ACFI330: Banking and the financial system - Pension economics

What is the Lifecycle Model (LCM)?

A model developed by Ando and Modigliani (1957) and extended by Merton (1969, 1971) where rational, well-informed individuals plan consumption over their entire lifecycle based on forecasts of lifetime earnings. The principal motivation for saving is to accumulate assets to support habitual consumption in retirement.

What is the key empirical observation that supports the LCM?

Per capita aggregate consumption is smoother than per capita aggregate income, suggesting individuals try to smooth their consumption over time.

What are the two main periods in the simple LCM?

1) Youth & work, and 2) Old age & retirement.

What happens in the absence of a pension system according to LCM?

Individuals must save adequately for retirement. Failure to save leads to sharply falling living standards. Borrowing is risky as there's no prospect of repaying.

What is the lifetime utility function in the LCM?

Λₜ = U(Cₜ) + (1/(1+ρ))U(Cₜ₊₁) + (1/(1+ρ))²U(Cₜ₊₂) + ... + (1/(1+ρ))ᴰU(Cₜ₊ᴰ), where ρ is the rate of time preference and D̄ is the length of life.

What is the intertemporal budget constraint in the LCM?

Lifetime consumption must equal lifetime income: ΣCs(1/(1+r))ˢ⁻ᵗ = Aₜ + ΣWs(1/(1+r))ˢ⁻ᵗ = Aₜ + W̄ₜ, where Aₜ is financial wealth, Wₜ is income, r is interest rate, and R is length of working life.

What is the rate of time preference (ρ)?

The personal or subjective discount rate (degree of impatience) that measures an individual's preference between current and future consumption. It can be interpreted as the personal interest rate. Individuals with high ρ "live for today" and discount the future heavily.

What is the intertemporal substitution elasticity (ISE)?

σ[Cₜ] = -U'(Cₜ)/(U''(Cₜ)Cₜ). It measures the willingness to substitute consumption across time (consumption smoothing). When ISE is low (below unity), willingness to engage in consumption smoothing is high.

What is log utility and why is it commonly used?

U(Cₜ) = Ln(Cₜ). With log utility, U'(Cₜ) = 1/Cₜ > 0 and U''(Cₜ) = -1/(Cₜ)² < 0, demonstrating positive but decreasing marginal utility. Log utility has an ISE of exactly 1.

What is the optimal consumption formula with log utility?

Cₜ = b(Aₜ + W̄ₜ), where b is the marginal propensity to consume from total wealth. b equals D̄⁻¹ for finite life or ρ for infinite lifetime.

What is the marginal propensity to consume (b)?

The proportion of an additional dollar of total wealth spent on consumer goods. It's a constant equal to D̄⁻¹ (for finite life) or ρ (for infinite lifetime).

What does the LCM predict about consumption over the lifecycle?

Consumption is stable over the lifecycle. As a consequence, savings are positive for working individuals and negative for retired individuals.

How does an unfunded state pension affect savings?

An unfunded state pension (pay-as-you-go) will reduce individual and national savings dollar for dollar. Each $1 taken from a worker and given to a pensioner increases the pensioner's consumption but doesn't change the worker's consumption—it simply reduces the worker's savings.

How does a private funded pension affect savings?

Every $1 placed in a private funded pension scheme exactly displaces $1 of private savings. Such schemes have no effect on national savings (the sum of discretionary and pension savings). Pension savings are inframarginal—less than what the worker would have saved anyway.

What is social security wealth?

The value of promised state pension benefits based on a worker's contributions while in work. It's the present value of future pension payments from an unfunded state scheme.

What is forced oversaving?

When pension contributions force individuals to save more than they otherwise would. In a perfect capital market, individuals could borrow against future pension savings to keep consumption unchanged, but capital market constraints prevent this.

What happens when capital market constraints are binding?

The individual's optimum point moves from an interior solution (point A) to a corner solution (point E₂). Total savings increase, but total utility falls. Non-pension savings become zero, and any increase in mandatory pension savings increases national savings dollar for dollar.

What are inframarginal vs. marginal pension savings?

Inframarginal: pension savings less than what the worker would have saved anyway (fully displaces private savings). Marginal: pension savings at or beyond what the worker would save (increases total savings).

How do tax breaks on pension savings affect behavior?

Tax breaks mean pension savings earn a higher after-tax return (r) than discretionary savings (r(1-τ)). This creates a pure income effect: consumption rises in both periods, total savings fall, but retirement savings rise due to the value of the tax break.

What is the effect of forced oversaving with tax breaks?

Consumption in youth falls, retirement consumption rises, and depending on the pension size, utility might rise or fall. It's possible for a worker to gain from a suboptimal pension plan due to the tax benefits. Non-pension savings remain zero.

What factors make retirement more likely according to LCM?

Workers are more likely to retire if they are older, sicker, wealthier, have lower wages, or can get higher promised social security benefits.

What factors delay retirement?

Retirement is delayed for those on higher salaries and having more flexible working hours.

How does a private funded pension affect retirement decisions?

A private pension creates an additional budget constraint after retirement. Complete retirement is more likely if: the pension is larger, the wage difference between main and part-time jobs is larger, and the minimum hours for part-time work are higher.

What are the budget constraints with a private pension?

Before retirement: TAD (same as without pension). After retirement: TEHG (with pension P and part-time wage wₜ). Effective combined constraint: CFH plus point E.

What does empirical evidence show about pensions and savings?

1) State pension reduces the need for saving privately for retirement, 2) The effect of state pension on inducing early retirement is weak, 3) Private occupational pensions increase savings and encourage early retirement.

Why is empirical study of LCM challenging?

Due to measurement issues and omitted variables biases.

In the simple numerical illustration, what were the key assumptions?

No uncertainty, zero interest rate, 25-year-old working for 40 years, retired for 10 years, earning $25,000/year = $1,000,000 total human capital.

In the numerical example, how much did the person save and spend?

Spent $20,000/year (smooth consumption), saved $5,000/year while working, accumulated $200,000 retirement fund, drew down $20,000/year in retirement.

What happened when the person inherited $250,000 in the example?

Total wealth became $1,250,000 ($1,000,000 human capital + $250,000 financial). Could now spend $25,000/year and still die with zero assets.