# How “Economists” Calculate Child Support

By Dr. David Garrod

Nov 28, 2004, 02:31

Summary: What we want to know is the true cost of raising children as a function of the income of the parents. However no such precise data exist. We have to infer the cost of raising children from the consumer expenditure surveys (which were never intended to be used for this.) Once we have figured out the “cost of raising children” we can set up guideline tables and deduce which parent should pay what amount.

[Reprinted with permission, circa 1997.]

A Simplified Explanation of how the “Economists” Calculate Child Support

What we want to know is the true cost of raising children as a function of the income of the parents. However no such precise data exist. We have to infer the cost of raising children from the consumer expenditure surveys (which were never intended to be used for this.) Once we have figured out the “cost of raising children” we can set up guideline tables and deduce which parent should pay what amount.

The first problem is that children`s expenditure items are not separated out (except for child care and children`s clothing) in the consumer expenditure surveys. So what economists do is to use an interpolation technique based on the difference in costs between a family with children and a family without children at the same standard of living. This is often called the marginal cost technique. Depending on the economist (or his mood at the time of calculation) a measure for standard of living is chosen. In the Rothbarth technique the measure (proxy) for the standard of living is expenditure on adult-only goods. If the families with and without children spend the same amount on adult goods they are theorized to have the same standard of living. The difference in total expenditure between the family with children and the family without children, given an equal expenditure on adult goods, is considered to be the “cost of raising the children” in monetary terms.

Many different proxies for the standard of living have been used over the last century, but NONE of the proxies have ever actually been shown to measure the standard of living. Further, none of these marginal cost techniques have ever been shown to actually produce accurate figures for the cost of raising children.

To demonstrate the difficulty of developing marginal cost techniques, we will use an example of several proxies for standard of living and demonstrate that the specific choice of proxy will have such a dramatic effect as to invalidate the technique as a whole. The following calculation is simplified so as to be intelligible to anyone with an understanding of simple mathematics. Thus the actual numerical results should not individually be taken as meaningful, but rather that the extreme variation that can result should be taken as a demonstration of the difficulty/impossibility of choosing any appropriate measure of standard of living.

Further, to simplify actual numbers we will use percentages rather than explicit dollar amounts. Let us assume that, at the $25,000 family expenditure level, we obtain the following expenditure breakdown percentages from the Consumer Expenditure Surveys:

Expenditures | Family without children |
Family with two children |
---|---|---|

Housing | 28% | 28% |

Transportation | 31% | 25% |

Food at home | 8% | 13% |

Food away from home | 5% | 3% |

Clothing | 5% | 5% |

Health care | 3% | 4% |

Entertainment | 6% | 6% |

Retirement | 8% | 8% |

Child care | 0% | 2% |

Alcohol & tobacco | 2% | 2% |

other | 4% | 4% |

(These numbers are actually close to being accurate for young families: See Family Economics Review Vol 5, p 12, 1992) Let us assume the percentages are exact, with no rounding errors. Further let us assume the percentages remain the same if income is increased. These assumptions are not true in the actual CES data, but what we are trying to show here is the invalidity of the technique; we are not trying to obtain accurate numerical results.

Rothbarth technique:

Suppose we take percentage of expenditure on alcohol & tobacco as a measure of the standard of living. The two families spend the same amount on alcohol & tobacoo and thus have the same standard of living as measured by this proxy…thus the marginal cost of the children is zero.

Food away from home proxy:

Suppose we take food away from home as a proxy for the standard of living. This time the family with children would would have to have an income of $41,666 to spend the same on food away from home as the family without children. (5% of $25,000 = 3% of $41,666) (Again making the simplification of no change in percentages with income.) This time the marginal cost of two children is $41,666 – $25,000 or 40% of expenditures.

Transportation proxy:

Suppose we take expenditure on transportation as the proxy for the standard of living, further, for simplicity let us make the assumption (not valid in real life) that the expenditure percentages do not change as expenditure increases. The family without children spends 31% of $25,000 = $7,750 on transportation; the family with children would have to have an income of $31,000 to spend the same amount. (25% of $31,000 = $7,750) Thus with transportation as a proxy we could deduce that the marginal cost of children is $31,000 – $25,000 or 19.35% of expenditures.

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The reader should recognize the fact that the mathematics have been simplified, but that the concept of the results obtained is true. The choice of the proxy will substantially determine the marginal cost of the children. The accuracy of the result will, in fact, have little real connection with the true cost of raising children. There has to date been NO PROVEN VALID PROXY. There has to date, in fact, been no calculation of the cost of raising children which has been shown to be accurate or even almost accurate. All the marginal cost methods depend on a choice of proxy for the standard of living. All are non-proven.

