A model of wealth distribution, falling interest rates, ZIRP, unemployment, and quantitative easing

I will sketch a simple model in which the distribution of wealth gets more unequal over time, how the equilibrium real interest rate falls over time, eventually leading to a zero nominal interest rate, and unemployment. I will then show that an increase in the money supply can increase employment, despite zero nominal interest rates.

Let me give you the intuition first.

People differ in how patient they are, along a continuum. In the initial equilibrium, the more patient save and the less patient dissave. Over time, the patient accumulate assets and the impatient reduce their assets. Eventually the impatient become borrowing-constrained.

The initial equilibrium real rate of interest depends on the average degree of patience of the whole population. But when the impatient become borrowing-constrained, the equilibrium real rate of interest depends on the average degree of patience of that subset of the population which is not borrowing-constrained. That subset excludes the less patient, which means the equilibrium real interest rate falls over time as more and more people become borrowing-constrained. Eventually the equilibrium real interest rate falls so much that the nominal interest rate hits the zero lower bound.

There are two assets: money and bonds. Money is a medium of exchange; bonds are not. When the nominal interest rate hits zero, the most patient continue to save, but can only save in the form of money. The least patient dissave, and slowly reduce their holdings of money.

Since the most patient now hold money purely as a store of wealth, at the margin, the average desired velocity of circulation of money across the population falls over time. As velocity falls over time, aggregate demand falls over time, and unemployment rises over time.

Unexpected deflation would prevent unemployment by allowing the real money stock to rise over time. But fully anticipated deflation might worsen unemployment by increasing the real interest rate above equilibrium. A permanent increase in the money supply would prevent unemployment for a long time, provided some of the money were given to the borrowing-constrained.

Here's a sketch of the model.

Agents are identical, except in their rate of time preference (patience). There is a continuous distribution of rates of time preference F(d). Otherwise agents are identical. They consume, and supply labour inelastically.

Labour produces consumption services. No investment or storage.

Let's start with a barter version of the model.

There is one asset: government bonds. Agents are unable to issue private bonds, so an agent who runs out of bonds is borrowing-constrained.

Each agent has a consumption-Euler equation (personal IS curve): C0 = C(C1,d-r). Where r is the real rate of interest.

The market rate of interest adjusts until aggregate savings equals zero. The more patient agents will be saving, and the less patient will be dissaving. So the stock of bonds flows from the less patient (r<d) to the more patient (r>d). Eventually the least patient person runs out of bonds, becomes borrowing constrained, and stops dissaving. Aggregate savings therefore rises, and so the rate of interest falls, and continues to fall over time as more and more people become borrowing-constrained. Eventually, the most patient person in the whole population will hold all the bonds, and everyone else is borrowing-constrained.

Now introduce money, as a second asset. Money pays no interest, but is a medium of exchange. Each agent has a cost of having a high personal velocity of circulation (low real balances relative to nominal expenditure). The marginal cost falls to zero when velocity gets below some minimum level (call it 1), at which point he is satiated in monetary services.

Some agents own bonds. They can separate their savings decision (consumption vs. savings) from their portfolio allocation decision (money vs. bonds).

Each agent who owns bonds has a personal LM curve, which defines velocity as a function of the nominal rate of interest. The LM curve has the normal slope, but suddenly goes horizontal at a zero nominal rate of interest.

But other agents do not own bonds, and are borrowing-constrained. Their savings decisions cannot be separated from their money demand decisions. If the real rate of interest is below their rate of time-preference, they will dissave, and slowly reduce their holdings of money over time. But as their money holdings get smaller, their level of dissaving will fall, so eventually their savings drops to zero, and their money holdings stop falling when they hit some lower bound (whether at a zero or positive level of money depends on their preferences).

The aggregate stocks of bonds and money stay constant over time.

At the beginning of time, the bonds and money are divided equally between all agents. Then play begins.

Over time, the patient agents save, the impatient agents dissave, and bonds flow from the impatient to the patient.

Eventually, the least patient agent runs out of bonds, his savings rate slowly falls, as his stock of money falls, and then he stops dissaving when his holdings of money hit the lower bound. As more and more agents hit the lower bound, the real rate of interest falls over time. Eventually the real rate of interest falls so low that the nominal rate of interest hits zero.

When the nominal rate of interest hits zero, and the real rate of interest can fall no further, desired aggregate savings at full employment is positive. Unemployment, initially at zero, now begins to rise. The more patient, who are saving, accumulate both bonds and money, past the point of satiation of money holdings.

After some time, there are four sets of agents. 1) The most patient are still saving, and hold bonds and money, and are past satiation in money (they hold "idle hoards"). 2)The slightly less patient are dissaving, and holding bonds and money. 3)The slightly less patient still are dissaving, and holding only money. 4) The least patient have stopped dissaving, and hold only money (the lower bound).

Unemployment would cause the price level to fall, if we assume flexible prices. A lower price level would help eliminate unemployment, by increasing the real value of all agents' holdings of money. The fourth group of agents would now join the third group, and would start dissaving again. (And the third group might dissave more). This will reduce aggregate savings, and help reduce unemployment. But expected deflation would increase the real interest rate, cause an increase in savings, and increase unemployment. The second effect would dominate (assume it doesn't and you get a contradiction, which would take me too long to prove).

So let's just assume the price level stays fixed once unemployment starts to appear.

Then the central bank decides to do something about unemployment.

An open market operation will not help (I think). But a helicopter increase in the money supply will help. The fourth group of agents will start dissaving again. The third group of agents will dissave more. So aggregate savings falls.

If the helicopter can increase the supply of money by a big enough amount to get to full employment, then the price level can start to rise if extra money is added. So the policy prescription is one big helicopter drop, to get to full employment, then steadily increase the money supply over time to make inflation positive, and allow the real rate to drop below zero.

Well, the model works, sort of. But I am not happy with it. A helicopter drop of bonds could have the same initial effect, since the borrowing-constrained could sell the bonds for some of the money held in idle hoards. The bond market (and that's the only asset market) is perfectly liquid, in that bonds can be swapped for money at zero cost. Put it another way: it's the wealth effect, as much as any liquidity effect, that's doing most of the work (I think).

But, the model does show that monetary policy could work, even at zero nominal interest rates. So I'm going to post it, even though it's not really doing what I want it to do.

Comments

[DW]

Nick,

Thanks for the post. Two questions:

1. Do you believe that one of the causes/uses of a recession is to correct a relatively significant reallocation of resources among the various sectors of the economy? Or is it entirely a confidence thing?

2. Doesn't a helicopter drop of money stop that process of creative destruction in its tracks and potentially perpetuates a misallocation of resources?

Thanks!

[pointbite]

"provided some of the money were given to the borrowing-constrained."

I read your words, but in my head all I heard was: "provided you subsidize reckless consumption and screw savers."

"So aggregate savings falls."

What if savings is already too low to begin with? The savings rate has jumped a little in the last few months, but let's be honest with ourselves, it's STILL too low by historic standards. How long can we survive with a zero or negative savings rate before people lose confidence? Barry Ritholtz posted an interesting discussion with Robert Shiller the other day, I don't agree with everything he says, but he makes an important point (that I agree with fully) regarding the influence of psychology on markets. All of your models ignore psychology and confidence. Please spend some time watching.

http://fora.tv/2009/02/18/Animal_Spirits_How_Psychology_Drives_the_Economy#chapter_01

[Adam]

Nick, not sure what you're complaining about in the last couple paragraphs. I think the model pretty much accomplishes what you want. The thing about a helicopter drop of bonds working just as well is entirely consistent with a liquidity trapped economy. The savers are willing to excahnge money for bonds because they see them as perfect substitutes. This assumes though that the total value of the bonds that fall from the sky doesn't exceed the total money stock, after that you do need money not bonds.

