) (21.84 “) (13.49 “) (5.64 “) 5.064 (D2xM11, (10.11 “)
x(ECOV,
-ECOV,m,))-11,842 (-5.60
(D2XECOV,/ECOV,_,)+ “)
0.525 (D3xTW,_,)+0.781 (D4xTW,_,)-281.4 D1+12,337 D2+193.1 D3 (17.32 “) (- 2.21 “) (5.63 “) (2.53 “) (21.96 “) F= 2210 a ln(PREM,)=
d
R2 = 0.985
Period = 7002 - 8704
n = 71
180”
874”
DW =1.240
3 ’
Period = 8304 - 8704
n =17
1
R2 = 0.792
= 0.188 + 0.848 MAVG(2, (0.559 “)(16.43 “) F=
TRAN,
530
= 0.030 BN -TN,(15.83 “) F=
I e
Durbin - h = - 0.098 ah
1.490+0.868 In (DIST,)+0.210 D8402 (4.00) (5.17) (32.40) F=
REIM,
a2 = 0.997
R2 = 0.986
4 Durbin - h = 1.65 ab BAL,) x MAVG(2,
R,m6)
Durbin - h = - 1.67 ab
Period = 7601-
8801
n = 49
j3 = 0.523
’
5
Period = 7604 - 8604
n = 41
8, =1.143
= -278.6 + 77.2 UR-tO.144 TRAN,m,+0.435 TRAN,_, (- 1.37 ‘)(2.14 “) (1.18 “) (3.65 “) F=
32.9 a
R2 = 0.611
Durbin - h = 1.65 ab
B2 = - 0.422 6
Period = 7203 - 8704
n = 62
Asymptotic statistic. A), where A is the set of independent variables. See Durbin t-statistic for the coefficient of e,_, in the equation e, = f(e,_,, (1970). Inconclusive DW. A Durbin-Watson test for first order autocorrelation, using the tables of Farebrother (1980). revealed that autocorrelation was present in this equation. The equation was re-estimated with an assumed AR(l) structure. The results shown reflect this re-estimation. This equation was estimated with an assumed AR(2) structure by the Hildreth-Lu search technique. MAVG( n, x) denotes an n-period moving average of x.
employment losses. Since this is predominately a cyclical phenomena, the percent change in employment is included in this equation as a proxy for the inherent inaccuracies. The negative estimated coefficient suggests that the overstatement is larger than the understatement. The components of equation 2 that are relevant in the third and fourth quarters could be constructed in a manner similar to the first and second quarter components. However, the distortions became more pronounced in later quarters so that this construction does not work well. Taxable wages in the last two quarters of the year follow taxable wages for the preceding quarter, so a simple lag was estimated for the third and fourth quarters. Notice that this structure still captures
the effects of an exogenous change in the per-employee ceiling in all four quarters because the change is passed through the lag structure to the later quarters. Moreover, despite the somewhat simplistic nature of equation 2 for the third and fourth quarters, the coefficients are significant and, as discussed below, the equation predicts well. Tax rates must be applied to the taxable wage forecast to obtain a premium forecast. Tax rates can be forecast either by an estimated equation for the average tax rate, or by using a distribution of firms across the reserve ratio continuum and then applying the legislated tax table to this distribution. If an average tax rate is used, the experience rating system is bypassed and the array of tax rates that are possible is not part of the
D.M. Mandy / Unemployment insurance trustfunds Table 1 Tesim revenue equations Variable B
BAL BN_TN D8402 Di DIST ECOV Ml1 Ml2 PREM R REIM TRAN TW UR W
a
385
(Cont.) Description
Units
Per-employee ceiling Trust fund balance Total benefits paid from the Tennessee UI trust fund Dummy variable; 1 in 198402 and after, 0 otherwise Dummy variable; 1 in ith quarter, 0 otherwise Sum of premiums over experience rating categories Employment in premium-paying industries Interest Min (B, W) Min (B - Mll, W) Premiums Prime rate Reimbursements Interstate transfers Taxable wages Seasonally adjusted Tennessee unemployment rate Average annual wage and salary income in premium-paying industries
Mil. Cur. $ Mil. Cur. $ Thou. Cur. $ _
,’ All variables are Tennessee Associates, Inc.
variables,
except
R. Exogenous
premium calculation. Also, since alternative tax tables are often considered for adoption, an average tax rate approach is not adequate for strategic planning purposes. For this reason, TESIM uses the distribution approach. Future distributions are forecast by applying the forecast growth rates of taxable wages and benefits to the taxable wages and benefits of each reserve ratio category. The reserve ratio calculation is then applied to each category to obtain a forecast reserve ratio for the category. Once the distribution is forecast, the (lagged) forecast trust fund balance is combined with the reserve ratio of each category to obtain the legislated tax rate for that category. Multiplying this by forecasted taxable wages for the category yields the premium forecast for the category. Aggregating across categories yields a total premium forecast. By using a different set of tax rates, the impact of proposed legislative changes in the tax tables can be assessed. Despite the advantage of alternative tax table simulation capability, this method suffers from several shortcomings. The assumption that each category will experience average growth in taxable wages and benefits is clearly inaccurate. Still, a solution to this problem entails estimating wages and benefits for each category separately, and this could involve several hundred equations, It may
values
of R were obtained
_ Thou. Cur. Jobs Mil. Cur. $ Mil. Cur. $ Mil. Cur. $ Thou. Cur. Percent Thou. Cur. Thou. Cur. Mil. Cur. $ Percent Mil. Cur. $
from Wharton
$
$ $ $
Econometric
Forecasting
be possible to disaggregate the gross wages and benefits forecasts across the categories by using some cyclical explanatory variables. This is an area for future research. Another shortcoming is that the premium-paying employers that are subject to special rates are not included in the available distribution. Hence, the distribution forecast always understates true premiums. The understatement is systematic, however, and true premiums are easily forecast as a function of the distribution forecast. The estimated relationship is given by equation 3 of table 1. A third problem is the significant data requirement of this approach. Barnow and Vroman (1986) discuss this problem as it applies to the Mercer model. For TESIM, only five years’ distributions were available, limiting estimation of equation 3 to seventeen observations. This prohibits simultaneous estimation of TESIM, but the need for policy simulation in the UI environment is important enough to warrant the distribution approach. Equations 4-6 forecast the remaining three revenue categories. Equation 4 forecasts reimbursements, which are repaid one quarter after the benefits are paid. The benefits paid to employees of reimbursing employers is a relatively stable proportion of total benefits, as reflected by equation 4. Equation 5 forecasts interest as the product of the average balance over the quarter with an
D. M. Mandy / Unemployment insurance trust funds
386 Table 2 Tesim benefit equations BN, = AVGBN, In (AVGBN,)
7
x TOTWKS, = 0.009 + 1.27 In (AVGNB,_,)-0.339 (0.27 “) (9.99 “) (-2.88 F=8182a
TOTWKS,
‘
R* = 0.998
= -49.62 +l.lll (- 2.11 “)(26.23 F=
672a
R’ = 0.978
= 8,515 -8,346 E,/E,_, (12.74 “) (- 12.67 “)
REGWKS,
F=
iI* = 0.947
592a
Durbin-h=-l.40ab
REGWKS, “)
8
In (AVGBN,_,)+O.063 In (MBA,) (1.93 “) “) Period = 7203 - 8801
n = 63 9
+73.60 DEXTBN, (4.50 “) Durbin - h = 1.40 ab + 0.782 REGWKS,_ (26.19 “) Durbin - h = 0.26 ab
Period = 7203 - 8801
n = 63
fir = 0.756
& = - 0.336 10
r Period = 7102 - 8704
n = 67 11
EXTWKS,
= DEXTBN,
x (TOTWKS,
REGBN,
= REGWKS,
x AVGBN,
12
EXTBN,
= EXTWKS,
x AVGBN,
13
+ PCT, x EXTBN,
14
BN _TN, d = REGBN, 1 DEXTBN,
=
if (DEXTBN,_, or (REGWKS,_,
0
- REGWKS,)
= 1 and EXTWKS, > 10) -REGWKS,_,
2100) 15
otherwise
Asymptotic statistic t-statistic for the coefficient of e, _, in the equation e, = f (e,_ 1,A), where A is the set of independent variables. See Durbin (1970). This equation was estimated with an assumed AR(2) structure by the Hildreth-Lu search technique. Note that the RHS variables in this equation are seasonally adjusted, while the LHS variable is unadjusted. In practice, forecast seasonal factors are used to express all variables in unadjusted form before this equation is calculated.
