Modified Lee-Carter Methods with LASSO type Smoothing and Adjusting for Lifespan Disparity

Abstract

Extrapolative methods like Lee-Carter and its later variants are widely accepted for forecasting mortality in industrial countries due to simplicity, both for single population forecasting and coherent forecasting. This model assumes an invariant age component and a linear time component for forecasting. The latter requires a second level estimation to increase forecast accuracy. We propose to apply the Lee-Carter method on smoothed mortality rates obtained by LASSO type regularization and hence to partially adjust the time component to match the observed lifespan disparity ($e_0^\dagger$). Smoothing by lasso produces less error during fitting period compared to other spline based smoothing techniques. Also matching with $e_0^\dagger$ - a more informative indicator of longevity than $e_0$, made the time component more reflective of countries' mortality patterns. We further extend this methodology for coherent forecasting as well. In this setting, choosing the appropriate reference population remains an arbitrary process. We propose to obtain the reference population on the basis of closest $\bar{e}_0^\dagger$. Hence the common factor of coherent model is estimated utilizing only a subset of the available years (the best fitting period), and these same years are considered as country-specific fitting period as well. Both of the proposed methods have been found to be more accurate during out-of-sample evaluation compared to corresponding existing models and provide more optimistic forecasts