This is my fourth and last Chuck Norris post. I'm getting bored with the metaphor too. But there is something many people missed in my last posts. It's important. Andy Harless explains it in his post. I'm going to explain it my way.
Suppose Chuck Norris keeps on fighting for an NGDP level path target year after year. Suppose year after year you bet that Chuck will lose his fight. Your losses if Chuck eventually wins his fight get bigger and bigger every year, while your gains if he loses his fight stay the same. Eventually you will stop betting against Chuck, even if you think there is only a very small chance he will win next year. If everybody else switches their bet before you switch yours, then Chuck wins his fight, and you lose your bet. So you want to switch your bet just before everybody else switches theirs. So do they. So switch your bet now.
Eventually the US economy will return to normal. Something will turn up, and the economy will escape the liquidity trap. Utterly boring conventional monetary policy will work again. If Chuck is still fighting, because NGDP is below his target level, he would have no difficulty in getting NGDP up as high as he likes to hit his target. Even a skinny kid could do it. But maybe the chances of that happening next year are always small.
The beauty of an NGDP level path target (or a Price level path target) that is growing at (say) 5% per year, is that the longer actual NGDP grows at less than 5%, the bigger the upward jump in NGDP when it finally does hit the target path. If Chuck loses year after year, but eventually wins, the longer it takes him to win the bigger the eventual jump in NGDP.
Suppose, just to keep the math simple, that target and actual NGDP start out the same. Then target NGDP grows at 5%, and actual NGDP grows at 4% as long as Chuck loses his fights. The gap between target GDP and actual GDP is 0% of NGDP originally, 1% of NGDP after 1 year, 2% of NGDP after 2 years, 3% after 3 years, and so on. (OK, I've ignored compounding). Until Chuck eventually wins, and NGDP jumps up to the target level path.
You are trying to forecast next year's NGDP growth. Each year, when you make your investment decision, you are making a bet on what NGDP growth will be for the coming year. Your losses if your forecast is wrong are proportional to the amount by which your forecast is wrong.
If you bet that Chuck will lose his fight, and he loses, you win 1% of NGDP. Same 1% of NGDP again if you make the same bet next year and he loses again. And so on, every year.
If you bet that Chuck will lose his fight, and he wins in the first year, you lose 1% of NGDP. If you make the same bet and he eventually wins in the second year you lose 2% of NGDP. If you make the same bet and he eventually wins in the third year you lose 3% of NGDP. And so on.
Even if you think Chuck has a small chance of winning, how long do you want to keep rolling the dice, betting Chuck will lose again next year? It's even odds the first year; two to one in the second year; three to one in the third year, and so on. The odds get worse and worse every year. Eventually you will stop betting that Chuck will lose.
And remember, if everybody else stops betting against Chuck, Chuck wins, and you have already lost your bet. Because investment decisions based on expected future NGDP have a very big influence on current NGDP. So you want to switch your bet just before everybody else does. And remember that everyone else will also want to switch their bet just before everybody else does too. So better switch your bet immediately.
This seems like a very clever and original way of saying ... there is never mispricing in asset markets.
The price of an asset goes up, seemingly unrelated to fundamentals. Next period it may continue to go up, or it may return to its fundamental level. Maybe the chance of its returning to the fundamental level is small. But every period your gain from correctly betting on continued increase stays the same, and your loss if it returns to the fundamental grows. So eventually you'll stop betting against fundamentals. So will everyone else. So now you want to stop betting against fundamentals before everyone else. But so does everyone else. So switch your bet to fundamentals immediately.
There is no such thing as a bubble, or momentum trading, or this. QED.
Posted by: JW Mason | October 25, 2011 at 04:28 PM
Nick,
The expected payoff from a short NGDP futures bet is asymmetrical. If I win, the "upside" is as large as the potential shortfall between realized and targeted NGDP levels. If I lose, the "downside" is fixed at the (smaller) current difference between NGDP and target, assuming that the Fed does not allow an overshoot.