However, in order to maintain full employment going forward you do need to keep on expanding the money supply, otherwise the same dynamics repeat and you end up with unemployment again. So inflation is still required, it just seems as though the mechanism is different.

The real issue though is that you haven't specified a process for aggregate consumption. I suppose you probably had in mind that it's constant, but what if it's not? If aggregate consumption is going to be sufficiently lower in the future then we're back to my story. You need the promise of inflation to maintain full employment and although the helicopter drop increases aggregate demand it doesn't get you all the way.

My contention all along has been that the consumption path of the entire western world requires a negative real rate to support full employment. This means that future consumption will be relatively scarce, the key being relatively. I don't think we will be impoverished (thus the world running out of oil examples were just devices) but I think consumption was way overabundant for most of this decade due to the Chinease and other asian countries pretty much giving us everything they could manage to produce on credit. Thus, consumption will be relatively scarce even at full employment.

This also brings up what, I think, really should happen to rectify the situation. Inflation means your currency depreciates in real terms, if the western currencies depreciate enough then the asian countries (China in particluar) might finally start buying our stuff. Thus, western consumption falls, as it must, but at least there is no recession because total demand for our goods stays high. In all casses though, if aggregate consumpion in the western world is going to decline then inflation/real depreciation is the only way to maintain full employment. Either the west stops saving (and we basically inflate away our debts to the developing world) or the developing world stops saving and spends all their USD reserves buying stuff from us.

[bob]

Adam, great comment. I agree 100%. It also clears up why I was misunderstanding your earlier comments. When I wrote "structural reforms" in the earlier posts, mainly what I had in mind was the appreciation of asian currencies, lowering of asian savings, and reduction of trade imbalances, so I think we're pretty much on the same page.

Nick, I think the model is good. On an earlier post you had mentioned something about the international distribution of debt possibly having a similar effect, along the lines of what Adam is referring to. I would love to see a post applying this concept internationally.

I think Keynes realized this a long time ago, but maybe he never made the fundamental case explicit enough to convince everyone?

"Volume 25 of his collected writings is full of his plans for the institution that would regulate the world economy after World War II. His institution was to have very different requirements for trade surplus countries and trade deficit countries (pages 79-81), with the goal of keeping trade in balance. Here is what his institution would require of trade surplus countries:

"A Surplus Country shall discuss with the Governing Board (but shall retain the ultimate decision in its own hands) what measures would be appropriate to restore the equilibrium of its international balances, including
(a) measures for the expansion of domestic credit and domestic demand:
(b) the appreciation of its local currency ... or, if preferred, an increase in money-wages;
(c) the reduction of excessive tariffs and other discouragements against imports;
(d) international loans for the development of backward countries.

On the other hand, countries with a trade deficit would be allowed to take the following actions:

(i) restrictions on the disposal of receipts arising out of current trade and ‘invisible’ income.
(ii) import restrictions, whether quantitative or in the form of ‘duty-quotas’ (excluding however prohibitions genuinely designed to safeguard e.g. public health or morals or revenue collection);
(iii) barter arrangements
(iv) export quotas and discriminatory export taxes;
(v) export subsidies either furnished direction to the state or indirectly under schemes supported or encouraged by the state; and
(vi) excessive tariff.""

http://tradeandtaxes.blogspot.com/2009/02/keynes-trade-surplus-countries-should.html

[bob]

One thing though:

"Either the west stops saving (and we basically inflate away our debts to the developing world) or the developing world stops saving and spends all their USD reserves buying stuff from us."

I don't think the first option is possible because China is pegged, and Japan etc. manage their currencies, so they will buy as many dollars as necessary to neutralize an attempted depreciation of the US dollar. So it really is in Asia's hands right now to shift the balance. The west can't really do much besides putting up tariffs and trade barriers, and no one wants a trade war right now.

[pointbite]

Adam and Bob, I feel like we're going in circles. If we're experiencing deflation because people are determined to save, you won't change their mind by printing money. I think you're way too focused on the equations and forgetting the humanity. If people want to save and they're given an ultimatum, "spend your savings or I'll destroy them" the more likely outcome is a rush to alternate forms of savings. I still think you're all missing a critical component in your analysis, the PEOPLE.

I sometimes wonder if low interest rates are discouraging people from buying homes because with ZIRP there's an implicit assumption that prices are being artificially propped up and that somehow foreshadows an impending devaluation. A short story, today I went shopping with a family member and she saw an interesting book, but when she noticed it only cost $8 she assumed it must be terrible and lost interest. What you're all forgetting is that we have an innate sense of what constitutes a fair price. When something is too low, or too high, it raises alarm bells and people step back. In a way, the low interest rates are almost causing apprehension... "Wow, they must really be desperate! The market must be terrible! I'll wait another few years."

[bob]

pointbite: on your first point, what we're saying (I think) is that in order for debt to be too high and savings too low in America (which we all agree with you on), savings have to be too high and debt too low somewhere else. Savings have been too low in america, and too high in asia, but aggregate debt throughout the entire world is 0 by definition. What matters is the distribution of debt, if everyone has a bit of debt and a bit of savings (other peoples debt) that is healthy. When one set of people do all the saving, and the other set of people are in all the debt, that is bad. So when you say that there is "too much debt" what you really mean is that there is an excessively skewed distribution of savings and debt. You just see the debt half of it because you are in north america, if you went to China you would see the effects of excessive saving. the two are tied together.

on your second post, you have discovered the Paradox of Thrift. That insight into psychology is one of Keynes' great ideas and informs all of the analysis that you see going on here. He saw it as being a very tough problem for the same reasons that you do. As I was saying on a previous post: it is self-reinforcing. The thing is that Keynes figured out a way to break that cycle before we hit rock bottom. That was his great discovery.

[bob]

sorry, I should explain what I meant with the second part there:

Because a person, say a photographer, sees that prices are falling, they decide to wait to buy the house. BUT because they decide to wait, the real estate agent doesn't get paid. If the real estate agent is also a customer at the photographer's business, he will not have the money to buy anything, so the photographer's income drops. Maybe the photographer lowers his prices to try to get more business, but then the real estate agent says "aha! he's getting desperate. I know the price is going to be lower next week" so he decides to wait to buy anything. It turns into a standoff where no one buys anything from anyone else, because they know that the price is going to drop, but their incomes keep dropping faster than the prices, so it just keeps going and going. That's what we call the deflationary spiral.

What all the stimulus, quantitative easing, threatening inflation etc. is meant to do is break this cycle, and change the overall psychology.

[Nick Rowe]

Thanks a lot for your comments guys! I don't have time to reflect and answer them properly right now, since I'm about to head out.

What I don't like about it: I think it was a comment that either Paul Krugman, or Brad De Long, or someone made about quantitative easing: if you are relying on a wealth effect from throwing money at the economy, at zero interest rates, you would have to throw a few trillion $ for the US, and a few hundred billion, for Canada, to get any action. And I think (not sure) that's the channel through which helicopter money is working in my model.

