Monthly Archive for August, 2010

The Idea of the Decade

gplaneWhat is the largest (non-human) animal that’s ever found its way onto an airplane?

Someday Google (or its successor) will be able to answer that question. It will understand what you’re asking, it will perform relevant searches for old newspaper items, it will sift through the results, it will know (or know how to find out) whether a vole is larger than a ferret, and it will give you an answer. We’ll call it the semantic web.

When the Chronicle of Higher Education asked me for a few hundred words on the defining idea of the next decade, this was the first thing that came to mind. Another was the partial conquest of cognitive bias through better understanding of the systematic ways our brains let us down, together with software designed to compensate for our own mental shortcomings.

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Efficiency Experts

Is it better to tax consumption or to tax income? Is it better to tax carbon or to mandate fuel efficiency? Is it better to foster global competition or to protect local industries?

Today, I will attack none of these questions. Instead, I will attack the meta-question of how to attack such questions. For economists evaluating alternative policies, the industry standard is the efficiency criterion, also known as the welfare criterion. (I’ll illustrate what that means as I go along.) But now comes Princeton Professor Uwe Reinhardt with a piece in the New York Times that questions the orthodox approach found in virtually all modern textbooks (including one in particular).

Let’s first dispense with the straw man. I’ve never heard of an economist who believes that every efficient policy is good, and I’ve heard of very few who believe that every inefficient policy is bad. It’s true that most economists do seem to believe that any good policy analysis should start by considering efficiency. That doesn’t mean it should end there.

I think economists are right to emphasize efficiency, and I think so for (at least) two reasons. First, emphasizing efficiency forces us to concentrate on the most important problems. Second, emphasizing efficiency forces us to be honest about our goals.

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Weekend Roundup

roundupIf there’s one thing I wish everybody understood about economics, it’s that wise resource allocation requires truly vast amounts of information, and that prices do an excellent job of summarizing that information. We led off the week by applying this principle to grocery shopping. A rather silly column in the New York Times had seemed to suggest that socially responsible shoppers should care about the energy costs of producing vegetables to the exclusion of all the other costs. The column was focusing, in other words, on the seen as opposed to the unseen. But the unseen costs of growing a tomato in one location rather than another are just as important as the obvious ones, and because they are unseen (and unseeable) the only feasible way to account for them is to look at prices. We followed up with a 25 year old application of exactly the same principle, this time to the problem of resource extraction.

We moved on to the perils of interpreting data, in this case with regard to the ingredients of a happy marriage. Then a look back to what the world of 1985 thought would constitue a marvelous future; we seem to have met expectations pretty well. And finally, we came in a sense full circle — from lamenting those focus single-mindedly on energy costs to the exclusion of all else to lamenting those who fault others for failing to focus single-mindedly on one political issue to the exclusion of all others.

I’ll be back next week with some thoughts on why we should care about economic efficiency, a little more on the foundations of arithmetic, and some surprises.

The New Parochialism

So a former chairman of the Republican National Committee comes out as gay, and endorses gay marriage, but continues to support politicians who oppose gay marriage. For this he is labeled (on blogs too numerous to link) a first-class hypocrite.

I missed the memo about the new criteria for hypocrisy, so I’d like a little clarification here. Are Catholics now required to vote solely on the basis of Catholic issues, and union workers solely on the basis of union issues, and billionaires solely on the basis of billionaire issues? Or is it only gays who are forbidden to prioritize, say, foreign affairs and tax policy? And what’s to become of the multifaceted? If you’re a gay Jewish small business owner, to which brand of parochialism are you now in thrall? Please advise.

Living In the Future


My treasured copy of the humor classic Science Made Stupid, copyright 1985, contains a Wonderful Future Invention Checklist. Who in 1985 would have thought that just 25 years later, I could check off a third or so of the entries?

The Match Game

Robin Hanson reports that success in marriage is quite uncorrelated with the match between your personality traits and your partner’s. Your traits matter (it pays to be happy, for example) and so do your partner’s, but the combination makes no difference. In other words, being a happy person (or an extrovert, or a stickler for detail) affects the quality of your marriage in exactly the same way whether you marry Ruth Bader Ginsberg or Lady Gaga. (This applies specifically to personality traits, not to religion, politics, wealth, intelligence, etc.)

Edited to add: The original version of this post misstated the result; I’ve changed a few words in the preceding paragraph so it’s accurate now.

From this, Robin concludes:

If you want a happy relationship, be a happy person and pick a happy partner; no need to worry about how well you match personality-wise.

NO!!!! That’s not the right conclusion at all, and it’s worth understanding why not. Suppose we lived in a world where personality matches had a huge effect on the success of marriages. In that world, why would two people with clashing personalities ever choose to marry? Presumably because there’s some special value in the match — like, say, an extraordinary mutual attraction — that overrides the personality clash.

So a survey of married couples — which is exactly the sort of evidence Robin is reporting on — is not at all a random sample of couples. Instead, it consists, for the most part, of couples with matched personalities on the one hand, and couples with mismatched personalities who are exceptionally well suited to each other for some other reason on the other hand. It’s not too surprising to find similar success rates in those two classes of couples. The third class — the couples with mismatched personalities and no redeeming match characteristics — never gets married and therefore never gets surveyed.

Conclusion: The results Robin quotes are perfectly consistent with a world where personality matching doesn’t matter — but also perfectly consistent with a world where it matters very much.

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LocoVore Followup: A Blast From the Past

By way of followup to yesterday’s post on locavores, I present this letter to the editor of Science, written in 1976 by Harvard economist Robert Dorfman. You can think of Earl Cook, to whom Dorfman is responding, as the Steven Budiansky of his time.

The article by Earl Cook, “Limits to exploitation of nonrenewable resources”, is extremely informative. In fact, I should like to assign it to my class except that it is marred by an egregious fallacy. Since this fallacy has been turning up repeatedly in writings about environmental and natural resource problems, I wish to call it to the attention of Science readers.

The mistake has to do with the nature of social cost. Cook, for example, writes “To society … the profit from mining (including oil and gas extraction) can be defined either as an energy surplus, as from the exploitation of fossil and nuclear fuel deposits, or as a work saving, as in the lessened expenditure of human energy and time when steel is used in place of wood … “. A number of other authors also equate social cost with the expenditure of energy.

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Loco-Vores

bugsSteven Budiansky, the self-described Liberal Curmudgeon, thinks there’s something wrong with the locavore movement, and says so in the New York Times. But he misses the point just as badly as the locavores themselves.

The locavores, in case you don’t follow this kind of thing, are an environmentalist sect who make a moral issue out of where your food is grown — preferring that which is local to that which comes from afar. For example, as Budiansky puts it, “it is sinful in New York City to buy a tomato grown in California because of the energy spent to truck it across the country”.

Ah, says Budiansky, but let’s look deeper — the alternative to that California tomato might be one grown in a lavishly heated greenhouse in the Hudson Valley, and at a higher energy cost. This leads him off on a merry chase through what he calls a series of math lessons, adding up the energy costs of growing and transporting food in different locations. The implicit recommendation seems to be that when you’re choosing a tomato, you should care about all the energy costs.

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Weekend Roundup

roundupIt was a week of mathematics here at The Big Questions. I am still reeling from the momentous events that inspired Monday’s post; we now know that the Internet has changed mathematics forever. On Friday, we celebrated the momentous achievenments of the new Fields Medalists.

In between, we began what will be an occasional series on the foundations of arithmetic. In Part I, we distinguished truth from provability. In Part II, we distinguished theories (that is, systems of axioms) from models (that is, the mathematical structures that the theories are intended to describe). A theory is a map; a model is the territory. In Part III we talked about consistency and stressed that it applies only to theories, not to models. A purported map of Nebraska can be inconsistent; Nebraska itself can’t be.

It turns out (a little surprisingly) that any consistent map must describe multiple territories. (That is, any consistent set of axioms must describe many mathematical structures — or in other words, any consistent theory must have many models.) (This assumes the map has enough detail to let us talk about addition and multiplication.) These territories—i.e. these mathematical structures, all look very different, even though they all conform to the map. Conclusion: No map can fully describe the territory. No set of axioms can fully describe the natural numbers.

I’ll continue this series sporadically, and eventually we’ll get into some controversial philosophical questions. So far we haven’t.

Speaking of controversy, I’ve increased the default font size for this blog. Tell me if you like it.

Wikipedia Fail

Congratulations to the 2010 Fields Medalists, announced yesterday in Hyderabad. Elon Lindenstrauss, Ngo Bau Chau, Stanislav Smirnov, and Cedric Villani have been awarded math’s highest honor. (Up to four medalists are chosen every four years.)

My sense going in was that Ngo was widely considered a shoo-in, for his proof of the Fundamental Lemma of Langlands Theory. Do you want to know what the Fundamental Lemma says? Here is an 18-page statement (not proof!) of the lemma. The others were all strong favorites. Nevertheless:

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Basic Arithmetic, Part III: The Map is Not the Territory

Today let’s talk about consistency.

Suppose I show you a map of Nebraska, with as-the-crow-flies distances marked between the major cities. Omaha to Lincoln, 100 miles. Lincoln to Grand Island, 100 miles. Omaha to Grand Island, 400 miles.

You are entitled to say “Hey, wait a minute! This map is inconsistent. The numbers don’t add up. If it’s 400 miles straight from Omaha to Grand Island, then there can’t be a 200 mile route that goes through Lincoln!”

So a map can be inconsistent. (It can also be consistent but wrong.) Nebraska itself, however, can no more be inconsistent than the color red can be made of terrycloth. (Red things can be made of terrycloth, but the color red certainly can’t.)

With that in mind, suppose I give you a theory of the natural numbers — that is, a list of axioms about them. You might examine my axioms and say “Hey! These axioms are inconsistent. I can use them to prove that 0 equals 1 and I can also use them to prove that 0 does not equal 1!” And, depending on the theory I gave you, you might be right. So a theory can be inconsistent. But the intended model of that theory — the natural numbers themselves — can no more be inconsistent than Nebraska can. Inconsistency in this context applies to theories, like the Peano axioms for arithmetic, not to structures, like the natural numbers themselves.

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Basic Arithmetic, Part II

Today’s mini-lesson in the foundations of mathematics is about the key distinction between theories and models.

The first thing to keep in mind is that mathematics is not economics, and therefore the vocabulary is not the same. In economics, a “model” is some sort of an approximation to reality. In mathematics, the word model refers to the reality itself, whereas a theory is a sort of approximation to that reality.

A theory is a list of axioms. (I am slightly oversimplifying, but not in any way that will be important here.) Let’s take an example. I have a theory with two axioms. The first axiom is “Socrates is a man” and the second is “All men are mortal”. From these axioms I can deduce some theorems, like “Socrates is mortal”.

That’s the theory. My intended model for this theory is the real world, where “man” means man, “Socrates” means that ancient Greek guy named Socrates, and “mortal” means “bound to die”.

But this theory also has models I never intended. Another model is the universe of Disney cartoons, where we interpret “man” to mean “mouse”, we interpret “Socrates” to mean “Mickey” and we interpret “mortal” to mean “large-eared”. Under that interpretation, my axioms are still true — all mice are large-eared, and Mickey is a mouse — so my theorem “Socrates is mortal” (which now means “Mickey is large-eared”) is also true.

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Basic Arithmetic

With the P=NP problem in the news, this seems like a good time to revisit the distinction between truth and provability.

Start with this P=NP-inspired question:

Question 1: Is it or is it not possible to write a computer program that factors numbers substantially faster than by trial-and-error?

I don’t need you to answer that question. I just want you to answer an easier question:

Question 2: Does or does not Question 1 have an answer?

If you said yes (as would be the case, for example, if you happen to be sane), then you have recognized that statements about arithmetic can be either true or false independent of our ability to prove them from some set of standard axioms. After all, nobody knows whether the standard axioms of arithmetic (or even the standard axioms for set theory, which are much stronger) suffice to settle Question 1. Nevertheless, pretty much everyone recognizes that Question 1 must have an answer.

Let’s be clear that this is indeed a question about arithmetic, not about (say) electrical engineering. A computer program is a finite string of symbols, so it can easily be encoded as a string of numbers. The power to factor quickly is a property of that string, and that property can be expressed in the language of arithemetic. So Question 1 is an arithmetic question in disguise. (You might worry that phrases like “quickly” or “substantially faster” are suspiciously vague, but don’t worry about that — these terms have standard and perfectly precise definitions.)

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O Brave New World!

complexitySomething momentous happened this week. Of this I feel certain.

A little over a week ago, HP Research Scientist Vinay Delalikar claimed he could settle the central problem of theoretical computer science. That’s not the momentous part. The momentous part is what happened next.

Deolalikar claimed to prove that P does not equal NP. This means, very roughly, that in mathematics, easy solutions can be difficult to find. “Difficult to find” means, roughly, that there’s no method substantially faster than brute force trial-and-error.

Plenty of problems — like “What are the factors of 17158904089?” — have easy solutions that seem difficult to find, but maybe that’s an illusion. Maybe there’s are easy solution methods we just haven’t thought of yet. If Deolalikar is right and P does not equal NP, then the illusion is reality: Some of those problems really are difficult. Math is hard, Barbie.

So. Deolalikar presented (where “presented” means “posted on the web and pointed several experts to it via email”) a 102 page paper that purports to solve the central problem of theoretical computer science. Then came the firestorm. It all played out on the blogs.

Dozens of experts leapt into action, checking details, filling in logical gaps, teasing out the deep structure of the argument, devising examples to illuminate the ideas, and identifying fundamental obstructions to the proof strategy. New insights and arguments were absorbed, picked apart, reconstructed and re-absorbed, often within minutes after they first appeared. The great minds at work included some of the giants of complexity theory, but also some semi-outsiders like Terence Tao and Tim Gowers, who are not complexity theorists but who are both wicked smart (with Fields Medals to prove it).

The epicenter of activity was Dick Lipton’s blog where, at last count, there had been been 6 posts with a total of roughly 1000 commments. How to keep track of all the interlocking comment threads? Check the continuously updated wiki, which summarizes all the main ideas and provides dozens of relevant links!

I am not remotely an expert in complexity theory, but for the past week I have been largely glued to my screen reading these comments, understanding some of them, and learning a lot of mathematics as I struggle to understand the others. It’s been exhilarating.

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Weekend Roundup

More posts than usual this week as I was motivated twice to add a mid-day post to my usual morning fare. As a result, I’m afraid Jeff Poggi’s remarkable sonnet to Darwin got less attention than it should have; I hope you’ll go back, read it, and spot the hidden Darwin references.

The mid-day posts were motivated by a pair of (in my opinion, of course) outrages — first Paul Krugman’s suggestion that if we control for education and a few other demographic factors, we can make a meaningful comparison of private and public sector wages, ignoring all the ways in which public and private sector jobs differ. (And ignoring, too, all the ways in which one college degree might differ from another.) I suggested that a better metric is the quit rate in each sector; some commenters rightfully pointed out that that’s also an insufficient statistic. I bet it still comes a lot closer than Krugman’s attempt, though.

The second outrage was the Administration’s willingness to act as the equivalent of a Mafia enforcer for firms who prefer not to compete with foreign labor. Some commenters asked how this differed from any other case of the American government enforcing American laws while asking the beneficiaries to contribute to the costs. That’s easy. This law, unlike, say, the laws against murder, has as its primary purpose the restraint of trade (as opposed to oh, say, the general welfare).

We talked about how to estimate the peak of the Laffer curve (answer—it’s at about the 70% marginal tax rate, though I indicated some reasons why it might be somewhat leftward of that), mused about the value of a good CEO, and gave new meaning to the phrase phone sex when we reported on the fact that iPhone users have many more lifetime sex partners than Android users.

Incidentally, those readers who thought the flashy iPhone pays off in the mating market can’t be right (or at least can’t have hit on the key story), because the effect holds even for 40 year olds, who surely did not acquire their iPhones until long after they’d acquired most of their sex partners.

And we noted in passing the announcement of a proof that P does not equal NP (where you can look here for a very rough idea of what this means). Over the course of the week, this developed into a story of, I think, monumental significance, which I will surely revisit early next week. See you then.

The Protection Racket

Say you run a restaurant. And say a competitor announces plans to set up shop just across the street. What can you do to minimize the impact on your business?

Well, you could lower your prices. Or you could work on providing better service. Or you could send over a couple of guys who are really good at convincing people it’s not in their interest to compete with you.

Or say you run a personnel company that brings foreign workers into the United States. And say you’re worried about competitors who cross the border without your help. One option is to try doing a better job. Another is to send over about 1500 guys with unmanned aerial vehicles, new forwarding operating bases and $14 million in new communications equipment to tamp down the flow.

President Obama, with support from both sides of the political aisle, will be signing a bill today that allocates $600 million for “border security”. According to CNN, “The bill is funded in part by higher fees on personnel companies that bring foreign workers into the United States”.

I imagine the personnel companies will consider it money well spent. Let’s not lose sight of how ugly this is.

On Darwin’s 200th

Our reader Jeff Poggi sent me a sonnet he wrote in honor of Darwin’s 200′th birthday, and kindly allowed me to reproduce it here. How many hidden Darwin references can you spot?

