Lunch with Jeremy Bentham
I finally got to visit my old friend Jeremy Bentham today. We had lunch together. He didn't talk much, but he was pleasant company nonetheless. Here, you can see both of us in this picture I took - he's the one behind the glass, and I'm the one in front of it.
If you ever visit UCL, I'm sure he'll be happy to see you too - and isn't happiness what it's all about? Here's more on where to find him and his busy schedule since his death 175 years ago:
At the end of the South Cloisters of the main building of UCL stands a wooden cabinet, which has been a source of curiosity and perplexity to visitors.
The cabinet contains Bentham's preserved skeleton, dressed in his own clothes, and surmounted by a wax head. Bentham requested that his body be preserved in this way in his will made shortly before his death on 6 June 1832.Not surprisingly, this peculiar relic has given rise to numerous legends and anecdotes. One of the most commonly recounted is that the Auto-Icon regularly attends meetings of the College Council, and that it is solemnly wheeled into the Council Room to take its place among the present-day members. Its presence, it is claimed, is always recorded in the minutes with the words Jeremy Bentham - present but not voting. Another version of the story asserts that the Auto-Icon does vote, but only on occasions when the votes of the other Council members are equally split. In these cases the Auto-Icon invariably votes for the motion.
Bentham had originally intended that his head should be part of the Auto-Icon, and for ten years before his death (so runs another story) carried around in his pocket the glass eyes which were to adorn it. Unfortunately when the time came to preserve it for posterity, the process went disastrously wrong, robbing the head of most of its facial expression, and leaving it decidedly unattractive. The wax head was therefore substituted, and for some years the real head, with its glass eyes, reposed on the floor of the Auto-Icon, between Bentham's legs.
However, it proved an irresistible target for students, especially from King's College London, who stole the head in 1975 and demanded a ransome of £100 to be paid to the charity Shelter. UCL finally agreed to pay a ransome of £10 and the head was returned. On another occasion, according to legend, the head, again stolen by students, was eventually found in a luggage locker at a Scottish Station (possibly Aberdeen). The last straw (so runs yet another story) came when it was discovered in the front quadrangle being used for football practice, and the head was henceforth placed in secure storage.
Friday Special 47
Surfing video on a wave of similar magnitude
The Face of Tomorrow: the effects of globalization on identity
Desktopography exhibits various nature themed wallpapers
Beluga SkySails proves concept on its maiden voyage
Chinese smart phone runs 1 year in standby
Kurt Cobain About A Son
Niloufar
From Marjane Satrapi's Persepolis.
A girl argues with God
This is from the superb Persepolisby the Iranian Marjane Satrapi. If you read one thing this year, this should be it.
I will be posting a couple more excerpts from the book and commentary in the following days.
A free lunch tastes better
Dan Ariely, author of Predictably Irrationalsays that free! is not just another price.
Thanks to James for the pointer.
21 accents
Impressive.
Friday Special 46
Start your daily all-in-one web experience simple with Symbaloo
Reported oil reserves and other interesting charts
Because adventure is a big part of life: Steep
Google office in Zurich, Switzerland
In the long run it's only redistribution, and redistribution is a good thing: Thoughts on the subprime crisis, part 1
Assume house prices fall by 50%. Heck, assume stock prices also fall by 50%. As Tyler Cowen notes, no houses are dynamited. No factories are burned to the ground. No people are shot. In short, no resources are used up. We, as a society, have exactly as much material wealth as we did before.
At the end of the day, a massive fall in asset prices is nothing more than a transfer of resources from people that hold a lot of assets to people that hold few assets.
In fact, it is very difficult to argue that a fall in asset prices is not in fact a good thing. Asset-heavy individuals tend to be rich(er) than asset-light individuals. We, society, value redistribution. In fact, we value it so much that we impose highly distortionary taxes to achieve it. A massive fall in asset prices means that we now get a lot of redistribution with none of the distortionary effects.
One more thing: Tyler says 'Most of the costs of overinvestment in housing already have been borne in the form of lower living standards, namely we have fewer non-housing goods and services.' Of course, this implies that as P went up, Q supplied went up as well - but the housing market is a bit different to regular markets. In crowded European cities at least, Q is constained by the planning system, which responds to price changes very slowly and not necessarily in the direction a profit maximising supplier would. Given that the opportunity cost of utilising your land for housing is extremely low (how much do you think agricultural land is worth?) if you can get permission to build you do so as long as construction costs are less than the price the house will command (a near certainty for any development reasonably near to civilization).