average of recent interest rates. Finally, equation 6 forecasts interstate transfers. There is no obvious structure that links to TEM that can be used to forecast this variable. It is subject to seasonal and cyclical variability as well as potential structural
Table 2 Tesim benefit Variable
a
AVGBN BN BN_TN DEXTBN E EXTBN EXTWKS MBA PCT REGBN REGWKS TOTWKS d All variables
equations
changes in the commuting patterns between states. While several alternative specifications were examined, equation 6 is the best fit obtained. On the expenditure side, both regular and extended benefits can be expressed as the product of
(Cont.) Description
Units
Seasonally adjusted average benefit payment for all benefits Seasonally adjusted total benefits Total benefits paid from the Tennessee UI trust fund Dummy variable; 1 in extended benefit periods, 0 otherwise Seasonally adjusted total nonagricultural employment Seasonally adjusted total extended benefits Seasonally adjusted extended weeks compensated Legislated maximum benefit amount Proportion of extended benefits paid by Tennessee Seasonally adjusted total regular benefits Seasonally adjusted regular weeks compensated Seasonally adJusted total weeks compensated
Cur. $ Thou. Cur. % Thou. Cur. S
are Tennessee
variables.
Thou. Jobs Thou. Cur. $ Thou. Weeks Cur. $ Rate Thou. Cur. $ Thou. Weeks Thou. Weeks
D.M. Mandy / Unemployment insurance trust funds
‘weeks compensated’ and the average weekly benefit. Weeks compensated is simply the number of UI payments issued in an average week during the quarter. Thus, total benefits are given by equation 7 of table 2. Extended weeks compensated and average extended benefits are the most difficult variables to estimate and forecast. They are volatile series and only limited observations exist since these variables are zero except during extended benefit periods. Estimating total and regular benefit variables provides more reliable equations. Then, when an extended benefit period is in force, extended benefits can be treated as a residual. Accordingly, average benefits across both regular and extended benefits are predicted by equation 8, and total weeks compensated are predicted by equation 9. Equation 8 reflects the fact that the benefit formula depends on the legislated maximum benefit amount. This provides another outlet for policy simulation, as the effects of changes in the maximum benefit amount can be investigated by using different exogenous values for the maximum benefit amount. Total weeks compensated are predominately determined by regular weeks compensated. In addition, total weeks compensated increase during extended benefit periods as indicated by the extended benefits dummy. It is necessary to disaggregate benefits into extended and regular benefit outlays so that the effect of the federal sharing rule is reflected in the forecast trust fund balance. Equation 10 predicts regular weeks compensated and, given this forecast, extended weeks compensated are given by the identity shown as equation 11. Regular and extended benefits, respectively, are then determined by identities 12 and 13. Finally, total reductions in the trust fund balance are given by equation 14. If the extended benefit dummy is determined exogenously, equations 7-14 can be used to predict benefits. Aternatively, the occurrence of extended benefit periods can be determined endogenously. In practice, extended benefit periods are determined by a complicated rule that examines changes in weekly unemployment rates. This is cumbersome to incorporate into TESIM, creating the need for a proxy rule if extended benefit periods are to be endogenously determined. Historically, extended benefit periods were always preceded by a sharp increase in regular weeks
387
compensated. Once an extended benefit period is in effect, it remains in effect until unemployment decreases. This usually coincides with a decrease in extended weeks compensated to a relatively low level. This leads to the proxy rule given by equation 15. The threshold value of 100 was chosen because it perfectly predicts every extended benefit period.
3. Performance
of TESIM
Three separate sets of simulations were conducted to evaluate the forecasting accuracy of TESIM. For the first two sets, TESIM was reestimated using only part of the data and then a forecast was generated over the withheld observations. Each set consists of ten eight-quarter forecasts generated in this manner, beginning in each quarter from 8304 through 8601. Data limitations prevent simulations of quarters prior to 8304. Estimation was conducted using data through the quarter preceding the first forecast quarter in each case. Equation 3 was not re-estimated for these simulations due to the lack of observations for this equation. Thus, the transformation from distribution-based premiums to the premium forecast is more accurate in these simulations than can be expected in a true forecasting environment. The distinction between the first two sets of simulations lies in the source for the exogenous variables. For the first set of simulations, exogenous values were provided by old TEM forecasts wherein the beginning forecast quarter corresponded to the beginning forecast quarter of each TESIM forecast. These are the forecasts that were actually produced using TEM at the time. One problem with these simulations is that data have been revised since the TEM forecasts were produced, and TESIM is estimated using current data over the appropriate time period. To make the data consistent, growth rates were calculated from the TEM forecasts and then applied sequentially to the last historical observation of the current data. The exogenous values created in this way were then used to drive each TESIM forecast. For the second set of simulations, true values for the exogenous variables were used. As a basis for comparison, a third set of simulations was generated using a univariate HoltWinters technique to forecast only the trust fund
D. M. Mandy / Unemployment insurance trust funds
388
balance. The model consists of level, trend, and seasonal components, and the parameters were chosen optimally to minimize the sum of the squared forecast errors in the first forecast quarter. The data consist of quarterly observations on the trust fund balance from 7101 through 8704 (68 observations). In 8301, the UI trust fund in Tennessee became insolvent, so the observation for that quarter is slightly negative. Since the seasonal adjustment calculation does not work for negative values, this observation was arbitrarily set at 1. The first nine years of data (36 observations) were used to allow the effects of the starting values to die down. Thus, the sum of squared errors was calculated from the thirty-seventh observation through the end of the history for each simulation. This procedure is described by Granger and Newbold (1977, pp. 164-167). Ten eight-quarter forecasts were generated with this model, corresponding to the forecasts generated with TESIM. The parameters were recalculated for each forecast, using only data through the end of the historical period. For each forecast, percent forecast errors for each endogenous variable were calculated. These errors were then aggregated into mean absolute percent errors (MAPE) by forecast quarter, and the MAPE’s are reported for the most important
Table 3 Tesim mape by forecast
TESIM variables in table 3. Together, the three sets of errors provide a substantive test of the accuracy of TESIM. The first set of errors measures the accuracy of the entire forecasting system, while the second set measures the accuracy of TESIM independent of the errors generated by TEM. The third set provides a benchmark for the first two sets. The average benefit payment exhibits the smallest forecast errors, averaging 1.4% over all forecast quarters. Note that the errors for this variable are the same for the first two sets of simulations because, by equation 8, the average benefit forecast is independent of exogenous assumptions. A less favorable performance is displayed by total weeks compensated, as the MAPE increases from 5.3% in the first forecast quarter to 8.4% before decreasing to 7% in the eight forecast quarter. This variable performed particularly poorly when the exogenous values were provided by TEM, with errors averaging 14.8%. Clearly, a large proportion of the errors here result from inaccurate employment forecasts produced by TEM. These two variables combine to produce an average error in total benefits of 7.5% over all forecast quarters in the second set of simulations and 14.8% in the first set of simulations, and an error pattern that mirrors total weeks compensated.
