Stochastic modelling in policy analysis

Danne Mikula, SSIA

* Swedish PAYG pension scheme* The Balance Mechanism

Designing rules for distributing of surplus of the Swedish NDC Pension Scheme

But first we need a crash course in

Notional Defined Contribution (NDC)

Pay As You Go scheme (PAYG)

Contribution rate 18.5% -> 16%

Total Liability = 2.5 x GDP

Buffer Fund = 10 % of Total Liability

“Autonomous system”

Main source of income for elderly

The Swedish pension reform defines

a financially stable pension system

• Average wage indexation

• Contribution = Entitlement

• Annuity Capital / ”remaining life length”

• Balance mechanism

BR = Assets

Liabilities

Assets? But the system is of PAYG type…

Balance Ratio (BR)

BR =Funds + ....

Pension liability

In Steady State:

Over-consolidation(could be removed) Pension Liability

Balance Ratio an intuitive explanation

BR =Funds + “Pension Liability in SS”

Pension liability

Define

Balance Ratio

Pension Liability in Steady State = Contribution Asset (CA)

CA = C * T

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Contributions (C)

TTurnover duration

”...time is money”

age

Pensions

Average age of contributor

Average age of retiree

AssetsBR =

Liabilities

CA + FBR =

D

Balance Ratio

C * T + FBR =

D

BR >= 1.0

Balance Mechanism

Balance ratio, Demography = Baseline, growth = 2%

0,90

1,00

1,10

1,20

1,30

1,40

1,50

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

5.0% 3.25% 2%

Rate of return

3.25%

5.0%

2.0%

2.0%, with balancing

Big surplus could be accumulated

Asymmetric design

over-consolidation ?

”Automatic balance mechanism”, some properties

• No forecasts, nerveless early reaction to protect liquidity bookkeeping based on well defined, observable historical facts, increases transparency

• Allow less stable (“more socially attractive”) systems deviation from desired indexation only if it is financially necessary

• Secure financial stability regardless magnitude or type of financial strain

• Asymmetric construction can allow exploding buffer fund we need rule indicating when the assets are to big

0,90

1,00

1,10

1,20

1,30

1,40

1,50

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

Balance Ratio Ceiling (BRC)

Task: Find the proper BRC level

• Relatively small increase in risk for balancing caused by earlier distribution (<5%)• Consider the intergenerational fairness

Two guiding principles:

1.00 <= BR <= 1.00

Balance Mechanismrestoring the symmetry

1.00 <= BR <= 1.01 1.00 <= BR <= 1.02

1.00 <= BR <= 1.19 1.00 <= BR <= 1.20

… … …

“Ru

le s

pace

”

SwedishPensionModel(Micro)

UTÖModel

(Cell based)

Randomization of• Labour participation• Real return on Buffer Fund• Inflation

Different rules for asset distribution1.00, 1.01, …, 1.20, none

Pension liabilities

Base Line assumptions

With & Without the rule XBuffer FundContributionsPension benefitsBalance Ratio (assets & liabilities)

Aggregate sums, counts,(Average Gain & St. Dev.)

Repeat it “lot of times”

Analyse & make your choice

The framework

Ready!

Here next: Excel based analysis

1.00 <= BR <= 1.10

Recommendationfor the symmetric

mechanism