The choice of proxies has varied over the last century. The inversepercentage of expenditure on food (Engel methodology) was first chosen, but this has since been shown essentially equivalent to the per capita method of attributing equal shares of the expenditure to each family member. The Rothbarth methodology (adult expenditures) typically produces results considerably lower than per capita. If housing costs were used, the apparent cost of children would go negative. (It would be zero on the above example.) (This is probably why no one has suggested using housing as a proxy, although almost everything else other than transportation has been suggested.)

Further, there are some assumptions which are often glossed over or incorrectly stated in papers discussing the cost of raising children.

We will explicitly now examine some of those assumptions.

Inherent in any marginal cost technique for measuring the cost of raising children, it is assumed that the lifestyles of parents without children are the same as those with children, except for the cost of children and the effect this has on consumption. This assumption can be stated in various ways, but basically comes done to a statement that parents with or without children are assumed to have the same value system, the same spending patterns were it not for the effect of the children.

I would suggest this is not a valid assumption, and its effect of non-validity will vary depending on the proxy chosen. For example, studies have shown that adult consumption of alcohol and tobacco may decrease after the family has children. (Some mothers have been known to give up smoking totally after the arrival of a baby.) Thus the consumption of adult goods may well be affected by lifestyle decisions which are unrelated to economics. If the reduction of consumption of adult goods were true and of a significant amount, then the Rothbarth proxy could seriously over-estimate the cost of children. (The reader should contrast these thoughts with comments made by Lewin/ICF that suggest that substitution might cause the Rothbarth choice of proxy to under-estimate the cost of children.) As a further comment regarding substitution; most authors assume that substitution takes place in a manner which would indicate a selfish nature of the parents. That is to say that parents might change their consumption patterns so that when they have children they buy more goods that adults might use more of than children. If this were to be true, the marginal cost of children might underestimate the cost of children.

However, the very same authors when comparing the cost of raising children in single parent families versus two parent families often explain their conflicting results by saying that the single parent chooses to spend more on the children and deprive themselves out of unselfish behavior. I would suggest there is a conflict on the one hand of suggesting two parents act in a selfish way but that on the other hand a single parent tends to act in an unselfish way. This is in direct conflict with human nature and observations of parents with children. On average the tendency should be in the same direction regardless of marital status, and the tendency is that parents with children tend to be less selfish than parents without children. The less selfish tendency of parents thus yet again suggests an error in the direction of an over-estimate of child costs, not an under-estimate.

Finally many economists have given a reason for validity of their particular pet calculation as being correct becuase it lies within the bounds of reasonable limits. They cite Rothbarth as a lower bound because of substitution and Engel or Espenshade as an upper bound because it is essentially per capita or equal shares. Both bounds are wrong. First the Rothbarth or adult items proxy is not a lower bound, because first substitution if it takes place is probably not (according to sociologists) in the direction in which economists suggest. Secondly economists have overlooked behavior pattern changes on having children which would tend to reduce not increase adult item expenditure. Both of these effects suggest that Rothbarth techniques would over-estimate child costs. There is no calculation representing a lower bound at this time. Thirdly, it obvious that per capita or equal shares estimates would totally overestimate child raising costs. In fact, they so over-estimate child raising cost that to suggest such estimates represent upper bounds is a true but utterly useless statement. The upper bound is simply too high to be useful.

A better upper bound might be the Family Economics Research Group calculations of Mark Lino, et al. Here the economist attempt to actually estimate the costs directly. The results are known to be in error and by the authors own admission, when in doubt they choose to err on the side of an overestimate. Lino`s results are in error because two of the higher cost items, namely housing and transportation are estimated on a per capita calculation with some minor adjustments. To use Dr. William`s comments in Georgia recently; “If a single adult can rent a one-bedroom apartment for herself/himself at $400 per month, and a two bedroom apartment for a single adult with a child is $450 per month, the per capita cost is $225 per month, but the marginal cost, the true cost we should use in child support calculations, is $50 per month.”

Given significant errors in housing and transportation on the high side in the FERG calculations, not only should it be realized that the FERG calculations represent an upper bound, but, in fact, this upper bound is probably more than 20% too high. One cannot, of course, justify at this point in time the 20% number without actually knowing the true cost of raising children. It should be noted that spending patterns on housing do not show a strong correlation with the number of children. Most families tend to spend about the same fraction of their income (about 30%) on housing regardless of the number of children.

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