Thursday, August 31, 2006

Monty Hall again

John Kay offers a surprising solution, though no resolution, to the Monty Hall paradox.

The extraordinary feature of the two-box problem is that there is a strategy that seems better than always switching or always sticking, one that beats random choice even in a situation of almost total ignorance.

Well, it is a remarkably simple strategy.

Nicely done

Chris Dillow has an excellent post on when it is efficient for a society to have property rights.

Tuesday, August 29, 2006


Via Edge, an editorial and an article in the New Scientist on Loop Quantum Gravity. Loop Quantum Gravity hypothesizes that the elementary particles are braids made of space-time, thus dissolving the difference between space-time and the matter that "warps" it in the General Theory.

The origins of loop quantum gravity can be traced back to the 1980s, when Abhay Ashtekar, now at Pennsylvania State University in University Park, rewrote Einstein's equations of general relativity in a quantum framework. Smolin and Carlo Rovelli of the University of the Mediterranean in Marseille, France, later developed Ashtekar's ideas and discovered that in the new framework, space is not smooth and continuous but instead comprises indivisible chunks just 10-35 (Rajeev: 10 to the power of -35) metres in diameter. Loop quantum gravity then defines space-time as a network of abstract links that connect these volumes of space, rather like nodes linked on an airline route map.

From the start, physicists noticed that these links could wrap around one another to form braid-like structures. Curious as these braids were, however, no one understood their meaning. "We knew about braiding in 1987," says Smolin, "but we didn't know if it corresponded to anything physical."

Some models developed in the 1970s hypothesised that the elementary particles (electrons, photons, neutrinos, etc.) are made of smaller particles they called preons, which carried charge and interacted with one another. The models were abandoned when it was discovered that these preons would ave more energy than the particles that are built up of them. Sundance Bilson-Thompson approached the problem differently.

Instead of thinking of preons as particles that join together like Lego bricks, he concentrated on how they interact. After all, what we call a particle's properties are really nothing more than shorthand for the way it interacts with everything around it. Perhaps, he thought, he could work out how preons interact, and from that work out what they are.

To do this, Bilson-Thompson abandoned the idea that preons are point-like particles and theorised that they in fact possess length and width, like ribbons that could somehow interact by wrapping around each other. He supposed that these ribbons could cross over and under each other to form a braid when three preons come together to make a particle. Individual ribbons can also twist clockwise or anticlockwise along their length. Each twist, he imagined, would endow the preon with a charge equivalent to one-third of the charge on an electron, and the sign of the charge depends on the direction of the twist.

The simplest braid possible in Bilson-Thompson's model looks like a deformed pretzel and corresponds to an electron neutrino (see Graphic). Flip it over in a mirror and you have its antimatter counterpart, the electron anti-neutrino. Add three clockwise twists and you have something that behaves just like an electron; three
anticlockwise twists and you have a positron. Bilson-Thompson's model also produces photons and the W and Z bosons, the particles that carry the electromagnetic and weak forces. In fact, these braided ribbons seem to map out the
entire zoo of particles in the standard model.

Smolin, Bilson-Thompson and Fotini Markopoulou then used a radical version of quantum mechanics which Fontini was working on, which treats the Universe as a giant Quantum computer.

In Markopoulou and Kribs's version of loop quantum gravity, they considered the universe as a giant quantum computer, where each quantum of space is replaced by a bit of quantum information. Their calculations showed that the qubits' resilience would preserve the quantum braids in space-time, explaining how particles could be so long-lived amid the quantum turbulence.

Smolin, Markopoulou and Bilson-Thompson have now confirmed that the braiding of this quantum space-time can produce the lightest particles in the standard model - the electron, the "up" and "down" quarks, the electron neutrino and their antimatter partners

So, once again, we return to the idea that existence is a computation.

