Roger F. Gay, PICSLT, September 28, 1999
 

Changes:

990930: Added simplified versions of the equations.
991007: Added the general formula for cross-crediting (section 9
991007: Added the Conclusion (section 10)
991007: General editing of the text
991007: Added examples using the simplified cc formula
 

The basic formula for adjusting a child support award to account for visitation or shared parenting is relatively simple. The form of the equation does not depend upon one's views with regard to whether the adjustment should be made directly in relation to time children spend with each parent because "fixed" and non-fixed expenses can be treated separately. Nor does the calculation depend on the type of legal custody. The form of the cross-crediting equation is constant. Adjusting the outcome for fixed expenses and other variable policy considerations will also be discussed.
 
 

Sections:

Introduction

What is wrong with a simple credit?

What is cross-crediting?

A very simple example

A second example

A better model of Ability to Pay and what it means in practice

Fraction of what?

Comment

A More General Cross-Crediting Formula

Conclusion

Introduction

In his book; Divorced Dads: Shattering the Myths, Sanford Braver recounts a court case in which children had nearly equal time with each parent. The "mother" (mother) had the children only one night per week more than the father. Both parents had a reasonably good income, yet this small difference in the parenting schedule meant that the father was making a large child support payment each month. The court recognized that if the parenting schedule was shifted by only one night per week, the mother would instead be paying a relative large amount. It was easy for the court to recognize that one night per week could not reasonably account for such a huge difference in the child support award.

The case described above illustrates one of the problems in child support guidelines today. Popular designs do not accurately account for circumstances of parents and children. Thus, the method of accounting for support contributions by both parents described here is quite relevant to a necessary discussion on calculation of child support awards.

The traditional cross-crediting method was developed in the context of children's need to have a primary home. Some old statutes specifically stated that child support is an amount paid by the parent not awarded custody to the custodial parent. The entrenched notion underlying the traditional cross-crediting formula is consistent with the traditional concept of child support; that it is a reimbursement for expenses in the primary home.

A dramatic shift in the view of custody is taking place, virtually worldwide. New research shows that contact between both parents is extremely important to child development. The presumption that joint custody is best whenever possible and that children are better off spending more time with the other parent is the norm in more countries than ever before. The section entitled, "A More General Cross-Crediting Formula," the assumption that child support is a simple reimbursement to a primary or custodial parent is changed. The result is a more general cross-crediting formula. Until then however, this report is concerned with the special version of cross-crediting that fits the traditional reimbursement philosophy of child support awards.

The method described below for adjusting child support awards to account for visitation and shared parenting can be used with any child support calculation method, percent-of-income, Income-Shares, cost sharing, Melson, PICSLT, or whatever. However, PICSLT has consistently criticized many of the models mentioned above and strongly recommends rejection of - especially - percent-of-income, Income-Shares, and even simple cost sharing models except when appropriate. State courts are beginning to recognize in the post-federal-reform era what they had consistently recognized in the pre-federal-reform era. That which we call "child support" should be for the purpose of supporting children. Therefore, arbitrary methods such as percent-of-income and the currently popular Income-Shares model must surely go out of fashion.

As with all the work presented by PICSLT, this formulae and analysis presented in this paper are based on the following three principles.

Child support is for the care and maintenance of children.

Both parents have an equal duty to support their children.

All relevant circumstantial information may effect the amount of the award

For an earlier discussion on cross-crediting, see How to Calculate Child Support, Maurice Franks, Case & Comment, January-February, 1981.
 
 

What is wrong with a simple credit?

Simple credit for visitation might be defined as deducting an amount from the payment to account for the expenses paid directly by a non-custodial or non-primary parent during visitation. Credit for the time children spend with the parent that pays child support is especially well justified when the "visitation" results in financial relief for the child support recipient who would otherwise pay the expenses. If credit is not given, one would have to ask why one parent is paying the expenses directly while simultaneously reimbursing the other parent for those same expenses.

An equation for a simple credit is easy to create. If we give simple credit, the parent that pays child support (ncp) would pay to the recipient parent (cp) his or her share of the cp's child raising expenses in proportion to the ncp's ability to pay. The simple credit equation is simply the ncp's relative ability to pay times the fraction of time the children spend with the cp. The result of the simple credit equation would be multiplied by the total child support need. The total child support need is the total that would be needed by the custodial parent amount (from both parents and any other source such as welfare) to support the children if the children live full time with the custodial parent (i.e. no visitation).