Money is wealth, but it's more than just wealth, when there's a shortage of liquidity.

I don't think the model proves quite what I wanted it to!

[bob]

to get back to Nick's original model, I think the domestic inequality is actually compounding the global effect of excessive saving in Asia. So while it has been happening on a global scale (although it is not really exactly the same in terms of wealth distribution: it's more like a forced system where poor people are forced to save, as if they were rich), it has also been happening domestically, increasing the deflationary pressure twofold.

I think this is something that has been known intuitively for a long long time, but no one wants to believe that equality is actually good for overall growth, and inequality is bad.

If you look at the Jubilee tradition, it seems like a rudimentary policy to correct this: pronounce all debts null and void every 49 years. I'd file it under "superstitious traditions that actually made a lot of sense". It's like letting fields lay fallow once every 7 years - seemed like a crazy counter-productive superstition but it turns out there are good scientific reasons supporting it. Even though the ancients probably didn't have a firm rationale, the stigma attached to avarice and money lending probably has something to do with repeated experiences of rising inequality followed by a crash.

I'm not sure if this happened with all previous depressions, but the Great Depression and this crisis both were proceeded by periods of increasing inequality, leading to excessive saving in one half of society, and excessive borrowing in the other half, leading to deflating prices and collapse. I think Nick's model explains this basic phenomenon quite nicely, even if it doesn't do everything he wanted it to wrt monetary easing.

[pointbite]

Bob, if you agree that low savings in North America are a problem, wouldn't the more appropriate solution be to raise interest rates? Or print Chinese RMB instead of Canadian dollars? Or the gold standard to automatically settle imbalances of trade? What about Europe, rates are dropping there too but savings have always been much higher. Is it possible that savings are a consequence of culture more than finance?

When I follow your arguments step by step they make sense, but people don't walk in a straight line. I keep going back to Nassim Talib, as you can tell I loved his books... I'm going to paraphrase because I don't remember the details, but in The Black Swan he tells a story of a mathematician given the assignment of predicting the exact movement of a billiard ball after being struck by another ball. Imagine all the variables and the precision that would be required. Now imagine the struck ball hit another ball and his task is now to predict the movement of the 3rd ball. Then the 4th, 5th, 6th... etc. Imagine how much data, to what precision, would be required by the time you reached the 10th ball. You would need to take the gravitation pull of distant stars into consideration, the exact imperfections of the table... At some point, this task becomes impossible. Now my little addition to the story, imagine if each ball had free-will and didn't always obey the known laws. Game over. And that's with 10, imagine 6 billion. The conclusion of course is that to some extent economics a guessing game. We don't really know as much as we think we know.

With stable money supply bubbles are limited because diverting large portions of the money supply into one area causes shortages of demand in other areas, resulting in price declines that eventually re-balance demand. This time around, the amount of inflation required to remedy the last recession was so massive it created a bubble in everything. The inflation didn't solve the underlying problems last time and it won't be any more useful this time.

In my opinion, the spiral you talk about is only a problem if the supply of money is shrinking. I'm not alarmed by falling prices... prices for typewriters fell off a cliff decades ago, the world moved on. It can sometimes just reflect changes in society over time. Perhaps we went a little over the top with home ownership and now that must correct. Interfering without reversing cultural shifts won't stop the trend, but it may cause irreparable collateral damage. I always keep one eye on the real estate market, I have felt for years that prices were unjustifiably high. I can tell you personally there is a price at which I become interested. We're not there yet. If prices start rising again it won't increase the likelihood I will buy. With all the maths and models, don't forget about the people. I believe inflation will actually prevent economic recovery and make our problems worse. If you want more demand, let the prices drop.

[bob]

"If you want more demand, let the prices drop."

I think you already figured out why this doesn't happen in your earlier post: if prices drop one time, or for a limited period, that does increase demand (ie a one day sale). But what if you know that prices will be lower the day after tomorrow? And even lower the day after that? Then it never makes sense to buy, so the constantly falling price actually kills demand.

that's why Monetarists want to at least trick people into thinking that we are going to unleash an inflationary holocaust (don't worry, we don't actually want one, we just want people to think that). even if people are buying gold as a hedge, at least then they are buying something, and at least the income of gold miners would go up. we want people to try to hedge against inflation, but it is hard to get them to do that if they see that rates are at 0% but prices are still falling. Its kind of like threatening someone with a revolver, but they can see that there are no bullets in it. Not a very credible threat.

Because traditionary monetary policy can't create the threat of inflation at this point, that is why Nick is exploring QE, and judging by your response yesterday, it seems like he might be able to generate a pretty credible threat of inflation. We want people to think "That Fed chair Nick is one crazy mofo! He doesn't care, he just loves to print money and he will never stop! I'm trading all my dollars for goods or services because soon they will be worth nothing!" but as soon as you do that, Fed Chair Nick stops printing money, raises interest rates and says "haha, fooled you!".

I agree that falling prices aren't always bad. You want certain prices to fall so that its sends the message to producers "Stop making typewriters! We don't want them anymore." When you're designing stimulus, you want to avoid interfering with those processes, but also avoid a general falling price level so that people don't stop making useful things and good companies don't go out of business. I don't think we had a bubble in everything.

In the current context: housing prices need to come down. This we know. Income to price ratios are way out of whack. Schemes to prop up housing prices are terribly misguided.

The problem is that falling house prices set off the chain reaction in my post above: because the photographer didn't want to buy the overpriced house (a good rational choice) that was falling in value, this starts having a deflationary effect on the economy as a whole. the real estate agent stops buying his morning coffee at the local diner, the diner stops ordering photographs from the photographer etc. etc. and everyones incomes start falling faster than the prices. The housing prices DO need to come down, and the real estate agent probably does have to get himself another more productive job, but we want to make sure that the photographer and the diner owner who did nothing wrong and run good businesses don't get clobbered by the slowdown and falling prices that the collapsing housing bubble sets off.

Same thing with the banks. Geithner wants to save them because he knows that their collapse entails even more deflation, but he is blocking a very important rebalancing and restructuring from taking place. They screwed up and they need to pay the price. That's how a market works. Bailing out house-flippers to keep housing prices up and bailing out bankers to keep the price of financial assets up is just about the worst meddling you could possibly do right now.

The important thing is to let the prices that need to fall go down on their own, while insuring that the general price level doesn't start falling rapidly and taking out innocent bystanders. Also, I do share your caution: we don't know exactly how people will react to every policy. To my mind, fiscal stimulus like infrastructure is more tried and true and depends less on assumptions about how people will react, so I tend to favor those kinds of Keynesian policies, rather than Monetarist policies like quantitative easing.

[pointbite]

Bob, if you scare people by threatening an inflationary holocaust you won't re-create demand for discretionary items, encourage people to take more vacations or get a fancy hair cut. It will encourage them, if anything, to hoard food and precious metals, which is totally unproductive. That would probably be the worst policy you can pursue. I actually think the exact opposite would be preferable -- secretly creating actual inflation. Although ideally I would rather the government take a vacation for a few years.

The world would be much better off without any inflation and without anybody feeling a need to panic-spend their savings unproductively or hoard anything, ever. I'm not happy buying gold, I would rather buy a house or start a business, but I can't justify the cost or investment right now. The government is forcing me to hurt the economy against my will.