quarter. 1st Quarter
Exogenous values provided Trust Fund Balance Taxable Wage Average Premium Rate Premiums Total Weeks Compensated Average Benefit Payment Benefits
by TEM
Exogenous values provided Trust Fund Balance Taxable Wage Average Premium Rate Premiums Total Weeks Compensated Average Benefit Payment Benefits Holt-Winters forecast Trust Fund Balance
by actual
2nd Quarter
3rd Quarter
4th Quarter
5th Quarter
6th Quarter
7th Quarter
8th Quarter
Average
4.67 2.57 5.81 5.91 10.89 0.83 11.11
5.60 2.87 5.76 5.71 9.49 1.05 9.59
3.90 3.05 7.20 6.72 4.86 1.40 4.33
4.14 4.57 8.46 7.36 9.16 1.46 9.49
5.60 4.23 7.71 9.55 14.08 1.72 14.18
7.07 6.12 5.73 9.35 15.99 1.64 15.93
9.23 7.09 5.53 8.00 22.76 1.49 22.66
12.08 10.34 12.39 8.05 31.51 1.29 31.05
6.54 5.10 7.33 7.58 14.84 1.36 14.79
4.18 2.07 5.92 5.91 5.34 0.83 5.85
5.94 2.62 5.78 5.00 5.68 1.05 6.13
4.88 2.79 6.94 6.18 6.63 1.40 7.33
5.94 3.47 8.35 7.97 7.79 1.46 X.27
7.57 3.41 8.06 10.12 8.42 1.72 8.88
X.67 4.28 4.66 9.18 7.67 1.64 8.16
9.37 4.84 4.45 7.26 7.46 1.49 8.07
10.17 6.43 7.16 7.46 7.03 1.29 7.53
7.09 3.74 6.41 7.38 7.00 1.36 7.53
34.69
41.79
23.88
41.68
36.19
39.85
26.01
57.94
56.62
D.M. Mandy / Unemployment
On the revenue side of the trust fund, in the first set of simulations the MAPE for taxable wages increases from 2% to 5% before jumping in the last quarter of the forecast period to 6.4%. The transformation to total premiums increases the average error in total premiums to 7.4%. When the exogenous values are provided by TEM, the MAPE for taxable wages increases from 2.6 to 7.1% before increasing to 10.3% in the last forecast quarter. The average error for premiums is 7.6%. The errors displayed by the trust fund balance summarize the errors of its component parts. The MAPE for the balance increases steadily with one exception from 4.2% to 10.2% from the first to the eighth forecast quarters. When the exogenous values are provided by TEM, the MAPE for the balance increases from 3.9% in the third to 12.1% in the eight forecast quarter. Surprisingly, the overall average is lower than the average produced by using actual values for the exogenous variables. The fact that the trust fund balance is a stock that is forecast by estimated flows reinforces the tendency for forecast errors to increase in later forecast quarters. Any errors in the balance forecast become cumulative unless the errors in the component flows change direction. In general, premiums are greater than their forecast values and benefits are less than their forecast values. Thus, the change in the trust fund balance is usually larger than the forecasted change. A change in the direction of this error is rare, so that errors in the trust fund balance accumulate, leading to a large MAPE by the eighth forecast quarter. From the standpoint of minimizing the risk of trust fund insolvency, this is not a significant problem since the direction of the error implies that the trust fund balance will be larger than the forecast value. Hence, the model tends to err on the conservative side. These errors compare quite favorably with the benchmark Holt-Winters forecasts. In general, the Holt-Winters technique performed very poorly, with forecasting errors averaging almost 40%. Moreover, this technique is not useful for simulations since it ignores the institutional structure of the forecasting environment. That is, another measure of the performance of a model is its ability to provide decision support for strategic planning. TESlM meets this goal by construction, since the taxable wage ceiling, tax rates, maximum benefit amount, and experience rating rule are all explicitly present in the model. Changes in these
389
insurance trusf funds
variables can be simulated by simply changing the parameters of the model. To illustrate how TESIM can be used for strategic planning, the first three of these parameters were altered and three new simulations were generated over the last simulation period, 8601-8704. In all cases, the exogenous variables were provided by the actual values, so the appropriate baseline for comparison is the last of the second set of simulations described above. The results of these simulations are presented in figs. 2-6, each of which presents the alternative scenarios that affect a particular UI variable. The series are labeled according to the parameter that was altered in each case. TAX TABLE represents a 10% increase in tax rates relative to BASELINE effective 8601 on only those employers with negative reserve ratios. MBA results from holding the maximum weekly benefit amount constant at $120 instead of providing the increases to $145 that actually occurred during this period. Finally, B results from increasing the taxable wage ceiling from $7,000 to $8,000 effective 8601. All three of these changes cause the forecasted trust fund balance to increase. Figure 2 illustrates that the increase in the taxable wage ceiling has the most significant impact, while the change in MBA had little effect. The effects on taxable wages of the change in the ceiling can be seen by examining fig. 3. Figure 4 illustrates how changing the ceiling and the tax tables affects premiums. Figures 5 and 6 show how changing the maximum benefit amount affects total benefits and the average benefit payment, respectively. A significant weakness in the simulation capability of TESIM is the lack of policy variables related to the benefit formula and eligibility. The
L L
r
500..
0
Iw 8
480..
0 F
40000-.
S
I : 01
a?
03 19m
84
oi
Fig. 2. Trust fund balance.
82
03 W8?
04
D.M. Mandy / Unemployment msurance trwtfundr
390
02
Fig. 3. Taxable
-
SASELIN
a3 I%7
s4
01
wages.
si?
03 I%s
Fig. 6. Average
s4
benefit
II,
w
03 Inn
04
payments.
-S TM TALE
T
I
0
F
m..
I :
III
02
w
04
Pl
92
1986
93 1987
a4
porate the rules into the model must use a distribution of beneficiaries to simulate the impact of rule changes. This could be similar to the approach currently in use on the revenue side of the model. Alternatively, behavioral modeling of individual claimants may be necessary. As experience is gained with distribution methods in general, a reformulation of the benefits side of the model may be in order.
Fig. 4. Premiums.
4. Summary -SASQDlE --%A
I :
91
02
w
04
19m
01
a?