When deflation tail risk is high, the short futures bet is highly asymmetric to the upside and therefore very attractive. To change the payoff distribution, the Fed must appear to allow an NGDP overshoot to occur. In other words, it must be seen as acting, "irresponsibly". This is also the essence of non-contingent future Fed Funds rate commitments (btw, the Fed's recent one is contingent): by virtue of their non-contingency, they create a scenario in which the Fed fails to act to contain inflation.
Posted by: David Pearson | October 25, 2011 at 04:53 PM
The problem (which I didn't get to in the body of my post but mentioned in the comments and in my hoisted comment on Brad DeLong's blog) is that once Chuck Norris finally wins, his opponent comes back for a re-match the next year. And there's no guarantee that Chuck will win the re-match in the early rounds. If the natural interest rate is R, the growth rate of target NGDP is G, and the growth rate of potential RGDP is P, then smoothness requires (I think) that P-G < R, and there is nothing (other than choosing a sufficiently high value of G) to guarantee that this condition will be satisfied in the long run. If it's not satisfied, you get an endless cycle of stagnant NGDP alternating with dramatically rapid NGDP growth.
Posted by: Andy Harless | October 25, 2011 at 05:00 PM
Andy: Yep. I saw you mention that potential problem. My view is that G=5% or above would be enough to eliminate that risk. Just make sure the implied equilibrium inflation rate is around 2%, and not less, because that allows an equilibrium real rate as low as minus 2%.
David: you lost me a little there. Presumably there already exists some tail risk of deflation today, yet we are in some sort of (ugly) equilibrium in asset markets. By adding an upside tail risk to NGDP growth that gets bigger over time for as long as Chuck loses, we don't just offset that downside tail risk, we offset it by larger and larger amounts.
Or did I misunderstand you?
JW: If people have RE they will switch to the new fundamental value immediately Chuck appears. If they don't, it may take some time. But the potential risks of being away from fundamental get bigger over time. The anti-Chuck bubble has to burst eventually. But what you say is neat. I never thought of the anti-Chuck expectation as being a "greater fool" bubble.
Posted by: Nick Rowe | October 25, 2011 at 05:22 PM
Nick, you are close the abyss about what is understood about probability, and probably within the abyss of non-zero game theory. On top of which you are getting tired of Chuck. I am, too. I thought of Dirty Harry, "Do you feel lucky, punk?"
Let's simplify even further. Suppose that there are two players, Alice and Betty. (Chuck is outside the game). Also suppose that the game only lasts one year. (I know that you mean for the game to last until Chuck succeeds, but that is illogical. You cannot posit that Chuck succeeds, even if, in the long run, the chance that he will approaches 1 in the limit.)
The payoff for each player is the same. If both Alice and Betty bet against Chuck, they each get a payoff of 1. If Alice bets against Chuck and Betty bets for Chuck, Alice loses 1 and Betty gains 0, and vice versa. If they both bet for Chuck, they both gain 0.
No, that can't be right, because if Chuck wins, they both win.
How about this payoff for each? If both bet against Chuck, they both gain 1. If Alice bets against Chuck and Betty bets for Chuck, Alice gets a payoff of 0 while Betty gets a payoff of 2, and vice versa. If both bet for Chuck, they both get a payoff of 2.
OK. In this case both Betty and Alice get 2 if they bet for Chuck. That can't be right, either, because then there is no question that betting for Chuck to succeed is best.
My first point is as stated before. You can't assume that Chuck eventually wins. My second is that the payoffs matter.
Another point, which I will not belabor, is that the sudden jump is unrealistic. As I recall, I once saw a graph that showed that the U. S. GDP eventually returned to the trend line from **before** the Great Depression! Amazing! But there was no jump when it happened.
Posted by: Min | October 25, 2011 at 05:22 PM
Min: I see where you are going. You need a game with 3 or more betters. If the majority bet that Chuck will win, Chuck does win, and they all gain, except the minority that bet against Chuck.
It's a cross between an American beauty contest and a non-zero sum game. If the majority bets that Chuck will win, he does win, and the total payoffs are positive, but the minority make transfers to the majority. If the majority bet that Chuck will lose, then he does lose, and the total payoffs are zero, but the minority who bet Chuck will win get negative payoffs which are paid to the majority. But the longer Chuck loses, the more the odds are skewed to those who bet he wins.