Meanwhile, Markopoulou's vision of the universe as a giant quantum computer might be more than a useful analogy: it might be true, according to some theorists. If so, there is one startling consequence: space itself might not exist. By replacing loop quantum gravity's chunks of space with qubits, what used to be a frame of reference - space itself - becomes just a web of information. If the notion of space ceases to have meaning at the smallest scale, Markopoulou says, some of the consequences of that could have been magnified by the expansion that followed the big bang. "My guess is that the non-existence of space has effects that are measurable, if you can only see it right." Because it's pretty hard to wrap your mind around what it means for there to be no space, she adds.


Intelligent leaders

This week's issue of the Economist has a letter from a professsor at HEC Lausanne

It might interest you to know that not a single serious study has ever been able to demonstrate a link between “emotional intelligence” and leadership effectiveness. The most robust and consistent single predictor of leadership effectiveness is, simply, intelligence. Emotional intelligence sells well, but scientific evidence supporting it is almost as solid as that supporting the effectiveness of homeopathy.

I don't know the details of the studies which led to this conclusion, but I wonder if they suffered from a version of the Sample Selection Bias described by Michael Stastny at Mahalanobis. Tyler Cowen once referred to a paper by Shane Frederick to the effect that

Expressed loosely, being smart makes women patient and makes men take more risks

Most senior managers are men. Intelligent men take greater risks than less intelligent men. Men who take risks will be either exceptionally successful or spectacular failures, while men who avoid risks will perform middlingly. If there is Sample selection bias, it will then appear that intelligence correlates with management ability. Just thinking aloud.

Monday, August 28, 2006

On Terrorism

Nitin Pai brought this article to my attention. Interesting read, but I could not agree with the thesis:

1. Taleb is wrong when he says

"you may believe, say, that financial markets will probably go up, while you behave, sensibly, as if they will go down. The reason? Because you think it very likely that they will go up a little, but, in the unlikely event that they go down, you think they will go down a great deal."

After all, markets have a bottom- they can go down to zero, but not below that. However, they can go up to infinity. The conventional explanation for why people behave this way is that they maximize expected utility, rather than expected wealth, and that this leads to risk aversion. Indeed, this is the very issue that led Bernoulli to come up with the idea of utility.However, even this is seriously controversial.

2. "successful suicide bombings became even slightly more common, can we really be confident that other fundamentalists would not copy that behaviour". This is quite correct- we should be preventing these attacks, but we also need to realize that there are other serious problems. If its really our intention to save lives, rather than simply political PR, we should see where our efforts can actually save most lives. By all means, prevent these attacks, but prioritize.

3. People are tough. I have seen half-dozen attacks on Mumbai. The latest was the train atrocity. People are back on the trains now. I can't imagine the terrorists believe they are any closer to their objectives because of their crimes. That must be pretty frustrating for them, and that should help prevent this: "Potential offenders catch the idea of offending from each other. And just like a disease that starts with only a few people and becomes an epidemic, once it reaches a tipping point the amount of criminal behaviour explodes". The American and British
responses are far more encouraging to them. Why give them the satisfaction of letting them think we consider them a huge issue? They are not.

I think this article in the Financial Times is also in favor of a more low-key approach to the "War on Terror". I also think Chris Dillow makes good sense here.

Friday, August 25, 2006

May I bring to your attention my paper

A wonderful article in the New Yorker, by Sylvia Nasar and David Gruber, on the Poincare hypothesis, and the battle for priority. A person like Perelman is almost certain to feel lost in this maze.

Perelman, by casually posting a proof on the Internet of one of the most famous problems in mathematics, was not just flouting academic convention but taking a considerable risk. If the proof was flawed, he would be publicly humiliated, and there would be no way to prevent another mathematician from fixing any errors and claiming victory. But Perelman said he was not particularly concerned. “My reasoning was: if I made an error and someone used my work to construct a correct proof I would be pleased,” he said. “I never set out to be the sole solver of the PoincarĂ©.”

And Chinese mathematics comes across as some sort of weird cult.