RAPncp = Relative Ability to Pay of the person who normally pays child support
Fcp = Fraction of time the child(ren) spend with the parent who normally receives child support
 

For example, let us say that total amount that is required to support a child full time in the custodial parent home is $400 per month. This means that the total contribution from both parents needs to be $400 per month to meet the needs of the child(ren). The children spend two weekends and every Wednesday night with the non-custodial parent, which we take to be 0.2 of each month (in terms of meal count). Calculating strictly in terms of time, 20% of the expenses are borne out-of-pocket by the non-custodial parent. (This strict time assumption is changed in the section below entitled; "Fraction of what?") The non-custodial parent should then only be reimbursing the custodial parent for his or her fair share of 80% of the total expenses.

The fair share is also taken to be in proportion to each parent's ability to pay. Let us say that the non-custodial parent has twice as much ability to pay (discussed below) as the custodial parent. The ncp's normal contribution then should be two thirds of the total child support need. (Her once plus his twice is three of something.) The ncp's contribution, taking the visitation credit into account should be:

The fraction of the total child support need that the non-custodial parent should pay is two-thirds of two-fifths (0.8) of the total. (In the sections below, the fraction reimbursed to the custodial parent will be called the "Adjusted Fraction.")

Put another way: For the 80% of the time the child is with the custodial parent, the theoretical cost is 80% of $400, or $320. Using the simple credit approach, the non-custodial parent pays her a share in proportion to his relative ability to pay. He pays two-thirds of $320.

She receives $213.33 as a child support payment, leaving $106.67 of the total need of $400. This is exactly the amount we would get if we applied the formula, using one third (her relative ability to pay) times 80% of $400.

The non-custodial parent also pays out-of-pocket support during visitation. Assuming he spends at the same rate, it costs him 20 percent of $400 out-of-pocket; i.e. $80.

The monthly cost for the non-custodial parent would include $80 per month in out-of-pocket expenses plus $213.33 paid in child support, for a total of $293.33. We have said though that the non-custodial parent should pay two thirds, and that the custodial parent should pay one third in proportion to their abilities to pay. That is to say that the non-custodial parent should provide twice the amount of support because he has twice the "ability to pay." In fact, he would pay nearly three-quarters. (0.73 verses 0,67)

Obviously, something isn't quite right. Using the simple credit, the non-custodial parent's contribution is more than twice as much. The equation needs to be adjusted. What has been left out is the custodial parent's contribution to child support while the child is with the non-custodial parent.
 
 

What is cross-crediting?

The equation for credit for visitation and shared parenting can be seen as involving two parents, just as the rest of the child support calculation should be. Which parent reimburses the other depends at least partly on who is paying the expenses out-of-pocket. Normally, this means that the non-custodial or non-primary parent pays the custodial or primary parent. Cross-crediting applies the same logic to expenses paid out-of-pocket by the parent that usually pays child support. It credits the payer for out-of-pocket expenses and also accounts for the custodial parent's share of those expenses.

The custodial parent's share of the expenses that are paid out-of-pocket by the non-custodial parent is in proportion to the amount of time children spend with the non-custodial parent (Fncp) and her relative ability to pay (RAPcp).

The expanded form of the cross-crediting equation is constructed by subtracting the cp's share of his out-of-pocket expenses from the simple credit equation above.

This Adjusted_Fraction is the fraction of the total support need that should be paid by a non-custodial parent to reimburse the custodial parent once visitation or shared parenting arrangements are accounted for.

The most popular child support guideline formula in the United States today, uses income to represent ability to pay. Relative income is then used in place of relative ability to pay. The equation for calculating relative income is:

A better model of ability to pay and the consequences of its use will also be discussed below. (See also, New Equations for Calculating Child Support and Spousal Maintenance With Discussion on Child Support Guidelines)

By recognizing that the relative ability to pay of both parents must sum to one (RAPncp+RAPcp=1), and that the fraction of time children spend with each parent must also sum to one (Fncp+Fcp=1), the equation can be simplified.

The simplified form of the equation is:

In application, the Adjusted Fraction is multiplied by the total child support need (N).

