Thursday, July 05, 2012

Excess volatility and NGDP futures targeting

Steve Williamson has a post arguing against NGDP targeting. I just wanted to throw my two cents in, and consider an issue that Steve didn't mention.

When he talks about "NGDP targeting", Scott Sumner actually means the following (quoting Williamson):
In its current incarnation, here's how NGDP targeting would work, according to Scott Sumner. The Fed would set a target path for future NGDP. For example, the Fed could announce that NGDP will grow along a 5% growth path forever (say 2% for inflation and 3% for long run real GDP growth). Of course, the Fed cannot just wish for a 5% growth path in NGDP and have it happen...One might imagine that Sumner would have the Fed conform to its existing operating procedure and move the fed funds rate target - Taylor rule fashion - in response to current information on where NGDP is relative to its target. Not so. Sumner's recommendation is that we create a market in claims contingent on future NGDP - a NGDP futures market - and that the Fed then conduct open market operations to achieve a target for the price of one of these claims.
So basically, the Fed would do its utmost to keep NGDP futures prices on a certain path.

I have a problem with that. The problem is called "excess volatility". According to some theories, asset prices should be an optimal forecast of (discounted) future payouts - for example, the price of a stock should be an optimal forecast of discounted future dividends, etc. An optimal forecast should not respond to "noise"; in other words, if something happens that doesn't affect dividends, it shouldn't affect the forecast. This means that actual dividends should be more variable than prices - the dividends should have lots of "surprises".

But we can actually look at whether or not this is true! All we have to do is wait for actual dividends to come in, and then see whether past prices bounced around less than the dividends, or more. Robert Shiller was one of the first to do this, and here is what he found:

The jagged black line is the S&P 500, and the lighter, less jagged lines are dividends discounted by various discount rates. It's easy to see that no matter what discount rate we use, stock prices are a lot more variable than the fundamental value of stocks. This means that there is "noise" in stock prices - prices may respond to information about dividends, but they also respond to some other stuff that has nothing to do with dividends. They display "excess volatility". Lots of researchers have tried to kill the excess volatility puzzle, but none have really succeeded. In other words, markets may be "efficient" in the sense that you can't predict future returns, but those returns are probably going to depend partly on things other than fundamental value.

Now back to NGDP futures targeting. An NGDP futures price will probably experience excess volatility too. It will bounce around more than changes in actual NGDP. This means that the Fed will be trying to hit a very volatile moving target. One quarter, futures prices will soar, the next month they will crash, and the Fed will be trying to keep up, tightening dramatically in the first quarter and loosening dramatically in the second. This will happen even if a true optimal forecast of NGDP (which of course no one really knows) is relatively stable! Asset market volatility will cause policy volatility.

If you think that policy volatility has no costs, this is fine. But if you think that the Fed bouncing around wildly from quarter to quarter sounds scary, you should be scared of NGDP futures targeting. For example, volatile Fed policy, even if it adheres rigidly and credibly and permanently to an NGDP futures targeting rule, may cause expectations to become more volatile if a substantial number of economic actors fail to believe that NGDP targeting will succeed in hitting the target. That could cause volatility in things like inflation and real GDP.

Of course, this is also true of any Fed policy rule that takes market prices as a measure of expectations (for example, using TIPS spreads as a measure of inflation expectations) and then responds to those "expectations". This is one reason why, contra John Taylor, I support combining rules with judgment. But even in terms of rules, we can make guesses about excess volatility. If excess volatility is an increasing function of actual volatility, then using NGDP futures should worry us more than using inflation expectations. Real GDP bounces around a lot more than inflation, as this graph from Stephen Williamson shows:

If excess volatility is, say, 50% of actual volatility, then using NGDP futures in Fed policy is going to cause a lot more bouncing around than using inflation futures alone.

Anyway, this is not to say that NGDP targeting is a hopeless idea. But the futures-market aspect of what Scott Sumner is proposing relies on a version of market efficiency that is much stronger even than what most finance professors would accept.

Update: In an email exchange, Scott Sumner has clarified the nature of his NGDP futures market proposal. In a nutshell, he proposes that the Fed act as a market maker, buying and selling infinite quantities of NGDP futures at the target price. Demand for NGDP futures would then be used to determine Fed policy; if NGDP futures demand increased, the Fed would commence open-market operations to bring down expected NGDP. The price of NGDP futures would not move, but demand would swing from positive to negative, moving Fed policy as it swung.

It seems to me that the concerns expressed in this blog post apply to this sort of market as well. In the stock market, prices move in response to demand (not, generally, supply); we can infer from excess price volatility that demand exhibits excess volatility as well. Now, if prices could not move (which is really the same thing as banning resale), it's possible that excess volatility would diminish or even vanish. However, this is far from obvious. For example, if excess volatility is caused by overconfidence, as many behavioral finance theories predict, excess volatility would persist in Sumner's proposed setup. 

If people believe that noise is actually information, that noise will directly feed through into Fed actions, causing Fed actions to bounce around too much.


  1. Anonymous2:38 PM

    Am I the only person that gets nervous about the notion of a single , market-based determinant of FED monetary policy , especially in light of the recent Libor scandal ?

    1. John Hall10:10 AM

      The difference is that this would be like a futures contract, where rather than 18 banks you would have potentially thousands or millions of different participants.

    2. Anonymous1:08 PM

      Small numbers of big players manipulate futures markets with regularity. The idea that all the bit players will keep them honest is a pipedream.

  2. Target a threshold and try to keep the forecast within this threshold (say between 3% and 4% NGDP growth). Also, you could use some inferred market forecast metric (averaging over time) which would presumably be more stable, than using directly the price of a futures contract in real time.

  3. Very good post. I understand now what I saw only intuitively.
    There are other objections, as the continous revisions of te National Account. That is one more reason for volatility of expectations; But This once seems to me definitive, because in te rare case of not data revisions, we get volatitilty.

  4. ...And I agree whith you that a mix of rules and judgment is Inevitable. Foolish Will be other decision.

  5. Scott actually advocates having the Fed make a market in NGDP futures (much as the Treasury used to make a market in gold). In this case, there won't be any volatility in the price of the futures, because the Fed will absorb the impact of excess buy and sell orders onto its own balance sheet. But then Scott advocates having monetary policy respond mechanically to changes in the Fed's NGDP futures position. That's where I see a danger: if the Fed is reacting to the same noise that generates excess volatility, then the Fed's instrument (the monetary base, in Scott Sumner's version, but I think it could just as easily be the interest rate) will be excessively volatile. An alternative possibility is to do it without this mechanical step and just have the Fed use its judgment about when to absorb buy and sell orders, just as it did (roughly speaking) under the gold standard. The Fed had to make sure we wouldn't run out of gold completely, but it had a lot of leeway about how much of a buffer it thought was necessary and essentially unlimited ability to abosrb (or make the Treasury absorb) excess supply of gold from the private sector. With NGDP futures, the potential leverage makes the risk greater, but, unlike with gold, there are no absolute limits: the Fed will never "run out" of NGDP futures the way the Treasury could run out of gold. The real danger then comes if the Fed tries but is unable, via open market operations &c, to staunch a huge flow of sell orders. (It's not a problem with buy orders, because the Fed can always raise interest rates further if it's trying to kill high NGDP expectations.) If you get into an extreme liquidity trap, where everyone believes NGDP will be below target no matter what the Fed does and everyone is willing to put a lot of money where their mouth is, then the Fed will eventually go broke. That might be OK, though, because a broke Fed -- a Fed with no assets to sell to reduce the base money stock -- would presumably increase inflation (and therefore NGDP) expectations, which is what they were trying to do in the first place. Hopefully before you get to that point, people would start to anticipate the Fed's insolvency and raise their NGDP expectations, thus eliminating the flood of sell orders.

    1. I think what you're suggesting just ends up being either the Fed using pure judgment, or targeting its own internal NGDP forecast, or some combination of those two. Which sort of kills the rationale for futures price targeting in the first place...

    2. I don't think it kills the rationale, although my rationale may be different from Scott's. Futures price targeting has a couple of advantages: (1) it keeps the Fed accountable, because they'll know they're going out on a limb if they have to absorb a large position, so they won't do it unless they have a good reason, whereas, if you just say, "This is the target," there's a lot of room for self-deception; (2) it gives the private sector a chance to hedge, so they can make plans based on the target rate of NGDP growth, even if they don't have a lot of confidence in it.