Paying the price

Biology can tell some of the most compelling stories of Economics at work. This post by Carl Zimmer is a great example of the problem of Public goods. The question here is why some of these critters "willingly" sacrifice themselves so that others may breed.
The theory of altruism pioneered by Haldane and Hamilton can explain such behavior when the parties are closely related, but not when they are totally unrelated. Any gene that leads to such behavior would quickly die out. "The evolution of virtue" by Matt Ridley had a great discussion of such issues.

Bow down

Seems tall guys are smarter, and generally cooler.
Thought that was obvious- guess the shorties need everything spelt out. :-)

The man that hath no music in himself

This seems like a book for me.

Tuesday, August 22, 2006

Monty Hall is back

John Kay describes a problem that involves a probability distribution that is not well-behaved.

This problem is real. Anyone who has changed jobs, bought a house or planned a merger has encountered a version of the two-box game; keep what you know, or go for an uncertain alternative. But familiar problems are not necessarily easy to model.

Of course, this is better known as the two envelopes problem, and there are other paradoxes in probability theory.

Sunday, August 20, 2006

Two on India

The Economist recently published two articles on India- one in this issue, and the other in Economics Focus from the previous issue.

The second is subscription only, and is about the World Bank's India Development Policy Review.

Look at the detail, however, and you may despair at the depth and complexity of the problems India faces. For all its achievements, poverty remains entrenched. Some 260m people survive on less than one dollar a day. Nearly half of the country's children below the age of six are undernourished. More than half of its women are illiterate. Half its homes have no electricity, and in one state, Chhattisgarh, 82% are not even connected by road. Nor is there a huge pot of money to throw at these shortages. The government's average budget deficit, from 2000 to 2004, was exceeded only by that of Turkey. Even when it does spend money, the pipeline between government coffers and the intended beneficiaries is corroded by corruption, and cash seeps out.

Thus, the report argues that the "rampant" optimism about India is not justified by fundamental changes, that the performance of the public sector is going from bad to worse, and that the gap between the best of India and the worst keeps growing.

India, for example, has a government committed to providing all its people with health care. But there are only five countries in the world where a lower proportion of spending on health comes from the government—just 21% (compared with, for example, 45% in America). So even the poor are paying for private health care. A survey has also found that health care absorbs a bigger share (27%) of low-level “retail” bribery than any other government function...Another found that between 1999 and 2003 the percentage of children fully immunised against childhood diseases had fallen from 52% to 45%.

Inequality keeps getting worse, partly because the worst-performing states are falling further behind the best.

Although India has, compared with other countries, a relatively equal distribution of income, it is a deeply unequal society, partly because of its legacy of social stratification and exclusion. The caste system is proving resilient, and there is evidence that, in some respects, the prejudice against girl children is worsening. In rich areas, sex-selective abortion is leading to highly skewed sex ratios at birth. Nor is the bias any less among the poor. A girl born in the early 1990s was 40% more likely than a boy to die between her first and fifth birthdays

Thus, it argues that the problems of the country boil down to two big, inter-related issues: "to make the public sector better at delivering basic services; and to sustain growth at high levels and extend its fruits to more people". Alas, no indication of how it can be done.

The article in the new issue is about the Maoists in India. Not suprisingly, the epicenter is in the very parts, including Chattisgarh, which are falling further behind the rest of the country. These, though, are no defenders of the poor

Several hundred had mounted a co-ordinated attack on a police station, a paramilitary base and a relief camp for displaced people. They killed more than 30 of the camp's residents, mostly by hacking them to death with axes. The scholarly Mr Ueike did boast that his army relied on “low-tech weapons”.

This was the latest battle in a year-long civil war in Dantewada district, in which more than 350 people have been killed, and nearly 50,000 moved into camps such as the one at Errabore.

