Meseguer 2010 — Forecasting Vital Rates and Population with Bayesian Vector Autoregressions

Unpublished SSA manuscript, February 2010. No published version; circulated as an internal working paper.

Summary

Meseguer (2010) extends the mortality-only Bayesian vector autoregression (BVAR) framework of Meseguer 2006 — Long-Range Forecasts of Mortality and Life Expectancy Using Bayesian Vector Autoregressions to a full demographic system forecasting mortality, fertility, and population jointly through 2100. Using Office of the Chief Actuary (OCACT) data (mortality 1928–2008; fertility 1917–2008), the paper estimates a gender-specific BVAR for 22 mortality age groups and a separate BVAR for 7 fertility age groups, then feeds these into a population projection. Two variants are contrasted: a diffuse-prior BVAR (Diff-BVAR, anchored to the data alone) and an informative-prior BVAR (Inf-BVAR, whose steady-state means are constrained toward the Social Security Administration (SSA) Alternative 2 (Alt 2) trajectory). The central finding is that Lee-Carter's (LC) confidence intervals are implausibly narrow for elderly population projections — Alt 2's female population aged 65+ falls entirely outside the LC 90% interval from 2009 all the way to 2088.

Key Claims

LC interval failure for elderly population: Female population 65+ from Alt 2 is outside the LC 90% confidence band from jump-off to 2088. This is a more dramatic version of Meseguer (2008)'s dependency-ratio coverage failure: not just miscalibrated, but completely non-overlapping with the official forecast for 80 years.
Life expectancy at birth (2100): Male — Alt 2 = 84.1, LC = 84.4, Diff-BVAR = 84.6 (90% confidence interval [CI]: 79.3–89.9), Inf-BVAR = 83.1. Female — Alt 2 = 87.3, LC = 90.3, Diff-BVAR = 90.1, Inf-BVAR = 87.5. LC and Diff-BVAR give nearly identical point forecasts; Inf-BVAR is anchored closer to the SSA official trajectory.
Aged dependency ratio (65+/20–64) in 2100: Alt 2 = 0.433, Inf-BVAR ≈ 0.436–0.438, Diff-BVAR ≈ higher, LC = 0.466. The LC point forecast for the aged dependency ratio is also elevated relative to Alt 2, reinforcing the pattern from Meseguer (2008).
Total dependency ratio (2100): Alt 2 = 0.88, Inf-BVAR = 0.891, LC = 0.914, Diff-BVAR = 0.916. All models agree direction; LC and Diff-BVAR highest.
Fertility (total fertility rate, TFR, 2100): LC = 2.01 (constrained by design), Inf-BVAR = 2.01, Diff-BVAR = 2.13. The informative prior pulls fertility toward the Alt 2 TFR assumption.
Cross-equation weights: $\lambda_2(i,j) = 0.8 \times \mathrm{Corr}[\Delta\log(y_i), \Delta\log(y_j)]$ , identical to Meseguer (2006). Correlation-calibrated weights capture the strong co-movement among adjacent age groups without requiring separate model selection.
Informative prior via Villani (2006): The Inf-BVAR uses mean-adjusted BVAR (Villani 2006 Riksbank working paper), which allows priors on the unconditional mean of the process — directly encoding SSA Alt 2's long-run trajectory as the steady-state prior rather than merely as a constraint on the autoregressive (AR) coefficients.
Markov chain Monte Carlo (MCMC) estimation: Three-block Gibbs sampler (steady-state means, AR coefficients, error covariance), 12,000 iterations, 2,000 burn-in. Minnesota prior hyperparameters: mortality $\lambda_1 = 0.2$ , p = 1; fertility $\lambda_1 = 0.05$ , p = 2 with AR(0.8) prior.
Full system coherence: Unlike running mortality and fertility models independently and summing, the joint framework preserves cross-component correlation structure — important for dependency ratio uncertainty, which depends on the joint distribution of old-age survivors and working-age births cohorts.

Concepts Introduced or Extended

Lee-Carter Model — demonstrates interval collapse: Alt 2 female elderly population outside the LC 90% CI for 80 years
SSA Mortality Forecasting — extends Meseguer (2006/2008) critique from mortality alone to full demographic system
Period Mortality — LC's $b_x$ structure implicitly assumes a single common mortality factor; BVAR relaxes this

Entities Mentioned

Quotes

"The 90 percent confidence interval of the Lee-Carter projections for the female population aged 65 and over does not cover the SSA Alternative 2 projections from 2009 to 2088."

My Take

This paper completes the Meseguer trilogy (2006: BVAR theory; 2008: LC interval failure out-of-sample; 2010: full system extending the failure to fertility/population). The most striking result is the 80-year LC interval non-coverage for elderly female population — this is not a marginal miscalibration but a catastrophic failure for the most policy-relevant demographic group. The informative-prior BVAR is methodologically attractive because it provides a principled way to incorporate SSA's own actuarial judgment (Alt 2) as a prior mean while still allowing the data to update the trajectory and widen uncertainty bounds appropriately. That the Inf-BVAR dependency ratios closely track Alt 2's point forecast while having substantially wider uncertainty bands than LC is the ideal outcome for policy use: consistent with the official projection in expectation, but honest about uncertainty. The paper is unpublished and circulated only internally at SSA; it has not been subject to external peer review.