Too damn complicated!
Posted by: Nick Rowe | October 25, 2011 at 05:38 PM
Nick,
I think you might have misunderstood. Take the case where we have a shortfall of 3% of NGDP from target levels. The downside from a short NGDP futures bet is 3%; the upside, say, in a severe deflation scenario, is 10-20%. This is an asymmetrical payoff distribution. To make it symmetrical, the Fed needs to provide a downside of 10-20%, which would require allowing (or perceiving to allow) a significant, "irresponsible" NGDP/inflation overshoot.
To dislodge deflation expectations, the Fed needs a symmetrical payoff. This is what the gold standard exit accomplished in 1933; by removing the binding constraint on future policy, it "shocked" the distribution of payoffs to a deflation bet. This is one reason why the gold standard exit is not comparable to policy easing today: no such binding constraint exists.
Basically, I don't think you change behavior by committing to a 5% (implied level) target. This is like Chuck Norris with the stomach flu; I'm not sure it will really scare anyone into acting. The real Chuck Norris -- the open a can of you-know-what fighter -- threatens severe inflation as a counterweight to the possibility of severe deflation. The more deflation tail risk exists, the more that Chuck Norris has to bulk up on steriods (higher inflation targets) to be believed.
You can dislodge deflation expectations, or you can promise to be forever responsible and not allow high inflaiton, but you can't do both.
Posted by: David Pearson | October 25, 2011 at 06:07 PM
Thanks, Nick. :)
How is this for the first year? There are three players, whose payoffs are symmetrical.
If all three bet against Chuck, the payoff for each is 0. If two bet against Chuck, they each get a payoff of 1, while the other gets a payoff of -2. If one bets against Chuck, he has a payoff of -1, while the others get a payoff of 2. If no one bets against Chuck, all three get a payoff of 1. Thus, if Chuck succeeds, the total payoffs are 3, if Chuck fails, the total payoffs are 0.
Hmmm. Each player can guarantee a payoff of 1 by betting on Chuck. It is complicated.
Posted by: Min | October 25, 2011 at 08:41 PM
Min. OK. It's probably easier if there are a large number of small players.
David: OK. I think I see your point now. And going off gold in 1933 must have shifted those risks considerably, as you say, in a way that cannot be replicated today.
But presumably the existing set of risks, even before Chuck arrives on the scene, has some deflationary tail risk, and yet that risk must be balanced by some inflationary risk, otherwise we wouldn't be where we are now. And Chuck's arrival on the scene can only increase the upside risk.
Posted by: Nick Rowe | October 25, 2011 at 09:14 PM
Nick Rowe: "And going off gold in 1933 must have shifted those risks considerably, as you say, in a way that cannot be replicated today."
What about going off the Euro? Is that something like going off the gold standard?
Posted by: Min | October 25, 2011 at 09:55 PM
Nick, off topic, but I wanted to thank you. My car battery died yesterday and I suspect the alternator, and I put off dealing with it because I couldn't get a tow to a mechanic open in the evenings, but then thinking of a recent post of yours I realized that I could just hail a cab to an auto supply store and and replace the battery myself, then drive to the mechanic. In fact I've read it's not hard to test the alternator, so I'll be doing that before having it replaced.
Posted by: adjacent / q | October 25, 2011 at 09:56 PM
Min: it would be like going off gold, except you would need a totally new set of notes, so a lot more difficult.
adjacent/q: Finally! Now I know I've actually given some good policy advice on this blog!!
Nearly always, when the alternator dies, the "no charge" light (usually a picture of a battery) on your dashboard will light up. If that red warning light didn't come on, your alternator is probably OK.
Don't use the old-skool test of seeing if the engine dies when you disconnect the battery.
Spend $10 on a cheap digital multimeter from any auto supply store. With the engine idling, you should get about 13-14 volts across the terminals, if the alternator is good. 12-13 volts means bad alternator. If above 15 volts stop the engine immediately and replace the alternator.
Your battery will have a date on it. If it's over about 7 years old, it's probably bad.