03 Ien
04
Fig. 5. Benefits.
only explicit parameter is the maximum weekly benefit amount. Eligibility requirements and benefit rules can be complicated and difficult to model. However, changes in these formulas are often considered, and the strategic planning capabilities of the model would be significantly improved if the impact of alternative benefit legislation could be easily evaluated. The problem is that the benefit rules affect individual claimants differently, so that any attempt to explicitly incor-
The TESIM model is constructed to fulfill two major goals. The first is to provide the most accurate forecasts possible for the UI system. The second is to incorporate important policy variables into the model so that policy changes can be simulated. These goals are not necessarily congruous. To the extent that model structure is dictated by simulation capability, forecasting accuracy may be sacrificed. TESIM incorporates most of the significant policy variables and is constructed to minimize forecasting error within this framework. The result is larger forecasting errors than could be achieved if the only goal were accuracy. However, the model lends itself to policy simulation and uses well-founded exogenous assumptions. Many alternatives were investigated while building the TESIM model, and the forecasting errors are testimony to the difficulty of modeling the UI system in a way that meets the needs of UI policy makers. Despite the inaccuracies, TESIM fulfills these needs within a consistent framework, making it a potentially useful framework for policy makers nationwide.
D.M. Mandy / Unemployment
References Bamow, Burt and Wayne Vroman, 1986, An analysis of UI trust fund adequacy, final report submitted by ICF Incorporated for contract no. 99-5-3024-04-090-01, Employment and Training Administration, U.S. Department of Labor, Washington, D.C. Durbin, J., 1970, Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables, Econometrica 38, 410-421. Farebrother, R.W., 1980, The Durbin-Watson test for serial correlation when there is no intercept in the regression, Econometrica 48, 1553-1563. Fox, William F. and David A. Hake, 1984, Economic forecasting in Tennessee, Suruey of Business 19, 30-37. Granger, C.W.J. and Paul Newbold, 1977, Forecasting economic time series (Academic Press, New York). Hultman, Charles W. and Charles G. Renfro. 1979, Analysis of an unemployment insurance projection model, Office of Re-
insurance trust funds
391
search, College of Business and Economics, University of Kentucky (Lexington, KY). Ladin, Jay, 1986, Simulating the impact of the next recession on unemployment trust funds: The Matyland case, Department of Fiscal Services, Maryland General Assembly. Mercer Associates, 1977, State unemployment insurance user’s manual for projection program and financial forecast program, 2 volumes, prepared for the Division of Actuarial Services, UI Service, U.S. Department of Labor.
Biography: David MANDY is a Research Assistant Professor at the Center for Business and Economic Research, the University of Tennessee, Knoxville and Assistant Professor of Economics, The University of Tennessee, Knoxville. He is director of the Tennessee Economic Forecasting Service and received the Ph.D. in Economics from the University of Illinois/ Urbana-Champaign in 1987. His fields of specialization are applied microeconomics and econometrics.
Journal
of Forecasting
381
5 (1989) 381-397
Forecasting Unemployment Insurance Trust Funds: The case of Tennessee David M. MANDY * The University of Tennessee Knoxville,
TN 37996-4170,
USA
Abstract: Many state unemployment insurance (UI) trust funds have reached levels inadequate to fund UI programs, resulting in renewed efforts to forecast UI variables. This paper describes efforts in Tennessee to formulate a UI forecasting model that overcomes the weaknesses of existing models. The intent is to help forecasters in other states cope with the problems of UI forecasting and to provide a framework to build upon. The two major goals of the model are to provide accurate forecasts and to facilitate strategic planning. Forecasting errors illuminate some important inaccuracies in the model. However, the model captures the variables most frequently subject to legislative change. Keywords: Forecasting
accuracy,
Model selection,
.A deteriorating solvency position in many state unemployment insurance (UI) trust funds has recently prompted renewed efforts to forecast UI variables. The major goal of these forecasting efforts is to anticipate low trust fund balances so that appropriate changes can be made to avoid insolvencies. For example, states may limit benefits, expand the tax base, and/or increase tax rates in response to an inadequate trust fund balance. Ladin (1986) describes efforts in Maryland to anticipate the effects of a recession on the trust fund. Barnow and Vroman (1986) develop the annual simulation model (ASM), which is easy to use but does not capture the institutional structure of the UI system as well as some other models. The most comprehensive UI forecasting model was developed by Mercer Associates (1977) for the U.S. Department of Labor. Much of the institutional structure of the UI system is captured * Research
assistance from Timothy Ferguson and Martha Miles of the Tennessee Department of Employment Security and Melissa Wood of the Center for Business and Economic Research, the University of Tennessee-Knoxville is gratefully acknowledged. This work was partially funded by the Tennessee Department of Employment Security. Opinions expressed are exclusively the author’s, Any errors or omissions are the author’s.
0169-2070/89/$3.50
0 1989, Elsevier Science Publishers
Strategic
planning,
Unemployment
insurance.
by this model, making it possible for states to simulate the effects of various policy changes. One application of the Mercer model is described by Hultman and Renfro (1979). States using these models must make assumptions regarding future unemployment rates, wages, and the labor force. Depending on the methods used by a particular state, these assumptions may or may not be well-founded and based on sound econometric forecasts of the state. This limitation caused the Tennessee Department of Employment Security to take an alternative approach to UI forecasting. The sensitivity of trust fund activity to economic performance and the simultaneity of many UI variables suggested that an econometric model is the appropriate forecasting tool. However, a UI forecasting model should provide support for strategic planning through the simulation of policy changes. Hence, the Tennessee Employment Security Insurance Forecasting Model (TESIM) is primarily a simultaneous equation econometric model, but policy variables are explicitly incorporated into the model to provide simulation capabilities. This behavioral approach to UI forecasting contrasts with the deterministic approaches used by most UI models. The economic forecasts that drive TESIM are derived
B.V. (North-Holland)
382
D.M. Mandy / Unemployment msurance trust funds
from the quarterly Tennessee Econometric Model (TEM) (Fox and Hake, 1984). This arrangement reflects the environment in which the UI system operates and makes the exogenous assumptions underlying TESIM forecasts more broadly based than the assumptions that underlie a typical use of the Mercer or ASM models. In the sections that follow we provide a general overview of UI systems, describe TESIM, and evaluate its performance. The intent is to help forecasters in other states cope with the problems of UI simulation and forecasting, and to provide a framework to build upon.
1. Overview
of UI systems
Changes in the balance of an UT trust fund can be divided into two basic parts: flows into and flows out of the fund. The flows into the fund are further separated into four revenue categories: premiums, reimbursements, interest, and interstate transfers. Flows out of the fund consist of two expenditure categories: regular and extended benefits. The following paragraphs describe each of these components. Premiums contribute most of the trust fund revenues. These payments come from a tax rate applied to the ‘taxable wages’ of covered employers. Taxable wages are the wages paid to each employee in a calendar year up to a prescribed ceiling, currently $7,000 in Tennessee. Tax rates are determined by the unemployment history of a firm and the solvency of the trust fund. States devise an ‘experience rating’ rule that compares the premium and benefit histories of each firm. Rarnow and Vroman (1986, p. 3) discuss several alternative experience rating formulas. In Tennessee and most other states, the premiums paid by a firm and the benefits received by its employees are aggregated over the entire UI history of the firm. The difference between aggregate premiums and benefits is divided by the average taxable wages of the firm over the most recent three years. This quantity is called the reserve ratio. Firms with low reserve ratios are charged at higher tax rates. However, the rates imperfectly reflect the reserve ratios of the firms so that firms with low average unemployment rates subsidize those with high average unemployment rates.
