Household formation process in simulation

In this simplified process of household formation through marriage it is assumed that the household formation process is a function of age, sex and location. An individual gets married and forms a new household with the new spouse (and their existing household members if they are the HRP or Household Reference Person) if

) , , ( ) 1 , 0 ( P hf a s l Ran ≤ (Equation 4.27)

where Ran (0,1) is a random number, a is the age, s is the sex and lis the location of the individual and P(hf a,s,l) is the probability of household formation occurring to an individual of age a, sex sat location l. This model does not differentiate cohabitated population from the singles, so there is a limitation on individual household structure modelling. However, this will not have much impact on processes as reported in this thesis, which are modelled independent of household structure.

The simplified household formation process is illustrated using the marriage process as an example as in Figure 4.11.

2

Married? no

18

Update household statuses b yes 1 Formal care? yes no yes 3 16/younger? yes no 8 Probability is bigger? yes no 7

Assign one preset random number that is between 0-1 no

5

Get probabilities of marriage for men in this age

6

Get probabilities of marriage for women in this age

no

11

Update the marital status of both

13

Update household size

12

HRP household?

14

Household is vacant

15

Update number of all dependents

10

Marry yes

16

Update person statuses a

19

Update area statuses c

17

Create the new household

9

Marriage candidate?

4

Man?

Figure 4.11 The marriage and household formation process

Notes: the pre-super-scripts in diagrams represent the simulation steps and the post-super- scripts are:

a. HRP status, current and previous locations etc.

b. household size, household member type and count, family roles etc. c. total population in area, total households in area etc.

Other types of household formation can be generated through similar processes. First a set of marriage candidates needs to be generated based on a set of marriage probabilities by age, sex and location. Once an individual is available to get married, the program then tries to find a suitable candidate with the opposite sex and a suitable age (this model does not study the household formation of same-sex couples). The space within which a partner is sought is randomly decided to be either within the same location or another different location as the candidate, due to limited data. The matching of the ages of the husband and wife is based on probabilities calculated from the age distribution between the husband and wife from the commissioned table from ONS that are described in data section in Chapter 3. Based on this matrix of the single year ages of husbands and wives, probability of a man at a certain age to marry a woman at a certain age can be calculated. Five year age bands were used for practical reasons. Then the marriage candidates were sorted by age and sex into two lists and one candidate was matched to the closest aged candidate of the three from the search in another list. If a spouse cannot be found, the candidate remains unmarried and enters the marriage market again in next year (Figure 4.12).

In both “marrying” and “after marriage” processes, various HRP (Household Reference Person) scenarios need to be considered for each couple: one is the HRP, both are HRPs and neither is an HRP. The first case is straightforward and the no one’s HRP status will be affected. In the second scenario, the wife’s status will be changed to spouse and the husband will be appointed as the HRP (Figure 4.13). In the model, children always follow their current HRP. Therefore there are 3 scenarios for children upon marriage: no changes to children of a non- HRP, they stay with the current HRP and only the non-HRP moves out; no changes to children of an HRP, while new household member(s) join in and adopt(s) the current household statuses; in the case that children of the current HRP follow he/she to join a new household (when two HRPs get married), all members of this household update their household statuses according to the new household information.

Figure 4.12 Matching candidates in marriage process

1

Same location search? yes no

7

Aged 16-99?

9

Put in the candidate list

13

Put the searcher in the list and sort by age

2

Finding an area

14

Compare the age difference with 2 neighbours on both sides

17

Match with the older candidate

5 In formal care? yes 4 Opposite sex? 6 Married? no no yes no yes 15

Older candidate has smaller age difference? no

8

Last person in area?

10 Search candidates in different locations? no yes no yes 16

Match with the younger candidate

yes

12

Candidates in the list?

no yes

yes

3

Finding a candidate in the area

yes yes

no

11

Last area?

*Notes: the pre-super-scripts in diagrams represent the simulation step numbers

2 One HRP? yes 1 Both HRPs? 3No HRP? M yes no yes 4

Change the woman HRP to Spouse

6

Mark her household as Spouse Household

9

Join spouse household in HRP household

5

Appoint the man as HRP

7

Mark the woman as Spouse no

8

Mark her household as Spouse Household

no

Figure 4.13 HRP status updating

Notes: the pre-super-scripts in diagrams represent the simulation step numbers