Belloni and Maccheroni 2006 — Actuarial Fairness when Longevity Increases

Summary

Belloni and Maccheroni evaluate the actuarial properties of the Italian pension system before and after the 1995 Dini reform, which replaced a defined-benefit (DB) formula with a Notional Defined Contribution (NDC) system. Using money's worth measures — Social Security Wealth (SSW), the Net Present Value Ratio (NPVR), and the implicit tax/subsidy rate (TAX) — they show the DB system was neither actuarially fair (NPVR up to $1.5$) nor actuarially neutral (TAX up to $50\%$), while the NDC system comes close to both (NPVR $\approx 1.0$, TAX $\approx 4\%$). However, because the NDC transformation coefficients rely on 1990 period life tables updated only every 10 years, cohort mortality improvements generate a persistent $\approx 6$ percentage points (pp) actuarial overpayment — with two-thirds attributable to using cross-sectional rather than longitudinal tables and one-third to the revision lag.

Key Claims

• DB vs. NDC actuarial neutrality gap: Under the DB system, implicit taxes at the margin of continued work reached $50\%$ at certain ages, creating strong incentives for early exit. Under the NDC system, the TAX falls to approximately $4\%$, close to — but not exactly — neutral.
• NPVR under DB and NDC: DB NPVRs reached as high as $1.50$ ($50\%$ overpayment on discounted contributions). NDC NPVRs converge to approximately $1.0$ by design, but remain slightly above 1 due to the period-table bias.
• Period table distortion — magnitude: Because transformation coefficients are computed from the 1990 Istituto Nazionale di Statistica (ISTAT) period life tables (updated every 10 years), and because cohort life expectancy exceeds period life expectancy under improving mortality, the system systematically overpays. Total distortion $\approx 6$ pp of NPVR; $2/3$ ($\approx 4$ pp) from using cross-sectional rather than longitudinal mortality tables; $1/3$ ($\approx 2$ pp) from the 10-year revision lag.
• Pre-revision spikes: In the years just before a scheduled 10-year update to the transformation coefficients, TAX spikes by $30$–$40$ pp: workers have a strong incentive to delay retirement until the revision takes effect (which will assign them a higher coefficient reflecting improved longevity), creating a large departure from actuarial neutrality at those ages.
• Intragenerational redistribution shift: DB redistributes toward higher earners (wage-indexed benefits, long contribution histories); NDC shifts redistribution toward longer-lived individuals (women live longer, so same contributions → more SSW), reversing the direction of intragenerational transfers.
• Weibull mortality projections: The paper uses an ad hoc Weibull model ($q_x = A \times B^x$, limiting $e_0 = 110$, $\omega = 120$) to project future mortality. Projected $e_0$ by 2030: male $81.8$, female $86.1$ (1990 base: male $\approx 74$, female $\approx 80$).
• Long transition: The full NDC system applies only to workers with no pre-1996 contributions (entering the labor force from ~2010+). Workers with mixed careers fall under a pro-rata DB/NDC formula. Full NDC coverage reaches the majority only around 2030.

Concepts Introduced or Extended

• Actuarial Neutrality — core concept formalized: TAX $= 0$ at all ages within retirement window; distinct from actuarial fairness; Italian DB fails, NDC approximately achieves
• Notional Defined Contribution — Italian NDC architecture, transformation coefficient computation, actuarial implications
• Period vs. Cohort Life Expectancy — Italian pension application: period tables understate cohort life expectancy (LE) $\to$ transformation coefficient set too high $\to$ systematic overpayment; $2/3$ from cross-sectional/longitudinal divergence, $1/3$ from revision lag

Entities Mentioned

• Michele Belloni
• Carlo Maccheroni

Quotes

"The NDC system is actuarially neutral only if the transformation coefficients correctly reflect the actual mortality the cohort of retirees will experience. When period tables are used and mortality is improving, the system systematically overpays."

"We find that the 1995 reform dramatically reduced both the actuarial unfairness and the actuarial non-neutrality of the Italian pension system, but did not eliminate them."

My Take

The core contribution is methodologically sharp: the distinction between actuarial fairness (NPVR $= 1$ on average) and actuarial neutrality (TAX $= 0$ at the margin) clarifies what the Dini reform achieved and what it left unsolved. The period-table bias analysis is essentially an application of the period-cohort LE distinction to pension design — a natural but underappreciated connection. The ad hoc Weibull mortality projections are the weakest part: they lack uncertainty quantification and use a fixed limiting age ($\omega = 120$) rather than an empirically grounded model, making the projected TAX spikes before each 10-year revision sensitive to model choice. The paper does not address political economy (why a 10-year revision cycle? why period tables?), which matters for whether the distortion is likely to be corrected. Overall, a clean and policy-relevant demonstration that NDC is not a complete solution to actuarial incentive problems — it trades one set of distortions for another.