The reserve ratio calculation is not sensitive to the balance in the trust fund, but tax rates for all firms increase automatically as the trust fund balance decreases. This is a safety factor designed to maintain solvency, but makes the UI tax procyclical during a sustained recession since tax rates may increase before the recession trough occurs. It also shifts the relative burden of the UI tax to low-risk firms. Hence, trust fund insolvencies have undesirable consequences due to the structure of the UI system, in addition to the interest on funds that must be borrowed to pay unemployment benefits during an insolvency. Some employers may be subject to special rates if their history is too short to determine an experience rating or if they are in an industry with unusual unemployment experience. Reimbursements are made by government and nonprofit institutions that choose not to pay the premiums tax. These employers simply reimburse the trust fund for any benefits paid to their employees. Reimbursements are usually repaid one quarter after the benefits are dispersed. Interest accumulates from investment of the trust fund balance and is credited to the trust fund in the next period. The significance of this revenue source declines during recessions as the trust fund balance decreases. Higher interest rates can bolster these revenues, however. In general, interest revenues depend on the portfolio of assets that is purchased with the trust fund balance, but since all state UI trust funds are deposited with the U.S. Treasury, the interest return is not controlled at the state level. The last revenue category is interstate transfers. Interstate transfers are payments between states to compensate for claims made in one state when the associated premiums were paid in a different state. This occurs when an employee crosses state lines between home and work, or when an employee has earnings in more than one state. Only the net transfers are relevant in determining the trust fund balance. These transfers depend on the net migration of benefit recipients, which varies greatly with no clear pattern. The largest expenditure component is regular benefits, which are paid to an unemployed claimant according to a benefit formula. To receive UI benefits, the claimant must be eligible, and the requirements vary among states. Meeting the eligibility requirements entitles the claimant to a
D.M.
Mandy
/
Unemployment
specific number of weeks of UI benefits. The amount of the weekly benefit is based on the claimant’s previous earnings, subject to some maximum and minimum amounts. Weekly benefit amounts are also influenced by part-time work and, to varying degrees across states, by the number of claimant’s dependents. Extended benefits are paid during cyclical downturns when the duration of unemployment increases. In practice, extended benefit periods are determined by a rule that compares current and past unemployment rates. During an extended benefit period, eligible claimants who have exhausted their regular benefits can receive UI payments for additional weeks. The cost of extended benefits is shared between the federal government and the states. Hence, the sum of regular and extended benefits overstates the flows out of a state UI trust fund.
2. The estimated model In order to forecast the trust fund balance, each of the components described in the previous section must be forecast. This is reflected by equation 1 of table 1, which is the identity that aggregates the components into the trust fund balance. Table 1 also shows the revenue equations, while the benefit equations are given in table 2. The system of equations given in tables 1 and 2 cannot be simultaneously estimated, primarily due to the lack of observations on the independent variable in equation 3. The source for this variable is discussed below, but the implication for estimation is that with only 17 observations there are more predetermined variables than observations. Hence, the equations discussed below are estimated individually, although forecasts are produced with the entire simultaneous system. On the revenue side, premiums are the most important component, and there are two important policy variables involved in the premium forecast. Hence, a substantial portion of the discussion of this section centers on the premium equations. The first step in developing a premium forecast is to forecast the taxable wages that underlie premiums. The pattern of taxable wages is dependent on the taxable wage ceiling. The ceiling becomes binding on many employees in the first quarter and on the average employee in the second quarter
insurance
383
trust funds
of the year; this introduces strong seasonality into the taxable wage data (see fig. 1). Since the ceiling causes taxable wages for each quarter to be generated by a different set of circumstances, slope and intercept dummy variables were used to fit the taxable wage equation. Equation 2 captures the way in which the per-employee ceiling affects taxable wages, on average, by using the minimum of the ceiling and the average wage. In the first quarter average wages are usually higher than the ceiling, so a change in the per-employee ceiling probably would not affect the predicted value for taxable wages. However, the ceiling is undoubtedly binding on some employees in the first quarter. For this reason the ceiling is explicitly included as an additional independent variable in the first quarter. The integration of the ceiling into this equation provides an important policy variable since the effects of legislative changes in this variable can be easily simulated by changing the exogenous assumption. Ideally, the components of equation 2 that are relevant in the second quarter should consist of two terms. The first is any wages below the ceiling paid to employees that were employed in the first quarter. The second is wages below the ceiling paid to new employees. This structure cannot be captured because the net change in employment cannot be empirically disaggregated into additions to and subtractions from employment. Equation 2 approximates the correct structure by treating the net change in employment as if it were all new employment in the second quarter. This overstates taxable wages due to continuing employment and understates taxable wages due to new employment; the magnitude of these inaccuracies depends upon gross employment growth relative to
0 F
ZSOO..
oJ: 01 1070
: 01 1972
01
1974
01
197E
01 ma
Fig. 1. Taxable
ot
01
19110 1902
wages
01
01
ls4
19s
384
Table 1 Tesim revenue equations BAL,
=BAL,_,+(PREM,+REIM,+TRAN,-BN_TN,)xl,OOO+I,_,
1
TW,
=
2
-89.7 + 0.586(D1xMl1,~ECOV)+0.218(D1~B,)+0.430(D2xM12,xECOV,)+ (- 1.60 “) (21.84 “) (13.49 “) (5.64 “) 5.064 (D2xM11, (10.11 “)
x(ECOV,
-ECOV,m,))-11,842 (-5.60
(D2XECOV,/ECOV,_,)+ “)
0.525 (D3xTW,_,)+0.781 (D4xTW,_,)-281.4 D1+12,337 D2+193.1 D3 (17.32 “) (- 2.21 “) (5.63 “) (2.53 “) (21.96 “) F= 2210 a ln(PREM,)=
d
R2 = 0.985
Period = 7002 - 8704
n = 71
180”
874”
DW =1.240
3 ’
Period = 8304 - 8704
n =17
1
R2 = 0.792
= 0.188 + 0.848 MAVG(2, (0.559 “)(16.43 “) F=
TRAN,
530
= 0.030 BN -TN,(15.83 “) F=
I e
Durbin - h = - 0.098 ah
1.490+0.868 In (DIST,)+0.210 D8402 (4.00) (5.17) (32.40) F=
REIM,
a2 = 0.997
R2 = 0.986
4 Durbin - h = 1.65 ab BAL,) x MAVG(2,
R,m6)
Durbin - h = - 1.67 ab
Period = 7601-
8801
n = 49
j3 = 0.523
’
5
Period = 7604 - 8604
n = 41
8, =1.143
= -278.6 + 77.2 UR-tO.144 TRAN,m,+0.435 TRAN,_, (- 1.37 ‘)(2.14 “) (1.18 “) (3.65 “) F=
32.9 a
R2 = 0.611
Durbin - h = 1.65 ab
B2 = - 0.422 6
Period = 7203 - 8704
n = 62
Asymptotic statistic. A), where A is the set of independent variables. See Durbin t-statistic for the coefficient of e,_, in the equation e, = f(e,_,, (1970). Inconclusive DW. A Durbin-Watson test for first order autocorrelation, using the tables of Farebrother (1980). revealed that autocorrelation was present in this equation. The equation was re-estimated with an assumed AR(l) structure. The results shown reflect this re-estimation. This equation was estimated with an assumed AR(2) structure by the Hildreth-Lu search technique. MAVG( n, x) denotes an n-period moving average of x.
