# 6 Life 20Tables by 2rwZZG

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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
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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