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# How Rival Marriage Is

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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/2a

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.
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:

 Method Effective Consump. High-Earner's Gain Low-Earner's Gain SUBJ \$84,090 \$24,090 \$44,090 CONS \$77,916 \$17,916 \$37,916 PROG \$68,302 \$8,302 \$28,302 STAT \$60,710 \$710 \$20,710

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?

Chris writes:

Because

1) It's a big no-no to interfere with anyone else's marital affairs or offer advice unless asked.

2) Liberals couldn't stand the idea of saying that one lifestyle (marriage) is better than another (being single or merely cohabiting).

3) Liberals think marriage is patriarchal; facts don't matter as long as people carry cultural baggage into their marriage.

Kinanik writes:

What implications does this have for discussions of income inequality over time? Russ Roberts, for instance, points to the increased number of single person households to support the claim that median income stagnation is, in part, an artifact of the changing composition of households (of course, marriage is not the only situation where multiple people live in a household).

Greg writes:

How is this different to sharing a flat with a friend?

Kinanik writes:

On the other hand, if being single is a luxury, then an increase in being single is evidence of increased income, even if it isn't measured.

libertarianinchina writes:

I got married at 36, and was amazed at how non-rivalrous the house and household goods actually are. When I was single I ate out every day; now I eat out twice a week and eat 100x better at home. Unless you have a very unusul personality, being single in your thirties and forties is a bad, bad decision.

BC writes:

It's interesting that the two government estimates, which help determine benefit levels, underestimate the effective consumption gain from marriage relative to the other two estimates. Presumably, this bias in the government estimates implies that married couples' need is overestimated with respect to means-tested benefits, and married couples' ability-to-pay is underestimated with respect to progressive taxation. Would that suggest that married couples may have disproportionate political influence relative to singles, i.e., married couples may be a more powerful special interest group? If so, could that indicate that the marriage premium may partially result from rent seeking and, in turn, would that suggest that we should encourage marriage or that we should combat the effects of such rent seeking? Food for thought.

NZ writes:

I hit command+F and tried the following search strings:

"child"
"children"
"baby"
"offspring"
"youngsters"
"ankle-biters"
"mouths to feed"
"TFR"
"replacement"

Nothing came up. Are we really talking about marriage?

[NZ: Command-F searches this web page and only this web page. If you think every discussion of marriage ought to include keywords on that same webpage such as "ankle-biters" or "replacement," etc., I think your comments do not belong on EconLog. Or at least they don't belong in the comment section of this blog post. Not every discussion about the economics of marriage is about children. If you want to discuss children, try a blog about children. EconLog is an economics blog.--Econlib Ed.]

John Thacker writes:

@BC:

Presumably, this bias in the government estimates implies that married couples' need is overestimated with respect to means-tested benefits, and married couples' ability-to-pay is underestimated with respect to progressive taxation... If so, could that indicate that the marriage premium may partially result from rent seeking and, in turn, would that suggest that we should encourage marriage or that we should combat the effects of such rent seeking?

First note that many of the consumption sharing benefits are attainable, as noted above, by cohabitating (whether with a romantic partner or a roommate-- Bryan has praised living with a roommate before). Therefore, if anything, the need that is overestimated (and ability to pay underestimated) is that of cohabitating unmarried people. There already is a strong incentive in certain cases to, say, divorce in order to obtain more benefits, and the PPACA/Obamacare extends this to a greater proportion of the working class. There's a large cliff for benefits, and thus a married couple each making \$40k is eligible for thousands more in benefits by divorcing, for example. Any attempt to "solve" this problem would have to account for the unmarried cohabitants, including simple roommates.

However, aside from that, it's still unlikely we would want to discourage people from engaging in the more efficient behavior. The existing government regulation splits the difference, and thus the gains between the married couple and taxpayers as a whole-- it does reduce benefits somewhat based on need to pay and ability to pay, but not as much as the benefit to the married couple, thus preserving some incentive for efficient behavior. Of course this breaks down since people can still choose marriage in all but name, and (hypothetically) get the same benefits on consumption but retain more government benefits. (In the short run; in the long run it may well make for a more unstable relationship.)

