Monthly Archive for November, 2010

How to Decide

kieferMany years ago, when I was teaching at Cornell, my then-colleague Nick Kiefer kept me endlessly amused with the creative assignments he dreamed up for the students in his Decision Theory class. I’m reporting this from memory, so I don’t guarantee that I have it exactly right, but I think this was one of those problems:

  • On Day Zero (before classes start), Nick uses his pocket calculator to generate, at random, a secret number between 0 and 100. This number is drawn from a uniform distribution, which means (roughly) that the drawing is unbiased, so any number is as likely to come up as any other. The students’ job is to guess this number.
  • On Day One — the first day of class — Nick uses his pocket calculator to generate a Number of the Day. He doesn’t tell the students what the Number of the Day is, but he does tell them whether it’s larger or smaller than the secret number.
  • On Days Two, Three, and so forth, he does the same thing. He generates a Number of the Day and announces whether it’s bigger or smaller than the secret number.
  • You, the student, can submit your guess on the day of your choice.
  • You are then assessed two penalties. The first penalty is equal to the square of the error in your guess. So if the correct number is 3 and your guess is 5, your penalty is 22, or 4. The second penalty is equal to the natural logarithm of the day when you submit your guess. So if you submit your guess on Day 7, your penalty is the log of 7, which is 1.94591.
  • These penalties are subtracted from some some fixed number of points that you’re given to start out with (say 1000). The result, after the subtraction, is your score for the assignment. This score counts for a significant fraction of your course grade.

Continue reading ‘How to Decide’



When I review the blessings of my extraordinarily blessed life, this one always appears near the top of my list: I am an adult male who has never been to war. I have always assumed — without thinking about it too hard — that in the historical scheme of things, this is a great privilege, and a great rarity.

Am I right about that? Over the course of human history, what is your estimate of the fraction of males who have reached adulthood without participating in a military conflict?

(Obviously, there’s some fuzziness about what counts as military conflict. I’m thinking here not about the occasional street fighter, but about the guy living in mud and getting shot at for weeks at a time — or things equally dangerous/traumatic/uncomfortable.)

Thanksgiving Break

Along with half of everyone else who works at a University, I’m starting my Thanksgiving break a little early. I’ll see you all after the holiday weekend, hoping to find you well fed, healthy, and reflective of your blessings.

Keep the Mortgage Interest Deduction

mankiwGreg Mankiw endorses the Bowles-Simpson recommendation to eliminate the mortgage interest deduction. I am not convinced. Here’s why:

I start from the position that capital income (including interest income) ought not be taxed. Unlike a tax on labor income, which (unfortunately) discourages work, a tax on capital income discourages both work and saving, and so is doubly destructive. Moreover, it effectively taxes the labor of the young (who earn, save for a while, and then spend) at a higher rate than the labor of the old (who earn, save for a shorter time, and then spend), which is both unfair and distortionary (in that in encourages young people to postpone their high-earning years).

Continue reading ‘Keep the Mortgage Interest Deduction’

Police News

My favorite news story of 2010, from the “Police News” section of the Hudson Hub Times:

Hudson — A Sullivan Road resident called police to report a “suspicious package” on his front porch Nov. 2 at 3:20 p.m.

The resident said he observed an unknown person leave the package and called police, according to the police report.

The officer said he could see the package was clearly labeled with the logo and asked the man if he had ordered anything from the firm recently.

The man reportedly said “Why yes, I did.”

The officer told the resident his order had arrived. The resident then said he was comfortable opening the box. The officer then left the scene, according to the report.

Hat tip to my sister.


ben-bernankeSome Q&A about quantitative easing, with a somewhat higher ratio of economics to cartoon characters than we had yesterday:

What is this quantitative easing stuff? What exactly is the Federal Reserve (a/k/a “the Fed”) doing?

They’re creating 600 billion new dollars and using those dollars to pay down the government’s debt.

They’re paying down the debt? I thought they were buying bonds.

It’s the same thing. Last year, Huey McDuck lent the government a dollar and received a bond. (A bond is the same thing as an IOU.) Today the Fed buys Huey’s bond. Now the government owes a dollar to the Fed instead of to Huey.

But the government still owes someone a dollar!

Well, yes and no. Unlike Huey, the Fed is subject to a 100% tax on profits. So the government can pay its one-dollar debt to the Fed and then turn right around and swoop that dollar back up again. That’s just as good as not owing anything in the first place.

Continue reading ‘QE2′

Quantitative Easing Explained by Cartoon Characters

I can’t really endorse the content, but I like the presentation:

Get the Flash Player to see this content.

(Original here .)

Did the Stimulus Work?

Did the stimulus create jobs?

