Legal marital status

Typically, a marital status projection will be subject to a number of external and internal constraints. Within these constraints, the projections will be determined by assumptions of future (a) marriage and remarriage rates, (b) divorce rates, (c) mortality differentials by marital status and (d) net migration by marital status.

External constraints
The marital status projections were constrained to agree with the 2003-based interim national (age and sex) projections for England & Wales. There were three separate constraints:

(i) the number of people entering the “population at risk” each year is the projected population aged 15 last birthday from the national projection, all of whom are assumed to be initially single (i.e. never-married);

(ii) the total number of deaths each year is constrained to agree, at each age and sex, with the national projection; and

(iii) the total number of net migrants each year is constrained to agree, at each age and sex, with the national projection.

Satisfying all these constraints, means that the total projected population for each future year, at each age and sex, is consistent with the national projections.

Internal constraints
The input rates for marriage and divorce were subject to further adjustment in order to satisfy the following standard two sex consistency requirements:

(a) the number of males marrying must equal the number of females marrying:

(b) the number of males divorcing must equal the number of females divorcing:

(c) the number of married males dying must equal the number of females becoming widowed; and

(d) the number of married females dying must equal the number of males becoming widowed.

Note, however, that as one partner in a marriage may be temporarily resident abroad, the number of married men and women are never exactly equal in population estimates and have not been constrained to be equal in these projections. Similarly, in reality, net migration of married men and women is never exactly equal. However, to avoid the risk of small annual differences accumulating into a significant long-term bias, it is sensible to assume that annual differences will cancel out and impose the further consistency condition:

(e) net migration of married males is assumed to equal net migration of married females.

These five consistency conditions are handled in different ways within LIPRO. The marriage and divorce consistency requirements (a and b) are met by taking the mean of the initially projected, and unequal, male and female events. This is justified on “market-mechanism” or bargaining grounds. If more women are willing to marry than men, say, then the actual number marrying will be a compromise between the two. These are termed active constraints.

The widowhood consistency requirements (c and d) are passive constraints. These are “mortality dominant” constraints where the number of people entering widowhood is set equal to the calculated number of married deaths and no further adjustment is required.

Finally, the net migration consistency requirement (e) is dealt with by simply specifying an assumed net migration distribution by marital status.

Cohabitation

As one partner in a marriage may be temporarily resident abroad, the number of married men and women are never exactly equal in population estimates and have not been constrained to be equal in the legal marital status projections. A similar argument could apply to the cohabiting population but the available data does not allow an accurate estimate to be made of any imbalance. Therefore, both the base year population estimates produced by ONS and these projections have been constrained so that the total number of cohabiting males equals the total number of cohabiting females.