And for the record I actually don't agree with your first paragraph. If I want to buy something, I will buy it when the price matches my utility. Knowing the price may drop on my favorite car $1000 between today and 365 days from now may not be sufficient to compensate me from not having it for those days. I strongly disagree that falling prices reduce demand, if anything the continually lower prices cause excitement and increase demand. The whole high tech sector is my proof, we all own many cell phones and computers and televisions, yet the prices fall every other month. Where is your evidence? This price-dropping-spiral story is a myth, in my opinion.

[Patrick]

It looks to me like Nick's patience continuum might be able to capture 'animal spirits'. Instead of patience, call it fear (or maybe 1/confidence?). People with high levels of fear save more, peoples with low levels of fear save less. Suppose people have more or less random basic/built in levels of fear plus a variable level of fear that changes with their liquidity and indebtedness. Their variable level of fear would drop as they became more liquid and less indebted, and rise as they become less liquid and more indebted. Also as fear rises, the propensity to consume would go down. I'm not an economist, so maybe I'm just talking rubbish, but might this model reality more closely?

[Adam]

Patrick, hits the nail on the head. Absolutely correct and we don't need to conjure animal spirits to see it. With no randomness subjective discount factors just measure impatience but in the random world we live in subjective discount factors also have a risk premium. The expected future consumption that determines the equilibrium real rate is a risk-neutral expectation. This what I had in mind in earlier comments when talking about people expecting/fearing lower future consumption. Of course, once the economy is in free fall like now then the fear factor gets much more important. Even if only 5% of us are going to lose our jobs every one of us might worry that we'll be one of the unlucky and cut back consumption. Risk premiums are high now, clearly, and there's nothing irrational about that.

[Adam]

pointbite, generally falling prices are different from prices falling in a single good. One problem is supply side, if wages are downward sticky then a fall in the price level drives up the real wage and decreases supply and employment.

Now, let's assume wages eventually adjust downward. Does that return us to full employment? NO. The second problem is the debt-deflation problem. For this let's tweek Nick's model a bit. Nick said that the disavers couldn't borrow, no private bonds at all, so their consumption could never exceed their current income even though they (perfectly rationally) wanted it to. Let's change that and say that instead they can only borrrow to a fixed multiple of current income (for example, mortgages (before countrywide) used to be limited to 4-5 times current income). Now, Nick's fourth class of agent borrow up to their constraint and are stuck while his third class borrow but maybe not all the way to their bound. But now, a deflation followed by a drop in wages (so the real wage ends up back where it started) has impoverished the fourth class of agent and reduced the wealth of the third class, perhaps up to their constraint. There has been a transfer of real wealth to the savers and in Nick's economy the savers have zero marginal propensity to consume! Thus we end up with a large drop in aggregate demand and recession. Furthermore, in this version the helicopter drop of money needs to be truely huge to work because the people who had debts that originaly they could service are now way underwater and the first bit of money they get just goes to pay off the debt. The new money ends up going entirely to the savers until enough has been dropped to get the debtors solvent again.

[Adam]

Nick, still not seeing your problem. As I read the model you wanted to exhibit an economy that was liquidity trapped where the trap is due to market incompleteness and where monetary policy could work without the interest rate channel. Seems to me you did all that.

The trap happens because a bunch of agents would prefer to lend than consume, but can't, and on the other side the ones who are willing to borrow and consume can't either. Market inocompleteness, check.

The helicopter drop works not by changing prices but by relaxing constraints on the ones who would like to borrow. They need not suffer from any form of money illusion, they may know full well that the extra money means future prices would be higher but it's ok with them. The wanted to trade a little less consumption tomorrow for a bit more today and so if they can afford a bit less tomorrow they don't mind. Effectively you gave them a loan and the inflation is how they pay it back. A loan is what they wanted.

It's not a wealth effect, it's relaxing a constraint that was due to the missing credit market.

[pointbite]

Adam, the entire high-tech sector is not a specific good. Generally falling prices do not decrease demand. This issue just couldn't be more clear, it's thoroughly debunked in my opinion.

Why are you pinning all your hopes on increasing the capacity of the poor and unemployed to spend money they don't have? Why are you trying to save us from a transfer of wealth to our most competent citizens? Isn't that how capitalism is supposed to work? You're assuming savers refuse to consume because it's their nature, perhaps they refuse to consume because prices don't accurately reflect value. Perhaps inflation is the cause of the problem as opposed to the solution. You're forgetting that savers can change their behavior in light of new information, they're not robots.

There's something fundamentally silly and unfair about this whole plan, put yourself in the shoes of a saver, the most likely response will be retaliation and that could mean the most responsible and wealthy individuals will disengage even further. If these people were smart enough to avoid the market traps, they will be smart enough to avoid the government traps. They're not going to take this sitting down. This scenario stinks of bank runs, civil unrest and $5000 gold. It's actually quite amusing to me how much our perspectives differ.

[Adam]

pointbite, you're not really reading the argument. I never said falling prices, on their own, decrease demand. The argument is that with stick wages, which seems to be there, falling prices decrease supply by driving up marginal costs. If wages fall with the prices then their is no effect on demand. You said falling prices would increase demand.

Furthermore, if there is a debt-deflation and if creditors have lower propensity to consume than debtors (as is the case in Nick's model and likely to be the case in reality) then falling prices can reduce demand.

Finally, sustained deflation and deflatonary expectations (as opposed to a one time fall in prices) will reduce demand because it drives up the real rate of interest, that's macro 101.

Also, where do you get the idea that debtors are any less competent than creditors? Like I keep saying, a major defaltion will be costly to debtors who in anything like normal times are perfectly good credits. This includes competent entrepeneurs that borrowed to finance a potentially valuable business but couldn't index the debt. Moreover, if you bankrupt the debtors then the creditors lose too.

My guess is that 25% unemployment will cause more civil unrest than 6% inflation.

[Adam]

actually, I should correct the first paragraph of my last comment:

With sticky wages, which seem to be there, falling prices drive up the real wage and decrease employment. Higher unemployment will decrease demand.

If wages fall with prices then there is no change in demand. In no case does a deflation increase aggregate demand.

[calmo]

Such a formidable discussion in this thread...how could Nick "head out"? I'm still heading in...and reluctant to muss (this excepted) with these fine comments...commenters...possibly real PEOPLE, who just know how to read arguments...a few more brain pills to aid the digestion, maybe, and I can add to this fire...and not douse it. I'm headin in, I am...waaaaait up for me!

[pointbite]

Adam, I'm not arguing there's a superior plan that will result in less pain. We have built up enormous imbalances over many years and they won't correct without causing enormous dislocations in the economy. The fact this problem is really bad doesn't mean anything you do is better than nothing, you can't cure cancer with cyanide. I know this makes economists feel useless, but that's life.

I'm not alarmed by falling prices when the supply of money isn't falling. Look at the numbers, M0, M1, M2 and M3 are growing rapidly, even M3 + credit is still growing. (http://www.nowandfutures.com/key_stats.html#m3_plus_credit). Sticky wages or not, the money exists, there is no spiral. This tells me the problem is not monetary, it's psychological. Your tools have failed to influence psychology as prices contract and there is no reason to believe they will be any more successful should prices begin to rise as a result of money printing. You will not convince savers who resisted temptations during the boom to somehow see the light during the bust by threatening to steal their wealth. On a strictly human level, it makes no sense. The more likely response will be retaliation, that's common sense 101. Sometimes you have to put down your textbook and look out the window. There have been bubbles in everything, prices do no reflect reality, forcing them up from current levels will only cause more distortions. Imagine how much worse these problem would be if the US treasury market implodes and the only refuge is cash and gold.

As an aside, I was asking a few months ago if one potential solution would be to allow gold to appreciate. The government wouldn't have to do anything, just stop selling from the central banks. If gold started to break out, there's no question it would generate a ton of excitement and get money moving again. Ordinary people are watching gold for the first time. Especially those frugal savers you want to destroy.

[pointbite]

* remove the cash from the end of my second paragraph. Just gold, and possibly silver.

[bob]

pointbite: I would take my earlier comment with a large grain of salt. It was pretty hastily written, hence my use of the term "traditionary". I'm oversimplifying, and overstating things for dramatic effect (inflationary holocaust), just to try to get some of the basic ideas across. No doubt I have somewhat misrepresented Nick's positions as well. I'm sure that what happens with quantitative easing is a lot more nuanced than I made it out to be there. Part of the idea is to create an expectation of inflation, but not necessarily hyper-inflation, and I don't think anyone wants to induce full-blown panic. I think you got the basic ideas though, even if you don't agree with them.

In terms of low prices inducing demand when they reach a level corresponding to some sort of fundamental value: values are always relative, and have to be judged versus a number of different factors such as prices for other goods, interest rates, reflexive market psychology, current vs. future supply, current vs. future demand, opportunity costs etc. etc. that are all inter-related. Failing to take into account the influence and variation of all these factors is why bottom fishers lose money so often after being lured in by low P/E ratios. the value of a good (its marginal utility) is dependent on and can only really be judged within a complex web of relationships that are ever-changing and inter-dependent.

Your Taleb billiards example is a good demonstration of this. In terms of calculating marginal utility, we never "really know as much as we think we know" because any single agent's information is always incomplete, and judgments are often biased towards extrapolating past experience (lack of black swans etc.) into the future. What seems like a 'fundamental' good price relative to past experience may turn out to be a horrible price for the rest of the future (buying a buggy-whip factory with an extremely low P/E ratio right before Ford invents the Model T)

Sure, a house may seem to be useful to you at a certain price that is very low relative to your income and historic housing prices, but what if the price of everything, including your income, changes after you sign for the loan? Even if you bought at a price that seemed good at the time, it could end up being a terrible choice and a huge liability if the price of all other goods and services including the goods you produce (and therefore your income) goes down after that, but the outstanding balance on your loan stays the same.

[Nick Rowe]

21 comments! Let me try to answer some:

DW: there has probably been some shift in relative demand, but on top of that (and the thing I'm scared of) a fall in aggregate demand. Monetary or fiscal policy should be aimed at the latter. I think it will neither help not hinder the reallocation of resources away from some areas into others. (A big recession increases loss of resources in declining sectors, but reduces gain of resources in growing sectors). But my model doesn't handle relative shocks.

pointbite: the problem (according to my model, and I think it's right in this, is not too much saving, nor too little saving, originally, in aggregate. It's that some people want to save, and keep on saving, and others want to dissave (spend/borrow) and keep on dissaving, until they can't borrow any more, and then have to stop dissaving (so that aggregate savings then automatically rises, and gets too high). It's the distribution across the population, not the average, that causes problems. If the patient said "I've saved enough, time to stop saving", and the impatient said "I've borrowed enough, time to start saving", the problem would not appear. But if only one side says this, then we get problems.

Adam: I think you understand my model better than I do! "The real issue though is that you haven't specified a process for aggregate consumption." OOOps! Damn! You are (mostly) right. In full employment, (when i>0), consumption = output = employment = exogenous labour supply. But when i=0 and we get unemployment, we need to specify what happens more precisely. If the Euler equation is something like C0/C1 = C(r-d) we have problems. The simplest solution is to assume (like PK and others) that we return to full employment at some exogenous future date. A bit ad hoc, but it works. Otherwise there's a danger that the only equilibrium is at zero employment. Or we could play with the utility function, or we could play with the distribution F(d), and get an interior solution (I think). My maths isn't up to the task.

Adam and bob: yes, at the back of my mind was the possibility that the "patient" are mostly China and Japan, and the impatient are mostly the US and others. I've then ducked the exchange rate issue, but I don't think that matters much.

pointbite: what bob said.

bob: is it inequality of income (earning capacity) that drives differences in savings rates? That's not obvious to me. I can't think of any theoretical reason why those with high wages should be more patent, and those with low wages less patient (unless we reverse causality and bring in human capital investment). (Of course, those with negative transitory income should dissave, and those with positive transitory income should save). Anecdotally, it wasn't just the (permanently) low wage people who were getting too deep in debt. Or was it?

Patrick and Adam on animal spirits: agreed. Actually (and this brings me back to Adam's point about my failing to solve for consumption, when i=0, you can see in my model, that as we approach i=0, and people see unemployment rising in future, they will increase savings today. So with perfect foresight, the date at which i=0 would be brought forward. The expectation of future unemployment would cause current unemployment. We might (or might not) get a sudden "crash" of falling interest rate and recession, as we approach i=0. (I can't quite figure out if this would happen).

Adam 7.25. Agreed. But is it really monetary policy that's doing the work, or is it a fiscal policy that happens to be money-financed? (I mean, the original big helicopter increase in the money supply). There's a bit of a semantics in arguing over what's monetary and what's fiscal, but a helicopter money (money-financed transfer payment) is a bit of both. My head is not clear on this. That's why I'm not explaining myself clearly.

Adam at 1.37. Remember though, wage = price in this model. The only good is backscratching. A a lower price level (holding expected inflation constant) will increase real money balances, and increase employment.

calmo: yep, it's a great discussion. But a night out with my gf took precedence, so I "headed out". ;-)

[pointbite]

Nick, why do some savers never change their habits? I know that's an unfair question because there's no way to know, but that's the core our disagreement, I think. Ignoring the cause of this behavior is tantamount to writing a conclusion without any observations. Perhaps they refuse to spend because of excessive inflation, prices are never allowed to correct. Add more inflation and rather than a wave of enlightenment causing money to flow, you will instead experience a wave of rebellion. I believe psychologists call this cognitive dissonance. Even if your model is right, you will be wrong.

As a side note, in a time average savings are too low, it would seem counter-productive to punish the few savers left, if even they're a bit too frugal. It's like taking out the smartest kid in class to lower the curve, in the end you may graduate but with dumber kids (ie. we'll have even less savings in the future). I don't believe the government has a right to overrule how I spend (or don't spend) my money. I have an issue with deceptively stealing an individual's life savings to benefit people who consumed their way into bankruptcy, and that includes corporate bailouts. It's bad capitalism and it's bad morality.

[bob]

"bob: is it inequality of income (earning capacity) that drives differences in savings rates? That's not obvious to me. I can't think of any theoretical reason why those with high wages should be more patent, and those with low wages less patient (unless we reverse causality and bring in human capital investment). (Of course, those with negative transitory income should dissave, and those with positive transitory income should save). Anecdotally, it wasn't just the (permanently) low wage people who were getting too deep in debt. Or was it?"

I'm not sure if it is really obvious, but my intuition goes something like this:

Say all those who are patient and impatient, skilled and unskilled, smart and stupid, strong and weak start at an equal position: everyone has a $1000 cash loan satisfy consumption needs etc. and $1000 in interest paying bonds. So $1000 in savings and $1000 in debt. Basically we create a currency system by everyone borrowing and lending an equal amount to each other. All things being equal, the interest due on the loan is equal to the interest made from the bond.

Throughout the course of normal economic activity & competition, the productive and unproductive bifurcate: the more productive members start getting an increasing amount of everyone else's consumption spending, because they are more efficient and provide a superior product. People that are patient are evenly split in both groups (there are just as many poor misers as there are rich misers - I don't think propensity to save necessarily has anything to do with individual productivity).

So, over the course of time, the patient amongst the productive start to earn increasing income from their bonds, because they are putting more of their income in bonds and paying down debts, and less in consumption. The median-patient among the productive make a lot of money, but they also spend a lot of money, so the distribution of their 'portfolio' stays even between their own debts and savings. They keep their debt level at $1000, and bond level at $1000, but they use the excess income to accumulate goods, and enjoy services. A productive person (think pro athlete) with low patience has no limit on his consumption, so even though his income is high, he runs up his debt and runs down his savings in order to consume. When he can no longer perform at age 30 he runs out of income, his debt load is high, and savings low, so interest payments on the debt will quickly impoverish him.

So what happens is that the patient, productive person starts to generate an increasing amount of income from bond coupons. Because of the low propensity to consume, he pays down his loan, then just keeps dumping the interest income back into more bonds. At this point, even though he is not being any more productive than before, his income just keep growing, and savings grow, and interest income keeps growing until the interest payments actually eclipse his original income from productive activity. At this point he might decide, hey, why bother even working anymore? So he stops working at age 30, lives off of part of his interest income, but keeps dumping part of it back into more bonds. Then he has kids, and they don't do anything productive, but he teaches them that they don't ever have to do anything productive, so long as they remember to NEVER spend all of the interest income, and always put some back in to buy more bonds. This is the power of "old money", which in America is pretty much synonymous with major bondholders. This is the accepted wisdom that gets passed down amongst old money families: So long as you never spend more than the bond coupons, and always remember to put some back in, you will never have to work.

So the unpatient athlete and the patient saver both do the exact same amount of productive work, both retire at age 30, but due to the cumulative effect of the difference in patience, the saver gets rapidly richer, and the athlete gets rapidly poorer.

On the other side:

The less-productive members of society do not have the skills, efficiency etc. to provide products that can compete initially, so the cash they spend on consumption start to outstrip their income: Their debt level of $1000 starts to grow, their savings start to shrink. The least patient will run down up their debt, and run down savings to satisfy consumption. The median patience actor will adjust his consumption so that it matches income, so his bond and debt levels stay constant, canceling each other out. The most patient will make up for falling income by drastically cutting consumption, and putting his meager savings in bonds and paying down his debt to reduce his interest expenses, even though the tiny amounts of interest would take a long long time to make up for what he continually lacks in income. He will probably die before his saving could ever pay off big enough to make up for the poor income, and leads a miserable frugal life, but he does become wealthier than the non-patient, non-productive person.

Both the spender and the miser are equally useless and unproductive, but one ends up in debtor's prison, and the other suffers a slightly less depressing fate.

Putting them both together:

The interest income of the rich misers starts to far outstrip that of poor misers, because their initial income allowed them to purchase a greater amount of everyone else's debt. Over time this imbalance compounds, and soon everyone is in increasing debt to the rich misers. An increasing share of the poor's income goes to paying interest, but it never comes back to them as income because it is saved. So the misers refuse to buy their goods, but will lend them money. Eventually so much of the consumers incomes are diverted into interest payments on their debts, and that money is never used to buy goods, so prices start to fall. Deflationary collapse ensues. The poor eat the rich. Maybe if the rich are really clever they cook up a war to get all the poor to kill each other, thus avoiding a revolution, but losing part (but not all) of their investment income because half of the debtors are now dead and those bonds default. This brings us back somewhere closer to starting position (think pre-depression gilded age vs. post-war USA). Rinse and repeat.

[Patrick]

Models aside, I think this is the liquidity trap in pictures:

http://research.stlouisfed.org/fred2/series/EXCRESNS?cid=123
http://research.stlouisfed.org/fred2/series/BOGAMBSL?cid=124

Just by eye (I didn't bother looking at the data tables in the raw), the increase in excess reserves looks to be about the same as the increase in M0. The money is in the vault.

I'm starting to suspect that broken financial intermediaries have way more to do with the liquidity trap than ZIRP would in isolation. During the GD banks were broken, in Japan banks were broken, and today banks are broken worlwide. Can anyone think of a modern instance where there was a debt-deflation spiral & liquidity trap without broken banks?

Anyway, since the Fed obviously can't use the usual channels to increase the money supply, the only option is the helicopter.

[bob]

"Anecdotally, it wasn't just the (permanently) low wage people who were getting too deep in debt. Or was it?"

This is where it gets interesting.

The rich realized a long time ago that they needed to establish some sort of checks to slow down the above process, hence the welfare state. The poor realized that if they banded together and demanded enforced patience via pensions that they can grab a greater share of that interest income. BUT because they always start out in a weaker position, they can never really catch up to the rich in terms of investment income. Those are the countervailing forces that slow but do not stop the advance of inequality and debt imbalances.

China has basically made a giant pension plan by forcing savings across the whole population, the biggest pension plan of all-time. Even though they are poor, what they lacked in initial income they have made up for in sheer numbers. It's so big that they managed to out-save many of the lower level american rich, but not the ultra-rich, who were still on top and got way richer under Bush. the top 0.5% you always hear about, whose incomes grew exponentially in recent years are those who are on top of the whole heap. The giant force of all those savers moved up the dividing line in America, so even many of the people we generally consider rich and patient, with high incomes ended up on the other side of the patience divide, and their debt started to grow vs. savings. Due to globalization, the patience/impatience divide is now determined by the global population, rather than just the divide within the United States itself. The huge amount of enforced patience in China means that far more people who used to be above the patience divide fall under the patience line in western countries. It's a lot more complex than this, when you start factoring in interest rates, exchange rates etc., but basically that is what I think is going on.

[Nick Rowe]

pointbite: If some people save a lot, and others spend a lot, the economy on average is in equilibrium, but trouble is brewing. The spenders are going deeper into debt to the savers. Eventually the spenders have to stop spending (or they will be unable to pay their debts). But if the savers don't start spending, the economy goes into recession. How do we get the savers to start spending?

bob: I think I follow you. You seem to be arguing that patience and earning capacity are sort of multiplicative in their effects, rather than additive. I will need to mull that over. Not obviously wrong; not obviously right.

Patrick: Yes! Your comment is jogging my mind in the right direction! Broken financial intermediaries create the spread between private and government borrowing rates, so the latter can be at 0%, while the former are not.

[pointbite]

Nick, let prices adjust and stop trying to micro-manage the economy. Nobody is smart enough or honest enough to do it right. The slightly more complicated answer that I'm still debating (apparently with myself) is to allow the appreciation of some asset savers would be willing to buy, perhaps gold. Reduce deficit spending to free up private capital then stop selling from central bank reserves. Set gold free and watch dollars fly, they'll rain down from the sky without a helicopter. If we're talking about psychology, there's nothing more gratifying than being right. If you want savers to spend, make them right.