On Darwin’s 200th
by
Jeff Poggi

Charles much under winter gray knew life
Would be back, be full, be gullible, need
Life. If inches crept by like miles rife
With their own history, then just a seed
Or stone therein would tell the story of
All this earth–all. He can’t let it be, sees
The earth make new earth, sees new stars above
Reflected, fits royal needs while he flees
Into his life in these new waters, lands.
Home in his garden he takes walks and writes,
Suffers loss most dear and is forced to hand
To them who will not hear what sorely smites
Their hallowed place, their no less hallowed birth—
From such simple forms we populate the earth.

Causation versus Correlation

phonesex

Data from 9,785 users of the dating site OKCupid reveal that iPhone users have 50% to 100% more sex partners than Android users, at every age.

This graph combines men and women, but the same pattern holds for each gender separately.

Explain this to me!

More info here (if you scroll down a couple of screens).

Laffering All The Way

The Washington Post’s Ezra Klein had a great idea this week: He asked a bunch of economists and pundits to tell him where the Laffer curve bends. In other words, what is the marginal tax rate above which higher taxes lead to lower revenues? Meanwhile, coincidentally or not, Paul Krugman blogged on the very same question.

There’s a lot worth mentioning here, but let me start with one point that will be relevant below: Imposing a 20% income tax is not the same as cutting your wage by 20%. That’s because the income tax grabs not just a chunk of your current wages, but also a chunk of the future interest and dividends those wages enable you to earn. So a 20% income tax will, in general, discourage work more effectively than a 20% wage cut. This is important if you’re using data on wage cuts to predict the effects of income taxes.

That having been said, let’s see what we can learn from the responses:

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P, NP and All That

The really big news from Hewlett Packard this week was not the dismissal of CEO James Hurd but the announcement by HP Labs researcher Vinay Deolalikar that he has settled the central question in theoretical computer science.

That central question is called the “P versus NP” problem, and for those who already know what that means, his claim (of course) is that P does not equal NP. For those who don’t already know what that means, “P versus NP” is a problem about the difficulty of solving problems. Here‘s a very rough and imprecise summary of the problem, glossing over every technicality.

Deolalikar’s paper is 102 pages long and less than about 48 hours old, so nobody has yet read it carefully. (This is a preliminary draft and Deolalikar promises a more polished version soon.) The consensus among the experts who have at least skimmed the paper seems to be that it is a) not crazy (which already puts it in the top 1% of papers that have addressed this question), b) teeming with creative ideas that are likely to have broad applications, and c) quite likely wrong.

As far as I’m aware, people are betting on point c) not because of anything they’ve seen in the paper, but because of the notorious difficulty of the problem.

And when I say betting, I really mean betting. Scott Aaronson, whose judgment on this kind of thing I’d trust as much as anyone’s, has publicly declared his intention to send Deolalikar a check for $200,000 if this paper turns out to be correct. Says Aaronson: “I’m dead serious—and I can afford it about as well as you’d think I can.” His purpose in making this offer?

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Krugman Phones One In

I rarely post in the middle of the day, but this seems to call for an immediate response:

Paul Krugman, feisty as ever, scoffs at the claim that public-sector employees are overcompensated. True, salaries are 13% higher in the public sector. But, says, Krugman, you’ve got to correct for the fact that public employees are (on average) better educated. After the correction, those public servants earn 4% less than the rest of us.

Well, Krugman is certainly right that you can’t take the raw data at face value. But, at least if you’re trying to be honest, you don’t get to pick and choose what you correct for either. Sure, let’s correct for education levels. Let’s also correct for the fact that public sector employees work fewer hours per week. And for differences in pension plans, and job security, and working conditions.

How can we ever be sure we’ve counted everything important? We can’t, as long as we do it Krugman’s way. So let’s do something sensible instead. Let’s look at quit rates. Quit rates in the public sector are about one third what they are elsewhere. In other words, government employees sure do seem to like holding on to their jobs. More than just about anyone else, in fact. Doesn’t that tell us everything we need to know about who’s overcompensated?

HP Falter

hpHow important is it to hire the best person for the job?

Here’s a data point: On Friday, Hewlett Packard’s CEO Mark Hurd resigned unexpectedly — and pretty much instantly the value of HP stock dropped by about $10 billion. If we assume Hurd would otherwise have been around for another 10 years or so, that means shareholders think his departure will cost the company about a billion dollars a year. Which, incidentally, makes his $30 million or so in annual compensation look like a hell of a bargain.

Now maybe some part of that $10 billion reflects expected short-term losses due to the turmoil of an unplanned transition. But even if that turmoil were to cost HP a full month of revenue (which seems like a pretty extreme assumption), that’s still less than a billion — leaving over $9 billion to represent the difference between what the market expected from Hurd and what it expects from his successor.