Daniel Wilson of the San Francisco Federal Reserve Bank has just released what might be the first real evidence-based effort to resolve this question. One apparent problem with drawing inferences from the experience of the past couple years is that we have only one experiment to look at. But Wilson points out that in some sense, we have 50 separate experiments because stimulus spending differed substantially across states. You can potentially learn a lot from 50 experiments.

Unfortunately, they’re not controlled experiments, because stimulus funds were not allocated randomly. States with particularly weak economies probably got more Medicaid funds. States with bloated and inefficient bureaucracies might have been slow to complete necessary paperwork and hence slow to receive funds. If those weak economies or shamblng bureaucrats also had an effect on job growth, then the experiments are not clean.

But fortunately there are substantial components of the funds that were distributed according to objective formulas (demographics, number of highway miles, and so forth). Wilson makes competent use of these components, together with standard econometric techniques, to zero in on the subset of stimulus spending that can be considered effectively random. Now that he’s got his fifty more-or-less controlled experiments, he also controls for other confounding variables that could plausibly affect state-by-state economic growth. All of which is the right way to do this.

Continue reading ‘Did the Stimulus Work?’

Yes, It Really Is This Easy

The New York Times invites you to eliminate the federal deficit by picking and choosing among 16 options. I agree with Arnold Kling and David Henderson about the takeaway message: It’s really really easy to cut the deficit to zero without raising taxes. And that’s without even eliminating any agencies.

Moreover, the Bowles-Simpson proposals include dozens of additional specific recommendations that are not listed on the Times site. So cutting spending is even easier than the Times makes it appear.

If you want to raise taxes, the Times offers some very good ideas, like reducing the tax break for employer-provided health insurance, though a far better idea would be to eliminate the tax break for employer-provided health insurance. It also offers some very bad ideas, like raising capital gains taxes and limiting the mortgage interest deduction. A good idea would be to reduce the taxes on capital and interest to zero.

Continue reading ‘Yes, It Really Is This Easy’

Weekend Roundup

We started the week with a few words about estate taxes.

Then it was on to the justice system. On Tuesday I offered a little quiz on recognizing reasonable doubt (or its absence) in an exceptionally simple environment. Some readers thought that environment was too simple to be interesting. On the contrary, it’s simplicity is what makes it so interesting. If we can’t recognize reasonable doubt in such a simple environment, how can we ever recognize it in the courtroom?

On Wednesday, we talked about the appropriate numerical cutoff for reasonable doubt, and on Thursday we took a step back and asked what principles we should apply in choosing that cutoff. On Friday, I decried the dereliction of duty by judges and legislators who refuse to tell us what cutoff they have in mind when they use the word “reasonable”.

Some commenters thought that giving jurors a precise numerical standard was asking them to think more “mathematically” (whatever that means) than we can reasonably expect. But there’s no mathematics involved in telling a juror that he should convict if he believes that in 100 similar cases, at least 93 of the defendants will be guilty. No mathematics, that is, beyond the ability to count to 100, which is, I think, something we already expect of our jurors.

If I don’t tell you what “reasonable” means, then “beyond a reasonable doubt” makes as much sense as “beyond a gribzle doubt”. Judges could, if they wanted to, tell juries to convict if the evidence convinces them beyond a gribzle doubt, and then refuse to reveal what “gribzle” means. I don’t see how that system would differ substantially from the one we have now.

Blinded Justice

blindjusticeIt’s been “reasonable doubt” week here at The Big Questions. We’ve talked about recognizing reasonable doubt when you see it, about what the standard should be, and about what the standard for determining the standard should be.

This raises the question: What is the standard? Here’s the weird part: Nobody knows. The judges won’t tell you and neither will the legislators. If you’re on a jury, you’re on your own.

Now you might say that that’s a fine thing. We want to leave it to jurors to set this standard. Under that theory, a juror has two separate questions to answer. One is “How doubtful am I?” and the other is “How much doubt counts as reasonable?”. But I don’t believe anyone actually subscribes to that theory.

Here’s why I say that: Suppose that in a murder trial, the foreman of the jury reports back to the judge that the jurors have agreed that there’s a 15% chance the defendant is guilty, and that they consider 15% to be beyond a reasonable doubt. Therefore they have unanimously voted to convict. I am not a lawyer, but I will cheerfully bet you that in any such case, the judge would throw the conviction out in a hurry, on the grounds that 15% is not at all beyond reasonable.

In other words, the judge does not subscribe to the theory that it’s entirely up to the jurors to set the reasonable doubt standard. Moreover, the judge would throw out the verdict at 16% or 17% or 18% and so on up to …. what? Well, up to some number. That number is a standard that the judge is prepared to enforce. What is that number? I bet the judge won’t tell you. The question is: Why not? Why doesn’t the judge say something like “You should convict if you are at least 90% certain the defendant is guilty”?

