The dark side of wage indexed pensions Evert Carlsson & Kalle Erlandzon FUR 2006

Rationale 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 pension 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 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.

Contribution 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 preferences C – consumption  – discount factor  – relative risk aversion p j – conditional probability to survive b – bequest parameter D – bequest amount

Model – Labour income l ikt – log labour real income f(t,Z it ) – deterministic function of characteristics  it ~N(0,   ) idiosyncratic temporary shock u it ~N(0,   ) permanent shock  t ~N(0,   ) group aggregate component  it ~N(0,   ) idiosyncratic component

Model – Mandatory savings & retirement benefits - NDC NDC – Notionally defined contribution account R l – Return of NDC pensions  l – Expected national income growth   ~N(0,   ) national aggregate component L – Gross labour income PO– Annualised payout from NDC

Model – Mandatory savings & retirement benefits – Defined benefit

Model – Taxes

Model - Assets R s - After tax real simple risky return R f - After tax real simple risk-free return  s - 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 & consumption X – Cash on Hand Two control variables:  – consumption share  – risky weight F – initial wealth

Model – Optimization Optimization problem now has 4 state variables t, v, X and NDC 2 choice variables  and  4 stochastic variables  u  and   V – Value function  – Vector of state variables

Risky and consumption weight at age 64 holding NDC constant v  X v X 

Calibration - 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 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.

Calibration 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 labour income profile – e f(t, Z)

Calibration – Key parameters Aggregate labour income growth ll 1.8% Risk-free rateR f -11.5% Expected risky premium ss 3% Asset volatility  20% Coefficient of relative risk aversion  5 Discount factor  0.98 Bequest parameterb1 Volatility in agg. labour income growth  2%

Averages from the simulated distributions

Frequency distributions – log of X log(X) Age

Frequency distributions – risky weight Age 

Frequency distributions – log of risky Age Log[  (X-C)]

Frequency distributions – consumption share  Age

Valuing the NDC account Forced saving when wage profile is increasing and consumption is preferred NDC account cannot serve the precautionary motive

Risk 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 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 account Group 3 is men with a university degree. Group 4 is women with compulsory school only.

Risk 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 account

Robustness & 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%.

Conclusion 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 grupp

Total inkomst över 10 basbelopp

Individual wealth – cross-section 2002

Robustness & sensitivity – Reference case

Robustness & sensitivity – Valuing NDC Higher 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 – Valuing 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 – Risk Characteristics Risk-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 consumption weight at age 64 holding NDC constant X vv  

Frequency distributions – marginal utility