Put another way:

If the award were not adjusted for visitation time at all, it would be equal to the first half of the equation. The non-custodial parent would pay a part of the total need in direct proportion to his relative ability to pay. The credit given in the cross-crediting formula is for that portion of the total need that he pays out of pocket while the children are in his care.
 
 

Introduction of the cross-crediting formula: A very simple example

An initial assumption is made that cross-crediting is done directly in proportion to the time children spend with each parent. (Deviating from this assumption is discussed below, in "Fraction of what?") In this first simple example, the parents' have equal ability to pay. Therefore, the relative ability to pay (RAP) of each parent is the same; equal to one half. Let us say then that a child spends one half of his/her time living with each parent.

The first part in the cross-crediting formula is:

Using the values given;

The terms given represent the non-custodial parent's relative ability to pay times the amount of time the child spends with the custodial parent. In this case, the amount the non-custodial parent would provide to the custodial parent would be one half the amount needed to support the child for one half the time.

The second part in the cross-crediting formula is;

In this very simple example, the second term gives exactly the same result. The custodial parent's relative ability to pay is also one half, and the fraction of time the child spends with the non-custodial parent is also one half. So the second set of terms yields the same result as the first.

The intuitive interpretation is that the custodial parent (a term that is actually inappropriate in this example, although the mathematics are not) owes as much to the non-custodial parent in child support as the non-custodial parent does to the custodial parent.

Returning to the full cross-crediting formula, the result of the second set of terms is subtracted from the first.

The Adjusted_Fraction is the fraction of an award that should be paid by the non-custodial parent. In this simple example, the answer is quite intuitive. The result of cross-crediting in relation to time, when both parents have equal income, and the child spends equal amounts of time in both households is cancellation of payment.

To apply the cross-crediting formula, an award calculated without consideration for visitation or shared parenting would be multiplied by the result of the cross-crediting formula. In this simple example, the amount of the initially calculated award would not matter. Any finite amount multiplied by zero is zero.

Of course, we could have arrived at the same conclusion using the simplified version of the cross-crediting formula.

Introduction of the cross-crediting formula: A second example

Let us for the moment continue to cross-credit in direct proportion to the time children spend with each parent. In this second example, we will use values that may seem typical in divorce cases and in updating awards.

Let us take the custodial parent's income (a mother in this example) to be equal to two thirds that of the non-custodial parent's income (a father). For example, the non-custodial parent's income is $30,000 per year and the custodial parent's income is $20,000 per year. (This should be net take home pay rather than gross, i.e. disposable income.) Their child spends one quarter of his time with the non-custodial parent and three-quarters with the custodial parent.

Using the simplified form of Ability to Pay (income), the non-custodial parents relative ability to pay is;

We can take a simplified approach to calculating the custodial parent's relative ability to pay (relative income) since the sum (RAPncp + RAPcp) must equal one.

The child (a son in this example) spends one quarter of his time with the ncp and three-quarters with the cp. In proportion to the time spent in each household, and with consideration for each parent's ability to pay, the Adjusted_Fraction (using the simplified formula) is:

This might at first not seem so intuitive. Could it be that the non-custodial parent should pay less than half the original amount when their son spends only one quarter of his time with his father?

Let us not forget however, that the ncp pays expenses out-of-pocket during visitation, which also contributes to his son's needs. During visitation, his share out-of-pocket expenses are estimated to be one quarter of the total child support need. His total contribution is therefore toward the total child support need is;

The result is exactly in proportion to the non-custodial parent's relative income.
 
 

A better model of Ability to Pay: What it means in practice.

In New Equations for Calculating Child Support and Spousal Maintenance With Discussion on Child Support Guidelines case citation and other references are given in support of a better model of Ability to Pay. Here it will be presented intuitively. Parents must be able to support themselves. They must survive if they are to take care of their children. Therefore, Ability to Pay is not equal to income. If 100% of a parent's income were used to support children, the parent would have nothing left with which to survive.

Ability to Pay is calculated by subtracting a basic self-support amount from each parents' net take home pay. For simplicity of example, $10,000 per year will be taken as the amount one adult living alone needs for basic subsistence. Using the second example above, Ability to Pay is recalculated.

The non-custodial parent's disposable income is $30,000. His ability to pay is

The custodial parent's disposable income is $20,000. Her ability to pay is

The relative ability of the ncp to pay child support is then;

The custodial parent's RAP is one minus the non-custodial parent's RAP, therefore one third.

