Couldn't Have Said It Better Department

Roderick Long has an excellent post on the philosophical contradictions of religious conservatives.  It’s like shooting fish in a barrel, of course, but Rod’s a mighty fine shot.  For instance, Rod observes that religious conservatives love to rail against the evils of moral relativism, and then points out:

[The religious conservatives] tend, for example, to accept "divine command theory," which holds that what makes something right (or wrong) is the fact that God commands (or forbids) it. The upshot of such a view, of course, is that God's commands must be viewed as completely arbitrary and random. After all, if God had reasons for commanding and prohibiting as he does, then those reasons, rather than God's will, would be the basis of the action's rightness or wrongness -- an intolerable restriction on God's "freedom." Hence such conservatives are as hostile as any relativist to the notion of a rationally intelligible moral order. They too regard morality as being a matter of groundless whim; they just think the whim is God's rather than ours.

Well put.  I am not a believer myself, but even if I were, I’d still have to wonder what authority other than argumentum ad baculum lies behind God’s commands.  For that reason, I’m inclined to think too much emphasis is put on the question, “Is there a God?” and too little on the question, “Why does it matter?”

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The (in)Significance of Significance

I do not intend for this post to be about the minimum wage. I don’t really have anything new to add to the subject, except to point to my VC post on it, and to voice my basic agreement with Tyler Cowen and Steve Horwitz. But the topic of this post was inspired by the blogospheric discussion of the minimum wage, especially Jacob Levy’s question about the statistical questions involved.

Everyone who takes an undergrad stats class learns how to perform statistical significance tests. They learn to choose a significance level of 95%, corresponding to an alpha of 0.05. Sometimes, they learn that you can select a higher or lower level of significance, like 99% (alpha = 0.01) or 90% (alpha = 0.1). But what I’ve gradually realized, from speaking to (and testing) many undergrads, is that they typically have no clue why – and more importantly, when – that’s the right level of significance to choose. And I’m increasingly of the opinion that lots of professionals don’t, either. (Maybe I’m one of the ignorant professionals – I’ll judge that from the reactions to this post. Also, nothing I say here is meant as criticism of Jacob, who addresses a related but different question.)

The fact is that alpha = 0.05 is essentially arbitrary. Technically, alpha is the probability that your testing method will lead you to incorrectly reject some “null” hypothesis. The null is the complement (logical opposite) of the “alternative” hypothesis, which is the claim you’re interested in supporting. To take the minimum wage example, the null hypothesis is that there’s no relationship between the minimum wage and employment. With alpha = 0.05, there’s a 5% chance you’ll incorrectly reject that hypothesis and conclude there is such a relationship (when in fact there is not).

But why should alpha be so small? Why put such high value on not incorrectly accepting our alternative hypothesis? The idea is that, as scientists, we ought not put our faith in a conclusion unless we have very strong proof. And, again as scientists, we must be satisfied to remain agnostic if we fail to get statistical significance for a proposition. And this is the key point: The absence of statistical significance should not lead us to accept the null hypothesis. It should lead us to be agnostic about both the null and the alternative hypothesis. To take the minimum wage example again, if studies fail to show the minimum wage causes unemployment, the appropriate conclusion is not that there isn’t a relationship, but that we just can’t say so with much confidence.

Think about it this way. Above, I supposed we were interested in showing that there is a relationship between the minimum wage and unemployment. In order not to make the task too easy on ourselves, we set a rather high bar: 95% confidence. But what if we were interested in showing there’s not a relationship? In that case, we are interested in supporting the null, not the alternative, hypothesis. If we set alpha = 0.05, and if we accept the null whenever we fail to accept the alternative, then what is the chance of incorrectly affirming that there’s no relationship? It is not 5%, but in fact something much larger – what statisticians call the beta value, corresponding to a Type II error (the error of incorrectly failing to reject the null hypothesis). The smaller is the alpha, the larger is the beta. And that means using an alpha of 0.05 makes it way, way too easy to claim to have proven the no-relationship hypothesis.

Using a small alpha makes a lot of sense if you’re choosing between belief and agnosticism, and you wish to give agnosticism the benefit of a doubt. Scientists don’t want to express support for something unless they’re pretty darn sure of it. But what if the choice is not between belief and agnosticism, but between one belief and another belief? In practical decision-making, that is usually the case. The owner of a movie theater has to decide whether students’ ticket-buying behavior differs from the rest of the public’s, and if he makes the wrong decision he will not make as much money as he could have. He has no choice but to pick a belief – either he thinks students are probably different and he charges different prices, or he thinks they are probably the same and he charges the same prices. Similarly, a government can either impose a minimum wage or fail to do so. It can’t remain purely agnostic like the scientist can.

