Significance Tests as Leading Questions

Under the common law, lawyers are not allowed to ask witnesses “leading questions,” as witnesses can be influenced by the way questions are asked. A leading question is one that suggests a particular answer, for instance, “Were you at the country club on Saturday night?” is a leading question, while, “Where were you on Saturday night?” is not.

Econometricians should be as careful as lawyers when questioning the most unreliable of all witnesses: economic data. Most statistical software will automatically spit out t-tests for whether the coefficients in regression models equal zero. This is equivalent to asking the data, “Data, given these modelling assumptions, can you deny with 95% certainty that this coefficient equals zero?” That’s a leading question, and the econometrician shouldn’t ask it unless he has special reason to suspect that the coefficient is zero.

For example, suppose an economist was attempting to test the effect on employment of an increase in the minimum wage (I choose this example only because I am familiar with it). If he observes many people working below the new minimum immediately before it goes into effect, he can believe with high certainty that the new minimum will be binding. Furthermore, if he observes many businesses employing low-skilled workers, as well as a stream of new businesses entering the market for low-skilled labour, he can believe with high certainty that the market for low-skilled labour is competitive rather than monopsonistic. Putting on his economist hat, he can infer from these two observations that the reduction in employment caused by the minimum wage will correspond to the elasticity of the demand curve for low-skilled labour.

Given this situation, would it be appropriate for this economist to ask the data, “Data, given these modelling assumptions, can you deny with 95% certainty that the minimum wage has zero effect on employment?” I hope the reader can see the problem with such a question. The economist has no special reason to believe that the demand curve for low-skilled labour is perfectly inelastic, any more than he has a special reason to believe that this demand curve has an elasticity of exactly 0.73. The question he should be asking is, in the case of this particular historical event, how much did the increase in the minimum wage increase unemployment? “Not at all” is a valid answer, but with no special reason to believe it is the correct answer, he should not bias his conclusion by phrasing the question in such a way that he leads his “witness” to favour zero.

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Significance Tests as Leading Questions

Under the common law, lawyers are not allowed to ask witnesses “leading questions,” as witnesses can be influenced by the way questions are asked. A leading question is one that suggests a particular answer, for instance, “Were you at the country club on Saturday night?” is a leading question, while, “Where were you on Saturday night?” is not.

Econometricians should be as careful as lawyers when questioning the most unreliable of all witnesses: economic data. Most statistical software will automatically spit out t-tests for whether the coefficients in regression models equal zero. This is equivalent to asking the data, “Data, given these modelling assumptions, can you deny with 95% certainty that this coefficient equals zero?” That’s a leading question, and the econometrician shouldn’t ask it unless he has special reason to suspect that the coefficient is zero. (more…)

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Assigning the Burden of Proof

Have you ever experienced learning a new word and then hearing it everywhere in the days after you learn it? I’ve had a similar experience since making my argument that the burden of proof that the minimum wage is beneficial falls on the law’s supporters. Now I’m seeing people making burden-of-proof arguments everywhere. Bryan Caplan, in a post on EconLog, quotes Mike Huemer making the argument explicitly:

[T]here is a kind of moral presumption against coercive interventions. Laws are commands backed up by threats of coercive imposition of harm on those who disobey them. Harmful coercion against an individual generally requires some clear justification. One is not justified in coercively harming a person on the grounds that the person has violated a command that one merely guesses has some social benefit. If it is not reasonably clear that the expected benefits of a policy significantly outweigh the expected costs, then one cannot justly use force to impose that policy on the rest of society.

Ryan P. Long, over at Open Borders: The Case, makes what is essentially a burden-of-proof argument for open borders:

[W]hile it’s easy to merely allege that “the immigrants” caused crime to increase in your neighborhood or property values to decrease, it is substantially more difficult to prove it. I leave the burden of proof for [the idea that the differences between people really do translate into a reduced quality of life] on immigration’s critics.