In other words, high house prices are unlikely to have had a massive effect on building activity, thus driving a misallocation of resources on a grand scale. Strictly speaking, it is the land price bubble that burst; not the housing bubble.
£139.50 a year for this?
How many billions are there in a billion? This is the top story on the BBC News website right now:
Ill health 'costs economy £1bn'
Ill health costs the British economy over £1bn a year - the same as the cost of running the NHS for a year, a report is set to say.
The calculation will appear in an analysis by Dame Carol Black, national director for health and work.
Dame Carol's report will say the total cost of ill-health to the British economy is around £103bn.
The bulk of that - £63bn - is made of the benefit costs and lost taxes for people who are not working due to illness or disability.
The rest of the bill is made up the cost of the care given by family and friends, the cost to an employer of having someone absent from work and other additional costs.
Next year I'll send them a check for £1.39. I'm sure they won't mind.
p.s. I would also comment on treating 'benefit costs and lost taxes' as a cost to the economy, but learning to count is a good starting point.
UPDATE: They have finally corrected the story. It took a while...
Visit Greece
Yes, I live in London and you could claim I'm biased, but this is heartfelt advice. By the way, this is datacharmer hijacking stardom's Friday Special.
There's more eye-candy here, and don't miss this great spoof TV campaign. It offers all the reasons you need.
The master economist
The master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher - in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician.
John Maynard Keynes, quoted by Timothy Taylor.
Addendum: Here is Keynes's 1946 obituary in Time magazine.
Individuals and firms do not set prices
Geddit? As an economist talking to non-economists, this has been the single most difficult fact to explain.
This is from Timothy Taylor's 'Principles of Economics' lecture series on video. Click the link and check the list - he is a big success on the web, and - though his speaking style is a tad bit overstated - I really like this guy!
If you clicked on the link and are perplexed, this may help explain things.
Friday Special 45
From the winners of black and white photography
Spy satellite discovers lost Maya temples
What are the odds?
You are on holiday in some strange land, and you bump into Sue, an old friend. What are the odds?
Well, the probability is 1. 100%. It's certain. It bloody happened.
OK, you say, fair point - but that's not what you meant. What you meant is what is the probability you would bump into Sue, assuming you hadn't just bumped into him. I reply that that's a silly assumption to make as you just did bump into him, but you insist.
Well then, the probability is whatever you want it to be - pick a number, and I'll explain to you why it's plausible. You look perplexed and ask what I mean.
I explain: first of all, you need to specify the probability of what you are interested in.
-Do you want to know the probability you'd bump into Sue at the time and place you did
-Do you want the probability you would bump into an old friend while on holiday in general
-Or do you want the probability that something 'remarkable' enough would happen to you at some point in your life that would make you start asking silly questions about 'what is the probability of that happening'?
You say the first, obviously, and that I should stop being clever. I wasn't done, I say, and proceed to ask what is the information set I should base my probability estimate at - quantum mechanics aside, randomness is in the eye of the beholder after all, and if I was all-knowing God the probability of whatever it is that happened would be 1 even before it happened.
You throw your pina colada on my head and vow never to speak to me again.
A few days later, you are kind of missing me but don't feel like talking to me yet, so you visit bluematter. as a first step in rebuilding the relationship. And the first thing you see is this delightful little story, via Andrew Gelman:
In the city of Syracuse, the strangest thing happened in Tuesday's Democratic presidential primary.
Sen. Hillary Clinton and Sen. Barack Obama received the exact same number of votes, according to unofficial Board of Election results.
Clinton: 6,001.
Obama: 6,001.
The odds of Clinton and Obama tying were less than one in 1 million, said Syracuse University mathematics Professor Hyune-Ju Kim.
Elaborating on Thursday, she [Professor Hyune-Ju Kim] noted: "The "almost impossible" odd is obtained when we assume the Syracuse voter distribution follows the New York state distribution. Since it is almost impossible to observe what we have observed, statistically we can conclude that Syracuse voter distribution is significantly different from the New York state distribution."
