Bias-Corrected Inference for a Modified Lee–carter Mortality Model

Abstract

As a benchmark mortality model in forecasting future mortality rates and hedging longevity risk, the widely employed Lee–Carter model (Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.) suffers from a restrictive constraint on the unobserved mortality index for ensuring model’s identification and a possible inconsistent inference. Recently, a modified Lee–Carter model (Liu, Q., Ling, C. and Peng, L. (2018) Statistical inference for Lee–Carter mortality model and corresponding forecasts. North American Actuarial Journal, to appear.) removes this constraint and a simple least squares estimation is consistent with a normal limit when the mortality index follows from a unit root or near unit root AR(1) model with a nonzero intercept. This paper proposes a bias-corrected estimator for this modified Lee–Carter model, which is consistent and has a normal limit regardless of the mortality index being a stationary or near unit root or unit root AR(1) process with a nonzero intercept. Applications to the US mortality rates and a simulation study are provided as well.

Modelling mortality: A bayesian factor-augmented var (favar) approach

“…Moreover, when applied to the (κ t ) process estimated from the LC model, the result of the tests should be interpreted very carefully, since κ t is not directly observed, but can only be indirectly estimated and is hence subject to estimation error. For instance, the unit root hypothesis in the LC model has recently been questioned by Leng and Peng (2016) and Liu et al (2019a); Liu et al (2019b). Furthermore, even if the I(1) assumption holds true, a model written on the improvement rates is not able to detect potential co-integration relationships.…”

Labor Force Participation Rate and Expected Length of Retirement 2001-2047: A Case Study in Malaysia

“…Some examples of these adjustments are using a Bayesian method [30] incorporating randomness or an error term into the model [30], [31], or employing a state-space model to get around the biodemographic constraint and using resampling method to improve forecasting accuracy [32]. Moreover, Lee-Carter model has been contrasted with other models, including the neural networks [33], autoregressive integrated moving average (ARIMA) model [34], and modified Lee-Carter model with bias-corrected estimators [35]. Although several improvements have been made, the Lee-Carter model is still commonly used for predictions.…”

Labor Force Participation Rate and Expected Length of Retirement 1989-2066: Comparison of Several OECD Countries

“…Some examples of these adjustments are using a Bayesian method [26] incorporating randomness or an error term into the model [26,27], or employing a state-space model to get around the biodemographic constraint. Moreover, Lee-Carter model has been contrasted with other models, including the neural networks ( [28]), autoregressive integrated moving average (ARIMA) model ( [29]), and modified Lee-Carter model with bias-corrected estimators ( [30]). Although several improvements have been made, the Lee-Carter model is still commonly used for predictions.…”