Continue reading ‘Blinded Justice’

Reasoning About Reasonableness

Two days ago, we asked whether lawyers (or anyone else) can recognize reasonable doubt (or its absence) when they see it. Yesterday we stepped back to ask the question: What is the right standard for “reasonable doubt”? Should you convict when the probability of guilt is 70%? 80%? 90%? Of course the answer might vary with the crime and the prospective punishment. To keep this discussion concrete, I’ll focus on capital punishment for murder, and to keep it simple, I’ll pretend that no other punishment is available (so that the only choices are “acquit” and “execute”).

Today I want to take yet another step back and ask: What is the right standard for deciding the right standard? Here are two possible meta-standards:

1. Minimize the suffering of innocents.

2. Minimize suffering.

The difference is in whether we choose to care about the suffering of murderers.

Continue reading ‘Reasoning About Reasonableness’

Reasonable Doubts

doubtYesterday, I posed these questions:

Here I have a couple of urns. The one on the left contains 70 red balls and 30 black. The one on the right contains 30 red and 70 black.
While you weren’t looking, I reached into one of these urns and randomly drew out a dozen balls…4 of them were red and 8 were black.

1. If you had to guess, which urn would you guess I drew from?

2. What’s your estimate of the odds that you’re right?

3. Do you think you’re right beyond a reasonable doubt?

I stole this problem from the decision theorist Howard Raiffa, with some minor changes (he used bags instead of urns, and green and white balls instead of red and black — and he drew his twelve balls with replacement, rather than all at once, which has only a tiny effect on the probability). Here, with appropriate minor wording changes, is what Raiffa had to say:

Continue reading ‘Reasonable Doubts’

Law School Admissions Test

Here I have a couple of urns. The one on the left contains 70 red balls and 30 black. The one on the right contains 30 red and 70 black.

While you weren’t looking, I reached into one of these urns and randomly drew out a dozen balls. As you can see, 4 of them were red and 8 were black.

Here are three questions that I think you ought to be able to answer if you want to be in the business of assessing evidence:

  1. If you had to guess, which urn would you guess I drew from?
  2. What’s your estimate of the odds that you’re right?
  3. Do you think you’re right beyond a reasonable doubt?

Further discussion to follow later in the week. (Hat tip to Howard Raiffa, who will also figure in the upcoming discussion.)

Click here to comment or read others’ comments.

Thaler on the Estate Tax

Dick Thaler, writing in the New York Times, says so many wrong things about the estate tax that I don’t know where to begin. But let’s begin here:

First, it is incorrect to say the estate tax amounts to double taxation. The wealth in many large estates has never been taxed because it is largely in the form of unrealized — therefore untaxed — capital gains.

This is just not true. Virtually all of the wealth in every large estate has already been taxed at least once. Namely, it was taxed when it was earned. You do not understand this issue unless you understand the following simple example: Scrooge McDuck earns a dollar, makes some fortunate investments, and leaves a hundred million dollars in unrealized capital gains to his ne’er-do-well nephews. If Scrooge has to pay 50 cents income tax on that dollar, then he invests half as much, earns half as much, and leaves his nephews half as much. Scrooge’s fifty cent tax bill has already cost his nephews fifty million dollars.

Continue reading ‘Thaler on the Estate Tax’

Hope and Change

I well remember the last time the Republicans rode into town to get our fiscal house in order and curb the growth of government. That was in 1994. Twelve years later, when our Republican heroes were themselves ridden out of town, they still hadn’t managed to eliminate the goddamned National Endowment for the Arts.

They did, however, cut its budget for a while — from $170 million to under $100 million, though it’s crept back up since then. The moral: If you want a lasting impact, don’t cut budgets. Cut agencies.

The NEA is, of course, small potatoes, but my point is that these guys never made a permanent debt in the small stuff, let alone the big stuff. This time around, maybe — just maybe — things will be different, especially if the Tea Party continues to hold some feet to the fire. With that in mind, here are a few bits of advice for the freshman class:

Continue reading ‘Hope and Change’

Is Obama a Keynesian?

I realize everybody else in the world has already posted this, but just in case mine is the only blog you read:

Get the Flash Player to see this content.

Hat tip to our frequent commenter Ken B., who pointed me to this before everyone else had posted it.

First Tuesday After the First Monday in November

I have my eleven spreadsheets. I have my three computers with their dozen open browser windows. I have the television I bought specially for this occasion. I have my XM Radio. I have my 20,000 calories worth of junk food. I have my remote control.

I also have my prognostications and my preferences, but I am not (quite) narcissistic enough to assume they’d interest you — especially when there is so much enlightened commentary available elsewhere on the net. I for one will be turning to Nate Silver for insights throughout the day.

I will go to the gym today, but aside from that I don’t expect to move much in the next 24 hours or so. Tomorrow, the web will be flooded with post-election commentary, with which I will not attempt to compete for your attention. I’ll see you Thursday, with something loftier to talk about.

I Knew It All Along!

Proof positive that Google is an idiot: