Meseguer 2006 — Long-Range Forecasts of Mortality and Life Expectancy Using Bayesian Vector Autoregressions

Summary

A Social Security Administration (SSA) Office of Policy working paper proposing Bayesian Vector Autoregression (BVAR) with the Minnesota prior as an alternative to Lee-Carter for long-range US mortality forecasting. Using Office of the Chief Actuary (OCACT) period life tables for males and females combined, 21 age groups, 1928–2001, the paper estimates two BVAR(1) models and benchmarks them against Lee-Carter (LC). The key finding is that BVAR credible intervals are substantially wider than Lee-Carter's — 1.8× to 3× wider at a 75-year horizon — because the Bayesian framework correctly incorporates parameter uncertainty in addition to sampling variability. Point forecasts converge across the two methods. The paper is the theoretical precursor to Meseguer (2008), which confirmed out-of-sample that Lee-Carter's intervals are catastrophically too narrow while a comparable frequentist autoregressive (AR) model is adequately calibrated.

Key Claims

• An unrestricted vector autoregression (VAR) with m=21 age groups requires 462 autoregressive parameters at p=1 — far more than 74 years of data can identify. The Minnesota prior solves this via shrinkage: four hyperparameters ($\lambda_1$ overall tightness, $\lambda_2$ cross-equation weight, $\lambda_3$ lag decay, $\lambda_4$ intercept) reduce the effective parameter count while centering the prior on a random-walk-with-drift specification.
• BVAR(1)-II — which sets $\lambda_2(i,j) = 0.8 \times \Omega_{i,j}$ using the empirical cross-age correlation matrix — dominates BVAR(1)-I (effectively univariate) by 202 log-likelihood units (4,478.7 vs. 4,276.5), decisive by any Bayesian standard. BVAR(1)-II reduces in-sample sum of squared residuals (SSR) by 2–22% in 20 of 21 age groups.
• Both BVAR specifications achieve ~90% empirical coverage of their nominal 90% credible intervals, confirming good in-sample calibration.
• Median life expectancy (LE) at birth in 2075: BVAR 85.64 vs. Lee-Carter 86.22 — ~7 months difference. Point trajectories are in substantive agreement; Lee-Carter is very slightly more optimistic.
• Interval widths in 2075: BVAR(1)-II is 1.84× wider than Lee-Carter at birth (9.67 vs. 5.26 years), 2.15× wider at age 65 (8.36 vs. 3.88 years), and 3.0× wider at age 80 (8.08 vs. 2.69 years). The disparity grows with both horizon and age.
• Lee-Carter's narrow intervals arise because it treats the fitted $\alpha_i$ and $\beta_i$ as known constants — parameter uncertainty does not contribute to interval width. Classical inference cannot properly characterize parameter uncertainty because the sampling distribution has support on the sample space, not the parameter space. This is a conceptual problem, not merely a practical one.
• Three empirical regularities in US all-cause mortality (1928–2001): (1) log mortality has an "elongated V" shape over ages — declining to ages 10–14, then rising near-linearly; (2) the Lee-Carter index $k_t$ declines approximately linearly over the sample period; (3) cross-age correlations in Δlog(mortality) decline with age distance — temporally adjacent groups predict each other better than distant groups.
• The accident hump: a sharp mortality increase at ages 15–19 from motor-vehicle fatalities is visible in the age profile from the second half of the 20th century onward.

Concepts Introduced or Extended

• SSA Mortality Forecasting
• Period Mortality

Entities Mentioned

• Javier Meseguer
• Office of the Chief Actuary

Quotes

"The Bayesian paradigm treats a model's parameters as random variables, [so] the generated predictive distributions account for variation due to both the sample and parameter outcomes."

"Generally, however, there are both practical and conceptual problems to the notion of parameter uncertainty within the classical inference perspective. This is due to the fact that the sampling distribution of a classical estimator has support on the sample space, not on the parameter outcomes."

My Take

This is the theoretical companion to Meseguer (2008). Together they make a two-part argument: (1) BVAR is theoretically better suited for long-horizon mortality forecasting because it handles parameter uncertainty coherently; (2) the empirical out-of-sample evidence confirms that LC intervals fail catastrophically, consistent with the parameter-uncertainty critique. The 2006 paper's specific contribution is the in-sample validation that BVAR(1)-II is well-calibrated and outperforms BVAR(1)-I, establishing that cross-age correlation structure carries genuine predictive content. The interval comparison in Table 3 is the most useful number: at age 80 in 2075, BVAR gives a 5th–95th range of 7.99–16.08 years vs. LC's 10.64–13.33. The LC model is essentially claiming near-certainty about old-age mortality improvement that the data cannot support. One limitation: the paper uses combined male/female data, which likely obscures the sex asymmetry in mortality improvement that matters for disability insurance (DI, predominantly working-age) vs. Old-Age and Survivors Insurance (OASI, retirement-age) solvency.