Does the pension system’s income statement really matter? A proposal for an NDC scheme with disability and minimum pension benefits

Figures & data

Table 1. Measuring liabilities (and assets) in (contributory) social security schemes: summary.

Approach	Time horizon (valuation period)		Number of new cohorts of contributors included	Projections (explicit)	Suitable for…Applied to…
	System	Actuarial perspective
Closed group without future accruals (CG)	Zero. The system is assumed to be closed.	Pensions in payment are estimated in present value terms. Years elapsed between the highest age to which it is possible to survive and the youngest cohort of pensioners.	Zero.	No	Fully-funded DC schemes or PAYG schemes when the decision is made for immediate closure. (Eurostat, 2011).
Closed group with future accruals (CGFA)	Years elapsed between the retirement age and the youngest cohort of contributors.	Future and current pensions in payment are estimated in present value terms. Years elapsed between the highest age to which it is possible to survive and the youngest cohort of contributors.	Zero. The system is considered as if it were operating until the last contributor dies.	Yes. Explicit projections of economic, financial or demographic variables must be made.	Fully-funded DB schemes or PAYG schemes when no new entrants are allowed.
Hybrid open group (HOG)	An arbitrary time period corresponding to the number of new cohorts of contributors allowed (from 50 to 75 years).	Years elapsed between the highest age to which it is possible to survive and the youngest cohort of contributors plus the arbitrary time period.	An arbitrary number (from 50 to 75). The system is considered as if it were functioning until the last contributor of the last cohort of entrants accepted as contributors dies.	Yes. Explicit projections must be made.	PAYG schemes when only a limited number of new cohorts of entrants are allowed.
Open group (OG)	An arbitrary time period from 75-95 years to infinite.	Under a cash flow approach, matches the system’s time horizon.	An arbitrary number from 75-95 years to infinite. An ongoing basis for the scheme is assumed.	Yes. Explicit projections of economic, financial or demographic variables must be made.	PAYG and partially funded schemes. (EC, 2018); (BOT, 2019); (AAD, 2017); (OSFIC, 2018)
“Swedish” open group (SOG)	Valuation formulas consider only pensioners and contributors at the valuation date, but…	…the use of the expected time between payment of contributions and receipt of pensions (turnover duration, TD) and other assumptions makes this approach equivalent to a perpetual time horizon.	Equivalent to an infinite number of cohorts.	There is no need for explicit projections. It is assumed that the system's rules and the economic and demographic conditions prevailing at the time of the valuation remain constant.	PAYG schemes, especially for NDCs. (TSPS, 2019)

Source: Own.

Table 2. The ABS for an already-functioning NDC scheme combining retirement and disability contingencies with an MPB.

ASSETS	LIABILITIES AND SPONSOR SUPPORT (CAPITAL)
Financial (and real) assets: FA	Financial liabilities: FD
	Sponsor support: Ss
Contribution asset for retirement: CA_(R)	Liability to contributors for retirement: Con_(R)
	Liability to pensioners for retirement: Pen_(R)
Buffer fund for retirement: BF_(R)	Liability to contributors for retirement: Con_(R)_NCR
	Liability to pensioners for retirement: Pen_(R) _NCR
Contribution asset for disability: CA_(D)	Liability to contributors for disability: Con_(D)
	Liability to pensioners for disability: Pen_(D)
Buffer fund for disability: BF_(R)	Liability to contributors for disability: Con_(D)_NCR
	Liability to pensioners for disability: Pen_(D)_NCR:
Accumulated deficit: Ad_(R + D)	Accumulated surplus: As_(R + D)
Actuarial losses for the period: L_(R + D)	Actuarial profit (gains) for the period: P_(R + D)
TOTAL ASSETS	TOTAL LIABILITIES

Source: Own.

Table 3. The income statement for an NDC scheme combining retirement and disability contingencies, with an MPB for the period.

FUND ASSETS (Changes)	LIABILITIES (Changes)
Pension contributions: C	New pension credit: C
Sponsor contributions for NCRs: SC	Recognition of NCRs: R
Pension disbursements: - PT	Pension disbursements: - PT
Net return on funded capital: D	Indexation: I
CONTRIBUTION ASSET (Changes)	Value of change in life expectancy: $\delta$e
Value of change in contribution revenue: $\delta$C	Value of change in discount rate: $\delta$G
Value of change in turnover duration: $\delta$TD	NET GAIN/LOSS
TOTAL DEBIT SIDE	TOTAL CREDIT SIDE

Source: Own.

Table 4. The ABS of an ${\mathit{NDC}}_{\mathit{dr}}^{25\%}$ scheme at the end of years t-1 and t with changes in net worth (monetary units).

Items/year	$\mathit{t}-1$	$\mathit{t}$	Variation
ASSETS
BF	11.500	11.730	0.230
BF_(R + D)_NCR	5.500	5.588	0.088
CA_(R)	80.120	81.963	1.843
CA_(D)	19.880	20.079	0.199
Ad_(R + D)	0.000	0.000	0.000
L_(R + D)	0.000	0.000	0.000
Total	117.000	119.360	2.360
LIABILITIES AND SPONSOR SUPPORT (CAPITAL)
Ss_(R + D)	10.000	10.000	0.000
Con_(R)	55.510	56.620	1.110
Con_(D)	12.260	12.505	0.245
Pen_(R)	24.610	24.856	0.246
Pen_(D)	7.620	7.772	0.152
Pen_(R)_NCR	2.200	2.222	0.022
Pen_(D)_NCR	3.300	3.366	0.066
As_(R + D)	1.500	1.500	0.000
P_(R + D)	0.000	0.518	0.518
Total	117.000	119.360	2.360
SOLVENCY, FUNDING AND LIABILITY STRUCTURE INDICATORS
${TD}_t^S$ $({TD}_t^R;{TD}_t^D$)	31.92 (34.03; 25.55)	31.60 (34.37; 23.78)	−0.3192
${BR}_t^S$	1.014	1.019	0.0046
${DF}_t^{}$%	16.11	16.13	0.0002
${LS}_t^{}$%	64.24	64.40	0.0016

Source: Own.

Table 5. The income statement for the period t-1, t (monetary units).

ITEMS	System	R	D
FUND ASSET (Changes)	0.318	0.197	0.121
Pension contributions	3.229	2.385	0.844
Sponsor support for NCRs	0.088	0.022	0.066
Pension disbursements	−3.164	−2.337	−0.827
Net return on funded capital	0.165	0.127	0.038
CONTRIBUTION ASSET (Changes)	2.042	1.843	0.199
Value of change in contribution revenue	3.057	1.036	2.021
Value of change in turnover duration	−1.015	0.806	−1.822
Total LEFT-HAND SIDE	2.360	2.040	0.320
LIABILITIES (Changes)	1.842	1.397	0.445
New pension credit	3.229	2.385	0.844
Recognition of NCRs	0.088	0.022	0.066
Pension disbursements	−3.164	−2.337	−0.827
Indexation	0.900	0.720	0.180
Value of change in life expectancy	0.030	0.010	0.020
Value of change in discount rate	0.759	0.597	0.162
NET WORTH (Change)	0.518	0.643	−0.125
Total RIGHT-HAND SIDE	2.360	2.040	0.320

Source: Own.

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