## 1. Overview

The population projections by marital status are made up of 2 separate sets of projections. One provides projections by legal marital status and the other for (opposite-sex) cohabitation. These are produced using different methodologies that are described briefly below.

Nôl i'r tabl cynnwys## 2. Legal marital status projections

Legal marital status projections are produced using a component methodology that is based on assumptions of underlying marriage, remarriage and divorce rates. The legal marital status projections classify a person as being either single (that is, they have never been married), married, divorced or widowed. The projections assume that everyone aged 15 and under is single.

The model adjusts for movements of people from one marital status to another subject to a number of constraints. This is known as a multi-state projection model, the starting point being the latest set of marital status estimates available at the time of production.

Nôl i'r tabl cynnwys## 3. Cohort component model by marital status

The single population at the end of a year would be calculated as:

- single population at the beginning of the year
- plus births (all assumed to be single) in the year
- minus marriages in the year
- minus deaths of single people in the year
- plus/minus an adjustment for migration of single people in the year

The married population would be calculated as:

- married population at the beginning of the year
- plus marriages (of single, divorced and widowed people) in the year
- minus divorces in the year
- minus deaths of married people in the year
- minus people widowed in the year
- plus/minus an adjustment for migration of married people in the year

The divorced population would be calculated as:

- divorced population at the beginning of the year
- plus divorces in the year
- minus marriages to divorced people in the year
- minus deaths of divorced people in the year
- plus/minus an adjustment for migration of divorced people in the year

The widowed population would be calculated as:

- widowed population at the beginning of the year
- plus people widowed in the year
- minus marriages to widowed people in the year
- minus deaths of widowed people in the year
- plus/minus an adjustment for migration of widowed people in the year

## 4. More on legal marital status projections

Each year the population are aged on; for example, the number of single men aged 45 projected for mid-2016 become the starting point in the model for the number of men aged 46 for mid-2017.

The number of single, married, divorced and widowed people is constrained so that for each year by every age/sex group this adds up to the total number of people in the principal national population projection for England and Wales. The number of migrants and deaths are also consistent with the corresponding components in the principal projection. A number of consistency constraints are also imposed. These include internal "two-sex" constraints, for example, that the number of men divorcing each year must equal the number of women divorcing.

The projections have been produced using the multi-dimensional dynamic projection model LIPRO (LIfestyle PROjections) developed by the Netherlands Interdisciplinary Demographic Institute (NIDI). The model requires assumptions to be made for all of the possible transitions between marital statuses and the marital status distributions for both deaths and net migration.

The assumptions used as inputs into the LIPRO model are constructed using an exponentially smoothed model of the recent trends in marriage and divorce rates calculated using registrations data; more details about the assumptions can be found in the documentation published with the marital status population projections. For the 2008-based projections this can be found in sections 2 and 3.

Since the 2006-based set, population projections by marital status have included an adjustment to account for both legal marriages of residents of England and Wales that take place abroad and marriages to overseas residents that take place in England and Wales.

Nôl i'r tabl cynnwys## 5. Cohabitation projections

Details about methods used to produce the cohabitation estimates used as a basis for these projections can be found in the article "Estimating the cohabiting population (128 Kb Pdf) " by Ben Wilson.

Ideally, projections of de facto marital status (cohabitation) would also be produced using a component methodology that includes transitions into and out of cohabitation within such a model. However, whereas detailed historical data on transitions between legal marital status categories are readily available from registration data, data on cohabitation formation and dissolution are very limited. Theoretically, estimates could be made from sample surveys; however, in practice, the data is not of sufficient quality for this purpose. In particular, sample sizes are far too small to produce reliable data for individual ages. As the model used for the legal marital status projections is a dynamic model, assumptions made about cohabitation transitions would affect the results for legal marital status. It would therefore be likely that the inclusion of necessarily speculative data on cohabitation would actually reduce the quality of the legal marital status projections.

Instead, assumptions have been made about the proportions cohabiting in each age/sex/legal marital status group and these have been applied to the results of the legal marital status projections. These proportions change over the projection period; more details about this can be found in documentation published with the marital status population projections.

Nôl i'r tabl cynnwys## 6. Variant projections

Variant projections are produced using the same method as that described above but the assumptions made about future marriage and divorce rates, or cohabitation proportions, gradually diverge from those assumed for the principal projection. The level of divergence from the principal assumptions can vary for different components reflecting where there is greater uncertainty in the trend or if it is suspected that a turning point has been reached. The level of divergence applied for each variant is discussed with external experts and reviewed by the statistician responsible for the projections.

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