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英文文献：A Parametric Factor Model of the Term Structure of Mortality-死亡率期限结构的参数因素模型
英文文献作者：Niels Haldrup,Carsten P. T. Rosenskjold
英文文献摘要：
The prototypical Lee-Carter mortality model is characterized by a single common time factor that loads differently across age groups. In this paper we propose a factor model for the term structure of mortality where multiple factors are designed to influence the age groups differently via parametric loading functions. We identify four different factors: a factor common for all age groups, factors for infant and adult mortality, and a factor for the "accident hump" that primarily affects mortality of relatively young adults and late teenagers. Since the factors are identified via restrictions on the loading functions, the factors are not designed to be orthogonal but can be dependent and can possibly cointegrate when the factors have unit roots. We suggest two estimation procedures similar to the estimation of the dynamic Nelson-Siegel term structure model. First, a two-step nonlinear least squares procedure based on cross-section regressions together with a separate model to estimate the dynamics of the factors. Second, we suggest a fully specified model estimated by maximum likelihood via the Kalman filter recursions after the model is put on state space form. We demonstrate the methodology for US and French mortality data. We find that the model provides a good fitt of the relevant factors and in a forecast comparison with a range of benchmark models it is found that, especially for longer horizons, variants of the parametric factor model have excellent forecast performance.
典型的李-卡特死亡率模型的特征是一个单一的常见时间因素，不同年龄组的负荷不同。在本文中，我们提出了一个死亡率期限结构的因子模型，其中多个因子通过参数加载函数被设计以不同的方式影响年龄组。我们确定了四个不同的因素:一个对所有年龄组都普遍存在的因素，婴儿和成人死亡率的因素，以及一个主要影响相对年轻成年人和晚些青少年死亡率的“事故驼峰”因素。由于这些因子是通过加载函数的限制来识别的，所以这些因子不是设计成正交的，而是可以相互依赖的，并且当这些因子有单位根时，它们可以协整。我们提出了两种类似于动态尼尔森-西格尔项结构模型的估计方法。首先，基于截面回归的两步非线性最小二乘程序与一个单独的模型来估计因素的动力学。其次，我们建议在模型置于状态空间形式后，用最大似然卡尔曼滤波器递归估计一个完全指定的模型。我们展示了美国和法国死亡率数据的方法。在与一系列基准模型的预测比较中发现，特别是在较长期的预测中，参数因子模型的变量具有良好的预测效果。
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