Automatic Balance Mechanisms for Notional Defined Contribution Accounts in the presence of uncertainty

Transcription

1 Automatic Balance Mechanisms for Notional Defined Contribution Accounts in the presence of uncertainty Jennifer Alonso García (joint work with Carmen Boado-Penas and Pierre Devolder) Université Catholique de Louvain (UCL), Belgium 27/01/2015

2 Overview 1 Introduction Why? Overview NDC 2 Aim OLG Setup Liquidity & Solvency Ratio ABM 3 Methodology No Baby Boom Baby Boom 4

3 Why? Overview NDC Why should we consider a pension reform? In Belgium the following demographic changes are observed: Rising longevity: people are living longer and longer but retire at the same age as 50 years ago. Life expectancy in 1960: 70 years Life expectancy in 2011: 80 years Drop in fertility Fertility rate in 1960: 2.58 births per woman. Fertility rate in 2011: 1.84 births per woman. Shortcomings of Defined Benefit (DB): Shifting from defined benefits to defined contributions seems better in terms of steady-state income per capita (Artige, Cavenaile & Pestieau, 2014) Lack of actuarial fairness: No direct link between the contributions made and amount of pension received at retirement.

4 Why? Overview NDC Change in gross public pension expenditure over (in % of GDP) Table : Change in gross public pension expenditure over (in % of GDP) Country Change BE 11,0 13,1 16,5 16,6 5,6 DE 10,8 10,9 12,7 13,4 2,6 IT 15,3 14,5 15,6 14,4-0,9 SW 9,6 9,6 10,2 10,2 0,6 PL 11,8 10,9 10,3 9,6-2,2 UK 7,7 7,0 8,2 9,2 1,5 UE27 11,3 11,3 12,6 12,9 1,5 Source: European Commission - The 2012 Ageing Report

5 Why? Overview NDC Overview of pension systems Basic financing techniques Pay as you go (PAYG): current contributors pay current pensioners (Unfunded schemes) Funding: contributions are accumulated in a fund which earns a market interest rate (Funded schemes) Benefit formulae Defined Benefit: Pension is calculated according to a fixed formula which usually depends on the members salary and the number of contribution years. Defined Contribution: Pension is dependent on the amount of money contributed and their return. Notional Accounts: Mix of PAYG and Defined Contribution!

6 Why? Overview NDC Notional Defined Contribution The non-financial defined contribution or notional model combines: Pay-as-you-go (PAYG) financing A pension formula that depends on the amount contributed and the return on it which is determined by the notional rate. The account is called notional because no pot of pension fund money exists as the system is PAYG financed. At retirement age: Accumulated capital Annuity The annuity takes into account: Life expectancy of the individual The indexation of pensions The technical interest rate

7 Aim OLG Setup Liquidity & Solvency Ratio ABM Aim of the Article The aim of this article is twofold: Show at what extent the liquidity and solvency indicators are affected by fluctuations in the financial and demographic conditions, Explore the issue of choosing the most suitable automatic balancing mechanism into the notional model to re-establish financial equilibrium.

8 Aim OLG Setup Liquidity & Solvency Ratio ABM Four-period Overlapping Generations Model Age: x = y, y + 1,y + 2, y + 3, y + 4 Active population Retired population y y+1 y+2 y+3 y+4 The highest age to which it is possible to survive is y + 4. Population at time t: l(x, t) = l(y, t x + y) } {{ } Birth cohort p(x, t) }{{} Survival prob. Wages at time t: S(x, t) = S(x, 0) exp t i=1 γ i = l(y, 0) exp ( t x+y i=1 R i ) p(x, t) These stochastic processes are defined in the probability space (Ω, F, P): R i =increase rate in the entrant population during period i 1 to i γ i = increase rate of the salaries during period i 1 to i Further assumption: no mortality risk until retirement.

9 Aim OLG Setup Liquidity & Solvency Ratio ABM Contributions and notional rate Active members contribute a rate π of their salaries to the pension system. C(t) denotes the total contribution: C(t) = πs(y, t)l(y, t) + πs(y + 1, t)l(y + 1, t) t t 1 = πl(y, 0) exp ( γ i + R i )K C (t) i=1 i=1 where : K C (t) = S(y, 0)e Rt + S(y + 1, 0) The notional factor I (t) is chosen as the rate of increase of total contribution base and is affected by both salary and demographic risks: I (t) = C(t) C(t 1) = +R K eγt t 1 C (t) = 1 + nrt (1) K C (t 1)

10 Aim OLG Setup Liquidity & Solvency Ratio ABM Pension calculation and expenditure Individual contributions are indexed by the notional factor. Its accumulated value at retirement age corresponds to the notional capital NDC CO (y + 2, t). The initial pension is based on this notional capital and the annuity a t at time of retirement t: P(y + 2, t) = NDC CO(y + 2, t) a t l(y + 2, t) The pension expenditures, denoted by O(t) depend on past notional capitals and life expectancy: O(t) = P(y + 2, t)l(y + 2, t) + P(y + 2, t 1)Λ (t)l(y + 3, t) = C(t)K O (t) Indexation design Λ (t) ensures actuarial fairness per cohort.

11 Aim OLG Setup Liquidity & Solvency Ratio ABM Liquidity Ratio Most natural way to study the liquidity is to compare income and expenses, i.e., where F (t)=is a buffer fund. LR t = C(t) + F (t) O(t) Liquidity ratio has a cash-flow approach (compares only in and out CF): Doesn t take into account the full amount of liabilities! We would like to compare the Liability level V (t) to the assets. How can we estimate this non-existent asset?

12 Aim OLG Setup Liquidity & Solvency Ratio ABM Solvency Ratio The assets are estimated according to some accounting measure called the Contribution Asset: CA(t) = C(t)TD(t) TD(t) denotes de turnover duration (time in years expected to elapse before all system liabilities are renewed): TD(t) = A R t A C t Liabilities are calculated as the sum of the notional capital for all pension participants: y+3 V (t) = NDC(x, t) x=y Health of the pension system can be assessed through the solvency ratio (based on the swedish system): SR t = CA(t) + F (t) V (t)

13 Aim OLG Setup Liquidity & Solvency Ratio ABM Automatic Balance Mechanisms Even if longitudinal equilibrium may be attained, cross-sectional equilibrium is not guaranteed. Liquidity or solvency are only found when the population is in steady state. The population in Europe is not in steady state but it is rather dynamic. Introduction of an Automatic Balance Mechanism. Purpose: provide automatic financial stability. It should adapt to shocks without legislative intervention. We introduce the ABM B x(t) through the notional factor: I x(t) = I (t)b x(t) For the liquidity case is: B LR (s) = C(s)+F (t) C(s)K O LR (s) For the solvency case is: B SR (s) = CA(s)+F (s) V (s)

14 Methodology No Baby Boom Baby Boom Methodology ABM preference stated in terms of expected value and variance. Random variables are supposed to be stationary. However, exogenous shocks mimicking the baby-boom have been added. Three mortality scenarios (base, up & down). ABM may be symmetric or assymetric (surpluses are cumulated and not shared). Two annuity cases taken into account: prospective (C. 1) and current (C.2). Monte Carlo simulations on 1 million scenarios.

15 Methodology No Baby Boom Baby Boom : No Baby Boom - N. Factor Figure : Ex Value N. Factor: no ABM (dotted black line), LR ABM (dark gray squares) and SR ABM (light gray rhombuses) (a) C.1-Sym (b) C.1-Non-sym (c) C.2-Sym (d) C.2-Non-sym Note: 1st row: base, 2nd: up and 3rd: down

16 Methodology No Baby Boom Baby Boom : No Baby Boom - Fund/Contributions Figure : Expected Value Fund/Contributions: no ABM (dotted black line), LR ABM (dark gray squares) and SR ABM (light gray rhombuses) (a) C. 1-Sym (b) C. 1-No-sym (c) C.2-Sym (d) C.2-No-sym Note: 1st row: base, 2nd: up and 3rd: down

17 Methodology No Baby Boom Baby Boom : Baby Boom Figure : Expected Value: no ABM (dotted black line), LR ABM (dark gray squares) and SR ABM (light gray rhombuses) (a) N. Factor-C. 1 (b) N. Factor-C. 2 (c) Fund-C. 1 (d) Fund-C. 1 Note: 1st row: base, 2nd: up and 3rd: down

18 Introduction of an ABM reduces the volatility of the fund. The Solvency Ratio ABM yields the lowest value of the notional factor s variance with lowest expected value. Symmetric ABMs seem better by means of expected value. Assymetric ABMs produce an over-accumulation of assets (in line w/ Auerbach & Lee). System almost auto-regulates itself after an exogenous fertility shock once that the shocked generation exits. However, the NDC system can t cope with longevity improvements in absence of ABM.

19 References Alonso Garcia, J., Boado-Penas, M. del C. and P. Devolder (2014). Automatic balancing mechanisms for Notional Defined Contribution Accounts in the presence of uncertainty. ISBA Discussion Paper, 2014/38. Artige, L., Cavenaile, L. and P. Pestieau (2014). The macroeconomics of PAYG pension schemes in an aging society. CORE Discussion Paper, 2014/33 Auerbach, A.J. and R. Lee (2007). Notional Defined Contribution Pension Systems in a Stochastic Context: Design and Stability. Berkeley Program in Law and Economics, Working Paper Series, UC Berkeley. Boado-Penas, C., Valdés-Prieto, S. and C. Vidal-Meliá (2008). An Actuarial Balance Sheet for Pay-As-You-go Finance: Solvency Indicators for Spain and Sweden. Fiscal Studies, 29 (1), Settergren and Mikula, B. D. (2005). The rate of return of pay-as-you-go pension systems: a more exact consumption-loan model of interest. Journal of Pensions Economics and Finance, vol. 4, pp Valdés-Prieto, S. (2000). The financial stability of Notional Accounts Pension. Scandinavian Journal of Economics, 102(3),

20 Thank you!