Recalculating the Adjusted_Fraction;

The effect in this example is that the Adjusted_Fraction has increased. (0.42 verses 0.35) The importance of this effect is best seen in an example in which the custodial parent's income is closer to the poverty level for one adult. To be very simple, let's say that it is. It is easy to verify that the Adjusted_Fraction becomes 1. In other words, assuming the non-custodial parent can afford to pay, he will pay 100% of the amount that he would pay if his son spent no time with him, supporting both households no matter what.

If we use relative income instead, the subsistence income of the custodial parent would result in a positive fraction of the support obligation, which she cannot afford.

Ability to Pay is also a factor in calculating the amount that would be awarded if children spend no time with the non-custodial parent. Here again, low-income custodial parents, assuming the non-custodial parent can afford to pay, benefit from the improved definition of Ability to Pay.

The poor definition of Ability to Pay in the popular Income-Shares model has been one of its great weak points. Child support guideline designers have often improperly compensated for this weakness in design by making a second error. The numeric tables in Income-Shares guidelines used today (as well as others) have been shifted upward arbitrarily, resulting in awards that typically have no relation to the parents' ability to pay or children's needs.
 
 

Fraction of what?

Some people do not agree that visitation credit, or even shared parenting credits should always be given strictly in proportion to the amount of time children spend with each parent. For one thing, they say, not all expenses transfer from one household to the other with the children. In particular, the housing payment for the children's primary residence must still be made regardless of which home the children are in just now. A day-care payment might also continue to be made by the parent who has the agreement with the day-care center, regardless of which home a child was in the night before. The same might be true when paying for health insurance.

Dealing with fixed expenses is not particularly difficult. It should first be pointed out what not to do however. It has been fairly popular, due to the recommendation of a single child support collection entrepreneur, to multiply the total child support amount by 1.5 before performing the calculation to credit visitation and shared parenting time. This is said to reflect his estimate that approximately 50 percent of child related expenses are fixed. A reader who has gotten this far, understanding the algebra in this section might reasonably be expected to recognize the flaw without further discussion.

There is of course, no logical reason to increase the amount needed by the child support recipient.

Another explanation given for multiplying the basic award by 1.5 is that it accounts for the increased cost associated with two households. It means that each household has a fixed child related expense (housing etc.) equal to 50 percent of the total child support need. Fifty percent times two households is 100 percent. Then there is the other 50 percent of the basic child support award that is spent where the children are (food, entertainment, etc.) The total then is 150% of the base amount -- thus the 1.5 multiplier.

It is quite well understood however, that child support is basically an amount paid by one parent to reimburse the other (plus an sol adjustment). What the multiplier accomplished however, is to increase the amount paid to the recipient for time children spend with the payer. This is nonsensical of course, since his own household expenses should not in any case be reimbursed to the parent that doesn't pay them.

The rational approach is to calculate payment for fixed expenses separately. Let us take a simple example in which a custodial mother's income is quite low. The judgement is to account for the fact that she needs 50 percent of the total child support amount full time so that she can continue making housing and car payments. It is quite simple mathematically to award the mother 50% of the child support award unadjusted plus some portion of the other 50 percent after adjustment for visitation.

(In cases in which the custodial parent's income is much higher, or the fixed expenses are paid in partnership and to the advantage of a spouse, fixed child related expenses may account for a much smaller fraction of the total need. The Arizona State Child Support Commission recently estimated an "average" percent of fixed expenses at 31.5 percent. (Source: "Divorced Dads: Shattering the Myths," Braver, page 71) The Oregon Supreme Court pointed out that at higher income levels "the needs of the children in reality do not increase in proportion to the increases in the parent's ability to pay." Smith v. Smith, 626 P2d 342, 1981)

If for example, the total child support need is $300 per month, the mother would receive the father's share of $150 per month, non-adjusted, plus some portion of the other $150 after adjustment for visitation.

For example, let us say that his ability to pay child support is three times hers. His relative ability to pay is three-quarters. He then pays a fixed $112.50 (three-quarters) of the fixed expense of $150. The mother's fixed share of that amount is $37.50 per month. We then apply the cross-crediting formula to the other $150. This is the portion of the total need that is not fixed, which will be referred to as the roving portion of expenses. Let us say that he has the same visitation schedule as in the example above, with a time division of 0.2 / 0.8.

