응용통계연구 (The Korean Journal of Applied Statistics)

  • 제34권3호
  • /
  • Pages.347-373
  • /
  • 2021
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

코호트 효과를 고려한 확률적 사망률 예측 모형의 비교 연구

A comparative study of stochastic mortality models considering cohort effects

  • 투고 : 2021.02.16
  • 심사 : 2021.05.25
  • 발행 : 2021.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

지난 50여 년 동안 우리나라의 사망률 감소 패턴에 대한 탐색적 연구에 의하면 연령별 사망률이 모든 연령에서 감소했지만, 특정한 사망률이 개선되고 있는 패턴은 연령과 기간에 따라 다르다는 것을 알 수 있다. 여자가 남자보다 사망률 개선이 뚜렷하고 특히 시간이 지나면서 특정그룹에서의 사망률 개선이 두드러짐에 따라 전반적으로 사망 시간 추세에 구조적인 변화가 존재함을 확인하였다. 이에 본 연구에서는 우리나라 여자 사망률 자료를 이용하여 미래 사망률 예측을 위해 코호트 효과를 고려한 다양한 확률적 사망률 모형을 살펴보았다. 또한 분석 결과를 바탕으로 2067년까지 연령별 사망률과 예측기대수명을 작성하고 통계청(KOSIS)에서 제공하는 장래 연령별 사망률과 기대수명과 비교하였다. 자료이용기간에 따라 최적의 모형이 상이하나 적합력과 예측력을 전반적으로 고려했을 때 우리나라 여자 사망률은 코호트 효과를 고려한 PLAT 모형이 적절하다 볼 수 있을 것이다.

Over the past 50 years, explorative research on the nation's mortality decline patterns has showed a decrease in age-specific mortality rates in all age groups, but there were different improvement patterns in specific mortality rates depending on ages and periods. Greater distinct improvement was observed in mortality rates among women than men, and there was a noticeable improvement in mortality rates in certain groups especially in the more recent decades, revealing a structural change in the overall trends regarding death periods. In this paper, we compare various stochastic mortality models considering cohort effects for mortality projection using Korean female mortality data and further explore the uncertainty related to projection. It also created age-specific mortality rates and life expectancy for women until 2067 based on the results of the analysis, and compared them with future age-specific mortality rates and life expectancy provided by the national statistical office (KOISIS). The best optimal model could vary depending on data usage periods. however, considering the overall fit and predictability, the PLAT model would be regarded to have appropriate predictability in terms of the mortality rates of women in South Korea.