There would be less than one in 1 million chance of a tie occurring between Clinton and Obama in voting by a randomly selected group of 12,346 New York Democratic voters, she said.
To which Andrew replies:
Not to pick on some harried mathematics professor who'd probably rather be out proving theorems, but . . . of course Syracuse voters are not a randomly selected group of New Yorkers. You don't need a statistical test to see that. Regarding the probability of an exact tie: I don't think that's so low: a quick calculation might say that either Clinton or Obama could've received between, say, 5000 and 7000 votes, giving something like a 1/2000 chance of an exact tie. That's gotta be the right order of magnitude.
If there was one thing you were ever certain about, it is that you don't want to read what I have to say on this. A baseball bat happens to lie next to you (what are the odds!?). You grab it with both your shaky hands and smash the computer monitor to pieces.
Roses are red, violets are blue, and correlation is not causation
Merv emails me this article:
Football clubs with red team strips are more successful than those with other colours, according to a study released Wednesday.
The fact that English clubs Manchester United, Liverpool and Arsenal regularly top league tables is not a coincidence, say the experts from Durham University and the University of Plymouth.
Red shirts give the team an advantage due to deep-rooted biological response to the colour. "In nature, red is often associated with male aggression and display," they said, giving the example of the red-breasted robin.
"It is a testosterone-driven signal of male quality, and its striking effect has even been harnessed by soldiers in the past," added the researchers, after analyzing data on English football league results since World War II.
The red-breasted robin? That's the most fearsome red beast they can think of?
I can't access the paper, but just reading the abstract is enough to convince me it's bonkers. The authors also have a 2005 paper - in Nature no less - entitled 'Red enhances human performance in contests'. If any reader has a access to Nature, would you be kind enough to email me the article so I can -ahem- review it?
Don't believe everything you read in the papers
Academic papers that is:
When I read an article in a reputable journal, I expect that a reviewer has double-checked the results. Am I naive?
I fear that you are. Except in the simplest papers, it is impossible to describe everything that has happened to the data in the text. Only the data themselves can do that, together with the computer code. Reviewers are usually not expected to reproduce all regressions. They usually trust the authors. In contrast, reviewers of theoretical analyses are expected to confirm all equations and proofs.
The pointer is from Marginal Revolution. The situation has been getting better, but estimation remains a laborious business. We'll get there eventually, but at least as far second tier journals are concerned it's not going be in a hurry.
A boy named Sue
My daddy left home when I was three
And he didn't leave much to ma and me
Just this old guitar and an empty bottle of booze.
Now, I don't blame him cause he run and hid
But the meanest thing that he ever did
Was before he left, he went and named me "Sue."
Well, he must o' thought that is quite a joke
And it got a lot of laughs from a' lots of folk,
It seems I had to fight my whole life through.
Some gal would giggle and I'd get red
And some guy'd laugh and I'd bust his head,
I tell ya, life ain't easy for a boy named "Sue."
Well, I grew up quick and I grew up mean,
My fist got hard and my wits got keen,
I'd roam from town to town to hide my shame.
But I made a vow to the moon and stars
That I'd search the honky-tonks and bars
And kill that man who gave me that awful name.
Well, it was Gatlinburg in mid-July
And I just hit town and my throat was dry,
I thought I'd stop and have myself a brew.
At an old saloon on a street of mud,
There at a table, dealing stud,
Sat the dirty, mangy dog that named me "Sue."
Well, I knew that snake was my own sweet dad
From a worn-out picture that my mother'd had,
And I knew that scar on his cheek and his evil eye.
He was big and bent and gray and old,
And I looked at him and my blood ran cold
And I said: "My name is 'Sue!' How do you do!
Now your gonna die!!"
Well, I hit him hard right between the eyes
And he went down, but to my surprise,
He come up with a knife and cut off a piece of my ear.
But I busted a chair right across his teeth
And we crashed through the wall and into the street
Kicking and a' gouging in the mud and the blood and the beer.
I tell ya, I've fought tougher men
But I really can't remember when,
He kicked like a mule and he bit like a crocodile.
I heard him laugh and then I heard him cuss,
He went for his gun and I pulled mine first,
He stood there lookin' at me and I saw him smile.
And he said: "Son, this world is rough
And if a man's gonna make it, he's gotta be tough
And I knew I wouldn't be there to help ya along.
So I give ya that name and I said goodbye
I knew you'd have to get tough or die
And it's the name that helped to make you strong."
He said: "Now you just fought one hell of a fight
And I know you hate me, and you got the right
To kill me now, and I wouldn't blame you if you do.
But ya ought to thank me, before I die,
For the gravel in ya guts and the spit in ya eye
Cause I'm the son-of-a-bitch that named you "Sue.'"
I got all choked up and I threw down my gun
And I called him my pa, and he called me his son,
And I came away with a different point of view.
And I think about him, now and then,
Every time I try and every time I win,
And if I ever have a son, I think I'm gonna name him
Bill or George! Anything but Sue! I still hate that name!
Testable theories
Jan Tinbergen - the first person to be awarded the Nobel Prize in Economics - became known for his 'Tinbergen Norm'. This states that if the difference between the lowest and highest income in a company exceeds a rate of 1:5, that will not help the company and may indeed be counterproductive.
In 2000, the ratio of average-CEO-to-average-worker was 525 to 1.
Disclaimer: I could not find an original source for the Tinbergen Norm. I'll have another go at it and report back soon.
Economics
All humans (and I mean everybody - positive scientists, social scientists, artists, white and blue collar workers, and of course non-human organisms too but I won't be expanding on that here) observe and estimate. In order to understand the world (and, in some cases, to use this knowledge for specific ends) they feed information obtained by observation through estimators of various kinds.
Economics is nothing more than logical reasoning on steroids. Similarly, econometrics - a fundamental part of economics - is nothing more than the efficient processing of 'objectively coded' information on an industrial scale. For a piece of scholarly work or for a thought process to be categorised as 'economics', the estimator utilised has to have a relatively high 'objectively coded' component, as well as possess a degree of testability regarding the accuracy of its predictions. Of course, in economics you never get a 100% 'objectively coded' system: at the very least, you have to assume some mapping of reality to a mathematical model, and usually much more. It is still the case, however, that at the heart of any economic estimator lies an explicitly set out system.
Economics is a method, or if you prefer a tradition, not a topic; and if you confuse it for a topic it is because the method is more relevant to some areas than others. What does the method consist of, and how is it different to positive science and what other social scientists do?
'Sociologists, psychologists, historians, and anthropologists' and also journalists, astrologists and agony aunts are different to economists to the extent they utilise 'objectively measured' variables to test their theories of how the world works and the causal mechanisms behind what we observe. Anthropologists (and artists seeking to maximize the 'aesthetic beauty' or popularity of their produce) hardly use any at all. Sociologists tend to settle for less than economists do, while physicists rely almost exclusively on 'objectively measured' variables.
That is not to say that the work and advice of anthropologists, historians or newspaper political editors cannot be useful: in many cases these guys generate good descriptions of reality and good predictions. In contrast to physicists however, and to some extent economists, their estimates are produced by an implicit, hard to describe and replicate, process; they rely on non-objectively coded information and are less suited to testing and verifying.
Churchill saw the threat from Hitler without running any regressions, without consulting any hard-coded data and without clearly laying out the constituent parts of his model. Similarly, if I throw a ball towards you, you will catch it without taking the time to record the ball's speed, the atmospheric density and other variables of interest and applying equations of motion. The problem with both these cases is that there was no way for Churchill to convincingly prove his case, and there's no way you can build a mechanical system that will be able to catch the ball without being more explicit about the way the system works.
For understanding the way society works, economics offers precisely this 'explicitization' of the estimators and it allows us to test the validity of different predictions. In many cases, it will still be preferable to go with implicit estimators: you may trust Henry Kissinger's advice on foreign policy more than the advice from an economic model utilising data on political attributes, simply because the 'subjective' portion of the latter estimator is enough to render it worse to Kissinger's fully subjective offering.
Overall, however, the greater availability of 'objectively coded', 'explicitly measurable' information, coupled with better and 'cheaper' well-defined estimator components can only mean that economics will become more, not less, important in the future. Expect news coverage of the Democratic primaries to take prediction markets more seriously and political pundits less so; expect military strategists to have economics degrees, and expect astrologists to be taken somewhat less seriously.
Economics has a bright future ahead.
Postscript: This is Exhibit B on the case for the continuing health of economics. Thanks to Ken Houghton at Marginal Utility for shaming me into posting this. Note to self: try to kick the habit of defining 'tomorrow' loosely.
How would a world without oil look like?
Many people think mistakenly that modern prosperity was founded on this fossil energy revolution, and that when the oil and coal is gone, it is back to the Stone Age. If we had no fossil energy, then we would be forced to rely on an essentially unlimited amount of solar power, available at five times current energy costs.
Our living standard would decline by about 11 percent.
At current rates of economic growth we would gain back the income losses from having to convert to solar power in less than six years.
This is Gregory Clark, via Economist's View.
Friday Special 44
Google Search: Who is a failure?
Nicely animated FX trading platform
Datacharmer's playlist
Good stuff I've been listening to the last few days:
Little Red Riding Hood, by The Meteors - from the album Mutant Monkey and the Surfers from Zorch.
Heartbeats, by Jose Gonzalez. A beautiful cover, the original by the Knife is fantastic too.
Irish Tour, by Rory Gallagher. One of my favourite albums ever, check out A Million Miles Away.
Imaginations from the Other Side, by Blind Guardian. I can't find a good-enough quality version of the best song in the album, but here is a particularly powerful if amateurish version by a random guitarist playing over the song. If you have an ear for this sound, more here.
Ridin, by Chamillionaire. The song isn't what I'd call amazing, but it reminds me of the scene of AJ's suicide attempt in the Sopranos. A powerful piece, far and away the best scene across all 6-ish Sopranos series.
One man
One man and the truth is a majority.
Milton Friedman
The end of economics, and the end of physics
Fabio Rojas, a top sociologist, believes economics is finished:
Economics, as understood for hundreds of years, has played out. The major problems of econ 101 have been solved. We know about supply and demand, marginal utility, choice under uncertainty, and budget constraints. We have a wide variety of tools, ranging from game theory to econometrics, that help us identify these processes in situations ranging from war, to car sales, to dating. We are also seeing how these processes plug into classic macroeconomic issues, such as growth and international trade.
However, the market system itself, as indicated by Tim’s concluding chapter, depends on population, innovation, and liberal economic institutions. These, in turn, depend on psychology, group culture, and networks, the domain of sociologists, psychologists, historians, and anthropologists. Economists have shown how the market system processes the inputs, but there’s still much, much more to be said about where the inputs come from. That’s what’s going to be exciting in the decades to come, and I can’t wait to see it.
Datacharmer, an occasionally tactless economist, says no way. Exhibit A is this quote by Albert Abraham Michelson, circa 1903:
The most important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplemented in consequence of new discoveries is exceedingly remote.
Exhibit B is less sensationalist, and more to the point. Stay tuned, it will appear here tomorrow.
Credible commitment
This landed on my inbox today. I doubt the incident ever took place, but does it really matter?
The following is the transcript of an actual radio conversation in October 1995, between a US Navy ship and the British authorities off the north coast of Scotland. The transcript was released by the MoD on the 10/10/95.
BRITISH: Please divert your course 15 degrees to the South. To avoid collision.
US Navy: Recommend you divert YOUR course 15 degrees to the North to avoid collision
BRITISH: Negative. You will have to divert your course 15 degrees to the South to avoid collision.
US Navy: This is the Captain of US Navy ship. I say again, divert YOUR course.
BRITISH: Negative I say again divert your course.
US Navy: THIS IS THE AIRCRAFT CARRIER 'USS LINCOLN' THE SECOND LARGEST SHIP IN THE UNITED STATES' ATLANTIC FLEET. WE ARE ACCOMPANIED BY THREE DESTROYERS, THREE CRUISERS AND NUMEROUS SUPPORT VESSELS. DEMAND THAT YOU CHANGE YOUR COURSE 15 DEGREES NORTH, THAT'S 15 DEGREES NORTH, OR COUNTER MEASURES WILL BE UNDERTAKEN TO ENSURE THE SAFETY OF THIS SHIP.
BRITISH: We are a lighthouse. F*** off.
The History of Economic Thought, cont.
If you enjoyed the previous post and would like to further extend your knowledge, here is an excellent resource. And if you suffer from attention deficit disorder and want people to get to the point without waffling about, try this excellent paper:
This paper tells you everything you need to know in order to impress your friends with your knowledge of the most famous people and the useful past of the subject of economics. It collects all the useful past possessed by the subject into one convenient, and therefore easy to plagiarise, source.
With thanks to Netsmith and Gabriel.
The History of Economic Thought in 10 easy steps
I recently tasked myself to produce a brief history of economic thought in 10 points and in 4 minutes (writing time). Here it is:
1. The ancient Greeks: Didn’t really do much, but they did try to think systematically about things, so we do have some microeconomic insights
2. St. Thomas Aquinas: Well, there wasn’t much thinking on anything in the Middle Ages, and this guy at least did some – making sure he framed it in Church-friendly terms too. Didn’t really say much either, but he did have a crack at the ‘fair price’ as well as why usury is bad, so we include him in books on history of economic thought
3. The Mercantilists: They said that exports are good, imports are bad. What idiots!
4. Adam Smith: What a nice bloke. Economics as we know it starts here. Hume was a good buddy of his, include him too for good measure.
5. Ricardo: Even nicer bloke. Did actual analysis. Comparative advantage, what a fantastic insight. He was also the first person to hold a chair of ‘political economy’ at university, at UCL. (Smith etc held chairs in ‘moral philosophy’ and other stupid sounding subjects)
6. Marx: Yes, he was an economist too. Not a particularly good one though. His theories generally have little basis to reality. His equations look funny too (but he had some equations, so he needs to get credit for that).
7. The Austrians: Government is bad, long live the market! These guys are still going today. I particularly like Boehm-Bawerk (can’t do the uemlauts, sorry), not least because his name sounds so cool
8. Modern economics: they pretty much start with Marshall. Pigou, Walras and several other guys also get honourable mentions. At the same time, important advances in statistics, but nothing to do with economics yet, so they are not covered. Knight, a very objectionable individual (he was fascist, racist etc) does some amazing work on statistics, and brings a lot of it to economics. Hypothesis testing and econometrics is born.
9. Keynes: Economists are allowed to give economic advice! The ‘profession’ is born. Macroeconomics too.
10. Post-war period. Rise of monetarism, rise of empirical economics (econometrics).. Economics turns mathematical and it becomes more than ‘political economy’ where moral philosophy plays a major role. Too many thinkers (Milton Friedman has to be mentioned), but this is the subject of a 'current economic thought' module.
Also: A lot of the old texts (Adam Smith, whatever we have from Ricardo etc etc) are available at Project Gutenberg. My favourite piece of 'old' economics, preceding Adam Smith by some 50 years, is this.
I know the list has ommissions (comments are open). A loyal reader has already mentioned Von Neumann and co., and another points to RBC theory.
There were also some contributions as to the future of economics. Forrest predicts that 'it will be the full systemisation of bounded rationality, with general theories of modelling cognitive biases' (an excellent suggestion if you ask me). And this prediction by another past contributor to Bluematter. is worthy of consideration too:
11. And in the future we have everyone caring about happiness. Hurrah! GDP maximisation gets killed by happiness maximisation, which means shorter working hours, learning to like family life, a reduction in ASBO-worthy behaviour, the rebirth of morality and being polite, plus better television.
11b. And if 11 doesn’t work, economics will advise the medical profession to develop soma-like drugs and we can all live in Aldous Huxley’s brave new world.
Alfred Marshall
In a letter to his protégée, A.C. Pigou, he laid out the following system: "(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often."
Here is more. While I can think of cases where the old master's advice applies, I disagree with everything other than 3 (and 4 in some cases).
You can't get more politically incorrect if you try
Israel's deputy defence minister has said Israel will have "no choice" but to invade Gaza if Palestinian militants step up rocket attacks.
Matan Vilnai said Palestinians risked a "shoah", the Hebrew word for a big disaster - and for the Nazi Holocaust.
"We're getting close to using our full strength. Until now, we've used a small percentage of the army's power because of the nature of the territory," he added.
From BBC News. And the follow-up:
[...] many of Mr Vilnai's colleagues have quickly distanced themselves from his comments and also tried to downplay, them saying he did not mean genocide.