The remaining $150 is multiplied by 11 divided by 20. The result is $82.50. The total amount to be awarded is then $112.50 plus $82.50, which is $195 per month.

The cross-crediting equation with a fixed expense set aside is:

The term Fixed is the fraction of expenses that the payer must continue to supplement to the recipient even while the children are with the payer. The term Roving is the fraction of expenses that transfer during visitation.

Recognizing that Fixed plus Roving must sum to one, the equation can be simplified, as the time version was above.

The example above could be calculated using the simplified form as follows.

 
 

There are other types of fixed expenses, that are quite often treated as "add ons." One example is the expense of day care. Dealing with expenses that are not included in the basic award calculation should be treated differently.

Let us say that a custodial mother pays $300 per month to a day care center regardless of how much time a child spends with each parent. This is the full amount of the day care payment. The non-custodial parent is paying nothing directly to the day care center. We will say that his ability to pay is twice that of hers. Assume his ability to pay is twice hers. (RAPncp=2\3 and RAPcp=1\3)

The share of the day care expense that he should reimburse to her is two-thirds of $300 ($200) regardless of the amount of time the child spends at his house. Her share is $100 per month. We would then deduct $200 from his monthly income and $100 from her monthly income because the expense of day care has reduced their actual abilities to pay for other things by those amounts. Their remaining income would be used to calculate the child support need in the same way as it would if there was no day care expense. The cross-crediting formula would then be applied to this child support need as before. The total award would be the result of that new calculation plus his $200 per month for day care.
 
 

Comment

Cross-crediting is not a new idea. Franks (see citation in the Introduction section) explained it in a paper in 1981 and it had been used by lawyers and judges before then. To someone who has thought through the logic, it is relatively obvious and not particularly difficult to derive.

The mathematical steps explained above should be sufficient to deal with most adjustments to child support awards to account for visitation and shared parenting arrangements. Do you think so?

What, you might ask yourself, should be done if the non-custodial parent is paying part of the day-care bill directly? Such might be the case when a young child has longer visits with a non-custodial parent who lives in a different state. If you have mastered an understanding of the mathematics above, you will probably feel that the answer is easy, or at least obtainable given enough effort.

There are 200 years of history behind traditional concepts and practices related to the award of child support in the United States. We have recently been thrown onto another track by federal interference, but this too shall pass. I would recommend to anyone wishing to be a real expert on child support to look to the statutes, and cases, and literature prior to 1985 before making judgments about policies and child support guidelines currently used in the states.

I would also recommend Sanford Braver's book; Divorced Dads: Shattering the Myths. Federal reforms dramatically changed the way that child support is determined. The myths produced by political propaganda that led to those reforms ought not to be an integral part of an expert's opinion.

A long-standing problem has recently been solved. In 1994, the mathematical solution to the standard of living adjustment problem was first presented; in the paper New Equations for Calculating Child Support and Spousal Maintenance With Discussion on Child Support Guidelines. The paper can be found by clicking on the hot-link on the project description and citations page. The PICSLT web site is located at the following www address.

http:www.geocities.com/CapitolHill/5910/index.html
 
 

A More General Cross-crediting Formula

When a child support commissioner in Kansas (Jim Johnston) reviewed my explanation of cross-crediting, he immediately responded with a request. "Now do it taking into account all factors in both households."

I admit that at first I felt slightly bemused. I had thought of doing it before, simply because not doing it seemed an incomplete review of the theory. I always felt pressed by what I thought to be more practical matters however, and politely told Jim Johnston that it would have to wait for another day.

Take for example, the idea of "fixed costs." There are some fixed costs that can and should be handled outside the cross-crediting formula, so they present no problem in applying a more general formula. Those other fixed costs seemed to present a problem.

My concept of fixed costs in the cross-crediting formula apply to situations in which a custodial parent needs continued reimbursement for expenses that continue even when the children are somewhere else. This idea fits the notion of reimbursement and that child support is related to the need children have of a primary home.

The appropriate need definition relates to the actual circumstances in which children live. Nothing else makes sense. It is no problem to extend the theory by using two different values of need, one for the primary residence and one for the other. But what if the paying parent spends much more per unit time on children than the recipient? Wouldn't a requirement for the primary parent to pay a fair share of a higher per unit cost in the other household than she normally spends further degrade the standard of living in the primary household?

Jim Johnston told me that he had already been through the exercise with a particular case example. In the case he considered, the income of the two parents were not far apart. Both made a reasonably high income. The mother, who had been designated as the primary parent in a joint custody arrangement, had remarried. Although the child support guidelines did not take her spouse's income into consideration, the primary household actually had a much higher standard of living than that of the payer.

The joint custody agreement provided very close to equal time living at each parent's home. In this situation, the concept of fixed costs in the primary parent household did not seem to fit the design concept of a relatively poor single mother who needed continued reimbursement to maintain the primary household even when the children were gone. In fact, the new household might best be considered as the property of the new couple, and much less the responsibility of the former spouse to maintain.

Considering such a scenario made it seem less appropriate to apply the reimbursement philosophy in all cases. With more emphasis (world wide) being placed on joint custody these days, it began seeming quite improper to restrict the vision used in calculating child support awards to one of simple reimbursement.

The standard of living in the primary residence in the case considered by Jim Johnston is not a problem. In my view, the percentage of fixed expenses should depend upon need. Low-income households spend a higher percentage of their income on housing. It is also clear that a low-income single custodial mother needs more help from a father in maintaining a household than an upper middle class remarried mother.

High-income households have a lower child related cost (as a percent of expenditure). Most truly child related costs in higher income homes are not fixed. Expenditure on housing does not typically increase as a result of children in the household. In fact, at income levels somewhere in between high and low, families spend less on housing as family size increases. Additional expenditure on transportation is primarily a function of the miles driven to transport children and not the size of the car or insurance payment.

Thus, it initially seemed to me to be fair enough to set fixed expenses to zero and apply the simplest cross-crediting formula for reimbursement.

Child support formulae in common use today however, do not provide for such fair share calculations. Many states actually increase the payer's obligation as part of their method of calculating visitation credits (multiplying the value from the numeric table by 1.5 for example). In addition, cost tables provide a generous standard of living increase for the custodial or primary parent.

Sanford Braver tells in his book, Divorced Dads: Shattering the Myths (page 72) about a 1997 New York Court of Appeals decision in the similar case of Gregory and Diane Holmes. The Court noticed that a change of only one night per week in the children's scheduled time in each household would make Gregory the primary parent. Child support had been set according to the state formula. Gregory had been ordered to pay Diane a little over $12,000 per year. A change of one night per week in the living arrangement would have meant that Diane would have been ordered to pay Gregory a little over $10,000 per year instead.

The Court recognized that a difference of $22,000 per year in child support was too much for only one night difference in the living schedule. They determined that Gregory and Diane were simultaneously both custodial and non-custodial parents. They applied the formula both ways and ordered each to pay the other. Perhaps in anticipation of the need recognized by the New York Court of Appeals, guideline designers really do need a more general cross-crediting formula.

Perhaps the results of a new PICSLT study will help put the question in perspective (as of October 8 -- soon to be released). The new study, addresses speculation that visitation credit might "put a double incentive on fathers to push for, and mothers to oppose, more visitation, and may well encourage court battles over visitation schedules." (Braver, page 73)

The results of the new study might be a great surprise to some. Applying the reimbursement form of cross-crediting above, it was found that the child support recipient always either breaks even or benefits from a higher standard of living. Unless none of the expenses are fixed, the payer always pays more in proportion to the amount of visitation. In other words, in terms of economic advantage, there is no such incentive.

Jim Johnston and I are still discussing what the general formula really means and under what circumstances it should be applied. This is an excellent question for the discussion forum at the PICSLT web site. Here is the general formula.

N :: The dollar amount needed to meet children's needs in each household
RAP :: Relative ability of each parent to pay
R :: The "roving" portion of need; i.e. the portion that travels with children.
F :: The fraction of time children spend in each household
FX :: The fixed portion of need; i.e. the portion of that does not travel with children.
 

The general formula corresponds to the special reimbursement formula when we ignore the ncp's fixed expenses and focus only on the needs of the cp household. (The terms ncp and cp are still being used for convenience, especially in comparing them with the other equations.) In addition to setting FXncp equal to 0, the value of Rncp will be replaced by Rcp. That is, we regard spending in the ncp's household as being a replacement for the roving expenditure that would otherwise take place in the cp's household.

