Tuesday, 18 May 2010

Intrafamily effects and externalities

If anyone knows of a serious treatment of intrafamily effects, I'd like to know about it.

I'm reading through the Australian tax review's notes on alcohol [The "Henry" Report]. At footnote 18, they write:
These costs [social costs of alcohol] are more limited in scope than those used in the cost of illness methodologies that have been developed in the public health literature (for example, Collins & Lapsley 2008), which also include many of the costs that individuals bear themselves. To estimate spillover costs relevant for setting rates of tax, it is necessary to exclude private intangible costs (such as pain and suffering), and the loss of household production from premature death or sickness. That said, the distinction between private costs and spillover costs is not always clear. For example, if a family utility and decision making model is used, alcohol-related violence against family members and the loss of family disposable income are private costs; but, if an individual utility and decision making model is used, costs borne by other family members are spillovers.
I agree of course than an economic approach, unlike a public health approach, discounts private costs. That's the method Matt and I used, and for which we were excoriated as harsh rationalists by those who like to find big numbers.

I've done a bit of searching, and I have found no adequate treatment of how to handle intrafamily effects. Here's my best cut at it, but if anyone can point to a better treatment, please let me know about it.

First, in the Coasean world, there can only be intrafamily effects, not intrafamily externalities, regardless of whether we take an individual or family level decision model. Why? Because husband and wife are in a contractual relationship. Just as it wouldn't be a positive externality on me if my employer decided to double the available staff parking spaces, it's also not a positive externality on Susan if I decide to cook a really nice Sunday dinner. The availability of parking wasn't something in the employment contract I signed with my employer, and the frequency of nice Sunday dinner provision wasn't in the marriage contract I signed with Susan; they're both effects within incomplete contracts. When Canterbury and I eyed each other up back in 2003, we each took our best estimate of the likely positive and negative amenities we'd provide for each other and decided that the bundle was worthwhile; should either of us be too disappointed, the relationship can always be terminated (albeit with more difficulty for my employer than for me due to labour law, but that just increased the minimum expected quality threshold required for hiring). Similar conclusions were reached when Susan and I eyed each other up starting back in 1999 and moving to contract in 2002.

Continuing in this Coasean line, the marriage market is a two-sided matching problem. Specify for the moment that men and women lie along a quality distribution. Quality is of course multidimensional: we're all Lancasterian goods. And, people can place greater or lesser weights on various characteristics so individual preference orderings may vary somewhat from aggregate rankings. But we'll keep to a simplified distribution for now without particular loss of generality. At the left tail of the distributions are hopeless violent cads, cheats and deadbeats of various persuasions. At the right tail are decent folks with steady jobs, good prospects, loving dispositions and other good qualities. Left of the median are lots of folks with bad characteristics but many redeeming qualities; at the far left side of the distribution, there are only the bad characteristics.

In this kind of two-sided matching problem, we generally expect folks to match up with a partner at a similar point on the opposite gender quality distribution (or same gender, if that's the preference). Somebody at roughly the 70th percentile ought to match up with someone roughly at the 70th percentile; somebody at roughly the 10th with somebody roughly at the 10th, and so on. There of course will be errors along the way - some information is only revealed with certainty post contract, and some people seem to willfully misperceive things or to vastly overestimate their ability to fix their potential partner's adverse characteristics. But we ought to see rough matching along the broad quality dimension.

Now, suppose that a couple partners up: they're at the 25th percentile. She's an alcoholic but has redeeming qualities; he's overweight and lazy but has redeeming qualities as well. Each is the very best partner that the other could afford given each person's endowment of characteristics. He would have preferred a woman much like his partner who didn't drink as much; she would have preferred a man who exercised more and helped more around the house. But those folks weren't in either person's budget set.

After the contract is signed, the husband starts complaining of the effects of the wife's drinking on the marital environment. Now, this may well be a harmful effect within the marriage, and the husband certainly would be happier if the wife drank less. But so too would she be happier if he went on a diet and helped out more around the house. Again, each was the best partner the other could afford at time of contract. You might as well complain that the Honda you could afford didn't have the heated seats of the Mercedes you couldn't afford.

In the Coasean world, it's very hard to see any case for inter-spousal externalities.