In cases like these, the arbitrary setting of a very small alpha doesn’t make sense, because both the alpha and the beta are important. Small alpha implies large beta. In the case of the minimum wage, a large beta means a high chance of assuming there’s no relationship between the minimum wage and employment even though there is.

Again, let me emphasize that I’m not trying to make a point about the minimum wage per se. The point I’m making here applies to business, public policy, and numerous other cases of practical decision-making in which one must choose between alternate strategies based on alternate beliefs about the world. The decision rules of pure science should not be confused with the decision rules of life.

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Self-Promotion

I have an op-ed in the East Bay Business Times (free registration required), discussing state bans on direct shipping of wine to consumers. I'm not sure if it's okay for me to post it here as well, so you'll have to follow the link.

I see that some mild editing has been done, but nothing too serious. I do have one concern about my own claims: I used the phrase "Sonoma Valley chardonnay" without actually checking to make sure they make chardonnay in Sonoma Valley. For all I know, they only make cabernets there. But hey, I'm an economist, not a sommelier.
 
UPDATE:  The piece has been picked up by the Tri-Valley Herald and the Argus.  Cool!  Also, Jason kindly informs me (in the comments) that I'm safe on the Sonoma Valley chardonnay issue.

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Unfriendly Amendments

A friend just forwarded me an email alert, which began with the following:

In less than 48 hours, Congress will vote on an amendment to the U.S. Constitution that would permanently deny marriage equality to same-sex couples. This is unprecedented -- never before has our Constitution been amended to take away anyone's rights. We've got to fight back.

The proposed amendment is a bad idea, of course. But it’s false to say the Constitution has never been amended to take away anyone’s rights. What about the 18th Amendment, which instituted the prohibition of alcohol? That definitely took away people’s rights. We might also include the 16th Amendment, which allowed Congress to institute an income tax.

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Does Divorce Encourage or Discourage Marriage?

The gay marriage debate has gotten me thinking about the effect of divorce on marriage. That divorce has a deleterious effect on marriage as an institution is a notion shared by both the advocates of gay marriage (“What’s really undermining marriage is divorce, not homosexuality”) and opponents (“Gay marriage, like divorce, will further the degradation of traditional marriage”). But is it really true that divorce is bad for marriage?

From an economic perspective, the answer is ambiguous. Marriage is a kind of contract. Divorce is a means of ending the contractual relationship. What happens when you make it easier to get out of a contract? On the one hand, people will be less inclined to enter a contract if the other party can bail out, potentially leaving you in a difficult situation (say, stranding your relationship-specific investments). On the other hand, people will be more inclined to enter a contract if they know they can end the relationship when it’s no longer beneficial for themselves. For example, if I like an apartment but I’m unsure I’ll enjoy living there, I’m more inclined to rent on a short-term lease. Likewise, if the landlord think I like a good tenant but can’t be certain, they’re more inclined to rent to me on a short-term lease. There’s a reason that business contracts often contain escape clauses: without such an option, some parties won’t contract in the first place.

The application to marriage is straightforward: easier divorce could increase or decrease the number of marriages performed. The participants in some potential marriages are made better off by divorce, others worse off. Now, the conservative defenders of marriage might argue that the total number of marriages, or the satisfaction of the participants, is not the issue – the real issue is having stable marriages, and easy divorce decreases stability through both the routes described above. People become less willing to make investments in a relationship that might end, and they become more willing to enter such relationships lightly because they have an escape hatch.

But why do we want marriages to be stable? The main argument is “the good of the children.” Realize that many couples who might consider marriage already have kids (or kids on the way). Being unsure about the lastingness of their relationship, they might be unwilling to marry if marriage is hard to quit, but willing to give it a try if it’s easy to quit. If they get married with an easy divorce option, the kids could end up better off because their parents are more inclined to stay together than if they hadn’t tied the knot. And even if the parents wind up getting divorced, arguably the kids are no worse off than if the parents had never married in the first place and eventually went their separate ways.

I’m not claiming the effect just described is significant enough to make easy divorce, on net, a good thing. But it is something to keep in mind, because it means that divorce’s effects are ambiguous in theory, even if we focus solely on its effects on children. In principle, it would make most sense to allow couples to choose the terms of their own marriage contracts. That would allow couples who feel the need for an escape clause to include one, without obligating other couples who want a stronger commitment to follow suit.

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