Because if you try to make them wrong, again, they won't cooperate.

[Patrick]

pointbite:

Have look at this:

http://oregonstate.edu/cla/polisci/faculty-research/sahr/sumprice.pdf

The, in my view quite wrong, Austrian/libertarian view of inflation only looks at the inflation graph and they immediately loose their grip on reality.

Yes, the inflation graph at first glance looks pretty scary. But go look at the real GDP graph. It's exponential too, and really takes off post depression. Also notice how flat GDP growth is pre-1915?

Now look at the graph for y/y changes in inflation pre-1915. Notice all the churn? Ok. Now look the 1915-present graph. See how the chop disappears? That corresponds to a period of massive increase in GDP and standard of living. It also happens to corresponds to the era of modern economics, which some would argue was ushered in by Keynes.

In human terms, the period of history that Austrian/libertarians would view as an inflationary holocaust corresponds to the largest gains in standard of living in the history of the human race. It also corresponds to a period of economic stability - all that inflation/deflation chop and churn in the pre-1915 period was not fun. Imagine prices swinging around that violently today? How could you run a business or a government in that environment?

I think there are serious issues raised by exponential growth/inflation; not the least of which is the simple fact that it isn't sustainable, but in my view it would be terribly foolish to revert to the dismal income inequality and price chop and churn of the pre-modern era. It'd be like throwing out antibiotics at the first appearance of MRSA.

[Patrick]

Brad Setser on the most impatient actors
here

[reason]

Nick
I don't think the model proves quite what I wanted it to!

But you have proved what I have been saying all along! We need a REAL helicopter drop (where money gets to those at the bottom, not a financial sector underwrite the fat cats bonuses helicopter drop).

And mostly, I think I should just let adam talk for me, we seem to pretty much agree and he says it better than I do.

[reason]

DW
1. No that is the cause of a boom as resources are pulled into the expanding sector (see 1990s).
2. No that is caused by the stagnant sector being outcompeted for resources and imploding.

[reason]

Nick
Sorry I didn't read your answer to DW before I posted. We both said the same thing, but you were much kinder.

Adam and bob: yes, at the back of my mind was the possibility that the "patient" are mostly China and Japan, and the impatient are mostly the US and others. I've then ducked the exchange rate issue, but I don't think that matters much.

But I do. I think it is crucial.

[bob]

"You seem to be arguing that patience and earning capacity are sort of multiplicative in their effects, rather than additive."

Yep. I'm also saying that there is a tipping point (when the patient person's investment income eclipses regular income & consumption) where the process accelerates because interest payments are then put back into more bonds, which increases investment income, which further increases bond holdings, on and on.

[pointbite]

Patrick, I'll take a look at the link later tonight, but just a quick comment:

"the largest gains in standard of living in the history of the human race"

Are you saying that without the Federal Reserve we wouldn't have micro-chips and airplanes? Talk about a stretch. The only saying applies: correlation doesn't prove causation. Furthermore, PLEASE read The Black Swan, that book was made especially for people with your perspective. When you get to the part about options traders, hold up a mirror.

[Patrick]

pointbite: I tried. When you start with the personal attacks, I'm done.

[pointbite]

Patrick, I didn't attack you. I'm saying Talib's section about options trading is a better response to your point then I could articulate on this forum.

[bob]

pointbite: If you left out the "mirror" part it would be fine. It's best to keep things civil. Case in point:

One year ago, on another blog, under another pseudonym, I was trying to make the exact point that Patrick makes at 8:08 and Nick makes in his new post: if the credit system (credit channels) is clogged with lemons ("AAA" securities that may or may not be junk) the credit transmission mechanism stops working. When you cut rates during this situation (before deflation starts) it ignites the threat of inflation causing people to rush into inflation hedges (the oil bubble) but it doesn't actually stimulate the rest of the economy, and hastens the onset of the liquidity trap. I was frothing-at-the-mouth, pulling my hair out trying to get this point across so that maybe someone would tell Bernanke "DON'T DO IT!!!!". It's too late now, but I am so so glad to see Nick and Patrick realizing this.

Right about now, I would love to link back to those posts, but here's the problem: on the same blog I made some disparaging comments about Nick that are incredibly embarrassing in retrospect. ("If I wanted to know about pareto-optimal keg-stand configurations or beer-pong rules, I'd ask a Carleton economist"). Now that I know what a great economist Nick is, and how willing he was to see my point of view without writing it off, I'm way too embarrassed to link back to those posts. Also, I have learned a lot from Nick, and makes me realize that a lot of the things I wrote at the time on that blog were wrong, making me a hypocrite, and furthering my embarrassment. Even though I had a real point, which Nick now agrees with, the ad hominem attacks were totally counter-productive. Sorry Nick!

[Adam]

Bob, ditto for me, see my first ever comment on the blog (last week) for an example. going after Nick and I didn't even know who he was yet.

And seriously Bob, if you live in Toronto you should be well aware that for pareto-optimal keg-stand configurations or beer-pong rules you go to Western.

[bob]

haha, true.

Well Nick does hold a PHD from Western AND teaches at Carleton. I'm sure that his parties are organized in such a way as to maximize aggregate wastage, while minimizing premature cases of individual agents passing out:)

[Adam]

:)

yes, yes, they wouldn't be optimal if they didn't.

[pointbite]

It actually wasn't ad hominem... it was a failed attempt at a joke.

[Nick Rowe]

bob: So that was YOU! (I originally thought you must have had the wrong Carleton). I survived, and have learned a lot from comments. No worries. But yes, if the blogosphere were more civil, people would probably find it easier to learn from criticism, and change their minds.

[Adam]

I for one believe that pointbite didn't mean to attack anyone. But yeah, I agree with what Nick said.

[bob]

True, I don't think he did either. It's just that when you say that Nassim Taleb says x about people like you, there's a 90% chance that it's a chapter filled with ridiculous insults.

I have read some Taleb, and I trade options on a regular basis, so since pointbite keeps bringing him up, here's my impression of Taleb:

He misunderstood what was causing the underpricing of risk. The savings glut caused risk to be underpriced across all markets. Most of Taleb's investing career has taken place in the shadow of the growing savings glut, but he would rather think that everyone who underpriced risk is just an idiot, who has never heard of a fat tail, rather than dig a bit deeper into figuring out why that is. No, it's not just "fooled by randomness", it's more like "fooled by the glut". Pointbite, if you're a libertarian, shouldn't you be saying that the underpricing of risk was caused by the Fed underpricing it? I don't agree, but I think that thesis is actually more right than Taleb's.

His investment strategy is pretty lackluster to say the least. He only returned 50% on average last october in his ideal scenario, after years of losses and a failed hedge fund. Compare that to John Paulson with 4,300% last year, or Andrew Lahde with 1000%. THAT'S how you bet on the Black Swan showing up - not by aimlessly buying put options (which killed Taleb's previous hedge-fund in 2006, although he likes to gloss over that point). Taleb's response, his defense for totally missing the boat:

"`We refused to touch credit default swaps,'' Taleb said. ``It would be like buying insurance on the Titanic from someone on the Titanic.''

That was a bad idea. Sub-prime CDS were the most underpriced risks out there (based partially on Taleb's own ideas re: flawed quant models), with a fantastic risk reward profile, even considering counter-party risk. He just totally missed it and is making up excuses ex post facto. Paulson and Lahde got paid and got out before the counter-party risk got excessive, clearly demonstrating that Taleb's excuse is wrong.

