Current status life tables (cont.)

As discussed in the session on the single decrement life table, the life expectancy at birth can be conceived as the area under the survival curve. This is no different here: the time that men and women can expect to life in a single state, or, the mean age at first marriage is equal to area under the survival curve.

John Hajnal (1953) used this property to develop the Singulate Mean Age at Marriage (SMAM). We first calculate the total number of person-years lived in single state (from data in 5-year age intervals) as 5 times the proportion single in each age group, nΠx:

P Y s (0,50)=  5  *   ∑ x=0,5 45 S 5 x N 5 x =5  *   ∑ x=0,5 45 ∏ x 5      

As mentioned before, not everyone marries, and we will subtract time spent single by those who do not marry by age 50 in numerator, and divide by the proportion that marries by age 50 (interaction Why is age 50 chosen as the cutoff? Internal link). The fraction that never marries at exact age 50 is estimated as the arithmetic average of the proportions never married in the two neighboring age groups:

∏(50)  =   1 2   ( ∏ 45 5   +   ∏ 50 5 ) 

With these two components, we can define SMAM as:

SMAM  =   n  *   ∑ x=0,5 45 ∏ x 5   −  50  *  ∏(50) 1−∏(50)
The assumption is that those who are not married by age 50 will never get married.