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65 Years Later

quartered65 years ago today, the world changed. In his magnificent World War II memoir Quartered Safe Out Here, George McDonald Fraser looks back on what might have been:

I led Nine Section for a time; leading or not, I was part of it. They were my mates, and to them I was bound by ties of duty, loyalty and honor… Could I say, yes, Grandarse or Nick or Forster were expendable, and should have died rather than the victims of Hiroshima? No, never. And the same goes for every Indian, American, Australian, African, Chinese and other soldier whose life was on the line in August, 1945. So [I'd have said]: drop the bomb.

And then I have another thought.

You see, I have a feeling that if—and I know it’s an impossible if—but if, on that sunny August morning, Nine Section had known all that we know now of Hiroshima and Nagasaki, and could have been shown the effect of that bombing, and if some voice from on high had said: “There — that can end the war for you, if you want. But it doesn’t have to happen, the alternative is that the war, as you’ve known it, goes on to a normal victorious conclusion, which may take some time, and if the past is anything to go by, some of you won’t reach the end of the road. Anyway, Malaya’s down that way … it’s up to you”, I think I know what would have happened. They would have cried “Aw, fook that!”, with one voice, and then they would have sat about, snarling, and lapsed into silence, and then someone would have said heavily, “Aye, weel” and got to his feet, and been asked “W’eer th’ ‘ell you gan, then?”, and given no reply, and at last, the rest would have got up, too, gathering their gear with moaning and foul language and ill-tempered harking back to the long dirty bloody miles from the Imphal boxes to the Sittang Bend and the iniquity of having to do it again, slinging their rifles and bickering about who was to go on point, and “Ah’s aboot ‘ed it, me!” and “You, ye bugger, ye’re knackered afower ye start, you!”, and “We’ll a’ git killed!”, and then they would have been moving south. Because that is the kind of men they were.

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Equal Protection

A U.S. District Court has overturned California’s Proposition 8 (the prohibition of same-sex marriage), which, says the court, violates both the Due Process and Equal Protection clauses of the Fourteenth Amendment. I am very happy to hear that the courts are open to overturning legislation that violates the Fourteenth Amendment. Next up, Title VII of the 1964 Civil Rights Act!

The issues are pretty much identical. Here is the District Court’s reasoning in the California case (this is the Court’s summary of the plaintiffs’ position, which the Court endorses):

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This is Just to Say…

William Carlos Williams is a really bad roommate and I’m tired of sharing an apartment with him.  

A hat tip to my buddy Rosa, with hat tips once and twice removed to Tim Pierce and Doctor Memory.

Click here to comment or read others’ comments.

Deflation Followup

Yesterday’s post on deflation prompted a flurry of comments and emails remarking on how much economists disagree. This, I think, misses the point. Indeed, what I was trying to emphasize was that we all agree on the advantages of deflation as spelled out in Milton Friedman’s essay on The Optimum Quantity of Money. (I’ve put a quick summary of the key points here.) Therefore, the commentators who are currently worried about deflation must fall into two categories: First, there are the ignoramuses, of whom there are plenty on all sides of all issues. Second, there are those who are clearly not ignoramuses. Those in the latter camp have surely digested Friedman’s analysis, and understand the upside of deflation, but believe it is outweighed by some downside. It is frustrating to me that many of those commentators have failed to explain exactly what downside they have in mind.

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Deflating the Deflation Scare

deflationSo apparently we’re all supposed to be worried these days about the specter of deflation. I am doubly baffled by this—I don’t see the problem in theory and I don’t see the problem in practice. Maybe there’s something I’m missing.

Start with the theory: We learned long ago from Milton Friedman (who might have learned it from Irving Fisher) that a little bit of deflation is a good thing. That’s because deflation encourages people to hold money, and people who hold money aren’t buying stuff, and when other people don’t buy stuff, there’s more stuff left over for you and me.

There are a couple of other ways to see this, though they all come down to the same thing. Here’s the first: falling prices are good for buyers and bad for sellers, but that all washes out. It washes out in the aggregate because each gain to a buyer is offset by an equal and opposite loss to a seller. And it more or less washes out for each individual, because each of us sells roughly as much as we buy (including the sale of our labor.) But over and above all that, deflation enriches the holders of money, because their money increases in value as it sits around. That part is pretty much (may Milton’s ghost forgive me for putting it this way) a free lunch.

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