The formula for 2nd family children
This is an HTML transcript of a paper I wrote in 1998 while using the name "John Ward".
It is still largely relevant. I haven't checked all the links  some of them may now fail.
Original paper, Word for Windows (RTF) format
"Children First" & Second Family Children:
Analysis of the issues and options.
Barry Pearson
version 2.0
11th September 1998
Summary
This paper analyses methods for modifying the maintenance liability in the case where the NRP of the 1st family has children in a 2nd family. It is concerned solely with financial matters and not other (more important) aspects of child support.
It is not "mathematically" obvious that a 2nd family modification is needed, or if so, what sort. The paper therefore examines cash flows for various 1st and 2nd household situations to see what sort of problems arise with the standard (unmodified) formula.
The conclusion is that there is no jusification for a universal modification for 2nd family children, and indeed sometimes it would be unsafe to use one, but there may be a need for one in specific cases.
Contents
Discussion & conclusions
Examples of household cash flows
Appendices
Discussion & conclusions
References
[1] "Children First" Green Paper for CSA Reform
[2] "Children First" & Sharing of Care:
Problems with the proposed formula, and a revised proposal.
Barry Pearson 1998
[3] House of Commons Research Paper 98/79
"Child Benefit"
Scope
This paper analyses methods for modifying the maintenance liability of the "Children First" Green Paper [1] in the case where the NRP has children in a 2nd family. It is concerned with financial matters and not other (more important) aspects of child support.
This paper has little to say about the basic formula for the case where there are no 2nd family children, and does not discuss the sharing of care, which is dealt with elsewhere [2].
The approach used here
It is not "mathematically" obvious that a 2nd family modification is needed, or if so, what.
(This contrasts with the way that it is mathematically obvious that a sharedcare modification is needed. The different implications of 51%49% caring compared with 100%0% caring are glaring).
The vital principle of treating all children with equal importance doesn't settle things. If the standard liability were 1%, the NRP's remaining 99% would be enough to spend at least the same on 2nd family children. If it were 50%, a modification would be needed to spend equally on both sets of children. But at 15/20/25% it is not obvious.
Typically other nations/states using a formula/guidelines don't appear to have a 2nd family modification, although some do  see Appendix B.
The starting point for discussing "2nd family modifications" to the GP formula is to analyse the basic formula without any such modification, to see whether problems arise. If one is needed, it must then be designed to overcome specific identified problems  perhaps the basic formula doesn't work in the 2nd family case, or is unfair (eg. treats certain children as more important than others), or causes hardship (eg. loss of home, job, etc).
This paper identifies an idealised "balanced expected spending" situation for two households, using just the basic formula, which appears to have the right attributes of fairness, equality, etc. The situation is intended to have the characteristic that if it can be achieved, this shows that there is no "mathematical" reason for such modifications (there may be other reasons), otherwise this is proof that a modification is needed.
Then the paper examines whether it plausible to achieve this situation, so that conclusions can be drawn. It also examines the proposed 2nd family options. Appendices discuss various aspects of the situation.
Balanced Expected Spending
Principles
This identifies household cash flows which attempt to achieve the following:
 1st family children and 2nd family children see an equivalent contribution from their common parent (the 1st family NRP), so they are seen to be equally important  a principle which must not be compromised;
 children see the same proportional contribution from each parent, so there is no bias towards PWC, NRP, or NRP's new partner, or by gender.
It is unlikely that this scenario will be achieved exactly in any particular case. It depends on the whims of the parents, and legislation can't ensure this. Any or all of the parents may be miserly or generous towards their children. Nothing except openbook family accounting, or eliminating human variability, will prevent this.
The key is whether the child support formula performs a redistribution which enables the various parents to achieve this fair balance if they choose to, without unbalanced hardship. That is probably the most that can be expected from a redistribution formula.
The cash flow across the two households
The starting point for this situation is the 15/20/25% which the NRP is expected to contribute towards the 1/2/3 1st family children. If this is reasonable, it is assumed reasonable for this person's contribution to the 2nd family children also to be 15/20/25% (according to how many there are). Given that all parents (not just the NRP) should contribute to their children, it is further expected that the other parents should also contribute 15/20/25% of their income to their children. This is an idealised cash flow for the two households which has equality of responsibility and importance explicitly designed into it. (This paper assumes no sharing of care [2]). So:
1st family NRP spends 15/20/25% of own net income on 1st family children (via the PWC), 15/20/25% on 2nd family children, and so has 50% to 70% for everything else.
1st family PWC spends 15/20/25% of own net income on 1st family children, and has 85/80/75% for everything else. (Also spends the money from the NRP on the 1st family children).
2nd family other parent spends 15/20/25% of own net income on 2nd family children, and has 85/80/75% for everything else.
1st family children receive money, goods & services to the combined value of 15/20/25% of the net income of each of their parents.
2nd family children receive money, goods & services to the combined value of 15/20/25% of the net income of each of their parents.