If we relax Coasean assumptions somewhat to allow transactions costs - gaining information about a potential spouse's characteristics is costly and exit also is costly - it still would be difficult to see these sorts of things as externalities rather than just effects within incomplete contracts. Again, nothing in my contract with Canterbury says how many parking spaces there must be; my employer may irritate me by continuing to replace parking lots with buildings, but it imposes no externality on me by doing so. If the employer chisels sufficiently on the bundle of uncontracted amenities, I can always exit in hopes of finding another employer. Information costs will make search a lengthier process and exit costs will make folks more wary of entering into contractual arrangements prior to gaining sufficient information. Exit costs will have each partner more willing to endure a given amount of post-contract opportunism by the other, but the present discounted value of those expected chiseling costs cannot exceed the one-off cost of exit or folks will exercise the exit option.

If we want to start calling all kinds of inter-spousal effects "externalities", we start to make a hash of the entire concept of externality. Starting at year one, we drill into our students that something can't be an externality if it's part of a contractual relationship: externalities have to be effects on external parties. And a marriage partner is hardly an external party.

This all sounds rather harsh. I'm certainly not endorsing bad behaviour within marriage; many of the bad effects partners can impose on each other are rightly criminal offences rather than simply grounds for contractual dissolution. But not every bad thing in the world is an externality, just like there are plenty of bad things in the world that aren't market failures.


  1. I completely agree with you when it comes to spousal arrangements, but what about kids? Although I think it is a stretch to try and make it policy relevant, I think it would not be unreasonable to say the effects of a person's drinking are an externality on their children, as children didn't really choose to be part of the family arrangement like the spouse did. Of course this brings up a whole lot of other issues about exactly what rights a child has and what rights their parents have with respect to how they treat them and trying to obtain a meaningful measure of the externality would be ridiculous, but in theory it seems to fit the definition of an externality. What do you think?

  2. @rsw37: I left that one to one side as it's rather more difficult; will mull it over more and post on it later.

    The first best is of course that all families be warm and loving and kind to their children. But not all parents can be made to be like that costlessly.

    I'd be a bit too courageous were I to post things too half-baked on this one.

  3. If a Canadian migrates to New Zealand in the full knowledge that the latter may inexplicably implement inefficient policies, are there are similarly no externalities?

    Also, when that Canadian dedicates a substantial amount to time to arguing against said policies without any significant probability of changing them and/or financial remuneration, but also claims that he doesn't vote due to his disdain of expressive utility, is he hypocritical?

  4. @Henry: Maybe I'm overoptimistic about chances of changing bad policies. We'll see.

  5. Well, even if you're very influential as far as individuals go, your expected instrumental benefits still won't be very high. Even if you personally reduced the probability that a bill with a $100 million net social cost would be passed by 10%, you'd only save a few dollars.

    Perhaps your writing does have instrumental benefits by giving you practice that increases your probability of eventually winning the Nobel (Memorial) Prize. Then again, this is like saying that voting has instrumental benefits in the form of exercise that will increase your probability of eventually winning the New York City Marathon. Perhaps it does to an extent, but there are better ways.

  6. If a Canadian migrates to New Zealand in the full knowledge that the latter may inexplicably implement inefficient policies, are there are similarly no externalities?

  7. @Henry: No chance that blogging affects chances of Nobels; that's outside my budget set anyway. But "critic and conscience" stuff is in the job description here.

    @Jar: Everyone has to choose a country; there's no option of staying single. I don't think there's the parallel here. Maybe in a few decades when there are lots of competitive seasteads out there from which to choose, but that's not our current world.

  8. Are externalities only internalised in perfectly competitive markets? If so, then they're not interalised in marriage markets. Where do you draw the line then? You do have the option of a seastead right now - it'd just be prohibitively expensive and unpleasant. Some would consider the option of remaining single to also be highly unpleasant, especially in cultures where there are very strong pressures to be married.

  9. This kind of reasoning worries me.

    While I recognise the sense in saying it's contractual, so therefore can't be an externality, your discussion of partner selection essentially occurring within the individual's budget set is a little too close to a "They get what they deserve," type of rationalisation for my liking. I'm totally uncomfortable with this.

    Sticking to economics, let's not forget the substantial difference in bargaining power that exists between the partners in an abusive relationship. And the exit costs you mention can be LARGE. Finally, you have the risk of market capture, where the possibilities of exit and reselection are controlled by the abusive partner through practical constraints.

  10. @Henry: They're internalized in contractual relationships entered into voluntarily. If we were in a country with forced arranged marriages, things would be different.

    @Matthew: Note that I did argue that there's decent reason that some things remain criminal rather than just breach of contract.