1 / 28

Using the Select Table to Model Mortality Rates of Domestic Immigrants

This study investigates the mortality rates of domestic immigrants in Kinmen County and Hsinchu County in Taiwan, and proposes a methodology for modeling these rates. The study aims to understand the impact of population migration on city development and resource allocation.

jhoward
Download Presentation

Using the Select Table to Model Mortality Rates of Domestic Immigrants

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Using the Select Table to Model Mortality Rates of Domestic Immigrants Twelfth International Longevity Risk and Capital Markets Solutions Conference Sep 29, 2016 Hsin-Chung Wang Jack C. Yue Tzu-Yu Wang

  2. Outline • Motivation • Methodology • Evaluation of Graduation Methods • Empirical Analysis • Application • Conclusion

  3. Motivation Motivation • Ageing population Taiwan entered into ageing society since 1993 and ageing population will be over 20% of the total population in 2025 entering into hyper-aged society • Lower fertility rates The total fertility rate (TFR) of Taiwan is around 1.2 for the past 5 years (2011–2015) How to balance the losses of population and work force? population migration is one of the key factors • Population distribution inequality in city and county -Urbanization became more obvious -Fewer international immigrations in Taiwan

  4. Motivation Motivation an important factor in city development and resource allocation ? Domestic Immigrants • Most counties and Taiwan’s overall population growth rate are decreasing. But, Kinmen county’s is increasing.

  5. Motivation Motivation • City and County Demographic Indicators (2014 ) Increased population cities or counties are mainly from social increase

  6. Motivation Motivation • Annual Immigrants and Emigrants of Kinmen County • Net migration population was mostly working population

  7. Motivation Motivation • Age and Population Percentages for people residedless than 10 Years in Kinmen and HsinchuCounty in 2014 (similar to 2012 and 2013)

  8. Motivation Motivation • Population Structures of Taiwan and Kinmen (1998–2014) • larger proportion of elderly population • work force (ages 15–64) has a larger increasing rate • younger generation (ages 0–14) decrease much faster than in Taiwan. Must be more immigrants at the age group 15–64 to Kinmen county.

  9. Motivation Methodology • The standard mortality ratio (SMR) - is the death number of small area at age of x • is the population of small area at age of x • is the mortality rate of standard population at age of x. • The SMR is calculated using the same age structure • The smaller the SMR, is usually the larger the life expectancy is. .

  10. Methodology • The Whittaker method is to minimize the following objective function, i.e., weighted sum of fit function F and smoothness function S: • and are observed and graduated mortality rates for age x • is the weight for age x - n is population size - h and z are the parameters to be decided. • is the z time difference.

  11. Methodology • The partial SMR: is one way to deal with estimating mortality rates of small populations, by adding information from other (large) population to correct possible bias - was the estimated value of the heterogeneity parameter via:

  12. Evaluation of Graduation Methods • The county-level population sizes often are small and their observed age specific mortality rates fluctuate a lot for consecutive ages. • First, 1,000 simulation to evaluate if the size of reference population makes any differences. • Suppose the mortality rates follow the Lee-Carter model • Use the population structure of Taiwan male in 1995-2014 • Assume the reference and small populations have the same age structure in Taiwan

  13. Evaluation of Graduation Methods • Average Errors of Different Sizes of Reference Population Mean Absolute Percentage Error ( MAPE)：%

  14. Evaluation of Graduation Methods • graduation methods can reduce the errors • The reduction rate decreases as the size of small population size increase. • The errors without graduation are smaller than 10% when the population size is over 500,000 • It seems that 2 million is sufficient for the reference population. • Tthepartial SMR generally have smaller errors In practice, it is difficult to find (and confirm) the reference populations have identical mortality rates as the small population.

  15. Evaluation of Graduation Methods • Next, 1,000 simulation again: • We treat the sum of historical data from small population as the reference population • The partial SMR has better performance

  16. Evaluation of Graduation Methods • Mortality rates of Kinmen County (2014) • It appears that the partial SMR reduce the fluctuations of age-specific mortality rates.

  17. Empirical Analysis • Standardized Mortality Rates of Taiwan Counties • The SMR’s of Hsinchu county are almost identical to those of Taiwan. • Kinmen and Hsinchu have different mortality behavior.

  18. Empirical Analysis • Percentages of Populations and Deaths for those Resided more than 10 years in Kinmen and HsinchuCounties: • about 43% of population, but almost 70% of deaths in Kinmen.

  19. Empirical Analysis • Age-specific mortality rates of people resided in Kinmen (2012–2014) --Resided less than 10 years have smaller mortality rates, and it is more obvious for the male. --For the female, resided less than 10 years have smaller mortality rates for ages 50 and over.

  20. Empirical Analysis • Resided in Kinmen1–4 years, 5–9 years, and more than 10 years. The results are similar and indicate that newer immigrants have lower mortality rates.

  21. Empirical Analysis • Age-specific mortality rates of people resided in Hsinchu(2012–2014) -Resided less than 10 years still have lower mortality rates at younger age groups -Have about the same mortality rates at ages 50 and over. -the differences are not much and they locate at the younger ages, we think the new immigrants might have longer life.

  22. Empirical Analysis • SMR’s of Taipei City, Kinmen and Hsinchu Counties (2012–2014).

  23. Empirical Analysis • Graduated Mortality Rates in Kinmen County (2012–2014) -The mortality curves are fairly smooth, for populations at most 40,000 each. - After graduation, the advantage of mortality rates for the new immigrants are more noticeable - The mortality curve of all residents are in-between those of less and more than 10 years.

  24. Application • Select and Ultimate Table: 1. Assume the calculated total population mortality rate is (similar to the Select Table with lower mortality rate after insurance underwriting) 2. The mortality rate resided in Kinmen more than 10 years is , the mortality rate select after the select effect disappeared (similar to the ultimate table that exceeded select period) If the select periods are years, when , the select death probability ; when , the select death probability

  25. Application • we used total population of males at age of 45 ( ) with resided more than 10 years( ) • Assuming the select periods are 10 years, then if a 46 years old male moved into, the mortality rate at age of 46 is =0.00285 and the mortality rate at age 47 is 0.00307 and so on. The mortality rate at age of 56 is =0.00537.

  26. Conclusion • The top two counties with largest proportion of immigrants in Taiwan show that: --The immigrants do have lower mortality rates for Kinmen county but it is not the case for Hsinchu county. --This partly confirmed the theory of Kibele and Janssen (2013), that the migration would significantly distort the mortality rates in that area. --The effect of immigrants cannot explain why the residents (especially the female) of Kinmen county have longer life than those of Taipei city. There should be other causes other than migration. • It is believed that at least three causes behind the longer life in Kinmen county: • “Mini Three Link”: A lot of people (ages between 40 and 60) move to Kinmen in order to enjoy the privilege to have direct trades .

  27. Conclusion • Social welfare: local government gives monthly pension to the elderly residents and students of Kinmen University have waiver of tuition ( they must register to become residents of Kinmen County). • Island effect: is related to the residents of Okinawa who have longer life expectancy in Japan • It is still too early and not possible to come out a solid conclusion, with the limited data in this study • we found that the graduation methods can help to provide more stable estimates of mortality rates • if the mortality rates are related to the time of migration, then we can propose an approach by modifying the estimation of select and ultimate table from commercial insurance

  28. Thank you for your attention.

More Related