In the special formula for reimbursement, there is also only one value of N considered, which is the dollar amount needed to meet children's needs if the children live with cp full time. When checking for correspondence with the reimbursement formula, it is most convenient to set N to one. In the expression of the reimbursement formula above, it has been assumed that the method of application will be to multiply the result of the cross-crediting formula by the dollar amount needed. The same form of equation can be obtained by setting the value of N to one (to later be multiplied by a real N in application).

The special conditions required for the general formula to correspond to the special formula for reimbursement are;

Ncp=Nncp=1
FXncp=0
Rncp=Rcp=Roving
 

Using these values in the general cross-crediting formula yields the special formula for reimbursement.

If we then consider all expenses to be roving expenses, the special reimbursement formula takes the form of the cross-crediting formula first introduced in this paper. When none of the expenses are taken as "fixed," Roving equals one.

Following are a few illustrative examples comparing the special reimbursement formula with the general formula.

GenCC :: using the full general formula
GenCC :: using the general formula, with FXcp and FXncp set to zero and R=1.
CC :: using the special formula for reimbursement
CC0 :: using the special formula for reimbursement with FXcp and FXncp set to zero and R=1
 
 

Example 1

The first example illustrates correspondence between the two formulae when the correspondence conditions are met.

Circumstances 1:

When the correspondence Circumstances are met, GenCC and CC are equal. The two equations also give equal Recommended Awards when FXcp is set to zero. Therefore GenCC0 and CC0 are equal.

Recommended Award 1:

Example 2

In the second example, the correspondence conditions are met because the households are nearly equal. Since they both have relatively high income, FXcp and FXncp are both zero.

Circumstances 2:

In this circumstance, the award recommendations are equivalent.

Recommended Award 2:

Example 3

The third example is similar to the second, except that the parents' abilities to pay and their time with children are equal.

Circumstances 3:

Recommended Award 3:

Example 4

In the fourth example, the two parents are nearly equal in their abilities to pay and the need is the same in both households. They also have nearly equal time with children.

Circumstances 4:

The results of the formulae are equivalent when fixed expenses are set to zero. The results of the general formula are nearly the same whether the fixed expenses are used or set to zero. The greatest difference occurs in the reimbursement formula when fixed expenses are not zero.

Recommended Award 4:

Example 5

In the fifth example, the effect of fixed expenses is shown again. In this example the circumstances of the parents are equal, both in ability to pay and time with children.

Circumstances 5:

The results in example five show the effect of fixed expenses in the reimbursement formula.

Recommended Award 5:

Example 6

The sixth example shows what some researchers might in the past have referred to as a "typical" situation.

Circumstances 6:

Recommended Award 6:

Conclusion

Intelligent discussion on calculation of child support awards has been interrupted, at least temporarily, by federal intrusion into family law. The popular methods of implementing federal requirements for the use of child support formulae have no logical foundation. Even to the extent that a theoretical origin of a particular calculation can be traced, it is soon found to be ridden with technical errors. The most popular model, developed by the child support collections company, Policy Studies, Inc., does not contain a single component that isn't completely wrong.

Traditional law and practice typically emphasized the need of children for a primary home. In that context, sole custody became the most common arrangement for children of divorce in the United States. Certainly tens of millions and probably hundreds of millions of fathers and children have experienced a relationship on Wednesday nights and every other weekend.

Traditional methods of calculating child support awards also developed in this context. Mom's house has typically been presumed to be the best primary home. Dad's primary obligation to his children, so far as the courts and legislatures were concerned, was to reimburse mom with his share of her financial burden in raising the children.

Dad, and the importance of children's relationship with their dads, has finally received some attention by the research community. The findings are what reasonable people expected. The relationship between children and their fathers is extremely important to children. Thus, based on this new research, the world is turning toward more equitable custody arrangements for fathers and children.

When in the United States, the corruption and newly developed special financial interests that now provide great political resistance against this change have been dealt with adequately, one should expect that intelligent discussion on the methods of calculating child support will resume.

In anticipation of that discussion, some final questions are posed in this paper. Should practical economic factors and the needs of children be the only factors used to determine a child support award? If we filter out the arbitrary reward for being designated custodial or primary parent, and minimize the difference in the parents' legal status in all custody arrangements, would that minimize the effect that the child support award would have on custody preference? Would attorneys and judges and even the parents themselves have less resistance to fairly sharing the full responsibility of parenting?