Conclusions from the Examples
The conclusions from the examples (see next major section) can be summarised:
1: For any particular NRP income:
(a) the PWC may be much poorer than the 2nd family, and it would be unjust for deprived 1st family children to have a modification;
(b) the PWC may be much richer, so there may be a case for a modification;
(c) all parents may earn about the same amount, in which case there is no jusification for such a modification; the 2nd family needs more money, but retains more anyway.
Since the formula works from just the NRP's income, cases 1(a), 1(b), & 1(c) cannot be distinguished, so a 2nd family modification to the formula would be unsafe.
2: If the NRP has no or low pay, there is little maintenance, so little effect from a modification.
3: There do appear to be cases where a 2nd family modification may be justified:
(a) if the 2nd family built up commitments before the assessment which they can't decommit from in time;
(b) if there are considerable arrears.
These cannot be detected from the NRP's income alone, so can't be targeted by a 2nd family modification to the formula. 3(a) & 3(b) may have to be identified explicitly and dealt with by some sort of appeals mechanism.
Examination of 2nd family options
The key factor affecting the relative importance of the 1st and 2nd family children is the standard percentage liability, not any modification of it
 if it were 1%, it would say "the 1st family children are so unimportant that it is easy to spend more than that on anything you choose (which could be a 2nd family)";
 if it were 50%, it would say "the 1st family children are so important that it is impossible to spend that much on anything else (including a 2nd family)";
 but at 15/20/25%, it says "it is possible to find this amount of money for a 2nd family if you can adjust your finances so that 50% to 70% is sufficient for everything except the children".
The effect of a 2nd family modification is to adjust the importance of the 1st family children downwards relative to "anything you choose" to make it easier to spend at least the same amount on 2nd family children. So a 2nd family modification has to consider the extra hardship to the 1st family caused by the reduction in maintenance, compared to the benefit to the 2nd family of being able to pay for essentials (housing, etc) from the retained income. This is not algebra, it is sociology, and needs to be based on suitable research.
The example cash flows don't appear to show a need for a universal modification  there is no evidence that the standard formula makes it impossible to spend as much on the 2nd family children as the 1st, nor evidence that the any extra hardship caused to 1st family children would simply result in more balanced spending on 2nd family children.
First option
The effect of this option is to reduce the liability to the 1st family children to 85/80/75% of the standard liability, depending on the number of 2nd family children.
No rationale for this can be detected from the example cash flows. There is no evidence that this reduction in liability is needed, or if so is the right amount. It appears to be a plausiblelooking formula desperately plucked out of thin air.
Second option
The effect of this option is to treat the children of both households as though they were a single household, to apply the standard formula to them all, then to spread the money evenly across all the children.
The sole logic behind this would be if the 2nd family could not afford to spend any of the 85/80/75% they were originally left with on their new children. But there no evidence of this. The example cash flows don't show that the 2nd family has no scope for spending any of that money on their new children. There are also other flaws with this option:
 There is a body of opinion that the 2nd child of a family costs significantly less than the 1st child, even if they are treated as equally important, and so on, [3]. So while 2nd children of both families ought to cost the same as each other, this amount should be less than the 1st children. This is partly reflected in the basic formula (15/20/25). Option 2 doesn't take this into account.
 The standard formula only caters for the most common number of children in one household (1/2/3), not for those of two households (2/3/4/5/6).
The conclusion is that neither option makes much mathematical (or other) sense, even if they were needed, which does not appear to be the case.
Examples of household cash flows
All incomes are net, per week. The nosharing case is assumed. Child Benefit & other benefits are included and treated as net income for all calculations (except NRP CSA formula liability, which is based on pure net income  gross income less tax & NI). Maintenance is assumed to be spent on the children.
Examples 1: NRP earns consistent income (say £300)
Example 1a: All parents earn about the same
All parents earn £300, 2 children in each family.
1st family PWC spends £64 on children, and retains £256.
1st family NRP spends £60 on 1st family children, £60 on 2nd family children, and retains £180.
2nd family other parent spends £64 on children, and retains £256.
1st family children receive the equivalent of £124.
2nd family children receive the equivalent of £124.
1st family retains £256 after spending on the children.
2nd family retains £436 after spending on the children.
Conclusion: all children benefit to the same degree, and there is no specific hardship in the 2nd family. The difference between the 1st family & 2nd family retained incomes is less than the difference between 1st family & 2nd family total net incomes, but given the responsibility of the NRP towards children in the 1st household, this is expected. There is no justification for a modification to the basic formula here.
Example 1b: PWC doesn't earn, NRPpartner earns
PWC has no income, 2nd family parents earn £300, 2 children (under 11) in each family.
1st family PWC spends £9 on children, retains £36.
1st family NRP spends £60 on 1st family children, £60 on 2nd family children, and retains £180.
2nd family other parent spends £64 on children, and retains £256.
1st family children receive the equivalent of £69.
2nd family children receive the equivalent of £124.
1st family retains £36 after spending on the children.
2nd family retains £436 after spending on the children.
