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Life Tables

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

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Life Tables

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  1. Life Tables September 15

  2. Life Table • A statistical model for measuring the mortality (or any other type of “exit”) experiences of a population, controlling for age distributions

  3. Types of Life Tables • Current/Period vs. Generation/Cohort • Complete vs. Abridged • Single vs. Multiple Decrement • Increment/Decrement Tables

  4. Period Life Table Construction • Step 1: Solving for age-specific death rates nmx ≈ nMx = nDx / nNx

  5. 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

  6. 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

  7. Period Life Table Construction • Step 4: Solve for npx (probability of surviving an age interval) npx = 1 - nqx p85 = 0.00

  8. Period Life Table Construction • Step 5: Set radix (l0) and solve for number alive at age x (lx). lx+n = lx * npx

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

  10. 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)

  11. Period Life Table Construction • Step 8: Solve for person years lived above age x (nTx) Tx = nLa

  12. Period Life Table Construction • Step 9: Solve for life expectancy at age x (e0x) e0x = Tx / lx

  13. 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

  14. 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

  15. The Life Table as a Stationary Population • Interpretation of functions • lo • lx • ndx • nLx • Tx • e0x • Crude death rate • Crude birth rate

  16. 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 x+n Remember: For the open-ended age interval, there is only a direct effect

  17. 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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