The dark side of wage indexed The dark side of wage indexed pensionspensions

Evert Carlsson

&

Kalle Erlandzon

FUR 2006

RationaleRationale

• This paper investigates some welfare effects of forced saving through a mandatory pension scheme.

• The framework for the analysis is a life-cycle model of a borrowing constrained individual’s consumption and portfolio choice in the presence of:– Uncertain labour income– Realistically calibrated tax and pension

systems.

The Swedish mandatory The Swedish mandatory pension schemepension scheme

• Launched in 1999, the reformed Swedish pension system has attracted a lot of interest around the world.

• 16 % of all wages and benefits are paid as contributions to an individual notional account.

• The return on these accounts are set to equal aggregate labour income growth.

• The system is actually a PAYGO system, but it is set up as a defined contribution system.

• Therefore, the system is called a Notional Defined Contribution system – NDC.

Past researchPast research

• Modigliani & Brumberg(54), Friedman (AER57): No correlation between predictable income changes and consumption. However, empirical data shows a positive correlation.

• Deaton (EM91), Carroll(QJE97), Gourinchas & Parker(EM02): Life-cycle models with borrowing constraints, stochastic labour income and consumption choice. These models reconcile PIH with data.

• Cocco et al. (ReFinStud05): Extends Carrol by including portfolio choice.

• Campbell et al. (2001): Extends Cocco et al. to include an additional state variable, retirement wealth.

ContributionContribution

Our model extends Campbell et al. by including a realistically calibrated tax and pension system. We can therefore:

• attribute a value to mandatory pension savings,

• analyse the welfare effects of pension returns being linked to aggregate labour income growth.Results:– Young constrained individuals attribute little

value to their pension savings.– The welfare loss associated with uncertain

pension returns stems primarily from the dependency between labour income growth and pension returns rather than the volatility of pension returns.

Model – Individual Model – Individual preferencespreferences

C – consumption – discount factor – relative risk aversionpj – conditional probability to survive

b – bequest parameterD – bequest amount

Model – Labour incomeModel – Labour income

likt – log labour real income

f(t,Zit) – deterministic function of characteristics

it ~N(0,) idiosyncratic temporary shock

uit ~N(0,) permanent shock

t ~N(0,) group aggregate component

it ~N(0,) idiosyncratic component

Model – Mandatory savings Model – Mandatory savings & retirement benefits - & retirement benefits - NDCNDC

NDC – Notionally defined contribution accountRl – Return of NDC pensionsl – Expected national income growth ~N(0,) national aggregate component

L – Gross labour incomePO– Annualised payout from NDC

Model – Mandatory savings Model – Mandatory savings & retirement benefits – & retirement benefits – Defined benefitDefined benefit

Defined benefit payout

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Payout

Model – TaxesModel – Taxes

Model - AssetsModel - Assets

Rs - After tax real simple risky returnRf - After tax real simple risk-free returns - Expected risk premium- Innovation in excess returns, ~N(0,)

- Correlation between excess returns and the aggregate component of permanent innovations to labour income

Model – Private savings & Model – Private savings & consumptionconsumption

X – Cash on HandTwo control variables: – consumption share– risky weightF – initial wealth

Model – OptimizationModel – Optimization

Optimization problem now has4 state variables , v, X and NDC2 choice variables and 4 stochastic variables u and

V – Value function – Vector of state variables

Risky and consumption weight Risky and consumption weight at age 64at age 64holding NDC constantholding NDC constant

v

X

v

X

Calibration - EstimationCalibration - Estimation

• Income is defined as all taxable social benefits and wages for an individual before taxes.

• The components of the labour income process were estimated using LINDA panel data 1992-2002.

• LINDA is a register based data bas covering 3.35 % of the Swedish population.

• The data was divided into six non-intersecting groups defined by sex and educational status.

CalibrationCalibration

Our estimates of transitory shocks are lower than in C&S and CGM:- LINDA is register based data while C&S and CGM used survey

data, which is less precise (measurement errors will increase estimated variance).

Calibration – deterministic Calibration – deterministic labour income profile – elabour income profile – ef(t, f(t,

Z)Z)

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Comp Wom

Calibration – Key Calibration – Key parametersparameters

Aggregate labour income growth

l 1.8%

Risk-free rate Rf-1 1.5%

Expected risky premium s 3%

Asset volatility 20%

Coefficient of relative risk aversion

5

Discount factor 0.98

Bequest parameter b 1

Volatility in agg. labour income growth

2%

Averages from the Averages from the simulated distributionssimulated distributions

Frequency distributions – Frequency distributions – log of Xlog of X

log(X)

Age

Frequency distributions – Frequency distributions – risky weightrisky weight

Age

Frequency distributions – log Frequency distributions – log of riskyof risky

Age

Log[(X-C)]

Frequency distributions – Frequency distributions – consumption shareconsumption share

Age

Valuing the NDC Valuing the NDC accountaccount

• Forced saving when wage profile is increasing and consumption is preferred

• NDC account cannot serve the precautionary motive

Risk in the NDC accountRisk in the NDC account

• The model has five assets: risk-free, risky, defined benefit, future wages and the NDC asset.

• In the reference case NDC return is volatile and correlated with future wages and defined benefits as well as with the risky asset.

• Volatility (2%) in the NDC return is low, but NDC is the largest asset at retirement.

Risk in the NDC accountRisk in the NDC account

• Two alternative regimes:– NDC return is risk-free– NDC return is independent (but volatile)

• Gain in consumption and bequest equivalent units(a 1% increase represents the increase in utility that would be produced by a 1% increase in cons. and beq. for the rest of the life)

Risk in the NDC accountRisk in the NDC account

• Group 3 is men with a university degree.

• Group 4 is women with compulsory school only.

Risk in the NDC accountRisk in the NDC account

• We note that 2/3 of the gains originates from the elimination of the dependency. This holds irrespective of age.

• Without a risky asset in the model, the gains would have been generally underestimated.– After retirement, the

gains from independency would have been zero and very small in the risk-free case.

Risk in the NDC accountRisk in the NDC account

Risky weight

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Risk-free NDC

Reference

Robustness & sensitivityRobustness & sensitivity

• Conservative parameterisation wrt. the valuation of the NDC account.– High NDC return, low equity premium,

high discount factor and low correlation.

• Two tests:– Lowering the risk aversion from 5 to 2.– Increasing the equity premium from 3%

to 4%.

ConclusionConclusion

• This paper contributes to the understanding of the risk characteristics and welfare effects of NDC pension systems.

• First, individuals attribute little value to their pension savings in early life.

• Second, it is the dependency rather than the

volatility of the NDC returns which is of most importance.

Total inkomst per gruppTotal inkomst per grupp

Total inkomst över 10 Total inkomst över 10 basbeloppbasbelopp

Individual wealth – cross-Individual wealth – cross-section 2002section 2002

Medi an 75% per cent i l e

1000 SEK

- 50

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Robustness & sensitivity – Robustness & sensitivity – Reference caseReference case

Robustness & sensitivity – Robustness & sensitivity – Valuing NDCValuing NDCHigher risk premium, makes the NDC asset less attractive.Lower risk aversion:• Higher acceptance of risk makes the NDC less

desirable and the short-sales constraint often effective.• Higher elasticity of intertemporal substitution makes

the agent willing to substitute consumption over time (variation across time is less disadvantageous).

Robustness & sensitivity – Robustness & sensitivity – Valuing NDCValuing NDC• In early life, these two effects cancel out.• In mid life, as consumption reaches the lifetime average,

the effect of a higher intertemporal substitution diminishes.

• Finally, in late life the ratio of private to NDC wealth increases giving a higher preference for risk-free assets.

Robustness & sensitivity – Robustness & sensitivity – Risk CharacteristicsRisk CharacteristicsRisk-free or independent NDC return

Higher premium is associated with more risky assets and hence larger gains from a risk-free or independent NDC.Making the NDC risk-free or independent for an agent with lower risk aversion has less effect.

The proportional gain that stems from independency is still 2/3.

Contour plots of risky and Contour plots of risky and consumption weight at age 64 consumption weight at age 64 holding NDC constantholding NDC constant

X

v v

Frequency distributions – Frequency distributions – marginal utilitymarginal utility