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Trends in Mortality Decrease and Economic Growth

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The vast literature on extrapolative stochastic mortality models focuses mainly on the extrapolation of past mortality trends and summarizes the trends by one or more latent factors. However, the interpretation of these trends is typically not very clear. On the other hand, explanation methods are trying to link mortality dynamics with observable factors. This serves as an intermediate step between the two methods. We perform a comprehensive analysis on the relationship between the latent trend in mortality dynamics and the trend in economic growth represented by gross domestic product (GDP). Subsequently, the Lee-Carter framework is extended through the introduction of GDP as an additional factor next to the latent factor, which provides a better fit and better interpretable forecasts.

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  1. See the section Economic Growth and Mortality Rates for an overview of related literature.

  2. In this regard, the probability of survival beyond age 99 will be set equal to 0. However, in this article, we focus on life expectancy at early ages so that the survival probability beyond age 99 has little impact.

  3. Hanewald (2011) performed similar unit root tests, with two main procedural differences. First, she used the Brouhns et al. (2002) Poisson variant of the Lee-Carter model, whereas we maintain the original settings. Second, she used real GDP in levels, whereas our analysis is based on real GDP per capita in logarithm. However, the main results are similar.

  4. Based on results from the augmented Dickey-Fuller test, most of ln(m x,t ) are I(1) processes.

  5. We multiply the test statistics by a factor (Tpk) / T, where p denotes the number of lags in the VAR model, and k denotes the number of variables. This is to correct small sample bias, as suggested in Ahn and Reinsel (1990).

  6. Furthermore, cohort life tables are based on the projections over a very long period. Thus, the forecast of cohort life tables is more sensitive to the underlying model and estimation methods.

  7. When used to better fit the in-sample mortality rates at different ages, the Lee-Carter is more volatile than the GDP series, possibly yielding better out-of-sample point forecasts but at the expense of a larger prediction interval.

  8. Compared with the Lee-Carter model, we add constraint (16): namely, . Constraint (16) is needed to identify . This constraint is also required in the Lee-Carter model to identify . If Eq. (16) is not satisfied—that is, =0—then our model reduces to Model (4).

  9. According to Eqs. (13), (14), (15), and (16), we have four constraints. However, constraint (16) is examined only ex post and is not included in the estimation, similar to the Lee-Carter model. Thus, the effective number of constraints is three.


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For comments and discussions, we thank two anonymous referees, the Editor, Makov Udi, Qihe Tang, and Jochen Mierau, as well as participants at the 7th Conference in Actuarial Science and Finance in Samos, the 2012 Tilburg University GSS seminar in Tilburg, and the 2012 Netspar Pension Day in Utrecht. We would also like to thank the Netherlands Organisation for Scientific Research (NWO) for financial support.

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Correspondence to Geng Niu.

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Niu, G., Melenberg, B. Trends in Mortality Decrease and Economic Growth. Demography 51, 1755–1773 (2014).

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