John Thacker writes:

@BC:

To give an analogy-- people who carpool and who drive more efficient cars have a lesser need for aid with their fuel spending, and a greater ability to pay higher gas taxes. People who have more efficient insulation in their homes need less home heating assistance. But none of that means that we want to discourage the more efficient behavior-- suggesting that people with carpools and efficient cars pay higher tolls or gas taxes seems crazy.

NZ writes:

Let me clarify my earlier comment.

By searching for "child" and its synonyms and finding none on the page, I concluded that Bryan's post contained no references to children. (I was wrong: I forgot to search for the word "kids," which Bryan uses once to specify that he is talking about "married couple[s] without kids.")

The reason I take issue with this is as follows:

Bryan's economic analysis of marriage is meant to support his argument that being single is a luxury. Thus, he is attempting to show that being married has a certain economic impact on the average person, the overall effect being that it saves them money.

I agree with that part, but I don't think the average person gets married without the intention of having kids. Most people do have kids, and a great many people believe that facilitating childrearing is the essential function of marriage.

So, for an economic analysis of marriage to be meaningful, it seems to me it should account for children.

John Thacker writes:

@NZ:

See that big "S" for household size? It's equal to 2 for the no-kids case, but is larger when you have kids. Bryan explicitly notes this in the post. ("My equation, which sets S=2 for a married couple without kids, is just a special case of (1).") The problem is that estimating the elasticity is tougher with kids; if you have one probably when they're young a lot of stuff is rivalrous, but if you have more a lot of stuff can be shared between them-- which Bryan could point to as a Reason to Have Kids.

I'm confused. Did you not see that in the post?

NZ writes:

@John Thacker:

It appeared to me that Bryan was only talking about the special case of no kids.

If the equation is scalable to include kids then why not focus on such a scenario, since that will be most people's scenario for most of their marriages?

MingoV writes:

One way around the higher economic utility of marriage is to live in a singles apartment complex or condo. Your private space is smaller, but you have the advantages of onsite pool, gym, cafe, lounges, etc.

NZ writes:

@MingoV:

Really, if you're a single person intent on remaining single but you want to economize, you might want to move around a bunch of married people. That way you can at least free-ride off their positive externalities.

John Thacker writes:

@NZ:

Here's a few reasons:

1) Because the math is simpler with two people. The last mathematics wouldn't make nearly as much sense with a child added in. You'd have to say that the child earns \$0 if not for the marriage, or have some way of accounting for not existing. Furthermore, there's a good chance that adding in the child would make at least one of the spouses look materially worse off, but that's because having children has an intrinsic value to people who want them.

2) Because people who want to have kids probably think that marriage is a good idea anyway. This math shows that even for people who don't want to have kids, marriage (or cohabitation) makes a lot of sense.

NZ writes:

@John Thacker

1) Isn't the practical real-world usefulness of a formula more important than its absolute simplicity? I'm not expert and I could be wrong, but this seems like a reasonable assumption.

2) We have an illegitimacy rate of about 40%, and it's well over 60% for non-Asian minorities. There are a lot of reasons why so many people are deciding to have kids outside of marriage, but I'm certain one of them is that men tend to consider marriage an unacceptably high-cost undertaking, one that would result in them having to share their income with at least one--and usually more than one--other person. If there is anyone who needs to hear that marriage (even with kids) will actually save them money, it is these men.

John Thacker writes:
1) Isn't the practical real-world usefulness of a formula more important than its absolute simplicity? I'm not expert and I could be wrong, but this seems like a reasonable assumption.

The formula as given works in practice for a family of any size. Bryan just gave an example for a two person family in the table, but he explicitly says that that's just a special case of the general formula.

He is absolutely not at all talking about only marriages with no kids. I'm sorry, I don't know how I can make this any clearer (and it seems perfectly clear in the original post.)

He (and I) perfectly agree with 2). That's the entire point of the post. The issue with kids is that part of what you get out of them is having kids (which Bryan says are great, if you look at his other book, Selfish Reasons to Have Kids.) It's difficult to say that having kids makes you monetarily better off than not having them; there are other reasons (though, as the formula argues, it's considerably cheaper than simply dividing your income by an extra person). But getting married by itself generally makes you monetarily better off.

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