    3. So if the Fed makes the market so the price doesn't move, how does the futures market generate a number that is used to set the NGDP target? Be concrete.

    4. Anonymous4:34 AM

      IIRC, in one of the earlier versions of Scott's proposal, there would be a mechanical rule to engage in OMOs parallel to each futures contract the Fed bought/sold. Speculators would shift the intermediate target (i.e. base money) by virtue of their trades with the Fed.

      "If a speculator chooses to buy a contract at the price of $15.90, the Fed will create and sell the contract for $15.90. At the same time the Fed sells the future, it will simultaneously make an open market sale. Presumably, it would sell treasury bills. Sumner proposes that it sell five times the dollar value of the contract, so $79.50 worth of T-bills would be sold per futures contract the Fed sells."

      Their discussion has long since moved past that so I don't think this best represents the kind of futures markets that they prefer now.

      Other links I dug up (Watch out, Bill Woolsey's posts are lengthy!):

    5. More generally, it's the same as with gold. Under the gold standard, if the Fed (or the Treasury) made the market so the price didn't move, how did the gold market generate a number that was used to set the gold price target? Under the actual gold standard, the Fed just used its judgment. If you wanted to have a "robust" gold standard, you could make a mechanical rule that says the Fed has to do certain OMO's in response to changes in the sovereign gold stock, thus forcing the Fed to keep the gold stock close to a constant. That's analogous to Scott's proposal. Except that NGDP is a more sensible thing to target than the price of gold.

    6. You still appear not to have answered my question, Harless! How does the futures market generate the target number?

    7. The target number is set in advance, of course, not generated by the futures market. What the futures market generates is order flow data, which is used by the Fed to determine whether the market thinks it is undershooting or overshooting its target. If there is an excess of buy orders, and the Fed is building a short position, it can conclude that the market thinks it will overshoot. And vice versa. Then, depending on whether you use Scott's version or mine, the Fed either mechanically responds to this information or else it has to make a decision whether it wants to speculate that the market is wrong.

    8. In Scott's version, excess volatility of orders might be a problem (causing the Fed's instrument to become excessively volatile). In mine, presumably, it would not be a problem; it would just be a source of profit for the Fed (assuming the bid-ask spread is wide enough), just as it would be for any market maker (particularly one that is in a position to manipulate the market via its actions in other markets).

      I would note a side issue: besides excess volatility, there is the possibility of bias in the futures, if, for example, there are a lot of short hedgers who are willing to pay a premium to get the hedge. Not a problem in my version (provided the Fed's own forecasts are unbiased), just more profit for the Fed, which gets paid to provide insurance. In Scott's version, though, it is a (minor) problem in that it means that the Fed will systematically tend to overshoot (or undershoot, if long hedgers dominate) the target. Actually, come to think of it, from my point of view as one who has higher inflation preferences than the general population, that's a feature rather than a bug, provided (as I would expect) short hedgers dominate.

  6. Anonymous4:04 PM


    I liked your post.

    I think micro-fragility leads to macro-resilience and you can see from the S-P500 graph you have posted that ever since the Fed has tried to "stabilize" the markets either by propping up assets or failed institutions, the volatility has significantly increased. Micro stability has lead to macro fragility.

    Here is a more detailed elaboration on this point.

  7. Harless has the right idea.

    I call it index futures convertibility.

    As he says, Sumner advocates pegging the price of the future. There is never any volatility in the futures price.

    Index futures convertibility is the same.

    I wonder if experience with stock prices, which do change, tell us much about the volatility in the net market position on a futures contract.

    (I admit that I know little about the research on stocks and so how they account for changing discount rates and for the fact that firms retain earnings rather than pay dividends. A constant discount rate? Why?)

    There would be wide swings in the net position on the contract when there is really only small deviations of nominal GDP from target.

    I agree with Harless that a mechanical rule controlling the monetary base according to Fed's position on a contract would be a mistake. The Fed have discretion subject to the constraint that it buy and sell the contract.

    As for fear of the liquidity trap, well, that only is a problem if you insist on targeting some safe and short interest rate. The "problem" of central banks refusing to make heroic open market operations because it is too "risky" would be beaten out of them. The risk of taking a vast long position on nominal GDP would make taking a long position on all sorts of other assets they might buy a smaller concern.