IMO, Taleb is a mediocre investor at best. If he publicized ALL of his returns, I think you would see that he is actually a really bad investor, but no one knows for sure.

Most of his ideas are right, but trivially so. Most of what he says, everyone already knew, if not from the get-go, then certainly by the time of LTCM. Other people have been able to arbitrage under-priced risk far more successfully than him, so that makes me think that they understood the "why" a lot better.

[Nick Rowe]

bob: (following you in going totally off-topic, but what the hell):

Suppose you knew that an asset price was a bubble, but you didn't know when it would burst.

For example: suppose the fundamental value of an asset is zero, the bubble has a 10% chance of bursting each year, and the price is growing at 10%. Do you run a "fat tail" risk if you short the asset?

It's like that gambler's paradox (St Petersburg?), where you double the bet every time you lose the coin toss. Or is it?

I'm not sure if this makes sense. Ignore if it doesn't.

[bob]

I don't follow entirely, but I think this might explain it:

Say you are Nassim Talib, but instead of betting on markets, you are betting on boxing, and you think that the odds are skewed towards the favorite, and underprice the risk of an upset victory.

The bookies give odds of 100-to-1 that your fighter will lose, but you know they are underpricing the risk of him winning, and that the true odds are 99-to-1.

You start a hedge fund with $100 in capital to exploit this.

If you put down 1 dollar on him everytime he fights, by the time it gets to the 99th fight, he wins, and you end up with $101. So you make $1 in "risk-free" reward.

Here's the problem: you are betting on the distribution of those black swans over time. What if he loses all of his first 100 fights, but then wins his 114th fight and his 115th fight? Or what if he loses his first 200 fights, and wins his 205th, and three more after that? Over 200 or 300 or 1000 fights, the probabilities might pay off, but it doesn't matter, because you have already lost all your money. That's what happened to Taleb in 2006.

His bets are not just that black swans occur, it's that they occur regularly in a predictable manner, at regular intervals. But why would you think that unpredictable events would happen at predictable intervals? If you analyze his strategy vs. his "philosophy", I think he ends up looking pretty hypocritical.

[bob]

To summarize: Taleb's strategy is only sure to pay off with infinite capital deployed over an infinite length of time. Neither of those things exist in the real world for a mortal investor, and that's why it's a poor strategy.

[Nick Rowe]

bob: thanks. That helps.

1. Shorting a bubble is very much like betting on your boxer with a 1% chance of winning. Suppose there is a 1% chance per month that the bubble will burst. And every month you bet $1 that the bubble will burst. Sort of like a dynamic shorting strategy.

2. So betting that a black swan will appear is a very risky strategy. Only if you are very long-lived, and have big capital reserves, would you do it. Which might explain why the market odds tend to be biased.

3. On the other hand, we see people buy lottery tickets (bet on black swans), even when the expected returns are negative. Firms (casinos) and lottery corporations, actually produce risk, and people pay them to produce risk. Pity someone can't figure out a way to get people to pay for the risk that e.g. weather produces, instead of having to pay people to accept that risk.

[Adam]

Nick, you hit the nail on the head in your third point. Taleb's story comes down to saying that an insurance company selling fire insurance is mispricing the risk if it ever happens that the payout from one house that burns down exceeds the premiums received from only that contract. This completely misunderstands how insurance works, the company is profitable as long as the total payout from houses burning down is less than the total premium received from all policies written. Thus, a well run insurance company is hugely profitable and Taleb's hedge fund failed.

Don't use AIG as the counterexample, they were stupid but in a different way. Basically what they did was like having too much of the policy portfolio tied to one very expensive house. If that house burns down the insurer goes broke even if they correctly priced the policy. This basically was what all of wall street did wrong.

Finally, there are many insurance writing strategies that are profitable if you don't lever up a million times. For example, there is a strategy known as "short gamma" which sells atm option straddles and delta hedges to maturity. The strategy has been horrible over the last little while, since about Aug. 08, but if you've been doing it since 1994 you're still way in the money. The fact that it sometimes does poorly doesn't mean the pricing of the risk is wrong, over a long time you make money so it seems the risk is well priced. You make 20 basis points a month in 95% of the months and in 5% of the months you lose 200 basis points. On average your making 9bp a month, the fact that you sometimes lose 200bp doesn't mean the risk is mispriced, it means the risk is correctly priced. If you never had the big loss then the mystery would be where the 20bp a month is coming from the rest of the time.

Doing the opposite, which Taleb recommends, would be proftiable over the last 5 months but if you try to do it for a long time you go broke.

[reason]

Adam
you are forgetting that insurance is a competitive market. If claims are highly correlated then the market price for that insurance may be too low. Anybody pricing the risk correctly would have no customers. It is a general problem with insurance.

[reason]

As for casinos etc - that doesn't prove that people are in general not risk averse, only that they have non-linear risk preferences. They actually would like a very small part of their portfolio to offer a chance of a very high return. Call it the hope investment (they get utility from knowing they have a chance to be very rich). They are not interested in the average return in this case.

[bob]

"you are forgetting that insurance is a competitive market. If claims are highly correlated then the market price for that insurance may be too low. Anybody pricing the risk correctly would have no customers. It is a general problem with insurance."

True, but there are some countervailing forces at work as well that address this problem. The dirty little not-so-secret of insurance is that it is priced by cartel, out of necessity.

In any given situation, one insurance company could undercut every other insurance company by under-pricing long-term risk for short-term gain. Eventually, the loss-runs would pile up and they would go belly up, but everyone else would already be out of business. For this reason, price-fixing is pretty endemic in the P&C insurance world. I think the most recent case was in Ohio, but most major insurance companies have been charged with price-fixing at one point or another. It's not entirely their fault though, as cartel pricing is born of necessity.

It is true though that cartel pricing never works 100% so the insurance market still cycles between soft market and hard market conditions. Sometimes risk is over-priced, sometimes it is under-priced and sometimes it is "correctly" priced. Insurance is a zero-sum game, so "correct" pricing really means moderately over-priced risks.

Most insurance companies (and option sellers) tend to insist on a pretty fat over-pricing/profit/error margin, so I think that Adam's point does still hold. If Taleb was right, Warren Buffett would be poor. Instead he has become incredibly rich, partially by insuring against low-probability high-loss events like natural disasters, risks that would be under-priced according to Taleb's grand theory of "why everyone besides me is a complete idiot". In reality it is just not true.

If anything, people are unduly terrified of those kinds of events, and over-estimate their prevalence (plane crashes etc.) so they drastically over-pay for the insurance. I think that might be the flip-side of Nick's lottery example. It's human nature to over-price options on both low-probability high-gain events, and low-probability high-loss events. Both the lottery industry and the insurance industry have profited from this, while Taleb failed by trying to bet against it.

[Adam]

Thanks Bob, your explanation was better than mine. When I wrote the comment I didn't really mean to refer to actual insurance markets, I had in mind perfectly functioning markets.

What I meant to say was that if Taleb were to observe a perfectly functioning insurance market he would notice that sometimes there is an earthquake in California and because the total payouts that year exceed the premiums collected that year, he would claim that the company must have stupidly underpriced the risk. Of course, Taleb would ignore the fact that for the previous 15 years the insurance company made more than enough to pay the claims and still be profitable.