# Fatal Accident Dependency Calculations

This article was originally published in the winter 1999 issue of the Expert Witness.

We occasionally review cases in which the defendant is arguing that, after a fatal accident, the surviving spouse is financially better off. This sort of argument can be somewhat appealing in certain circumstances, but upon closer examination the “logic” is always unsupportable. Of course, I am referring to the distinction between sole- and cross-dependency. In this article I will briefly explain what dependency rates represent, and then offer a fairly detailed explanation of the differences between the sole-dependency approach and the cross-dependency approach.

Dependency rates are used to estimate a person’s financial loss due to the death of his or her spouse or parent. In a two-person household, if the husband dies, then the wife will no longer benefit from her husband’s income. However, she does not need to be compensated for the loss of all of his income, since some would have benefited him only.

To properly compensate the surviving dependant, it is necessary to determine how much of the deceased’s income the survivor needs in order to maintain the same standard of living as if the accident had not occurred. To make this determination, one must estimate how much of the deceased’s income would be allocated to common expenditures (mortgage payments, for example), and how much would be allocated to each spouse’s personal expenditures (food, clothing, and hobbies, for example). Our research suggests that, in general, about 40 percent of after-tax family income is allocated to common expenditures, and 30 percent to each spouse’s personal expenditures. We make the reasonable assumption that each spouse allocates his/her income in this manner. Thus, the surviving spouse requires approximately 70 percent of the deceased’s “without-accident” income, in order to maintain the without-accident standard of living. That is, the survivor still needs the 40 percent of the deceased’s income that would have been spent on common expenditures, as well as 30 percent that would have been spent on the survivor’s personal expenditures, but does not need the 30 percent of the deceased’s income that benefited the deceased only. The 70 percent is the dependency rate. Thus, I would argue that if the deceased would have earned \$30,000 per year (after taxes and contingencies), had the accident not occurred, then the survivor now needs 70 percent of this income, or \$21,000 per year in order to maintain the without-accident standard of living.

This approach – known as the sole dependency approach – is very appealing in many cases, thanks to its simplicity and the intuitively reasonable results that it generates. However, it is often argued that it needs to be modified in order not to over-compensate the survivor. The issue is how to treat the survivor’s income that would have benefited the deceased only. One might argue that the survivor’s lost share of the deceased’s income should be offset against her financial “gain” because she no longer spends money on items which benefited her husband exclusively. This is known as the cross-dependency approach.

I will attempt to more clearly explain the distinction between sole- and cross-dependency through a series of tables in which we consider a range of possible incomes earned by a hypothetical couple. (For the purposes of this article, I ignore the effect of dependent children.)

Table 1 illustrates how a couple’s income is allocated among the three broad expenditure categories, for a range of different income levels. (The reason why several different income levels are presented will become apparent later.)

We can take the examples shown in Table 1 a step further by examining the more general case in which we consider the income earned by both members of the household. This is shown in Table 2. Note that the “total family income” figures in Table 2 are exactly the same as those in Table 1. As are the spending allocation figures.

We can take this example another step further by considering how each member of the household allocates his/her income. Presumably, both spouses follow the 40/30/30 percent pattern when spending their income. Thus, each allocates about 40 percent of his/her income to common expenditures, 30 percent to his/her own personal expenditures, and 30 percent to the spouse’s personal expenditures. In Table 3 I follow the examples from Table 2, except that I show the allocation of spending by each spouse. Note that the “total family income” figures in Table 3 are exactly the same as in Tables 1 and 2, as are the totals of the individual spending allocation figures.

Using the figures shown in Table 3, I can estimate the survivor’s financial loss upon the death of his or her spouse. It is clear that for the survivor to maintain the same standard of living as if the accident had not occurred, he or she will need enough income to fund the common expenditures shown (columns c & d), as well as the expenditures that were for his/her own personal benefit (columns g & h). Thus, what the survivor has lost, due to the death of his or her spouse is the sum of columns c and g. (The survivor has not lost columns d and h because he or she is still earning the income to pay for those expenses.) This is the sole-dependency approach.