employment losses. Since this is predominately a cyclical phenomena, the percent change in employment is included in this equation as a proxy for the inherent inaccuracies. The negative estimated coefficient suggests that the overstatement is larger than the understatement. The components of equation 2 that are relevant in the third and fourth quarters could be constructed in a manner similar to the first and second quarter components. However, the distortions became more pronounced in later quarters so that this construction does not work well. Taxable wages in the last two quarters of the year follow taxable wages for the preceding quarter, so a simple lag was estimated for the third and fourth quarters. Notice that this structure still captures
the effects of an exogenous change in the per-employee ceiling in all four quarters because the change is passed through the lag structure to the later quarters. Moreover, despite the somewhat simplistic nature of equation 2 for the third and fourth quarters, the coefficients are significant and, as discussed below, the equation predicts well. Tax rates must be applied to the taxable wage forecast to obtain a premium forecast. Tax rates can be forecast either by an estimated equation for the average tax rate, or by using a distribution of firms across the reserve ratio continuum and then applying the legislated tax table to this distribution. If an average tax rate is used, the experience rating system is bypassed and the array of tax rates that are possible is not part of the
D.M. Mandy / Unemployment insurance trustfunds Table 1 Tesim revenue equations Variable B
BAL BN_TN D8402 Di DIST ECOV Ml1 Ml2 PREM R REIM TRAN TW UR W
a
385
(Cont.) Description
Units
Per-employee ceiling Trust fund balance Total benefits paid from the Tennessee UI trust fund Dummy variable; 1 in 198402 and after, 0 otherwise Dummy variable; 1 in ith quarter, 0 otherwise Sum of premiums over experience rating categories Employment in premium-paying industries Interest Min (B, W) Min (B - Mll, W) Premiums Prime rate Reimbursements Interstate transfers Taxable wages Seasonally adjusted Tennessee unemployment rate Average annual wage and salary income in premium-paying industries
Mil. Cur. $ Mil. Cur. $ Thou. Cur. $ _
,’ All variables are Tennessee Associates, Inc.
variables,
except
R. Exogenous
premium calculation. Also, since alternative tax tables are often considered for adoption, an average tax rate approach is not adequate for strategic planning purposes. For this reason, TESIM uses the distribution approach. Future distributions are forecast by applying the forecast growth rates of taxable wages and benefits to the taxable wages and benefits of each reserve ratio category. The reserve ratio calculation is then applied to each category to obtain a forecast reserve ratio for the category. Once the distribution is forecast, the (lagged) forecast trust fund balance is combined with the reserve ratio of each category to obtain the legislated tax rate for that category. Multiplying this by forecasted taxable wages for the category yields the premium forecast for the category. Aggregating across categories yields a total premium forecast. By using a different set of tax rates, the impact of proposed legislative changes in the tax tables can be assessed. Despite the advantage of alternative tax table simulation capability, this method suffers from several shortcomings. The assumption that each category will experience average growth in taxable wages and benefits is clearly inaccurate. Still, a solution to this problem entails estimating wages and benefits for each category separately, and this could involve several hundred equations, It may
values
of R were obtained
_ Thou. Cur. Jobs Mil. Cur. $ Mil. Cur. $ Mil. Cur. $ Thou. Cur. Percent Thou. Cur. Thou. Cur. Mil. Cur. $ Percent Mil. Cur. $
from Wharton
$
$ $ $
Econometric
Forecasting
be possible to disaggregate the gross wages and benefits forecasts across the categories by using some cyclical explanatory variables. This is an area for future research. Another shortcoming is that the premium-paying employers that are subject to special rates are not included in the available distribution. Hence, the distribution forecast always understates true premiums. The understatement is systematic, however, and true premiums are easily forecast as a function of the distribution forecast. The estimated relationship is given by equation 3 of table 1. A third problem is the significant data requirement of this approach. Barnow and Vroman (1986) discuss this problem as it applies to the Mercer model. For TESIM, only five years’ distributions were available, limiting estimation of equation 3 to seventeen observations. This prohibits simultaneous estimation of TESIM, but the need for policy simulation in the UI environment is important enough to warrant the distribution approach. Equations 4-6 forecast the remaining three revenue categories. Equation 4 forecasts reimbursements, which are repaid one quarter after the benefits are paid. The benefits paid to employees of reimbursing employers is a relatively stable proportion of total benefits, as reflected by equation 4. Equation 5 forecasts interest as the product of the average balance over the quarter with an
D. M. Mandy / Unemployment insurance trust funds
386 Table 2 Tesim benefit equations BN, = AVGBN, In (AVGBN,)
7
x TOTWKS, = 0.009 + 1.27 In (AVGNB,_,)-0.339 (0.27 “) (9.99 “) (-2.88 F=8182a
TOTWKS,
‘
R* = 0.998
= -49.62 +l.lll (- 2.11 “)(26.23 F=
672a
R’ = 0.978
= 8,515 -8,346 E,/E,_, (12.74 “) (- 12.67 “)
REGWKS,
F=
iI* = 0.947
592a
Durbin-h=-l.40ab
REGWKS, “)
8
In (AVGBN,_,)+O.063 In (MBA,) (1.93 “) “) Period = 7203 - 8801
n = 63 9
+73.60 DEXTBN, (4.50 “) Durbin - h = 1.40 ab + 0.782 REGWKS,_ (26.19 “) Durbin - h = 0.26 ab
Period = 7203 - 8801
n = 63
fir = 0.756
& = - 0.336 10
r Period = 7102 - 8704
n = 67 11
EXTWKS,
= DEXTBN,
x (TOTWKS,
REGBN,
= REGWKS,
x AVGBN,
12
EXTBN,
= EXTWKS,
x AVGBN,
13
+ PCT, x EXTBN,
14
BN _TN, d = REGBN, 1 DEXTBN,
=
if (DEXTBN,_, or (REGWKS,_,
0
- REGWKS,)
= 1 and EXTWKS, > 10) -REGWKS,_,
2100) 15
otherwise
Asymptotic statistic t-statistic for the coefficient of e, _, in the equation e, = f (e,_ 1,A), where A is the set of independent variables. See Durbin (1970). This equation was estimated with an assumed AR(2) structure by the Hildreth-Lu search technique. Note that the RHS variables in this equation are seasonally adjusted, while the LHS variable is unadjusted. In practice, forecast seasonal factors are used to express all variables in unadjusted form before this equation is calculated.
average of recent interest rates. Finally, equation 6 forecasts interstate transfers. There is no obvious structure that links to TEM that can be used to forecast this variable. It is subject to seasonal and cyclical variability as well as potential structural
Table 2 Tesim benefit Variable
a
AVGBN BN BN_TN DEXTBN E EXTBN EXTWKS MBA PCT REGBN REGWKS TOTWKS d All variables
equations
changes in the commuting patterns between states. While several alternative specifications were examined, equation 6 is the best fit obtained. On the expenditure side, both regular and extended benefits can be expressed as the product of
(Cont.) Description
Units
Seasonally adjusted average benefit payment for all benefits Seasonally adjusted total benefits Total benefits paid from the Tennessee UI trust fund Dummy variable; 1 in extended benefit periods, 0 otherwise Seasonally adjusted total nonagricultural employment Seasonally adjusted total extended benefits Seasonally adjusted extended weeks compensated Legislated maximum benefit amount Proportion of extended benefits paid by Tennessee Seasonally adjusted total regular benefits Seasonally adjusted regular weeks compensated Seasonally adJusted total weeks compensated
Cur. $ Thou. Cur. % Thou. Cur. S
are Tennessee
variables.
