New approaches to study historical evolution of mortality (with implications for forecasting)

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CONTEMPORARY METHODS OF MORTALITY ANALYSIS. New approaches to study historical evolution of mortality (with implications for forecasting). Lecture 4 Dr. Natalia S. Gavrilova, Ph.D. Dr. Leonid A. Gavrilov, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA. - PowerPoint PPT Presentation

Transcript of New approaches to study historical evolution of mortality (with implications for forecasting)

  • New approaches to study historical evolution of mortality (with implications for forecasting)Lecture 4

    Dr. Natalia S. Gavrilova, Ph.D.Dr. Leonid A. Gavrilov, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA

    CONTEMPORARY METHODS OF MORTALITY ANALYSIS

  • Using parametric models (mortality laws) for mortality projections

  • The Gompertz-Makeham Law(x) = A + R e x

    A Makeham term or background mortalityR e x age-dependent mortality; x - ageDeath rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age.risk of death

  • How can the Gompertz-Makeham law be used?By studying the historical dynamics of the mortality components in this law:(x) = A + R e x

    Makeham componentGompertz component

  • Historical Stability of the Gompertz Mortality Component Historical Changes in Mortality for 40-year-old Swedish MalesTotal mortality, 40 Background mortality (A)Age-dependent mortality (Re40)

    Source: Gavrilov, Gavrilova, The Biology of Life Span 1991

  • Predicting Mortality Crossover Historical Changes in Mortality for 40-year-old Women in Norway and DenmarkNorway, total mortalityDenmark, total mortalityNorway, age-dependent mortalityDenmark, age-dependent mortality

    Source: Gavrilov, Gavrilova, The Biology of Life Span 1991

  • Changes in Mortality, 1900-1960Swedish females. Data source: Human Mortality Database

  • In the end of the 1970s it looked like there is a limit to further increase of longevity

  • Increase of Longevity After the 1970s

  • Changes in Mortality, 1925-2007Swedish Females. Data source: Human Mortality Database

  • Age-dependent mortality no longer was stableIn 2005 Bongaarts suggested estimating parameters of the logistic formula for a number of years and extrapolating the values of three parameters (background mortality and two parameters of senescent mortality) to the future.

  • Shifting model of mortality projectionUsing data on mortality changes after the 1950s Bongaarts found that slope parameter in Gompertz-Makeham formula is stable in history. He suggested to use this property in mortality projections and called this method shifting mortality approach.

  • The main limitation of parametric approach to mortality projections is a dependence on the particular formula, which makes this approach too rigid for responding to possible changes in mortality trends and fluctuations.

  • Non-parapetric approach to mortality projections

  • Lee-Carter method of mortality projectionsThe Lee-Carter method is now one of the most widely used methods of mortality projections in demography and actuarial science (Lee and Miller 2001; Lee and Carter 1992). Its success is stemmed from the shifting model of mortality decline observed for industrialized countries during the last 30-50 years.

  • Lee-Carter method is based on the following formulawhere a(x), b(x) and k(t) are parameters to be estimated. This model does not produce a unique solution and Lee and Carter suggested applying certain constraints Then empirically estimated values of k(t) are extrapolated in the future

  • Limitations of Lee-Carter method The Lee-Carter method relies on multiplicative model of mortality decline and may not work well under another scenario of mortality change. This method is related to the assumption that historical evolution of mortality at all age groups is driven by one factor only (parameter b).

  • Extension of the Gompertz-Makeham Model Through the Factor Analysis of Mortality TrendsMortality force (age, time) = = a0(age) + a1(age) x F1(time) + a2(age) x F2(time)

  • Factor Analysis of Mortality Swedish FemalesData source: Human Mortality Database

  • Preliminary ConclusionsThere was some evidence for biological mortality limits in the past, but these limits proved to be responsive to the recent technological and medical progress.Thus, there is no convincing evidence for absolute biological mortality limits now.Analogy for illustration and clarification: There was a limit to the speed of airplane flight in the past (sound barrier), but it was overcome by further technological progress. Similar observations seems to be applicable to current human mortality decline.

  • ImplicationsMortality trends before the 1950s are useless or even misleading for current forecasts because all the rules of the game has been changed

  • Factor Analysis of Mortality Recent data for Swedish malesData source: Human Mortality Database

  • Factor Analysis of Mortality Recent data for Swedish femalesData source: Human Mortality Database

  • Advantages of factor analysis of mortalityFirst it is able to determine the number of factors affecting mortality changes over time. Second, this approach allows researchers to determine the time interval, in which underlying factors remain stable or undergo rapid changes.

  • Simple model of mortality projectionTaking into account the shifting model of mortality change it is reasonable to conclude that mortality after 1980 can be modeled by the following log-linear model with similar slope for all adult age groups:

  • Mortality modeling after 1980 Data for Swedish malesData source: Human Mortality Database

  • Projection in the case of continuous mortality declineAn example for Swedish females.Median life span increases from 86 years in 2005 to 102 years in 2105Data Source: Human mortality database

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    2005

    2105

    Age

    log (mortality rate)

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