Migrants from poor countries often see a 20-fold increase in their earnings just by setting foot in a wealthy country, so you had better have a good reason for barring them from doing so. The people at Open Borders: The Case do a great job arguing for the positive benefits of increased migration, but if we assigned the burden of proof correctly, it would be open borders’ opponents who would have to do the hard arguing.

Finally, while he doesn’t make an explicit burden of proof argument, Bob Murphy’s recent EconLib article raises the important point of non-price allocation under a binding minimum wage:

Raising the minimum wage might represent a drastic harm to the most vulnerable and desperate workers if the specific employees who would be working for $10.10 an hour are different from those who would be working for $7.25 an hour. What could happen is that the higher wage would attract new workers into the labor pool, allowing firms to become pickier and, thus, to overlook the least-productive workers, who would remain unemployed or lose their jobs to more-highly-skilled workers.

Murphy constructs a scenario where the demand curve for low-skilled labour is particularly inelastic, but the supply curve is still elastic, meaning that while the number of job openings has changed little, the number of low-skilled workers chasing those jobs has increased.

Even though (by construction) our hypothetical minimum wage has not significantly reduced total employment, it has, nonetheless, drastically impaired the functioning of the labor market. The “glut” of workers on the market means that non-price allocation mechanisms must come into play. Since there are now multiple applicants for a given job opening, employers can rely on other criteria, including racial and class background, to choose which worker gets the job. It is much more likely that an applicant will need to “know somebody” to get hired, and that teenagers from “respectable” backgrounds will be the ones to work at fast food restaurants, displacing teenagers who might be in more desperate circumstances.

These concerns are not merely hypothetical. Even many economists in favor of the wage hike agree that raising the minimum wage will affect the turnover of workers. For example, one of the leading revisionist authors, Arindrajit Dube, says that in one of his earlier co-authored studies “we… find that both hires and separations of low-wage workers (teens, restaurant workers) fall in response to [a] minimum wage increase, but employment levels do not change noticeably.” [footnotes removed]

What Bob is saying is that there’s more to the minimum wage law than just employment. Even if the revisionist studies that show small employment effects are entirely correct (which is not at all clear) there’s still plenty of reason to think that the minimum wage hurts the very people it’s supposed to help.

But let’s suppose, for the sake of argument, that employment isn’t reduced by the minimum wage, and that the non-price allocation mechanisms are efficient, so it really does do more good than harm to low-skilled workers. Would this morally vindicate today’s supporters of the minimum wage?

I don’t think so.  As Mike Huemer argued in the article quoted above, interference bears a higher burden of proof than non-interference:

[W]hen the state actively intervenes in society–for example, by issuing commands and coercively harming those who disobey its commands–the state then becomes responsible for any resulting harms, in a way that the state would not be responsible for harms that it merely (through lack of knowledge) fails to prevent. Imagine that I see a woman at a bus stop opening a bottle of pills, obviously about to take one. Before I decide to snatch the pills away from her and throw them into the sewer drain, I had better be very certain that the pills are actually something harmful. If it turns out that I have taken away a medication that the woman needed to forestall a heart attack, I will be responsible for the results. On the other hand, if, due to uncertainty as to the nature of the drugs, I decide to leave the woman alone, and it later turns out that she was swallowing poison, I will not thereby be responsible for her death. For this reason, intervention faces a higher burden of proof than nonintervention.

Imposing a minimum wage before we have enough evidence to say it does more harm than good is morally questionable whichever way the chips fall. Saying to low-skilled workers, “we weren’t sure that banning all contracts that pay a wage between zero and ten dollars per hour would help or hurt you, but we imposed the minimum wage anyways, and it turns out it did help you,” is morally equivalent to saying to someone, “I wasn’t sure that I would win that hand of poker, but I bet your life savings on it anyways, and it turns out I did win!”

How good a hand would you need to morally justify such a bet? A pair of eights? Three jacks? A straight flush? Even if you’re as sure that the minimum wage will do more good than harm as you are that three jacks will win a round of poker, the fact that you’re gambling with someone else’s livelihood should make you think twice about taking that bet.

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