    By the way, shouldn't it at least be considered that actual nominal GDP was much more volatile under regimes where there was no effort to stablize it?

    As for inflation vs. real GDP volatility, with supply shocks, there is negative covariance, right?

    But I see no cost to volatility in base money. So? Now, I can see how volatility in short term interest rate be unpleasant.

    On the other hand, unless what happens is that this quarters nominal GDP is volatile because short term interest rates are volatile, I am not sure there is too much concern. Less investment because long term interest rates are higher because short term interest rates are more volatile? I guess it is possible.

    And, of course, rather than just talk about volatility, what this is really saying is that people would be willing to bet on nominal GDP being away from target when there was really no reason to expect it to be away from target.

    There would not be a problem of people buying futures, expecting the price to rise, and then sell out for a capital gain. The pay off only occurs if nominal GDP comes in above target.

  8. Noah, I'm afraid you are shooting from the hip here without doing your homework. Andy's right that you misunderstood what I was proposing, so your post doesn't really have any bearing on my proposal. The NGDP futures price never fluctuates at all in my proposal.

    I would also like to second Andy's comment that we might want to let the Fed trade on it's own account, if it thought the market was behaving irrationally. I've made that proposal before, and I believe Bill Woolsey did as well. And contrary to your claim in reply, that does not eliminate the whole purpose of futures targeting. An NGDP futures market keeps the Fed honest. In late 2008 I had no way to profit from the fact that the Fed was obviously going to undershoot its implicit NGDP target. If a NGDP market existed, even with the Fed trading on its own account, I could have easily gotten rich. Now you might argue I wouldn't have gotten rich because lots of other people would have tried to do the same, and that competition would boosted the base enough to have eroded away all the easy profits.

    Which is exactly my point . . .

    What's the worst case? That I 'm wrong and that you and I and Andy can get fabulously wealthy.

    1. OK, so if I've misunderstood, what number would be used as the forecast of future NGDP under your proposed policy regime? By which I mean, how exactly would the NGDP target be generated?

    2. OK, Scott, I have done my homework now. I deserve the rebuke. Having done my homework, I shall now rectify my error and quote from your blog:

      From September 8, 2011:

      "Easy money is a policy that pushes NGDP futures prices above target, and vice versa."

      If the price never moves, how can the price be pushed above target???

      From April 3, 2012:

      "Hence I’ll assume NGDP futures prices are the optimal policy target, as they are much more closely correlated with expected future NGDP than are any of the other proposed targets (interest rates, exchange rates, M2, etc.)"

      "If the NGDP futures price is above the Fed’s target then policy is too expansionary, and vice versa."

      "So that’s my grand theory of monetary economics. Use the base to target NGDP futures prices, with the hope of maintaining steady growth in actual NGDP." (emphasis mine)

      Again, how can the price be a target if it never moves??

      From April 11, 2012:

      "Wouldn’t targeting NGDP futures prices be much easier?"

      Also, just for fun, here is what you said on June 24, 2010:
      "I am not an expert on futures markets, so John and I would appreciate any advice on how best to set up the contracts."

      and on December 14, 2010:
      "I’m kind of amused to see Brad DeLong suggest I finally ”plump” for NGDP futures targeting. I’ve devoted my entire career to the idea. Indeed I presented this idea at the AEA meetings in 1987, and have 6 publications on the futures targeting idea."

      and on July 2, 2012:
      "I rarely discuss NGDP futures targeting in my blog[.]"

      But on Oct. 28, 2011:
      "I’ve also talked a lot about the idea of targeting the price of NGDP futures contracts."

      Actually, this is getting fun...

    3. Anonymous5:40 AM

      That's mean! D: Clearly, Scott's writing is sloppy.

      When Scott talks about hitting NGDP futures prices, I think he is framing it in terms of conventional futures markets, where higher futures prices indicate expectations of higher prices in the future.

      In his own proposal for a NGDP futures market, however, the price of NGDP futures is pegged. In the version I mentioned in your reply to Andy Harless, any implied market forecasts of off-target NGDP are fleeting because the ensuing purchases/sales of NGDP futures would lead the Fed to automatically adjust base money to hit the NGDP target.

      Nonetheless, without the automatic OMOs, the Fed's position on the futures contract will show whether market forecasts are consistent with its target.

