Life Tables

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Life Tables

• September 15

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Life Table

• A statistical model for measuring the mortality
  (or any other type of exit) experiences of a
  population, controlling for age distributions

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Types of Life Tables

• Current/Period vs. Generation/Cohort
• Complete vs. Abridged
• Single vs. Multiple Decrement
• Increment/Decrement Tables

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Period Life Table Construction

• Step 1 Solving for age-specific death rates
• nmx nMx nDx / nNx

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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

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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

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Period Life Table Construction

• Step 4 Solve for npx (probability of surviving
  an age interval)
• npx 1 - nqx
• ?p85 0.00

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Period Life Table Construction

• Step 5 Set radix (l0) and solve for number
  alive at age x (lx).
• lxn lx npx

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Period Life Table Construction

• Step 6 Solve for deaths experienced in each age
  interval (ndx)
• ndx lx lxn

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Period Life Table Construction

• Step 7 Solve for person years lived between x
  and xn (nLx)
• nLx n lxn nax ndx
• (open-ended interval ?Lx lx / ?mx)

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Period Life Table Construction

• Step 8 Solve for person years lived above age x
  (nTx)
• Tx ?nLa

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Period Life Table Construction

• Step 9 Solve for life expectancy at age x (e0x)
• e0x Tx / lx

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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

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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

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The Life Table as a Stationary Population

• Interpretation of functions
• lo
• lx
• ndx
• nLx
• Tx
• e0x
• Crude death rate
• Crude birth rate

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Age-Decomposing a Difference in Life Expectancies
n ? x
Indirect and interaction effects resulting from
the person years added by additional survivors in
future intervals
The direct effect of a change in mortality rates
between ages x and xn
Remember For the open-ended age interval, there
is only a direct effect
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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