If less than 7 years old, and the alternator is good, and the battery goes flat overnight, I suspect a drain. A light staying on, or a short circuit somewhere. Aftermarket stereos are notorious for doing this. Disconnect one battery terminal, set the multimeter to read amps, and measure the current between the disconnected battery cable and terminal with everything switched off. It should be less than 0,05 amps. (Or you can use a 12 volt light bulb instead; if it shines brightly there's a drain). If there's a drain, pull the fuses out one by one. When the drain stops you have found the bad circuit.
Posted by: Nick Rowe | October 25, 2011 at 10:19 PM
On the assumption that there is some optimum amount of investment for given GDP, altering the amount of investment with a view to altering GDP must lead to a misallocation of resources.
Posted by: Ralph Musgrave | October 26, 2011 at 03:54 AM
I have a revised Chuck Norris story. I hope it meets your approval. :)
Chuck Norris has become a Taoist Immortal with the title of Reenter, the Dragon. Like all dragons, he is filthy rich. In addition, he is benevolent. There is only one country, known as This Land, which has a constant population of 2*N - 1 inhabitants. (Nobody is born or dies in this story.) Every year Chuck Norris sets aside (2*N - 1) * (2*N - 1) * 1,000 Dragon Dollars, (2*N - 1) * 1,000 for each person. At the end of the year every person will receive what Chuck has set aside for them, as long as during the year at least N people have sent an email to Chuck thanking him in advance for his generosity. In addition, however, the people pay each other according to how many people sent thanks to Chuck. The people in the minority pay the people in the majority. Each person in the minority pays 1,000 Dragon Dollars to each person in the majority.
Besides being benevolent, Chuck Norris is also forgiving. If people do not get their set asides one year, he carries them over to the next year and adds them to the current year's set asides. So if in the first year a majority do not thank Chuck, but a majority does in the second year, the second year's payoffs are doubled. This also means that each person in the minority who did not thank Chuck pays $2,000 to each person in the majority. But if a majority does not thank Chuck, each person in the minority pays only $1,000 to each person in the majority. The more years that a majority does not thank Chuck, the more it costs to be in the minority that does not thank Chuck, if a majority does.
And so on. If a majority do not thank Chuck for two years, but do in the third year, the payoffs are tripled for that year, etc., etc. If a majority thank Chuck in one year, the next year's payoffs are the same as in the original year.
Now, Chuck Norris is a Taoist Immortal, which means that he is not really immortal. Each year he has an infinitesimal chance of dying. If he dies, he takes his fortune with him, leaving nothing behind, and there are no payoffs. Nor do the people pay each other that year.
Posted by: Min | October 26, 2011 at 12:18 PM
Nick, tell me how the hell you managed this. I came up with the Chuck concept and thought I would fast write 10 Chuck posts on my blog. I however is only at three and they are all pretty bad. You have managed four already. I am tired of writing about Chuck Norris, but truly enjoy reading yours! Please don't stop before we hit 10!! I will post every single of them on my blog as well! I f...ing good!
Posted by: Lars Christensen | October 26, 2011 at 05:14 PM
I'm sure I made a post on this before, but it along with some others seems to have vanished. Still, a little point, distribution matters. Isn't the problem here that this hyperdetermined central bank is subsidising some players - and those players are already rich (they can afford to bet). Isn't spreading the money around the plebs (i.e. fiscal policy underwritten by the central bank) fairer.
I also asked Nick whether he thought that making a fixed rule doesn't carry risks if something real changes (e.g. demographics or terms or trade or resource depletion).
Posted by: reason | October 27, 2011 at 03:36 AM
Reason: I think this was explained in previous blogs and the answer lies in reversibility of the policy. If CB buys bonds it may still sell them back to private sector the recession is over. The same applies for other asset purchases such as stocks or land with the total liquidity on the market as the only constrain. However when government does a helicopter drop or if they buy food for poor or they just dig holes, there is nobody in a private sector who would be able to buy these expenses back from the government. By doing such irreversible things you will have imposed real costs for a private sector in form of higher inflation and/or higher taxation.