      "If the market is bearish, with more speculators selling futures at the target price than are buying, then the monetary authority is left with a long position on the contract. The monetary authority, along with all the bull speculators, is taking a risk of loss if nominal expenditure is below target."

      I also don't think you're being fair on the last four quotes. Scott himself would be the first to admit that he isn't the best person to go to for setting up NGDP future contracts, but he has been publishing articles about it for a while. And in the reply to Williamson, I believe he refers to the mechanics required to set up NGDP futures targeting effectively, rather than the merits of the idea, which he has been consistent at pushing.

    4. John Hall10:15 AM

      I like the idea of NGDP (and RGDP and PGDP) futures markets, even if the Fed isn't actively involved in them. However, if the NGDP futures contract never moves, then what's the incentive for market participants to be involved in it?

    5. Noah,
      Since you admit that you deserve a rebuke isn't an update in order? Your post was included in today's links at Economist's View:

      Most never read the comment section and some may not even get past the headline.

    6. Well, Mark, read the excerpted quotes above. Many times, Sumner has explicitly referred to targeting "NGDP futures prices". Therefore my critique applies exactly as written.

      It also raises the question of how Scott's claim that "the NGDP futures price never fluctuates at all in my proposal" squares with the idea of targeting a futures price. I'm just waiting for Scott to respond and clarify...

    7. If there were a futures market for nominal GDP, Sumner would claim that prices above the Fed's target would be easy money and prices below would be tight money.

      We can imagine the Fed making periodic changes in the policy interest rate according to its observations of this futures market.

      So, if the futures price is above target, it would start raising the policy rate at every meeting. Once the futures price fell to target, it would stop raising the rate.

      Yes, this could be done if there were a futures market for nominal GDP.

      But if the Fed ignored that futures price, Sumner would still stay that when it was above target, there is loose money and below target there is tight money. (And I don't really think the "target" is essential.

      Sumner's reform proposal is for the Fed to buy and sell unlimited quantities of the contract at the target value.

      Surely you can see that this means that the price will never change.

      Rather than policy responding to changes in the price of this future (which never happens,) policy responds to the Fed's position on the contract.

      Now, maybe the market would do lots of trading of the contract, and there would be alot of volatility in the Fed's position on the contract. And so, when policy responds to those changes in position, maybe there would be lots of volatility in policy.

      But really, the usual issue raised is that no one would trade the futures, not that they would trade them too much.

  9. The obvious difference is that stock prices are infinite-lived assets, so they reflect an estimate of the discounted value of all future dividends. NGDP futures, on the other hand, would be defined on NGDP in just one time period, and would expire and settle when the NGDP for that period is known. They should suffer much less from excess volatility. There are, in fact, dividend swaps defined on dividend payments on an index in specific time periods, and their prices don't look excessively volatile.

    1. That's interesting. Do you have a link?

  10. Anonymous10:27 PM

    Great post as usual. (Add the "i" to targetng).

  11. Anonymous7:31 AM


    I was hoping you would ask a couple of more fundamental issues.

    First, what is the point of targeting NGDP?

    How will such create jobs, against the forces of oil prices and demographics. Stock/Watson 2012 Disentangling the Channels of the 2007-2009 Recession

    Second, Minsky made the point in several papers that we cannot run deficits or their equivalent indefinitely. Thus, NGDP might work, or at least better, if also we de-indexed social security and government pensions at the same time. The later is a Minsky idea based on the simple observation that inflation would then move gov't into a surplus position.

    Third, what good does NGDP targeting do for a "gangster" economy like the one we have, as explained by Stiglitz and others, where the key drivers are agents with information advantages.

    Related to that is the assumption that the targets should be revealed, etc. Isn't it time to wake up and smell the roses and to realize that in an economy where information advantages cause imbalances that, may be the best policy would be for the Fed to shut up.

    If the game is one of manipulating expectations, keeping your mouth shut is a very necessary first step to prevailing.

    Watch one episode of Squawk Box following a fed meeting and it becomes apparent that a group of people believe they can manipulate the information to the disadvantage of the whole.

  12. Schiller and Kamstra have also proposed "Trills" in case you have not seen this. The Trill pays, a coupon of one-trillionth of current dollar GDP.

    you are probably right there would be volatility depending on how its designed (Schiller's proposal is more likely to be implemented honestly) and the tax implications (futures can have peculiar tax problems). I don't think that's fatal to the idea - in fact judging which indicators move the market is probably pretty informative. Like TIPS, a useful guidepost.

