응용통계연구 (The Korean Journal of Applied Statistics)

  • 제31권5호
  • /
  • Pages.637-653
  • /
  • 2018
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

우리나라 사망력 모형의 변천과 가정 고찰 - Lee-Carter 류를 중심으로 -

Consideration on assumption and transition of mortality model for Korea - Discussion on the kinds of Lee-carter -

  • Oh, Jinho (Statistical Research Institute, Statistics Korea) ;
  • Kim, Soon-Young (Statistical Research Institute, Statistics Korea)
  • 투고 : 2018.07.23
  • 심사 : 2018.09.16
  • 발행 : 2018.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

빠른 고령화로 고령층의 증가는 인구구조 변화와 인구고령화에 영향을 미친다. 예전부터 선진국은 인구고령화를 주요현안으로 간주하여 고령화로 인한 연금 재정건전성, 건강 및 노인 복지 시스템의 지속 가능성에 집중하고 있다. 이처럼 고령층의 증가로 인구구조 변화와 인구고령화에 미치는 사망률 예측은 어느 때보다도 중요하다. 본 논문은 통계청 1970-2016년 각세별 생명표 자료를 활용하여 사망률 모형 6가지를 비교하였다. 이들 모형은 Lee-Carter(LC) 모형 (Lee and Carter, Journal of the American Statistical Association, 87, 659-671, 1992)에 근원을 두고 있으며, LC 의 가정을 수정하고 개선한 것이다. 이들 개선과정과 가정검토를 모형별로 살펴보고 우리나라에 적합한 사망률 모형을 모색했다. 분석결과 빠른 고령화와 연령별 사망률의 개선 효과를 보이는 우리나라의 경우 기대수명에 큰 변화를 주지 않고 이들 현상을 반영하고 연령별 사망률 패턴을 수정하는 LC-ER 모형 (Li 등, Demography, 50, 2037-2051, 2013)과 Li-Lee 모형과 LC-ER모형을 조합한 LL&LC-ER 모형으로 사망률을 예측하는 것이 바람직하다.

Rapid aging of the population affects population structure and population aging. Consequently, developed countries have focused on population aging as a major issue in regards to pension sustainability finances as well as health and the elderly welfare system. Mortality projections that result from population structure changes and population aging are increasingly important. This paper compares six mortality models using KOSTAT's life table from 1970 to 2016. The models are rooted in the Lee-Carter (LC) model (Lee and Carter, Journal of the American Statistical Association, 87, 659-671, 1992) and have been modified and improved on the assumptions of the LC model. We examined the improvement process and the check assumption by models in order to find a suitable mortality model for Korea. Korea shows rapid aging and declined mortality rate by age; therefore, it is desirable to estimate and predict mortality from LL&LC-ER models by combining LC-ER, LL, and LC-ER models that reflect the phenomena and modify age-specific mortality patterns without major changes in expected life expectancy.

