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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 n m x n M x = n D x / n N x

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Period Life Table Construction Step 2: Decide on method for estimating n a x (average person-years lived in the interval by those dying in the interval) Direct observation Graduation of the n m x function Borrowing values Rules of thumb

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Period Life Table Construction Step 3: Solve for n q x (probability of dying in age interval) n q x = n * n m x / 1 + (n – n a x ) * n m x q 85 = 1.00

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Period Life Table Construction Step 4: Solve for n p x (probability of surviving an age interval) n p x = 1 - n q x p 85 = 0.00

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Period Life Table Construction Step 5: Set radix (l 0 ) and solve for number alive at age x (l x ). l x+n = l x * n p x

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Period Life Table Construction Step 6: Solve for deaths experienced in each age interval ( n d x ) n d x = l x – l x+n

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Period Life Table Construction Step 7: Solve for person years lived between x and x+n ( n L x ) n L x = n * l x+n + n a x * n d x (open-ended interval: L x = l x / m x )

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Period Life Table Construction Step 8: Solve for person years lived above age x ( n T x ) T x = n L a

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Period Life Table Construction Step 9: Solve for life expectancy at age x (e 0 x ) e 0 x = T x / l x

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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 65 th 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 –l o –l x – n d x – n L x –T x – e 0 x Crude death rate Crude birth rate

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

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The Basics Populations rarely have a constant size Intrinsic Factors BIRTH IMMIGRATION DEATH EMIGRATION Extrinsic factors Predation Weather N t+1 = N t.

The Basics Populations rarely have a constant size Intrinsic Factors BIRTH IMMIGRATION DEATH EMIGRATION Extrinsic factors Predation Weather N t+1 = N t.

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