How Rival Marriage Is

Last month, I observed:

If you share your home with a spouse, you don’t have as much space for
yourself as a solitary occupant of the same property.  But both of you
probably enjoy the benefits of more than half a house.  If a
couple owns one car, similarly, both have more than half a car.  Even
food is semi-rival, as the classic “You gonna eat that?” question
proves.

Mathematically, married individuals’ utility looks something like this:
U=Family Income/2^a

a=1 corresponds to pure rivalry: Partners pool their income, buy stuff, then separately consume their half.  a=0 corresponds to pure non-rivalry: Partners pool their income, buy stuff, then jointly consume the whole.

Then I asked:

There’s little doubt that a<1.  This insight is even built into the official poverty line.  That’s why I say that being single is a luxury.  My question: Where does a typically lie in the real world?  Feel free to discuss variation by social class and nationality.  Please show your work.

In the comments, ce advised me to look into “Equivalence Scales.”  Bill Dickens subsequently did the same.  When I finally followed through, I found that my blog post successfully reinvented the wheel, functional form included.  From Buhmann et al., “Equivalence Scales, Well-Being, Inequality, and Poverty” (Review of Income and Wealth, 1988):

Concern with equivalence scale issues has led the authors to undertake an informal survey of equivalence scales in use in different countries…

The scales we have assembled can be represented quite well by a single parameter, the family size elasticity of need. We assume that economic well-being (W) or “adjusted” income, can be equated to disposable income (D) and size (S) in the following way:

The equivalence elasticity, e, varies between 0 and 1; the larger it is the smaller are the economies of scale assumed by the equivalence scale.

My equation, which sets S=2 for a married couple without kids, is just a special case of (1).  More importantly, though, Buhmann et al. review a large literature that actually estimates e (my a).  There are four distinct empirical strategies:

(1) Expert Statistical (STAT)

In this case the scales are developed only for statistical purposes-that is, in order to count persons below or above a given standard of living – minimum adequacy, for example. The Bureau of Labor Statistics family budgets are a good example, or the scales used by OECD or the European community to count the low income population.

(2) Expert Program (PROG)

The second type of expert scale is focused on defining benefits for social programs-the Supplementary Benefits scale, or the Swedish “base amount” are examples of scales use to calculate benefits under social protection programs. The U.S. poverty line was initially developed for statistical purposes but over the years had come to serve also as a guide to the adequacy of program benefits.

(3) Consumption (CONS)

 In this case the effort is to measure utility indirectly through the revealed preferences of consumer spending constrained by disposable income. The equivalence scales contained in the 1982 article in this journal by Van der Gaag and Smolensky [1982] which are shown in Line 19 of Table 2 are of this variety.

(4) Subjective (SUBJ)

Here the goal is to measure directly the utility associated with particular income levels for families of given characteristics. Different questions related to evaluation of own income (IEQ), to minimum income needed by others to get along (MIQ) or what money buys (PIE) are used to elicit these scales.

The results heavily depend on which of the four methods you use.  After reviewing the extant literature (which hasn’t grown too much since), Buhmann et al. reach the following rough values:

SUBJ – a scale with an elasticity of 0.25
CONS – a scale with an elasticity of 0.36
PROG – a scale with an elasticity of 0.55
STAT – a scale with an elasticity of 0.72

Notice: The subjective (asking people) and consumption (looking at spending behavior) approaches both give small answers, implying low rivalry of consumption.  Government statisticians’ approaches, in contrast, both give substantially bigger answers, implying moderate-high rivalry of consumption.  Assuming married couples share equally, these elasticities imply that couple’s effective per-capita consumption ranges from Family Income/1.19 (for e=.25) to Family Income/1.65 (for e=.72).

Who cares?  Imagine two singles: One earns $60,000 per year; the other earns $40,000 per year.  Here’s happens to their effective consumption if they marry and share equally:

As you’d expect, the low-earning spouse makes out like a bandit.  The surprise: The high-earning spouse gains as well – for all four ways to estimate real-world rivalry.  If consumption were 100% rival, in contrast, the high-earner would lose $10,000 – precisely the amount the low earner gains.

To be sure, the magnitude of the high-earner’s gain depends heavily on which of the four methods you use.  Is there any reason to prefer one method to the others?  Yes.  People have ample first-hand experience with household management, so the subjective approach is probably better than deferring to government statisticians’ opinions.  And looking at actual consumption behavior is probably better than asking people what they think.

So how rival is your marriage?  If you’re a typical couple, simply plug in your total family income, divide by 1.28, and you’re done.  Thus, if one partner outearns the other by 50%, share-and-share-alike marriage raises the high-earner’s effective consumption by about 30%, and the low-earner’s effective consumption by about 100%.  To quote Keanu, “Woh.”

Note: These calculations deliberately ignore all the evidence that marriage makes family income go up via the large male marriage premium minus the small female marriage penalty.  So the true effect of marriage on economic well-being is probably even more massive than mere arithmetic suggests.  Why then are economists – not to mention poverty activists – so apathetic?