    The *trend* is probably more important than the level. that is, its unlikely the Fed would hit the target exactly, as you point out its operationally difficult (they don't even do that for fed funds). But they will probably keep it within guardrails.

    Also, i doubt that actual NGDP would ever actually hit the target because *unexpected* events (like Tsunamis) would happen, however i strongly disagree with your statement: "For example, volatile Fed policy, even if it adheres rigidly and credibly and permanently to an NGDP futures targeting rule, may cause expectations to become more volatile if a substantial number of economic actors fail to believe that NGDP targeting will succeed in hitting the target"

    well, this is about credibility, which is a problem with any target. The only way to be 100% credible is to never set a goal. the Fed never hits 2% PCE YoY either. It's comes down to whether the market believes that the Fed will adjust if it oversteers and vice versa.

  13. Asset market volatility will cause policy volatility.

    Sure, but it's countercyclical volatility. That should tend to work in favor of NGDP stability -- markets see faster NGDP growth, they know the Fed will tighten, markets see slower NGDP growth, they know the Fed will loosen.

    As dwb says, they'll often miss the target, but the market will know what to expect, and we can tend to avoid both excess inflation and these alleged liquidity traps.

  14. Noah, The Fed is a market-maker in the NGDP futures market. It offers to buy and sell unlimited quantities of NGDP futures at a price equal to the policy goal. At a higher or lower price, one side of the transaction or the other would prefer to deal with the Fed. Hence the market price never budges. No transactions take place at any other price.

    I think what confuses people is that they think of the NGDP futures market as forecasting NGDP, where's it's more useful to think of it as a tool to forecast the instrument setting that achieves on-target expected NGDP growth.

    BTW, Some of the quotes you provide are taken out of context. When I suggest an easy money policy would push NGDP futures above target, I'm assuming that the Fed is not targeting NGDP futures.

    I've probably done 200 posts on NGDP targeting, and maybe 20 of them invloved NGDP futures targeting. So in absolute terms I mention NGDP futures targeting fairly often (as I said) and in relative terms I usually just focus in NGDP targeting (as the futures targeting is a side issue) as I said.

    Andy right about his gold standard analogy, BTW.

  15. Noah, The Fed is a market-maker in the NGDP futures market. It offers to buy and sell unlimited quantities of NGDP futures at a price equal to the policy goal. At a higher or lower price, one side of the transaction or the other would prefer to deal with the Fed. Hence the market price never budges. No transactions take place at any other price.

    OK, this I understand. Thanks! However, I still don't understand how this market helps to inform, create, or otherwise help establish the NGDP target itself. Does private-sector demand for NGDP futures help establish the target?

    1. The NGDP target itself is not determined by the market.

      Sumner's usual assumption is that it is set by the central bank.

      It is 1.25% more than the target for the previous quarter.

      And you have to start with some specified value.

      I must not understand what you are asking.

    2. (in case you miss my reply to earlier comment)

      Yes, if I understand you correctly, (net) private sector demand for NGDP futures is what tells the Fed whether the market thinks it will undershoot or overshoot the target. If the private sector is a net buyer of NGDP futures (so that the Fed itself is a net seller), the Fed would interpret this to mean that the market thinks it will overshoot its target. Vice versa for undershoots. In Scott's proposal (some versions of it, anyhow) the Fed responds mechanically to this information. My preference is to let the Fed do as it sees fit (since I think we can be confident that the Fed wouldn't want to build up an extremely large position and thus will eventually respond if the market continues to implicitly express the opinion that it will miss its target).

  16. Noah, Stocks are volatile because the discount rate fluctuates for discounting those dividends far out in the future. In contrast, we are talking about a relatively short term NGDP futures contract. I would regard a 1% risk premium as being about the outer limit of what would be plausible. Anything larger would represent lots of $100 bills on the ground. That's not true of stocks. And in macroeconomic terms all we really care about is whether the risk premium is time-varying. It's not even clear which way the risk premium would go. Because NGDP futures markets don't currently exist, there seems to be little demand for hedging purposes. If it's a pure gamble, you'd expect the market price to be awfully close to the expected future value of NGDP. And as I said, if the central bank saw any dubious trades, they would be free to jump right in and take the opposite position.

    1. Stocks are volatile because the discount rate fluctuates for discounting those dividends far out in the future.

      I'm not sure I buy that at all...

    2. Deniz3:04 PM


      There is nothing to buy. Price = cash flow / (1+discount rate) is a mathematical identity. It's a rather meaningless statement. If cash flow does not change and the price goes down, you could say the discount rate went up because of negative sentiment, low confidence, etc. Or you could say that risk aversion increased. Both statements (rational and behavioral) would be are consistent with the price going down.

      This is a problem for Scott. You actually do not need behavioral biases, confidence, sentiment to make your point.
      Risk aversion (or ambiguity aversion) can be time varying and perfectly rational.

      Let's say Scott thinks the NGDP futures price is off by 1% from what he thinks the actual NGDP will be. First to invest, 1% has to be greater than the money he would get keeping the futures amount (or the margin deposit) in his bank account earning interest.

      But what % of his wealth would Scott invest? 100%, 10%, 1%? Would that % be different in 2005 vs 2008 (assuming the futures minus forecasted NGDP value is 1% in both years)?

      So to invest, Scott will require = expected mispricing (futures - expected NGDP) + risk free rate + time varying risk premium.

      The risk free rate and premia will be negatively correlated in bad economic times and positively correlated in good times. I am not sure how the expected mispricing would vary over time.

      So Scott's demand would decrease with high short term rates and during recessions, when we need to get the NGPD futures price more correctly. I am not a macro guy, so I don't know what the full implications would be. Btw, none of this requires noise, sentiment, etc.

  17. Noah: imagine base money as an increasing function of the fed's futures holding. When lots of private actors think ngdp will be high, money is too loose, the fed will have a decreasing futures position and base money will shrink.

    While I'm here, I think "this is fun" is not entirely consistent with your recent team vs science post.

  18. I'llHaveADouble12:20 PM

    An optimal forecast should not respond to "noise"; in other words, if something happens that doesn't affect dividends, it shouldn't affect the forecast. This means that actual dividends should be more variable than prices - the dividends should have lots of "surprises".

    Coffee not hitting brain - could you expand on this? Wouldn't the price of the stock fluctuate with each "surprising" dividend - dropping or rising in sync with "surprising" size of the dividend?

    1. Wouldn't the price of the stock fluctuate with each "surprising" dividend - dropping or rising in sync with "surprising" size of the dividend?

      Maybe it would, maybe not. But it's a bit beside the point...the point of "excess volatility" is that prices also respond to other things - noise, stuff that has nothing to do with future dividends.

    2. I'llHaveADouble5:16 PM

      Thanks for the reply. I think the thing I don't get is why prices would necessarily be less variable than dividends if they constitute optimal forecasts - in the words of Killface, I think I'm missing a key reference here.

  19. it occurred to me that the closest benchmark we have for ngdp futures volatility is not the stock market but breakeven inflation volatility (driven by TIPS and bonds, which overall track interest rate and other volatility), about 60 bps annually (1 stdev of daily changes, annualized). volatility varies widely from product to product (prompt oil and natural gas vol is much higher than stock market volatility!).

    Also, keep in mind, 1) ngdp volatility itself becomes a measure of central bank credibility (just as BE TIPS inflation is now, to a certain extent); so the CB would act to make sure it remained in a band; 2) its a function of "unanticipated" or unexpected economic factors (like the Japanese Tsunami); 3)forecasts can be adjusted for any bias (TIPS are biased predictors of inflation due to tax and term premia).

  20. This is an excellent post, and reminds me of my days in the late-1990s as a finance student who was very resistant to the logic of CAPM and the notion that the value of a stock is derived primarily from the value of its future dividend payments. That was a hard thing to swallow in the midst of the capital appreciation phenomenon that was the tech bubble.

    I'm sure much more thought has gone into it since those days, but having going toward law myself, I haven't followed it at all. But regardless, the "excess volatility" Noah mentions seems related, as does Soros's notion of "reflexivity" or any number of other attempts to explain how asset prices can be influenced by herd behavior and/or changing preferences.

    Unfortunately, I don't really understand exactly how Sumner's proposal works yet, but this post helped a lot.