Conclusion: "PWC not working" is a common case. Here, the 2nd family children are much better off than the 1st family children. The 2nd family has vastly more to spend after looking after the children than the 1st family. A 2nd family modification would be a injustice added to a deprived situation for the 1st family.
Example 1c: PWC & NRPpartner don't earn
NRP earns £300, other parents don't earn, 2 children (under 11) in each family, hence Income Support for PWC.
1st family PWC spends £5 on children, retains £20.
1st family NRP spends £60 on 1st family children, £60 on 2nd family children, and retains £180.
2nd family other parent spends £4 on children, and retains £16.
1st family children receive the equivalent of £64.
2nd family children receive the equivalent of £64.
1st family retains £16 after spending on the children.
2nd family retains £196 after spending on the children.
Conclusion: given the bias towards the 2nd family there is no justification for a modification to the basic formula here. The 1st family are at poverty levels (they are probably totally dependent on Housing Benefit & Council Tax Benefit), and any modification would be unjust.
Example 1d: PWC earns much more than NRP
PWC earns £600, NRP earns £300, NRP's partner doesn't earn, 2 children (under 11) in each family.
1st family PWC spends £124 on children, retains £496.
1st family NRP spends £60 on 1st family children, £60 on 2nd family children, and retains £180.
2nd family other parent spends £4 on children, and retains £16.
1st family children receive the equivalent of £184.
2nd family children receive the equivalent of £64.
1st family retains £496 after spending on the children.
2nd family retains £196 after spending on the children.
Conclusion: (this is a rare case). The difference between the households in retained income is exactly the same as the difference in earned income. The PWC actually spends more than twice as much as the NRP on the 1st family children (although the difference arises from Child Benefit). The 1st family children are much better off than the 2nd family children, but this is simply because the 1st family parents earn three times as much in total as the 2nd family parents.
Examples 2: NRP on low pay or no pay
If the NRP has low pay or no pay the 2nd family is likely to be deprived (although this depends on the partner's earnings). It may appear that compensation for this is needed.
But in these cases the standard maintenance liability is £5, so no modification to the formula can make much difference. The problems of the 2nd household have to be catered for some other way.
Examples 3: Difficult cases
Example 3a: 2nd family with inflexible commitments
The NRP retains 85/80/75% of net income according to the standard formula. If a family really does cost 15/20/25%, this should normally be enough. But if the NRP has commitments (plus essential living expenses) that amount to the full 85/80/75%, there is no scope for a 2nd family (unless the new partner earns enough).
It is essential to avoid the impact of retrospective liabilities which drive the NRP into poverty (or worse) without time or options to adjust (as happened in 1993 with the current CSA scheme). Options include: apply a 2nd family modification for this case; or ensure that changes are phasedin over sufficient time for the NRP to adjust.
Example 3b: NRP has significant arrears
This is similar to example 3a, if there is no flexibility over the arrears. Perhaps similar options apply, or some arrears can be delayed or cancelled.
Appendices
Appendix A: Benefits
This paper analyses child support liability without reference to meanstested benefits such as Income Support.
The reasons include:
 many CSA cases (about 15%) are private, not involving benefits
 the influence of the formula on nonbenefit cases extends beyond this, because a suitable formula can help other nonbenefit cases come to private arrangements, in the knowledge of what would happen if they did involve the CSA
 benefitPWCs may move off benefits in future, eg. as a result of Government programmes such as New Deal
 starting off relying on benefits is a form of benefit dependency, which is known to lead to unemployment traps and poverty traps, encourage fraud, and generally lack incentives towards socially acceptable behaviour
 it is more likely to be the PWC rather than the NRP who is on meanstested benefits, and therefore relying on meanstested benefits tends to make the 1st family children appear less important than the 2nd family children, which is unacceptable
Meanstested benefits must be seen as lastresort povertyrelief, not as the basis on which child support is designed. They can be paid as a topup after the assessment if necessary.
Appendix B: International experience
This is restricted to the Englishspeaking "Western" world.
Nations/states known to have a 2nd family modification
New Zealand:
(A living allowance is subtracted from gross income before applying the formula; the living allowance is bigger if there is a 2nd family).
Hawaii:
("These guidelines consider ... other dependants ...").
Indiana:
("... there should be an adjustment to Weekly Gross Income of parents who have natural or legally adopted children living in their households that were born or adopted subsequent to the prior support order").
Massachusetts:
("The guidelines allow the judge to consider whether the noncustodial parent has another family to support").
Wisconsin:
(Appears to be based on time sequence; a later 2nd family won't affect an earlier assessment, but a late assessment will take an existing 2nd family into account).
Nations/states apparently without a 2nd family modification
Further investigation may reveal that some of these have a 2nd family modification.
Canada:
Alaska:
California:
Colorado:
Florida:
Maryland:
Minnesota:
Hennepin County (Minn):
Nebraska:
New York:
North Carolina:
Oklahoma:
South Carolina:
South Dakota:
