Tag Archive for 'Tyler Cowen'

Some random links

Several of these are via Tyler Cowen.

Reblog: Cranial Heat Sink

Hey, if you can retweet, you can reblog.  Jeff Ely:

Tyler Cowen tweeted:

Why do chess players hold their heads hard, with their hands, when they are thinking? If it works, why don’t more thinkers do it?

To prevent overheating of course.  You’ll notice that they typically extend their fingers and cover their foreheads which is the hottest part.  They are [unconsciously] maximizing surface area in order to increase heat dissipation.

Here is a suggestion for how to super-cool your cranium and over-clock your brain.  On a more serious note, here is a pipe that is surgically implanted in the skull of epileptics to reduce the intensity of seizures.

On interest rates

In what Tyler Cowen calls “Critically important stuff and two of the best recent economics blog posts, in some time,” Paul Krugman and Brad DeLong have got some interesting thoughts on US interest rates.  First Krugman:

On the face of it, there’s no reason to be worried about interest rates on US debt. Despite large deficits, the Federal government is able to borrow cheaply, at rates that are up from the early post-Lehman period … but well below the pre-crisis levels:

DESCRIPTION

Underlying these low rates is, in turn, the fact that overall borrowing by the nonfinancial sector hasn’t risen: the surge in government borrowing has in fact, less than offset a plunge in private borrowing.

So what’s the problem?

Well, what I hear is that officials don’t trust the demand for long-term government debt, because they see it as driven by a “carry trade”: financial players borrowing cheap money short-term, and using it to buy long-term bonds. They fear that the whole thing could evaporate if long-term rates start to rise, imposing capital losses on the people doing the carry trade; this could, they believe, drive rates way up, even though this possibility doesn’t seem to be priced in by the market.

What’s wrong with this picture?

First of all, what would things look like if the debt situation were perfectly OK? The answer, it seems to me, is that it would look just like what we’re seeing.

Bear in mind that the whole problem right now is that the private sector is hurting, it’s spooked, and it’s looking for safety. So it’s piling into “cash”, which really means short-term debt. (Treasury bill rates briefly went negative yesterday). Meanwhile, the public sector is sustaining demand with deficit spending, financed by long-term debt. So someone has to be bridging the gap between the short-term assets the public wants to hold and the long-term debt the government wants to issue; call it a carry trade if you like, but it’s a normal and necessary thing.

Now, you could and should be worried if this thing looked like a great bubble — if long-term rates looked unreasonably low given the fundamentals. But do they? Long rates fluctuated between 4.5 and 5 percent in the mid-2000s, when the economy was driven by an unsustainable housing boom. Now we face the prospect of a prolonged period of near-zero short-term rates — I don’t see any reason for the Fed funds rate to rise for at least a year, and probably two — which should mean substantially lower long rates even if you expect yields eventually to rise back to 2005 levels. And if we’re facing a Japanese-type lost decade, which seems all too possible, long rates are in fact still unreasonably high.

Still, what about the possibility of a squeeze, in which rising rates for whatever reason produce a vicious circle of collapsing balance sheets among the carry traders, higher rates, and so on? Well, we’ve seen enough of that sort of thing not to dismiss the possibility. But if it does happen, it’s a financial system problem — not a deficit problem. It would basically be saying not that the government is borrowing too much, but that the people conveying funds from savers, who want short-term assets, to the government, which borrows long, are undercapitalized.

And the remedy should be financial, not fiscal. Have the Fed buy more long-term debt; or let the government issue more short-term debt. Whatever you do, don’t undermine recovery by calling off jobs creation.

The point is that it’s crazy to let the rescue of the economy be held hostage to what is, if it’s an issue at all, a technical matter of maturity mismatch. And again, it’s not clear that it even is an issue. What the worriers seem to regard as a danger sign — that supposedly awful carry trade — is exactly what you would expect to see even if fiscal policy were on a perfectly sustainable trajectory.

Then DeLong:

I am not sure Paul is correct when he says that the possible underlying problem is merely “a technical matter of maturity mismatch.” The long Treasury market is thinner than many people think: it is not completely implausible to argue that it is giving us the wrong read on what market expectations really are because long Treasuries right now are held by (a) price-insensitive actors like the PBoC and (b) highly-leveraged risk lovers borrowing at close to zero and collecting coupons as they try to pick up nickles in front of the steamroller. And to the extent that the prices at which businesses can borrow are set by a market that keys off the Treasury market, an unwinding of this “carry trade”–if it really exists–could produce bizarre outcomes.

Bear in mind that this whole story requires that the demand curve slope the wrong way for a while–that if the prices for Treasury bonds fall carry traders lose their shirts and exit the market, and so a small fall in Treasury bond prices turns into a crash until someone else steps in to hold the stock…

For reference, here are the time paths of interest rates for a variety of term lengths and risk profiles (all taken from FRED):

interest_rates_1monthinterest_rates_3monthsinterest_rates_30years

To my own mind, I’m somewhat inclined to agree with Krugman.  While I do believe that the carry trade is occurring, I suspect that it’s effects are mostly elsewhere, or at least that the carry trade is not being played particularly heavily in long-dated US government debt relative to other asset markets.

Notice that the AAA and BAA 30-year corporate rates are basically back to pre-crisis levels and that the premium they pay over 30-year government debt is also back to typical levels.  If the long-dated rates are being pushed down to pre-crisis levels solely by increased supply thanks to the carry trade, then we would surely expect the quantity of credit to also be at pre-crisis levels.  But new credit issuance is down relative to the pre-crisis period.  Since the price is largely unchanged, that means that both demand and supply of credit have shrunk – the supply from fear in the financial market pushing money to the short end of the curve and the demand from the fact that there’s been a recession.

The death throes of US newspapers?

Via Megan McArdle’s excellent commentary, I discovered the Mon-Fri daily circulation figures for the top 25 newspapers in the USA.  Megan’s words:

I think we’re witnessing the end of the newspaper business, full stop, not the end of the newspaper business as we know it. The economics just aren’t there. At some point, industries enter a death spiral: too few consumers raises their average costs, meaning they eventually have to pass price increases onto their customers. That drives more customers away. Rinse and repeat . . .

[...]

The numbers seem to confirm something I’ve thought for a while: we’re eventually going to end up with a few national papers, a la Britain, rather than local dailies. The Wall Street Journal, the Washington Post, and the New York Times (sorry, conservatives!) are weathering the downturn better than most, and it’s not surprising: business, politics, and national upper-middlebrow culture. But in 25 years, will any of them still be printing their product on the pulped up remains of dead trees? It doesn’t seem all that likely.

For those of you that like your information in pictoral form, here it is:

First, the data.  Look at the Mean/Median/Weighted Mean figures.  That really is an horrific collapse in sales.

US_Newspaper_circulation_data

Second, the distribution (click on the image for a full-sized version):

US_Newspaper_circulation_distribution

Finally, a scatter plot of year-over-year change against the latest circulation figures (click on the image for a full-sized version):

US_Newspaper_circulation_scatterplotAs Megan alluded in the second paragraph I quoted, there appears to be a weak relationship between the size of the paper and the declines they’ve suffered, with the bigger papers holding up better.  The USA Today is the clear exception to that idea.  Indeed, if the USA Today is excluded from the (already very small!) sample the R^2 becomes 30%.

To really appreciate just how devestating those numbers are, you need to combine it with advertising figures.  Since newspapers take revenue from both sales (circulation) and advertising, the fact that advertising revenue has also collapsed, as it always does in a recession, means that newspapers have taken not just one but two knives to the chest.

Here’s advertising expenditure in newspapers over recent years, taken from here:

Year Expenditure (millions of dollars) Year-over-year % change
2005 47,408
2006 46,611 -1.7%
2007 42,209 -9.2%
2008 34,740 -17.7%

Which is ugly.  Remember, also, that this expenditure is nominal.  Adjusted for inflation, the figures will be worse.

So what do you do when your ad sales and your circulation figures both fall by over 15%?  Oh, and you can’t really cut costs any more because, as Megan says:

For twenty years, newspapers have been trying to slow the process with increasingly desperate cost cutting, but almost all are at the end of that rope; they can’t cut their newsroom or production staff any further and still put out a newspaper. There just aren’t enough customers who are willing to pay for their product what it costs to produce it.

Which, in economics speak, means that the newspaper business has a large fixed cost component that isn’t particularly variable even in the long run.

Tyler Cowen, in an excellent post that demonstrates precisely why I read him daily, says:

I believe with p = 0.6 that the world is in for a “great disruption.”  It has come to MSM first but it will not end there.  In the longer run I am optimistic about the results of this change — computers will free up lots of human labor — but in the meantime it will have drastic implications for income redistribution, across both individuals and across economic sectors.  For a core metaphor, the internet displacing paid journalism and classified ads is a good place to start.  The value of newspapers has been sucked into Google.

[...]Once The Great Disruption becomes more evident, entertainment will be very very cheap.

Which may well be true, but will be cold comfort for all of those traditional journalists out there.

An information-based approach to understanding why America let Lehman Brothers collapse but saved everyone afterwards

In addition to his previous comments on the bailouts [25 Aug27 Aug28 Aug], which I highlighted here, Tyler Cowen has added a fourth post [2 Sep]:

I side with Bernanke because an economy can withstand only so much major bank insolvency at once. Lots of major banks were levered up 30-1 or so. Their assets fell in value more than a modest amount and then they were insolvent, sometimes grossly so. (A three percent decline in asset values already puts you into insolvency range.) If AIG had gone into bankruptcy court, some major banks would have been even more insolvent. Or if Frannie securities had been allowed to find their non-bailout values. My guess is that at least 15 out of the top 20 U.S. banks would have been flat-out insolvent if, starting at the time of Bear Stearns, all we had done was loose monetary policy and no other bailouts. Subsequent contagion effects, and the shut down of short-term repo markets, and a run on money market funds, would have made even more financial institutions insolvent. The world as we know it then becomes very dire, both for credit reasons and deflation reasons (yes you can print up currency to keep measured M up and running but the economy still collapses). So we needed not just emergency lending but also resource transfers to banks, basically to put them back into the range of possible solvency.

I really like to see Tyler’s evolving attitudes here.  It lets me know that mere grad students are allowed to not be sure of themselves. :-)  In any event, let me present my latest thoughts on the bailouts:

Imagine being Bernanke/Paulson two days before Lehman Brothers went down:  you know they’re going to go down if you don’t bail them out and you know that to bail them out creates moral hazard problems (i.e. increases the likelihood of a repeat of the entire mess in another 10 years).  You don’t know how close to the edge everyone else is, nor how large an effect a Lehman collapse will have on everyone else in the short-run (thanks, in no small part, to the fact that all those derivatives were sold over-the-counter), but you’re nevertheless almost certain that Lehman Brothers are not important enough to take down the whole planet.

In that situation, I think of the decision to let Lehman Brothers go down as an experiment to allow estimation of the system’s interconnectedness.  Suppose you’ve got a structural model of the U.S. financial system as a whole, but no empirical basis for calibrating it.  Normally you might estimate the deep parameters from micro models, but when derivatives were exempted from regulation in the 2000 Commodities Futures Modernization Act, in addition to letting firms do what they wanted with derivatives you also gave up having information about what they were doing.  So instead, what you need is a macro shock that you can fully identify so that at least you can pull out the reduced-form parameters.  Letting Lehman go was the perfect opportunity for that shock.

I’m not saying that Bernanke had an actual model that he wanted to calibrate (although if he didn’t, I really hope he has one now), but he will certainly have had a mental model.  I don’t even mean to suggest that this was the reasoning behind letting Lehman go.  That would be one hell of a (semi) natural experiment and a pretty reckless way to gather the information.  Nevertheless, the information gained is tremendously valuable, both in itself and to society as a whole because it is now, at least in part, public information.

To some extent, I feel like the ideal overall response to the crisis from the Fed and Treasury would have been to let everyone fail a little bit, but that isn’t possible — you can’t let an institution become a little bit bankrupt in the same way that you can’t be just a little bit pregnant.  To me, the best real-world alternative was to let one or two institutions die to put the frighteners on everyone and discover the degree of interconnectedness of the system and then save the rest, with the nature and scale of the subsequent bailouts being determined by the reaction to the first couple going down.  I would only really throw criticism at the manner of the saving of the rest (especially the secrecy) and even then I would be hesitant because:

(a) it was all terribly political and at that point the last thing Bernanke needed was a financially-illiterate representative pushing his or her reelection-centred agenda every step of the way (we don’t let people into a hospital emergency room when the doctor isn’t yet sure of what’s wrong with the patient);

(b) perhaps the calibration afforded by the collapse of Lehman Brothers convinced Bernanke-the-physician that short-term secrecy was necessay to “stop the bleeding” (although that doesn’t necessarily imply that long-term secrecy is warranted); and

(c) there was still inherent (i.e. Knightian) uncertainty in what was coming next on a day-to-day basis.

A pragmatic libertarian defense of the bank bailouts

Tyler Cowen is defending the bank bailouts in America: 25 Aug, 27 Aug, 28 Aug.  I generally like what he says.  I want to highlight the third post in particular:

General pro-market or anti-government arguments don’t rule out the recent bailouts.  Let’s take the hardest, least Friedman-friendly case, the insolvent banks.  For insolvent banks (and for some of the illiquid banks, which might have failed without bailouts), the alternative to those bailouts is calling in deposit insurance and the bankruptcy courts, both of which are, for better or worse, forms of government intervention.  In particular today’s bankruptcy procedures are ill-suited for disposing of a large financial institution in a timely manner and this can be considered a form of gross government failure.

Note that even when the Fed “bails out” a large investment bank, or insurance company, they are checking a chain reaction which would likely spread to some commercial banks, thus bringing in deposit insurance as well, not to mention further bankruptcies.  And that’s not even considering that Congress probably would have stepped in, I’m just looking at laws already on the books.

So if you’re “opposed to financial bailouts,” as a libertarian, you’re not for the market.  You’re saying that one scheme for governmental disposition is better than another.  Of course you are entitled to that opinion but the sheer force of libertarian doctrine is not necessarily on your side.  The general pro-market and anti-government arguments are not necessarily on your side.  I think it is quite plausible for a libertarian to believe that the Fed is “less bad” than the bankruptcy courts and the FDIC.

Now, all things considered, I don’t see why this “libertarian two-step” move should be needed.  I think it’s enough to simply ask whether the bailouts were a good idea and proceed accordingly.  But if you’re concerned about compatibility with libertarian principle, this is one simple way of seeing why my view fits right in.  In fact I think it is the more libertarian of the views under consideration, as it keeps the very worst of the government interventions on the table at bay.

No doubt some libertarians will counter that the FDIC and bankruptcy courts ought not to exist either (I disagree with that – while neither is perfect, they’re both needed.  But then, I’m hardly a libertarian), but that misses the point of Tyler’s title for the post:  ”A second-best theory of libertarian bailouts”.  The world of second-best is the real world.  It accepts that things are currently as they are and asks what is best given the current state of the world, not in all possible worlds.

Demand for sex in Japan

Mentioning sex in a blog post is a great way to generate some interesting traffic.  The last time I filled some time writing about it (on the rise of public sexuality, the rationality of prostitution and the extent of human trafficking), I got hits via some very odd queries on Google.

Titillation aside,  prostitution is a tremendously interesting topic in economics .  As John Hempton discussed initially in July 2008 and more extensively in May 2009, the price of prostitution is enormously flexible, unlike prices (and wages) in most industries.  That means that when, as John discussed, a country is operating under a fixed exchange rate and only prices can adjust in response to a macroeconomic shock, the sex industry will almost certainly move both first and furthest.

But because prostitution has very flexible wages and prices, that also makes it a candidate proxy for estimating changes in the potential output of an economy — the output that would occur if all prices were perfectly flexible.  (Remember there are differences between potential and natural levels of output)

I mention this after reading that the Bank of Japan is conducting surveys to estimate changes in demand in the Japanese sex industry:

The survey of sex shops and restaurants was designed to better gauge demand for services, an area of the economy that’s becoming more important as exports slump. “Any study into services is most welcome,” said Martin Schulz, senior economist at Fujitsu Research Institute in Tokyo. “We’ve got hundreds of studies on exports and manufacturing. What’s needed is creative thinking on services and if that includes brothels, so be it.” … While services including restaurants and retailing make up about 60 percent of gross domestic product, Japan’s economy has risen and fallen with the strength of its exports.

(Hat tip:  Tyler Cowen).

Another important point

Tyler Cowen writes, in the midst of a discussion of Keynes’s General Theory, spending multipliers and the velocity of money:

You can’t just take a partial derivative of an accounting identity and call the result a causal relationship.

[My previous posts on spending multipliers and the velocity of money.]

Is economics looking at itself?

Patricia Cowen recently wrote a piece for the New York Times:  “Ivory Tower Unswayed by Crashing Economy

The article contains precisely what you might expect from a title like that.  This snippet gives you the idea:

The financial crash happened very quickly while “things in academia change very, very slowly,” said David Card, a leading labor economist at the University of California, Berkeley. During the 1960s, he recalled, nearly all economists believed in what was known as the Phillips curve, which posited that unemployment and inflation were like the two ends of a seesaw: as one went up, the other went down. Then in the 1970s stagflation — high unemployment and high inflation — hit. But it took 10 years before academia let go of the Phillips curve.

James K. Galbraith, an economist at the Lyndon B. Johnson School of Public Affairs at the University of Texas, who has frequently been at odds with free marketers, said, “I don’t detect any change at all.” Academic economists are “like an ostrich with its head in the sand.”

“It’s business as usual,” he said. “I’m not conscious that there is a fundamental re-examination going on in journals.”

Unquestioning loyalty to a particular idea is what Robert J. Shiller, an economist at Yale, says is the reason the profession failed to foresee the financial collapse. He blames “groupthink,” the tendency to agree with the consensus. People don’t deviate from the conventional wisdom for fear they won’t be taken seriously, Mr. Shiller maintains. Wander too far and you find yourself on the fringe. The pattern is self-replicating. Graduate students who stray too far from the dominant theory and methods seriously reduce their chances of getting an academic job.

My reaction is to say “Yes.  And No.”  Here, for example, is a small list of prominent economists thinking about economics (the position is that author’s ranking according to ideas.repec.org):

There are plenty more. The point is that there is internal reflection occurring in economics, it’s just not at the level of the journals.  That’s for a simple enough reason – there is an average two-year lead time for getting an article in a journal.  You can pretty safely bet a dollar that the American Economic Review is planning a special on questioning the direction and methodology of economics.  Since it takes so long to get anything into journals, the discussion, where it is being made public at all, is occurring on the internet.  This is a reason to love blogs.

Another important point is that we are mostly talking about macroeconomics.  As I’ve mentioned previously, I pretty firmly believe that if you were to stop an average person on the street – hell, even an educated and well-read person – to ask them what economics is, they’d supply a list of topics that encompass Macroeconomics and Finance.

The swathes of stuff on microeconomics – contract theory, auction theory, all the stuff on game theory, behavioural economics – and all the stuff in development (90% of development economics for the last 10 years has been applied micro), not to mention the work in econometrics; none of that would get a mention.  The closest that the person on the street might get to recognising it would be to remember hearing about (or possibly reading) Freakonomics a couple of years ago.

How to value toxic assets (part 6)

Via Tyler Cowen, I am reminded (again) that I should really be reading Steve Waldman more often.  Like, all the time.  After reading John Hempton’s piece that I highlighted last time, Waldman writes, as an afterthought:

There’s another way to generate price transparency and liquidity for all the alphabet soup assets buried on bank balance sheets that would require no government lending or taxpayer risk-taking at all. Take all the ABS and CDOs and whatchamahaveyous, divvy all tranches into $100 par value claims, put all extant information about the securities on a website, give ‘em a ticker symbol, and put ‘em on an exchange. I know it’s out of fashion in a world ruined by hedge funds and 401-Ks and the unbearable orthodoxy of index investing. But I have a great deal of respect for that much maligned and nearly extinct species, the individual investor actively managing her own account. Individual investors screw up, but they are never too big to fail. When things go wrong, they take their lumps and move along. And despite everything the professionals tell you, a lot of smart and interested amateurs could build portfolios that match or beat the managers upon whose conflicted hands they have been persuaded to rely. Nothing generates a market price like a sea of independent minds making thousands of small trades, back and forth and back and forth.

I don’t really expect anybody to believe me, but I’ve been thinking something similar.

CDOs, CDOs-squared and all the rest are derrivatives that are traded over the counter; that is, they are traded entirely privately.  If bank B sells some to hedge fund Y, nobody else finds out any details of the trade or even that the trade took place.  The closest we come is that when bank B announces their quarterly accounts, we might realise that they off-loaded some assets.

On the more popularly known stock and bond markets, buyers publicly post their “bid” prices and sellers post their “ask” prices. When the prices meet, a trade occurs.[*1] Most details of the trade are then made public – the price(s), the volume, the particular details of the asset (ordinary shares in XXX, 2-year senior notes from XXX with an expiry of xx/xx/xxxx, etc) – everything except the identity of the buyer and seller. Those details then provide some information to everybody watching on how the buyer and seller value the asset. Other market players can then combine that with their own private valuations and update their own bid or ask prices accordingly. In short, the market aggregates information. [*2]

When assets are traded over the counter (OTC), each participant can only operate on their private valuation. There is no way for the market to aggregate information in that situation. Individual banks might still partially aggregate information by making a lot of trades with a lot of other institutions, since each time they trade they discover a bound on the valuation of the other party (an upper bound when you’re buying and the other party is selling, a lower bound when you’re selling and they’re buying).

To me, this is a huge failure of regulation. A market where information is not publicly and freely available is an inefficient market, and worse, one that expressly creates an incentive for market participants to confuse, conflate, bamboozle and then exploit the ignorant. Information is a true public good.

On that basis, here is my idea:

Introduce new regulation that every financial institution that wants to get support from the government must anonymously publish all details of every trade that they’re party to. The asset type, the quantity, the price, any time options on the deal, everything except the identity of the parties involved. Furthermore, the regulation would be retroactive for X months (say, two years, so that we get data that predates the crisis).  On top of that, the regulation would require that every future trade from everyone (whether they were receiving government assistance or not) would be subject to the same requirementes.  Then everything acts pretty much like the stock and bond markets.

The latest edition of The Economist has an article effectively questioning whether this is such a good idea.

[T]ransparency and liquidity are close relatives. One enemy of liquidity is “asymmetric information”. To illustrate this, look at a variation of the “Market for Lemons” identified by George Akerlof, a Nobel-prize-winning economist, in 1970. Suppose that a wine connoisseur and Joe Sixpack are haggling over the price of the 1998 Château Pétrus, which Joe recently inherited from his rich uncle. If Joe and the connoisseur only know that it is a red wine, they may strike a deal. They are equally uninformed. If vintage, region and grape are disclosed, Joe, fearing he will be taken for a ride, may refuse to sell. In financial markets, similarly, there are sophisticated and unsophisticated investors, and unless they have symmetrical information, liquidity can dry up. Unfortunately transparency may reduce liquidity. Symmetry, not the amount of information, matters.

I’m completely okay with this. Symmetric access to information and symmetric understanding of that information is the ideal. From the first paragraph and then the last paragraph :

… Not long ago the cheerleaders of opacity were the loudest. Without privacy, they argued, financial entrepreneurs would be unable to capture the full value of their trading strategies and other ingenious intellectual property. Forcing them to disclose information would impair their incentive to uncover and correct market inefficiencies, to the detriment of all …

Still, for all its difficulties, transparency is usually better than the alternative. The opaque innovations of the recent past, rather than eliminating market inefficiencies, unintentionally created systemic risks. The important point is that financial markets are not created equal: they may require different levels of disclosure. Liquidity in the stockmarket, for example, thrives on differences of opinion about the value of a firm; information fuels the debate. The money markets rely more on trust than transparency because transactions are so quick that there is little time to assess information. The problem with hedge funds is that a lack of information hinders outsiders’ ability to measure their contribution to systemic risk. A possible solution would be to impose delayed disclosure, which would allow the funds to profit from their strategies, provide data for experts to sift through, and allay fears about the legality of their activities. Transparency, like sunlight, needs to be looked at carefully.

This strikes me as being around the wrong way.  Money markets don’t rely on trust because their transactions are so fast; their transactions are so fast because they’re built on trust.  The scale of the crisis can be blamed, in no small measure, because of the breakdown in that trust.

I also do not buy the idea of opacity begetting market efficiency.  It makes no sense.  The only way that information disclosure can remove the incentive to “uncover and correct” inefficiencies in the market is if by making the information public you reduce the inefficiency.  I’m not suggesting that we force market participants to reveal what they discover before they get the chance to act on it.  I’m only suggesting that the details of their action should be public.

[*1] Okay, it’s not exactly like that, but it’s close enough.

[*2] Note that information aggregation does not necessarily imply that the Efficient Market Hypothesis (EMH), but the EMH requires information aggregation to work.

Other posts in this series:  1, 2, 3, 4, 5, [6].