Life Tables

Sociology 215: Demographic Methods

1. The following table is part of a life table for the total (male and female) population of California in 1970.

Fill in the missing values in the third through fifth columns, and all the values in the sixth through ninth columns.

If I had failed to give you the l_x values at each age, you would not have been able to calculate the d_x, _nm_x, _nq_x, and _na_x columns-at least not without some strong assumptions. Assume that I had not given you the values in the l_x column, but instead had given you the values for one of the four other columns with omitted values (i.e., the d_x, _nm_x, _nq_x, or _na_x column): Show how-if possible-the entire life table could be derived-without any assumptions. General formulas are fine; there is no point in simply reproducing the same table over and over; I want to know how you would derive the other four columns (e.g., l_x, _nm_x, _nq_x, and _na_x if you were given d_x). And, yes, you can continue to assume that you know _nL_x, T_x, and _x.

This particular life table was calculated under the assumption that death rates within each age group are constant (i.e., the instantaneous death rate is assumed to be the same at each point within the interval x to x+n. If I had not told you this, how, on the basis of the life table you derived in response to part A, might you have suspected and/or deduced this?

For the _na_x values that you calculated, substitute a set of _na_x values that you borrow and/or derive from Tables 3.2 and 3.3 of Preston and Heuveline. (How exactly should you borrow and/or derive them? This is inevitably a judgment call-yours. Just have a rationale for whatever it is that you do.) With this new set of _na_x values, calculate a new value for life expectancy at birth (₀).

Imagine that the original life table (i.e., the one filled in under part A) were a stationary population.