키워드

참고문헌

  1. Bohk-Ewald, C., Ebeling, M., and Rau, R. (2017). Lifespan disparity as an additional indicator for evaluating mortality forecasts, Demography, 54, 1559-1577. https://doi.org/10.1007/s13524-017-0584-0
  2. Booth, H., Maindonald, J., and Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 325-336. https://doi.org/10.1080/00324720215935
  3. Brillinger, D. R. (1986). The natural variability of vital rates and associated statistics, Biometrics, 42, 693-734. https://doi.org/10.2307/2530689
  4. Cairns, A., Blake, D., and Dowd, K. (2006). A two-factor model for stochastic mortality: theory and calibration, Journal of Risk and Insurance, 73, 687-718. https://doi.org/10.1111/j.1539-6975.2006.00195.x
  5. Cairns, A., Blake, D., Dowd, K., Coughlan, G., 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
  6. Cairns, A., Blake, D., Dowd, K., Coughlan, G., Epstein, D., and Khalaf-Allah, M. (2011). Mortality density forecasts: an analysis of six stochastic mortality models, Insurance Mathematics and Economics, 43, 355-367.
  7. De Jong, P. and Tickle, L. (2006). Extending Lee-Carter mortality forecasting, Mathematical Population Studies, 13, 1-18. https://doi.org/10.1080/08898480500452109
  8. Doukhan, P., Pommeret, D., Rynkiewicz, J., and Salhi, Y. (2017). A class of random field memory models for mortality forecasting, Insurance : Mathematics and Economics, 77, 97-110. https://doi.org/10.1016/j.insmatheco.2017.08.010
  9. Guibert, Q., Lopez, O., and Piette P. (2017). Forecasting mortality rate improvements with a high-dimensional VAR, HAL-01613050, doi:hal.archives-ouvertes.fr/hal-01613050
  10. Horiuchi, S. and Wilmoth, J. (1995). Annual meeting of the population association of America. San Francisco, CA: Population Association of America.
  11. Hunt, A. and Villegas A. M. (2015). Robustness and convergence in the Lee-Carter model with cohort effects, Insurance: Mathematics and Economics, 64, 186-202. https://doi.org/10.1016/j.insmatheco.2015.05.004
  12. Jeong, S. and Kim K. W. (2011). A Comparison study for mortality forecasting model by average life expectancy, The Korean Journal of Applied Statistics, 24, 115-125. https://doi.org/10.5351/KJAS.2011.24.1.115
  13. Jung, K., Back, J., and Kim, D. (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
  14. Kannisto, V., Lauritsen, J., Thatcher, A. R., and Vaupel, J. W. (1994). Reductions in mortality at advanced ages: several decades of evidence from 27 countries, Population and Development Review, 20, 793-810. https://doi.org/10.2307/2137662
  15. Kang, J. C., Lee, J. C., and Sung, J. H. (2006). A study on methods for forecasting mortality considering longevity risk, The Journal of Risk Management, 17, 153-178.
  16. Kim, S. J. (2012). A comparison study on the stochastic mortality models for measuring longevity risk, Korean Insurance Journal, 93, 213-235.
  17. Kim, S. Y. and Han, M. J. (2017). Mortality forecasting for 2016 Korean Population Projection, Korean Journal of Population Studies, 40, 1-25.
  18. Kim, S. Y. and Oh, J. H. (2017). A study comparison of mortality projection using parametric and nonparametric model, The Korean Journal of Applied Statistics, 30, 701-717. https://doi.org/10.5351/KJAS.2017.30.5.701
  19. Kim, S. Y., Oh, J. H., and Kim, K. W. (2018). A comparison of mortality projection by different time period in time series, The Korean Journal of Applied Statistics, 31, 41-65.
  20. KOSIS (2016). Population Projections (2015-2065).
  21. Lee, R. D. and Carter, L. R. (1992). Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87, 659-671.
  22. Lee, R. D. 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
  23. Li, H. and Lu, Y. (2017). Coherent forecasting of mortality rates: a Sparse Vector-Autoregression approach, ASTIN Bulletin: The Journal of the IAA, 47, 563-600. https://doi.org/10.1017/asb.2016.37
  24. Li, N. and Gerland, P. (2011). Modifying the Lee-Carter Method to Project Mortality Changes up to 2100, the Population Association of America 2011 Annual meeting-Washington, DC, Session 125, formal Demography I: Mathematical Models and Methods.
  25. Li, N. and Lee R. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 575-594. https://doi.org/10.1353/dem.2005.0021
  26. Li, N., Lee, R., and Gerland, P. (2013). Extending the lee-carter 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
  27. Park, Y. S., Kim, K. W., Lee, D. H., and Lee, Y. K. (2005). A comparison of two model 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
  28. Renshaw, A. E. 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
  29. Sevcikova, H., Li, N., Kantorova, V., Gerland, P., and Raftery, A. E. (2015). Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections. Working paper no. 150, Center for Statistics and the Social Sciences University of Washington.
  30. Statistics Canada (2015). Population Projections for Canada(2013 to 2063), Provinces and Territories (2013 to 2038): Technical Report on Methodology and Assumptions.
  31. Thatcher, A. R., Kannisto, V., and Vaupel, J. W. (1998). The force of mortality at ages 80 to 120, Odense Monographs on Population Aging 5, Odense University Press.
  32. Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net, Royal Statistical Society, 67, 301-320. https://doi.org/10.1111/j.1467-9868.2005.00503.x