Thou. Jobs Thou. Cur. $ Thou. Weeks Cur. $ Rate Thou. Cur. $ Thou. Weeks Thou. Weeks
D.M. Mandy / Unemployment insurance trust funds
‘weeks compensated’ and the average weekly benefit. Weeks compensated is simply the number of UI payments issued in an average week during the quarter. Thus, total benefits are given by equation 7 of table 2. Extended weeks compensated and average extended benefits are the most difficult variables to estimate and forecast. They are volatile series and only limited observations exist since these variables are zero except during extended benefit periods. Estimating total and regular benefit variables provides more reliable equations. Then, when an extended benefit period is in force, extended benefits can be treated as a residual. Accordingly, average benefits across both regular and extended benefits are predicted by equation 8, and total weeks compensated are predicted by equation 9. Equation 8 reflects the fact that the benefit formula depends on the legislated maximum benefit amount. This provides another outlet for policy simulation, as the effects of changes in the maximum benefit amount can be investigated by using different exogenous values for the maximum benefit amount. Total weeks compensated are predominately determined by regular weeks compensated. In addition, total weeks compensated increase during extended benefit periods as indicated by the extended benefits dummy. It is necessary to disaggregate benefits into extended and regular benefit outlays so that the effect of the federal sharing rule is reflected in the forecast trust fund balance. Equation 10 predicts regular weeks compensated and, given this forecast, extended weeks compensated are given by the identity shown as equation 11. Regular and extended benefits, respectively, are then determined by identities 12 and 13. Finally, total reductions in the trust fund balance are given by equation 14. If the extended benefit dummy is determined exogenously, equations 7-14 can be used to predict benefits. Aternatively, the occurrence of extended benefit periods can be determined endogenously. In practice, extended benefit periods are determined by a complicated rule that examines changes in weekly unemployment rates. This is cumbersome to incorporate into TESIM, creating the need for a proxy rule if extended benefit periods are to be endogenously determined. Historically, extended benefit periods were always preceded by a sharp increase in regular weeks
387
compensated. Once an extended benefit period is in effect, it remains in effect until unemployment decreases. This usually coincides with a decrease in extended weeks compensated to a relatively low level. This leads to the proxy rule given by equation 15. The threshold value of 100 was chosen because it perfectly predicts every extended benefit period.
3. Performance
of TESIM
Three separate sets of simulations were conducted to evaluate the forecasting accuracy of TESIM. For the first two sets, TESIM was reestimated using only part of the data and then a forecast was generated over the withheld observations. Each set consists of ten eight-quarter forecasts generated in this manner, beginning in each quarter from 8304 through 8601. Data limitations prevent simulations of quarters prior to 8304. Estimation was conducted using data through the quarter preceding the first forecast quarter in each case. Equation 3 was not re-estimated for these simulations due to the lack of observations for this equation. Thus, the transformation from distribution-based premiums to the premium forecast is more accurate in these simulations than can be expected in a true forecasting environment. The distinction between the first two sets of simulations lies in the source for the exogenous variables. For the first set of simulations, exogenous values were provided by old TEM forecasts wherein the beginning forecast quarter corresponded to the beginning forecast quarter of each TESIM forecast. These are the forecasts that were actually produced using TEM at the time. One problem with these simulations is that data have been revised since the TEM forecasts were produced, and TESIM is estimated using current data over the appropriate time period. To make the data consistent, growth rates were calculated from the TEM forecasts and then applied sequentially to the last historical observation of the current data. The exogenous values created in this way were then used to drive each TESIM forecast. For the second set of simulations, true values for the exogenous variables were used. As a basis for comparison, a third set of simulations was generated using a univariate HoltWinters technique to forecast only the trust fund
D. M. Mandy / Unemployment insurance trust funds
388
balance. The model consists of level, trend, and seasonal components, and the parameters were chosen optimally to minimize the sum of the squared forecast errors in the first forecast quarter. The data consist of quarterly observations on the trust fund balance from 7101 through 8704 (68 observations). In 8301, the UI trust fund in Tennessee became insolvent, so the observation for that quarter is slightly negative. Since the seasonal adjustment calculation does not work for negative values, this observation was arbitrarily set at 1. The first nine years of data (36 observations) were used to allow the effects of the starting values to die down. Thus, the sum of squared errors was calculated from the thirty-seventh observation through the end of the history for each simulation. This procedure is described by Granger and Newbold (1977, pp. 164-167). Ten eight-quarter forecasts were generated with this model, corresponding to the forecasts generated with TESIM. The parameters were recalculated for each forecast, using only data through the end of the historical period. For each forecast, percent forecast errors for each endogenous variable were calculated. These errors were then aggregated into mean absolute percent errors (MAPE) by forecast quarter, and the MAPE’s are reported for the most important
Table 3 Tesim mape by forecast
TESIM variables in table 3. Together, the three sets of errors provide a substantive test of the accuracy of TESIM. The first set of errors measures the accuracy of the entire forecasting system, while the second set measures the accuracy of TESIM independent of the errors generated by TEM. The third set provides a benchmark for the first two sets. The average benefit payment exhibits the smallest forecast errors, averaging 1.4% over all forecast quarters. Note that the errors for this variable are the same for the first two sets of simulations because, by equation 8, the average benefit forecast is independent of exogenous assumptions. A less favorable performance is displayed by total weeks compensated, as the MAPE increases from 5.3% in the first forecast quarter to 8.4% before decreasing to 7% in the eight forecast quarter. This variable performed particularly poorly when the exogenous values were provided by TEM, with errors averaging 14.8%. Clearly, a large proportion of the errors here result from inaccurate employment forecasts produced by TEM. These two variables combine to produce an average error in total benefits of 7.5% over all forecast quarters in the second set of simulations and 14.8% in the first set of simulations, and an error pattern that mirrors total weeks compensated.
