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					Life Tables

September 15
                Life Table
• A statistical model for measuring the
  mortality (or any other type of “exit”)
  experiences of a population, controlling for
  age distributions
          Types of Life Tables
•   Current/Period vs. Generation/Cohort
•   Complete vs. Abridged
•   Single vs. Multiple Decrement
•   Increment/Decrement Tables
                                                         Grad School Cohort Life Lines


           15                                2.83

           14                                                                                  5.83

           13                                                                           5.5

           12                                                                                                    7.92

           11                                                                                                               9.83

           10                         2.42

            9                                                     4.08
Students




            8                                     3.08

            7                                                                                 5.75

            6                                                                                             7.33

            5                       2.25

            4                      2.17

            3       0.33

            2                                     3.08

            1                                                                  4.83

                0          1   2              3               4                 5               6     7          8      9   10
                                                                         Years in Program
 Period Life Table Construction
• Step 1: Solving for age-specific death
  rates


        nmx   ≈ n M x = n Dx / n Nx
 Period Life Table Construction
• Step 2: Decide on method for estimating
  nax (average person-years lived in the
  interval by those dying in the interval)
    •   Direct observation
    •   Graduation of the nmx function
    •   Borrowing values
    •   Rules of thumb
 Period Life Table Construction
• Step 3: Solve for nqx (probability of dying
  in age interval)


      nqx   = n * nmx / 1 + (n – nax) * nmx

                   q85 =   1.00
 Period Life Table Construction
• Step 4: Solve for npx (probability of
  surviving an age interval)


                 npx   = 1 - nqx

                 p85 =   0.00
 Period Life Table Construction
• Step 5: Set radix (l0) and solve for number
  alive at age x (lx).

                lx+n = lx * npx
 Period Life Table Construction
• Step 6: Solve for deaths experienced in
  each age interval (ndx)


               ndx   = lx – lx+n
 Period Life Table Construction
• Step 7: Solve for person years lived
  between x and x+n (nLx)


           nLx   = n * lx+n + nax * ndx

    (open-ended interval: Lx = lx / mx)
 Period Life Table Construction
• Step 8: Solve for person years lived
  above age x (nTx)

                 Tx = nLa
 Period Life Table Construction
• Step 9: Solve for life expectancy at age x
  (e0x)

               e0x = Tx / lx
    Mortality Analysis with Life Tables
• Expectation of life at birth
• Expectation of life at age 1
• Expectation of life at age 65
• Probability of surviving from birth to the
  65th birthday
• Median age at death
           The Life Table as a
          Stationary Population
• A population whose total number and
  distribution by age do not change with time
  – Conditions
     • Number of births per year remains constant
     • Each cohort of births experiences current observed
       mortality rates throughout life
     • Net migration = 0; or “closed” to migration
              The Life Table as
           a Stationary Population
• Interpretation of functions
  – lo
  – lx
  – nd x
  – nL x
  – Tx
  – e0 x
• Crude death rate
• Crude birth rate
Age-Decomposing a Difference in
      Life Expectancies

              l1            n Lx
                                     2
                                             n Lx
                                                      1
                                                               Tx2 n         1
                                                                             lx        1
                                                                                      lxn
   n∆ x       x
                   1
                       *(        2
                                                 1
                                                          )     1
                                                                        *(    2
                                                                                      2
                                                                                             )
              l0            lx               lx                 l0           lx       lxn

              The direct effect of a                             Indirect and
              change in mortality                                interaction effects
              rates between ages x                               resulting from the
              and x+n                                            person years added
                                                                 by additional
                                                                 survivors in future
                                                                 intervals

                                                      Remember: For the open-ended age
                                                      interval, there is only a direct effect
      Other Uses for Life Tables
•   Nuptiality (first marriage)
•   Migration from place of birth
•   Entering the labor force
•   Becoming a mother
•   Subsequent childbearing
•   Marital survival
•   Unemployment spells
•   Incarceration

				
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posted:11/10/2011
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