And the problem is big:

In nearly 1,600 violent incidents involving Naxalites last year, 669 people died. There have been spectacular attacks across a big area: a train hold-up last month involving 250 armed fighters, a jailbreak freeing 350 prisoners, a near-miss assassination attempt in 2004 against a leading politician. “Naxalism” now affects some 170 of India's 602 districts—a “red corridor” down a swathe of central India from the border with Nepal in the north to Karnataka in the south and covering more than a quarter of India's land mass.

As always, the reason for their success is that the "Indian State is almost invisible"

In one there is a hand-pump installed by the local government, but the well is dry. There are no roads, waterpipes, electricity or telephone lines. In another village a teacher does come, but, in the absence of a school, holds classes outdoors. Policemen, health workers and officials are never seen. The vacuum is filled by Naxalite committees, running village affairs and providing logistic support to the fighters camping in the forest.

And, predictably, the local people are caught between the Maoists and Salwa Judum

This is a dirty little war in which truth was long ago a casualty. Salwa Judum itself is also responsible for displacing people—a “scorched village” policy intended to starve the Maoists of local support. This recognises that the Naxalites' real strength lies not in their guerrillas in the jungle, with their peaked caps and “country-made” rifles, but in their civilian networks in the villages themselves....Even Mr Gill, who has seen more brutality than most, thinks the Maoists stand out in this respect: “Their ideology is that the manner of killing should frighten more than the killing itself.”

Salwa Judum, too, is accused of intimidation, extortion, rape and murder. Its thugs have been manning roadblocks, supposedly to hunt for Maoists, but also to demand money. Some SPOs—like some Naxalites—may be local hoodlums, who have signed up for the money on offer, and the shiny new bicycles and motorbikes still wrapped in plastic at the Dornapal police station. Some families refusing to join Salwa Judum on its “combing” operations—rampages of arson, thuggery and pillage—have been “fined” or beaten. A report on Salwa Judum produced in April by a number of civil-liberties groups concluded that its formation had “escalated violence on all sides...Salwa Judum and the paramilitary operate with complete impunity. The rule of law has completely broken down.”

However, the Maoists are not merely cruel

He (Ajai Sahni of the Institute of Conflict Management, a Delhi think-tank) also says that the Naxalites have been among the most principled of terrorist groups in selecting their targets. Their attacks are not random; though, because they so often use crude landmines, they may kill the wrong people. Their leaders are thinking far into the future, taking a 20- to 25-year view of their struggle. “Liberated” areas, such as their part of Dantewada, would be expanded until they pose a threat even to India's cities.

Nepal's Maoists, with whom the Indian party has “fraternal” links, are a model of how such a strategy can work. Having managed to exclude the state from virtually all the countryside, and waged war for a decade, the Maoists in Nepal are now negotiating, from a position of some strength, their share in government—a decision their Indian comrades quietly deplore, despite a pretence of solidarity.

Just as I am sure that the current wave of Terrorism will die out, I have no doubt that this threat too will pass, but at a very high price indeed. The Naxal threat is strongest in teh poorest parts of India, deterring investment and hence increasing the gap with the rest of the country, and the resulting frustration then feeds the Naxal movement. Some good could come out of this if it makes the Indian State more serious about delivering basic services to these poor people. The Indian State is immensely strong and resilient, but Indians are just flesh and blood.

No deal

When you can't pay. Greg Mankiw links to an article by Cass Sunstein in the Washington Post, on why we are unlikely to see a deal on Global Warming. The folks responsible for the warming are not the ones who will suffer the consequences.

In recent years the United States has accounted for about 21 percent of the world's greenhouse gas emissions. China comes in second at about 15 percent. While many countries have stabilized their greenhouse gas levels, emissions from both nations, but especially China, are growing rapidly. Current projections suggest that by 2025 total emissions from the United States will increase by about one-third. By that year, China's emissions are expected roughly to double.... It follows that if an international agreement requires reductions, China and the United States will have to bear the brunt of the expense.


the biggest losers from greenhouse gas pollution are likely to be India and Africa. Some of the most detailed, careful and influential projections have been made by Yale University's William Nordhaus and Joseph Boyer. Nordhaus and Boyer show that in terms of human health and agricultural loss, India and Africa are by far the most vulnerable regions on Earth. Because of an anticipated increase in malaria, Africa will probably be hit especially hard, and India is expected to suffer a large increase in premature deaths as well.

While the US will pobably not suffer seriously, and Chinese agriculture will actually gain.
The two nations now most responsible for the problem have comparatively little incentive to do anything about it.

Thursday, August 17, 2006

Beauty bare

More than 2 years ago, Tyler Cowen reported that a "Russian loner", Grisha Perelman may have solved the Poincare Conjecture. Well, it seems the proof hangs together after all.

And Scientific American has an article on Alain Connes and his hopes that non-commutative geometry could explain the structure of space-time.

As an example, Connes refers to the way particle physics has grown: The concept of spacetime was derived from electrodynamics, but electrodynamics is only a small part of the Standard Model. New particles were added when required, and confirmation came when these predicted particles emerged in accelerators.

But the spacetime used in general relativity, also based on electrodynamics, was left unchanged. Connes proposed something quite different: "Instead of having new particles, we have a geometry that is more subtle, and the refinements of this geometry generate these new particles." In fact, he succeeded in creating a noncommutative space that contains all the abstract algebras (known as symmetry groups) that describe the properties of elementary particles in the Standard Model.

I don't understand any of the details of the latter, and only the most basic concepts of the first, but it feels nice that creatures of flesh and blood can actually think such thoughts.

Monday, August 14, 2006

Retailing and Software

The New Economist reports that IBM is planning to expand massively in India, and that this scares Indian firms who will now face competition for their employees.
Wage inflation is real but not a problem.

Some commentators have expressed concern that wage inflation in India is blunting the country's competitive edge in software services. These fears are overstated. It isn't particularly worrisome from India's perspective that the country's software engineers are now only a sixth as cheap as their U.S. counterparts. In 1998, that wage difference was about twice as large. The skills gap between its computer programmers and those from developed countries is shrinking even faster.

However, supply side constraints remain

That doesn't mean that such jobs are open to everyone. "Only those individuals have been able to gain entry into this industry whose parents are both quite highly educated,'' says Anirudh Krishna, a professor of public policy at Duke University in Durham, North Carolina.

Krishna's research on three Bangalore-based software companies shows that undereducated parents, unaware of the potential in the software industry, fail to prepare their children for the available opportunities. Parental ignorance constrains the size of the talent pool.

Ricardo is alive and well, as other sectors of the Economy struggle as talented people opt for careers in IT. The Bangalore Bug is

term that International Monetary Fund Chief Economist Raghuram Rajan uses for the challenge India will face as rising software wages make engineers so expensive that other sectors of the economy, especially labor-intensive manufacturing, can't afford them.

The New Economist also describes Reliance's plans to become the 3rd largest retailer in the world, after Wal-mart and Carrefour.

Wednesday, August 09, 2006

Truth Serum

Nice article from the March 2006 of Scientific American on the use of Experimental Economics at Hewlett-Packard.
Companies that rely on Salespeople's inputs to forecast sales face problems of Asymmetric information, similar to those that are confronted by Insurance companies. Salespeople are tempted to undercommit, which could result in the company being underprepared for actual sales. The solution, very similar to the one devised by insurance companies.

have each salesperson choose a personal balance of fixed and variable compensation. For example, the salesperson can choose a high commission percentage with no fixed salary or, at the other extreme, a modest fixed salary and no commission--or some combination in between. Each choice implicitly reveals how much the salesperson plans to sell, much as an insurance subscriber's choice of deductible and premium reveals how sick she is. Based on a truth-telling mechanism from game theory, this design works on paper.