quarter. 1st Quarter
Exogenous values provided Trust Fund Balance Taxable Wage Average Premium Rate Premiums Total Weeks Compensated Average Benefit Payment Benefits
by TEM
Exogenous values provided Trust Fund Balance Taxable Wage Average Premium Rate Premiums Total Weeks Compensated Average Benefit Payment Benefits Holt-Winters forecast Trust Fund Balance
by actual
2nd Quarter
3rd Quarter
4th Quarter
5th Quarter
6th Quarter
7th Quarter
8th Quarter
Average
4.67 2.57 5.81 5.91 10.89 0.83 11.11
5.60 2.87 5.76 5.71 9.49 1.05 9.59
3.90 3.05 7.20 6.72 4.86 1.40 4.33
4.14 4.57 8.46 7.36 9.16 1.46 9.49
5.60 4.23 7.71 9.55 14.08 1.72 14.18
7.07 6.12 5.73 9.35 15.99 1.64 15.93
9.23 7.09 5.53 8.00 22.76 1.49 22.66
12.08 10.34 12.39 8.05 31.51 1.29 31.05
6.54 5.10 7.33 7.58 14.84 1.36 14.79
4.18 2.07 5.92 5.91 5.34 0.83 5.85
5.94 2.62 5.78 5.00 5.68 1.05 6.13
4.88 2.79 6.94 6.18 6.63 1.40 7.33
5.94 3.47 8.35 7.97 7.79 1.46 X.27
7.57 3.41 8.06 10.12 8.42 1.72 8.88
X.67 4.28 4.66 9.18 7.67 1.64 8.16
9.37 4.84 4.45 7.26 7.46 1.49 8.07
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On the revenue side of the trust fund, in the first set of simulations the MAPE for taxable wages increases from 2% to 5% before jumping in the last quarter of the forecast period to 6.4%. The transformation to total premiums increases the average error in total premiums to 7.4%. When the exogenous values are provided by TEM, the MAPE for taxable wages increases from 2.6 to 7.1% before increasing to 10.3% in the last forecast quarter. The average error for premiums is 7.6%. The errors displayed by the trust fund balance summarize the errors of its component parts. The MAPE for the balance increases steadily with one exception from 4.2% to 10.2% from the first to the eighth forecast quarters. When the exogenous values are provided by TEM, the MAPE for the balance increases from 3.9% in the third to 12.1% in the eight forecast quarter. Surprisingly, the overall average is lower than the average produced by using actual values for the exogenous variables. The fact that the trust fund balance is a stock that is forecast by estimated flows reinforces the tendency for forecast errors to increase in later forecast quarters. Any errors in the balance forecast become cumulative unless the errors in the component flows change direction. In general, premiums are greater than their forecast values and benefits are less than their forecast values. Thus, the change in the trust fund balance is usually larger than the forecasted change. A change in the direction of this error is rare, so that errors in the trust fund balance accumulate, leading to a large MAPE by the eighth forecast quarter. From the standpoint of minimizing the risk of trust fund insolvency, this is not a significant problem since the direction of the error implies that the trust fund balance will be larger than the forecast value. Hence, the model tends to err on the conservative side. These errors compare quite favorably with the benchmark Holt-Winters forecasts. In general, the Holt-Winters technique performed very poorly, with forecasting errors averaging almost 40%. Moreover, this technique is not useful for simulations since it ignores the institutional structure of the forecasting environment. That is, another measure of the performance of a model is its ability to provide decision support for strategic planning. TESlM meets this goal by construction, since the taxable wage ceiling, tax rates, maximum benefit amount, and experience rating rule are all explicitly present in the model. Changes in these
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variables can be simulated by simply changing the parameters of the model. To illustrate how TESIM can be used for strategic planning, the first three of these parameters were altered and three new simulations were generated over the last simulation period, 8601-8704. In all cases, the exogenous variables were provided by the actual values, so the appropriate baseline for comparison is the last of the second set of simulations described above. The results of these simulations are presented in figs. 2-6, each of which presents the alternative scenarios that affect a particular UI variable. The series are labeled according to the parameter that was altered in each case. TAX TABLE represents a 10% increase in tax rates relative to BASELINE effective 8601 on only those employers with negative reserve ratios. MBA results from holding the maximum weekly benefit amount constant at $120 instead of providing the increases to $145 that actually occurred during this period. Finally, B results from increasing the taxable wage ceiling from $7,000 to $8,000 effective 8601. All three of these changes cause the forecasted trust fund balance to increase. Figure 2 illustrates that the increase in the taxable wage ceiling has the most significant impact, while the change in MBA had little effect. The effects on taxable wages of the change in the ceiling can be seen by examining fig. 3. Figure 4 illustrates how changing the ceiling and the tax tables affects premiums. Figures 5 and 6 show how changing the maximum benefit amount affects total benefits and the average benefit payment, respectively. A significant weakness in the simulation capability of TESIM is the lack of policy variables related to the benefit formula and eligibility. The
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only explicit parameter is the maximum weekly benefit amount. Eligibility requirements and benefit rules can be complicated and difficult to model. However, changes in these formulas are often considered, and the strategic planning capabilities of the model would be significantly improved if the impact of alternative benefit legislation could be easily evaluated. The problem is that the benefit rules affect individual claimants differently, so that any attempt to explicitly incor-
The TESIM model is constructed to fulfill two major goals. The first is to provide the most accurate forecasts possible for the UI system. The second is to incorporate important policy variables into the model so that policy changes can be simulated. These goals are not necessarily congruous. To the extent that model structure is dictated by simulation capability, forecasting accuracy may be sacrificed. TESIM incorporates most of the significant policy variables and is constructed to minimize forecasting error within this framework. The result is larger forecasting errors than could be achieved if the only goal were accuracy. However, the model lends itself to policy simulation and uses well-founded exogenous assumptions. Many alternatives were investigated while building the TESIM model, and the forecasting errors are testimony to the difficulty of modeling the UI system in a way that meets the needs of UI policy makers. Despite the inaccuracies, TESIM fulfills these needs within a consistent framework, making it a potentially useful framework for policy makers nationwide.
D.M. Mandy / Unemployment
References Bamow, Burt and Wayne Vroman, 1986, An analysis of UI trust fund adequacy, final report submitted by ICF Incorporated for contract no. 99-5-3024-04-090-01, Employment and Training Administration, U.S. Department of Labor, Washington, D.C. Durbin, J., 1970, Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables, Econometrica 38, 410-421. Farebrother, R.W., 1980, The Durbin-Watson test for serial correlation when there is no intercept in the regression, Econometrica 48, 1553-1563. Fox, William F. and David A. Hake, 1984, Economic forecasting in Tennessee, Suruey of Business 19, 30-37. Granger, C.W.J. and Paul Newbold, 1977, Forecasting economic time series (Academic Press, New York). Hultman, Charles W. and Charles G. Renfro. 1979, Analysis of an unemployment insurance projection model, Office of Re-
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search, College of Business and Economics, University of Kentucky (Lexington, KY). Ladin, Jay, 1986, Simulating the impact of the next recession on unemployment trust funds: The Matyland case, Department of Fiscal Services, Maryland General Assembly. Mercer Associates, 1977, State unemployment insurance user’s manual for projection program and financial forecast program, 2 volumes, prepared for the Division of Actuarial Services, UI Service, U.S. Department of Labor.
Biography: David MANDY is a Research Assistant Professor at the Center for Business and Economic Research, the University of Tennessee, Knoxville and Assistant Professor of Economics, The University of Tennessee, Knoxville. He is director of the Tennessee Economic Forecasting Service and received the Ph.D. in Economics from the University of Illinois/ Urbana-Champaign in 1987. His fields of specialization are applied microeconomics and econometrics.