키워드

참고문헌

  1. Aro H and Pennanen T (2011). A user-friendly approach to stochastic mortality modelling, European Actuarial Journal, 1, 151-167. https://doi.org/10.1007/s13385-011-0030-4
  2. Alai DH and Sherris M (2014). Rethinking age-period-cohort mortality trend models, Scandinavian Actuarial Journal, 3, 208-227. https://doi.org/10.1080/03461238.2012.676563
  3. B'orger M, Fleischer D, and Kuksin N (2014). Modeling the mortality trend under modern solvency regimes, Astin Bulletin, 44, 1-38. https://doi.org/10.1017/asb.2013.24
  4. Booth H, Tickle L, and Smith L (2005). Evaluation of the variants of the lee-carter method of forecasting mortality: a multi-country comparison, New Zealand Population Review, 31, 13-34.
  5. Booth H, Hyndman RJ, Tickle L, and De Jong P (2006). Lee-carter mortality forecasting: a multi-country comparison of variants and extensions, Demographic Research, 15, 289-310. https://doi.org/10.4054/DemRes.2006.15.9
  6. Brouhns N, Denuit M, and Vermunt J (2002). A poisson log-bilinear regression approach to the construction of projected life tables, Insurance: Mathematics and Economics, 31, 373-393. https://doi.org/10.1016/S0167-6687(02)00185-3
  7. Butt Z, Haberman S, and Shang HL (2014). Ilc: lee-carter mortality models using iterative fitting algorithms, R package version 1.0, Retrieved from: http://CRAN.R-project.org/package=ilc
  8. Cairns AJG, Blake D, and Dowd K (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 687-718. https://doi.org/10.1111/j.1539-6975.2006.00195.x
  9. Cairns AJG, Blake D, Dowd K, Coughlan GD, Epstein D, Ong A, and Balevich I (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States, North American Actuarial Journal, 13, 1-35. https://doi.org/10.1080/10920277.2009.10597538
  10. Cairns AJG, Blake D, Dowd K, Coughlan GD, Epstein D, and Khalaf-Allah M (2011). Mortality density forecasts: an analysis of six stochastic mortality models, Insurance: Mathematics and Economics, 48, 355-367. https://doi.org/10.1016/j.insmatheco.2010.12.005
  11. Currie ID (2016). On fitting generalized linear and non-linear models of mortality, Scandinavian Actuarial Journal, 4, 356-383. https://doi.org/10.1080/03461238.2014.928230
  12. De Jong P and Tickle L (2006). Extending lee-carter mortality forecasting, Mathematical Population Studies, 13, 1-18. https://doi.org/10.1080/08898480500452109
  13. Haberman S and Renshaw A (2011). A comparative study of parametric mortality projection models, Insurance: Mathematics and Economics, 48, 35-55. https://doi.org/10.1016/j.insmatheco.2010.09.003
  14. Hunt A and Blake D (2015). Modelling longevity bonds: analysing the Swiss Re Kortis bond, Insurance: Mathematics and Economics, Retrieved from http://dx.doi.org/10.1016/j.insmatheco.2015.03.017
  15. Hunt A and Villegas AM (2015). Robustness and Convergence in the Lee-Carter model with cohorts, Insurance: Mathematics and Economics, 64, 186-202. https://doi.org/10.1016/j.insmatheco.2015.05.004
  16. Hyndman RJ and Khandakar Y (2008). Automatic time series forecasting: the forecast package for R, Journal of Statistical Software, 27, Retrieved from 00 00, http://www.jstatsoft.org/v27/i03/, 1-22.
  17. Jeong S and Kim KW (2011). A comparison study for mortality forecasting models by average life expectancy, The Korean Journal of Applied Statistics, 24, 115-125. https://doi.org/10.5351/KJAS.2011.24.1.115
  18. Jung KN, Baek JS, and Kim DG (2013). Comparison of mortality estimate and prediction by the period of time series data used, The Korean Journal of Applied Statistics, 26, 1019-1032. https://doi.org/10.5351/KJAS.2013.26.6.1019
  19. Kang JC, Lee DS, and Shung JH (2006). A study on the method for forecasting mortality considering longevity risk, The Journal of Risk Management, 17, 153-178.
  20. Kim SJ (2012a), A comparison study on the stochastic mortality models for measuring longevity risk, Korean Insurance Journal, 93, 213-235.
  21. Kim SJ (2012b), A study on the prediction of mortality rate using the lee-carter model, The Journal of actuarial science, 4, 47-66
  22. Kim S Y and Oh JH (2017). A study comparison of mortality projection using parametric and non-parametric model, The Korean Journal of Applied Statistics, 30, 701-717. https://doi.org/10.5351/KJAS.2017.30.5.701
  23. Kim SY, Oh JH, and Kim KW (2018). A comparison mortality projection by different time period in time series, The Korean Journal of Applied Statistics, 31, 41-65. https://doi.org/10.5351/KJAS.2018.31.1.041
  24. Kim SY (2020). A study on the decomposition of contributions by age to changes in life expectancy at birth in Korea and visualization of mortality improvement, Journal of The Korean Official Statistics, 25, 1-31.
  25. Lee RD and Carter LR (1992). Modeling and forecasting US mortality, Journal of the American Statistical Association, 87, 659-671. https://doi.org/10.2307/2290201
  26. Lee R and Miller T (2001). Evaluating the performance of the lee-carter method for forecasting mortality, Demography, 38, 537-549 https://doi.org/10.1353/dem.2001.0036
  27. Li N, Lee R, and Gerland P (2013). Extending the Lee-Cater method to model the rotation of age patterns of mortality decline for long-term projections, Demography, 50, 2037-2051. https://doi.org/10.1007/s13524-013-0232-2
  28. Lov'asz E (2011). Analysis of Finnish and Swedish mortality data with stochastic mortality models, European Actuarial Journal, 1, 259-289. https://doi.org/10.1007/s13385-011-0039-8
  29. McCullagh P and Nelder J (1989). Generalized linear models(2nd ed), Chapman & Hall, London.
  30. O'Hare C and Li Y (2012). Explaining young mortality, Insurance: Mathematics and Economics, 50, 12-25. https://doi.org/10.1016/j.insmatheco.2011.09.005
  31. Oh JH and Kim SY (2018). Consideration on assumption and transition of mortality model for Korea, The Korean Journal of Applied Statistics, 31, 637-653. https://doi.org/10.5351/KJAS.2018.31.5.637
  32. Park YS, Kim KW, Lee DH, and Lee YK (2005). A comparison of two models for forecasting mortality in South Korea, The Korean Journal of Applied Statistics, 18, 639-654. https://doi.org/10.5351/KJAS.2005.18.3.639
  33. Plat R (2009). On stochastic mortality modeling, Insurance: Mathematics and Economics, 45, 393-404. https://doi.org/10.1016/j.insmatheco.2009.08.006
  34. Renshaw AE and Haberman S (2006). A cohort-based extension to the lee-carter model for mortality reduction factors, Insurance: Mathematics and Economics, 38, 556-570. https://doi.org/10.1016/j.insmatheco.2005.12.001
  35. Villegas AM, Haberman S, Kaishev VK, and Millossovich P (2015). A Comparative Study of Two-Population Models for the Assessment of Basis Risk in Longevity Hedges, Working paper.
  36. Villegas AM, Millossovich P, and Kaishev VK (2017). StMoMo: An R Package for Stochastic Mortality Modelling, R package version 0.4.0, Retrieved from: http://CRAN.R-project.org/package=StMoMo