Monday, August 07, 2006

On inequality

Via New Economist, an article by Pranab Bardhan in the Financial Times, on Inequality in India.
Its important to realize that these statistics are for all of India- a huge place. There is a lot of variation within the country.
However, it is broadly true that your well-being, and the social status that you enjoy, is largely determined by the family that you are born in into.
In the long run, this could cause India to go the way of Latin America. While the US followed a policy of homesteading (read this article by Hernando De Soto on the squatters who built America), land in Latin America was distributed by the government. Naturally, the wealthy and powerful grew even more wealthy and powerful. This could be one reason why wealth in Latin America has been tainted, and society has bene torn apart by the conflict between ultra-conservative reactionaries and redistributionist radicals.
This is related to one reason why I am against restictions on immigration into the large cities. In a country that fails to provide basic health-care and education to its rural poor, the alternative to internal migration is revolution.

Here comes the sun

and blue skies, after 3 days of gloom.

Wednesday, August 02, 2006

On the workings of the Indian Economy

Nitin Pai points out that India is still a difficult place to do business. (Worse than Iraq, though?!)

The New Economist links to a World Bank working paper by by Franklin Allen, Rajesh Chakrabarti, Sankar De, Jun Qian and Meijun Qianon on "Financing Firms in India. "

Our evidence, including results based on a survey of small- and medium-scale private firms, shows that alternative financing channels provide the most important source of funds. We also find that informal governance mechanisms, such as those based on reputation, trust and relationships, are more important than formal mechanisms (e.g., courts) in resolving disputes, overcoming corruption and supporting growth.

This is typical of extremely immature market economies.
Now, how do businesses survive the corruption?

Perhaps one of the most effective solutions for corruption for firms in this sector is the common goal of sharing high prospective profits. This common goal can align interests of the investors and government officials with entrepreneurs and managers to overcome numerous obstacles.

Another potential effective solution for corruption is competition among local governments/ bureaucrats from different regions within the same country. Entrepreneurs can move from region to region to find the most supportive government officials for their private firms, which in turn motivates officials to lend "helping hands" rather than "grabbing hands," or else there will be an outflow of profitable private businesses from the region. This remedy should be typically available in a big country with multiple regions like India.

This is an interesting variant of Mancur Olson's "grabbing hand" theory of Government. Because the businesses can choose the "bandit" (the regional governments) they are subject to, the Bandits' rapacity is constrained.

Tuesday, August 01, 2006


Five books

What price peace?

David Warsh, author of Knowledge and the Wealth of Nations, and the best weekly commentator on Economics matters I know of, writes about the cost of the war in Iraq. There are potential lessons for us in India, in our war with terrorism. I have little to add where people brighter and more knowledgeable than I am have thought so long and so hard. However, Pakistan is clearly a failed state- and its failure is inflicting terrible suffering on its own people. Moreover, the place is a breeding ground for terrorist activity directed at India. It is tempting to think that our problems originate across the border, and that if we could only remake the place more to our own liking, using force if required, our problems would be solved. This piece should give us pause.
What is our greatest problem? There are 10,000 armed Maoists tormenting at least 170 of India’s 602 districts, and Diarrhoea is the second leading cause of death among children here. Economics suggest that we should spend our resources where the marginal returns are greatest. We spend 15% of our central government budget on defense, and 2% on health and education each. Containment looks like a better policy than ever.

It's probably fair to say that the economics of national security had its beginnings in an essay by William D. Nordhaus of Yale University that appeared in December 2002, first in a non-technical essay in The New York Review of Books, then as a publication of the American Academy of Arts and Sciences…

It might seem faint-hearted to take seriously beforehand the task of estimating war's potential cost, wrote Nordhaus, slyly anticipating his critics, "a sign of insufficient resolve at best and appeasement at worst," but in fact it was simply realistic. "...[M]ost people recognize that the costs in dollars, and especially in blood, are acceptable only as long as they are low. If the casualty estimates mount to the thousands, if oil prices skyrocket, if a war pushes the economy into recession or requires a large tax increase, and if the United States becomes a pariah in the world because of callous attacks on civilian populations, then decision-makers in the White House and the Congress might not post so expeditiously to battle."…

And after disentangling direct military spending from various follow-on costs -- occupation and peacekeeping, reconstruction and nation-building, humanitarian assistance, the impact on oil markets and macroeconomic impact, Nordhaus produced a pair of estimates of the war's likely cost over a the course of a decade, low and high --$99 billion after a short and favorably resolved battle, compared to $1,934 billion, or almost $2 trillion dollars, nearly 20 percent of GDP, in the event of a protracted war with an unfavorable outcome.

