On the Linearization of Bilinear Mortality Models

We propose a general framework that reduces the bilinear structure of the Lee–Carter mortality model and a broad class of its extensions to a fully linear form, enabling the direct application of standard linear modeling techniques. The key insight is that, once the time-varying mortality indices are obtained through an external procedure—most naturally as the first principal components from principal component analysis—the bilinear interaction terms become fixed. In the single-population setting, this involves extracting the common mortality index kₜ externally; in multi-population settings, both the common factor kₜ and the population-specific factors k_cgₜ are extracted externally. Conditioning on these factors eliminates bilinearity and yields a standard linear regression structure. With bilinearity removed, parameters are estimated using generalized estimating equations, allowing for principled modeling of serial dependence while relying on standard linear tools. The resulting PCA–GEE framework applies broadly to single- and multi-population mortality models, including cohort-augmented specifications, and provides a transparent and computationally simple platform for mortality forecasting. Using data from the Human Mortality Database, we show that the proposed approach delivers consistently improved out-of-sample forecast accuracy relative to classical Lee–Carter and Li–Lee models.