And I think this is quite a good way to differentiate fiscal and monetary policy. Monetary policy has a high degree of reversibility, that is why it is tolerated by those in power and it is what gives it institutional stability and credibility. Fiscal policy has irreversible redistributional effects, thus it should be controlled in a political process where the actor (government) is directly responsible to the public via elections.
Posted by: J.V. Dubois | October 27, 2011 at 05:24 AM
J. V. DuBois: "I think this is quite a good way to differentiate fiscal and monetary policy. Monetary policy has a high degree of reversibility"
Interesting point. :)
J. V. Dubois: ""However when government does a helicopter drop or if they buy food for poor or they just dig holes, there is nobody in a private sector who would be able to buy these expenses back from the government. By doing such irreversible things you will have imposed real costs for a private sector in form of higher inflation and/or higher taxation."
Well, first, whether that is so is questionable. Second, can you call inflation a cost overall? Overall, is not moderate inflation a boon? (Yes, it may favor some over others, but reason's point was that so does monetary policy.) Third, you have to consider the enormous costs of high unemployment and low growth.
Posted by: Min | October 27, 2011 at 07:47 AM
Min: I think your game nearly works. It's got the cumulative pot aspect in there. But shouldn't the bet be for what's in the pot, or at least proportional to what's in the pot, rather than a fixed amount per winner?
And man it's complex!
Ralph: take an extreme case. Suppose there is a fixed amount of profitable investment opportunities. All of them are worth doing under almost any conditions, but no additional ones are worth doing. (E.g. we need one new shovel for each one new worker born, no more and no less). Then consumption will do all the adjusting to ensure that C+I=Y at full employment. (Whether that consumption and investment should be done by private households and firms or by the government is a separate question, and fiscal policy should be used to hit that separate objective. And I've ignored net exports for simplicity).
Thanks Lars! Stuff keeps coming into my head. I wrote 3 posts, then Andy wrote his, and I saw I needed to write a fourth.
reason: the way I see it is in terms of the correct assignment of targets to instruments. Which does which job? The job of fiscal policy is to do fairness and public vs private provision of goods. Because that's what fiscal policy is good at and monetary policy is useless at. And if fiscal policy is doing that job right, it can't do a second job right at the same time. And the job of monetary policy, which has nothing else to do, is to get AD right.
Plus, there's the whole intertemporal/reversibility aspect too, as JV says. The G-T deficit/debt question, which deals with intergenerational fairness, is done with fiscal policy.
Posted by: Nick Rowe | October 27, 2011 at 08:30 AM
I don't see how subsidising someone is reversable. If you pump up the price of something so somebody is persuaded to sell, and then later buy it back at a price the counterparty likes - it seems to me the counterparty wins both times, since the CB is a price taker in both cases.
Posted by: reason | October 27, 2011 at 09:28 AM
Nick
"The job of fiscal policy is to do fairness and public vs private provision of goods. Because that's what fiscal policy is good at and monetary policy is useless at. And if fiscal policy is doing that job right, it can't do a second job right at the same time. And the job of monetary policy, which has nothing else to do, is to get AD right."
I don't think this answers the charge (even though in normal times I be sympathetic to the idea). Because the monetary policy isn't neutral.
Posted by: reason | October 27, 2011 at 09:30 AM
Nick Rowe: " I think your game nearly works. It's got the cumulative pot aspect in there. But shouldn't the bet be for what's in the pot, or at least proportional to what's in the pot, rather than a fixed amount per winner?"
OK. Suppose that everybody but one person bets one way. I have him pay off a set amount to each winner, depending on whether Chuck succeeds or not. Better to have a fixed total payoff for each condition that is shared equally by the winners, with the losers sharing the cost? The total payoff for being right when Chuck succeeds in F + 1 times the total payoff when he fails, where F is the number of years in a row that he has failed, right?
Posted by: Min | October 27, 2011 at 09:36 AM
For a real education, try this on the stock market. Winners are usually winners, and losers are usually losers. But if you think one particular loser is Chuck Norris, well, good luck with that.
Posted by: rp1 | October 27, 2011 at 01:31 PM