As it happened, a trio of University of Chicago economists also produced in 2003 an estimate of the costs of the war, which came to very different conclusions -- partly by taking the analysis a step further and asking, compared to what?...

Assuming that Saddam had the same kind of staying power as repressive regimes in North Korea and Cuba, the Chicago economists concluded that the invasion would be a bargain, for Americans and Iraqis alike. The cost of continuing to contain Saddam at the same level as the precious decade -- 30,000 troops, 30 ships and 200 aircraft and their crews -- would add up to $380 billion going forward. "This dwarfs any reasonable estimate of US war costs," they wrote -- even before the possibility of increased terrorism was over the next twenty years was added in.

What about the Iraqis? What about the cost of war to them? Since Saddam came to power in 1979, their economy had stagnated, the Chicagoans noted; income per person had fallen by as much as 75 percent. They toted up the loss of lives as well -- the war with Iran, the repression of the Shiites, the Kurds and the Marsh Arabs, something like half a million premature deaths over a quarter-century, and projected the record into the future (with a suitable discount rate of 2 percent, and a 3 percent probability of spontaneous regime-change) and concluded another 200,000 to 600,000 Iraqis could be expected to die under a policy of continued containment were Saddam and his henchmen to continue to rule for another 33 years.

In contrast, after a forcible regime change, the Iraqi economy begins growing again. The war itself costs no more than a half a year's GDP. Oil revenues swell, income per person grows enough to make up for the quarter-century decline. "At first, it may seem surprising that war can lead to a huge improvement in human welfare. But, in fact, this conclusion is hard to escape so long as regime change even partly undoes the collapse in living standards under Saddam" -- at least it does as long as the killing stops.

And what if doesn't? Last week the Chicagoans were back, with a revised and considerably expanded rewrite of their 2003 paper, presented by Davis to the NBER's Summer Institute. Gone were some of the slam-bang certainties of the earlier version ("...[T]he costs of containment dramatically outweigh the costs of war according to our analysis"). Added were a number of cost-of-capital subtleties in calculating the cost of various contingencies, and a broader view of the possibilities themselves. Unchanged was the insistence that any judgment of the cost and efficacy of the invasion of Iraq would have meaning only when compared to the cost of /not/ invading -- that is, to maintaining a policy of containment.

What was striking, however, was that somehow the Chicagoans' numbers had changed.

In his role as discussant, Yale's Nordhaus underscored the disparity. In 2003, he noted, on the eve of the war itself, the Chicagoans had rated the cost of containment as $630 billion, compared to a projected $125 billion cost of war -- a virtual no-brainer. In the 2006 version, with the advantage of "partial hindsight" creeping in despite their determination to write as though they were still looking forward from early 2003, their (backward-looking) forward-looking cost of containment had become $297 billion, against a best guess of the cost of the war of $414 billion -- a very dramatic swing.

The words with which Nordhaus closed his 2002 discussion of the economic consequences of a war with Iraq suggest just how imaginative a before-the-fact analysis must be in the future if it is to be persuasive:

"The cost of a war may turn out to be low, but the cost of a successful peace looks very steep. If American taxpayers decline to pay the bills for ensuring the long-term health of Iraq, America would leave behind mountains of rubble and mobs of angry people. As the world learned from the Carthaginian peace that settled World War I, the cost of a botched peace may be even higher than the price of a bloody war"