The cross-dependency approach asks the question, “What should happen with the share of the survivor’s income that the survivor would have spent on the deceased (column f)?” The cross-dependency approach finds that this income has been saved, and should be offset against the sum of columns c and g. It finds that the survivor’s loss equals c + g – f. (Instead of just c + g, which is the finding of the sole-dependency approach.)*

Note that the dependency losses using either sole- or cross-dependency are always reported as the total of c + g – f (for cross-dependency) or the total of c + g (for sole-dependency). This is conventional, but it would be equally reasonable to report the individual components under separate heads of damage. For example, considering the top row of Table 3, the results could be reported as follows:

With the total cross-dependency loss separated into its individual components (above), it is clearer why I disagree with that approach. First, I do not believe that it is economically correct to deduct the portion of the survivor’s income that would have been allocated to the deceased’s personal expenditures (\$10,500) from the other components of the loss. Second, I do not believe that this deduction is consistent with other forms of personal injury damage assessment.

From an economic standpoint, I do not agree that the survivor’s income that would have been allocated to the deceased’s personal expenditures (\$10,500 in the above example) should be deducted from the other components of the loss. I think most would agree that individuals spend part of their income on their spouses because they want to – in economic terms, they receive an offsetting benefit. Following the death of a spouse, the best that a survivor can do is spend this money on alternative goods. But, since the survivor had previously chosen to spend this money on his or her spouse rather than these alternative goods, these goods must represent a “second-best” choice. For example if a surviving wife had previously been spending \$3,000 on goods which benefited her (now deceased) husband alone, and she now spends that money on alternative goods then, at best, that expenditure leaves her no better off than before. She has simply transferred the \$3,000 from one set of expenditures to another. Hence, the \$3,000 should not be offset against her loss of dependency.

It is my view that the correct way to compensate the survivor in this case is for the defendant to provide her with the income contribution that her husband would have made, had the accident not occurred (that is, the contributions to common expenses and to expenses which benefited the survivor only). The portion of the wife’s own income that would have been spent on her husband should remain available to be spent elsewhere at its second-best use (on holidays, gifts, charitable contributions, or whatever). From an economic standpoint, this will not leave the survivor financially better off. To argue in favour of cross-dependency, one must surely explain why the survivor is expected to use a portion of her own employment income to offset the defendant’s obligation.

I also do not believe that the deduction component of the cross-dependency approach is consistent with other forms of personal injury damage assessment. Cross-dependency requires that a plaintiff’s losses due to an accident should be reduced by any “savings” due to the accident (see the discussion above). Similar “savings” are seen in other forms of personal injury damage assessment, but are not deducted from losses. For example, plaintiffs who will be forced to retire early (or are unemployable) due to their injuries will “gain” a great deal of leisure time during the years when they otherwise would have worked. The value of this gain in leisure is not deducted from their losses. A father who was injured in a car accident that killed his son will now “save” the money he would have spent on his son. That savings is not deducted from the father’s loss of income award. Quadriplegics will “save” money on shoes, golf memberships, ski passes, and so forth. That savings is not deducted from their other losses.

Another difficulty with the cross-dependency approach is that if one follows the methodology consistently, it leads to indefensible results in many cases. Following the examples shown in the tables above, we see – below – that if the deceased’s income was much less than the survivor’s then cross-dependency will show that the survivor’s loss is negative (a net gain).

As shown by the examples in Table 4 (above), the sole dependency approach yields results that are, intuitively, much more reasonable, given a wide range of income assumptions. The sole-dependency approach will never find that a survivor is financially “better off” following the death of his or her spouse. As shown, the cross-dependency approach will yield such a result in cases in which the deceased earned much less than the survivor.

The “negative loss” results generated by the cross-dependency approach are often ignored, and it is stated that the survivor has suffered “no net financial loss”. Of course the true result implied by the cross-dependency approach is that the survivor has experienced a net financial gain. Cross-dependency is always ignored when the deceased did not earn any income (and the survivor was the sole income earner), since the method – if followed – will always show that the survivor is financially better off. If the cross-dependency approach was accepted, it would seem that in such a case the survivor’s gain in net income should be offset against his or her loss of dependency on household services. Of course it is not. In my view, part of the reason why the cross-dependency approach has enjoyed some level of acceptance is because its supporters only use it when it yields results that seem intuitively reasonable. When cross-dependency leads to the nonsensical results described here, it is usually (if not always) abandoned.

## Footnotes

* Note that the above description of cross-dependency is sometimes stated differently, although mathematically it is the same. The other way to describe cross-dependency is that it is 70 percent of the couple’s combined pre-accident income, less the survivor’s income. That is, 0.7[a + b] – b, using the above table. This is the same as 0.7a + 0.7b – b. Note also that 0.7a = c + g; 0.7b = d + h; and b = d + f + h. Thus the cross-dependency loss equals c + g + d + h – [d + f + h]. This reduces to c + g – f, which is exactly the same as I noted above. [back to text of article]

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.