Goodhart’s Law and NGDP targeting

A commenter named Rob recently asked me this question:

Scott, long-time reader, first time commenter. How do you respond to the criticism, raised both in the comments on MR and somewhere else I can’t remember, that the problem with Sumnerianism is Goodhart’s Law? If the Fed targets NGDP, then NGDP will lose its significance as the relevant indicator-or something like that.

Goodhart’s Law is sort of a humorous riff on the Lucas Critique.  It says that as soon as the central bank adopts a particular intermediate target, then the relationship between that target variable and the policy goal will breakdown.  Thus suppose economists found that M2 was highly correlated with NGDP.  If the Fed began targeting M2, then according to Goodhart’s Law M2 velocity would suddenly become more unstable.  Goodhart’s Law is one of the strongest arguments for NGDP targeting, which is why I wanted to answer these scurrilous charges in a new post.

Under NGDP targeting there is no intermediate target, the central banks uses some sort of policy instrument, such as open market operations or interest on reserves, to target NGDP directly.  Without an intermediate target, Goodhart’s Law is not applicable.

It is possible that these critics were thinking of my proposal for a NGDP futures targeting regime, where the Fed stabilizes the price of NGDP futures along a 5% growth trajectory.  In that case I suppose you could consider the price of NGDP futures contracts to be the intermediate target, and actual future NGDP to be the goal variable.  I’m not even sure I’d be willing to concede that point, as I think it is more important to stabilize future expected NGDP (which influences wage contracts and asset prices) than actual NGDP.   But let’s concede the point for the moment.  Even if you view NGDP future prices as an intermediate target, however, Goodhart’s Law is not applicable.  There is no possibility of the relationship between NGDP futures prices and actual future NGDP breaking down, because NGDP futures contracts do not exist—thus there is no relationship to breakdown.

Furthermore, the EMH suggests that NGDP futures contracts would provide an optimal forecast of future NGDP.  On the other hand the EMH does not suggest that the other intermediate targets (money, interest rates, exchange rates) would be expected to maintain a stable relationship with NGDP after a regime change.

Goodhart’s Law provides one of the best arguments for targeting the forecast of the goal variable directly, without intermediate targets.  Obviously it doesn’t have to be NGDP, but in principle the target should reflect the social welfare costs of macro instability.

PS.  Sorry for the long blog malfunction.  The blog was getting a lot of attention last night; perhaps it couldn’t handle the stress.  Hmmm, where are those Cialis ads that used to always pop up?

PPS.  I like the term ‘Sumnerianism.’  I would appreciate if another blogger could add a prefix like “anti-.”  I’m shooting for something longer than ‘antidisestablishmentarianism.’  The longer the name, the greater the prestige.



22 Responses to “Goodhart’s Law and NGDP targeting”

  1. Gravatar of Doc Merlin Doc Merlin
    5. December 2009 at 12:31

    Isn’t NGDP is itself an intermediate target for GDP?

  2. Gravatar of Doc Merlin Doc Merlin
    5. December 2009 at 12:44

    I guess I should be less terse. If the fed does NGDP targeting, wouldn’t the Lucas Critique suggest that (actual) GDP and NGDP will begin to diverge more and more.

  3. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    5. December 2009 at 12:51

    Antidisestablishsumnerianism–which only ties for word length–would presumably describe economists who, in the event that targeting NGDP became official Fed policy, were committed to keeping that status quo in the face of organized dissent.

  4. Gravatar of rob rob
    5. December 2009 at 12:52

    Thanks. I guess I forgot to add the smiley face after the “first time commenter” remark. 🙂

  5. Gravatar of jean jean
    5. December 2009 at 13:12

    @Doc Merlin: GDP is not the target, because we always want more GDP.

    I would say that NGDP is the intermediate target for “output gap=0”. But output gap is a theoretical concept which is unlikely to be measured properly.

    As I said earlier, the problem I see with NGDP is that there could be fluctuations of NGDP which are not wishable to be smoothed (for seasonnal variations, but we could imagine other examples).

  6. Gravatar of Doc Merlin Doc Merlin
    5. December 2009 at 16:39

    @Jean: No, Scott has said that he wants a 3-5% NGDP growth target. Not a 0% NGDP growth target.

    My views:
    The main problem I see with fed targeting NGDP is the same problem with the Fed targeting anything. A public, monopolistic backwards looking firm can’t target. Its impossible. You need market targeting, but market targeting based on a separate non-convertible won’t work, because of circularity. I order for it to work properly, money must be convertible and the fed must have its hands tied, so it can neither inflate nor deflate the currency.

    How I would define some terms:

    Disestablishmentsumnerism: The idea that the Fed should be abolished, but also that money should be backed by NGDP future convertibility. Bill Woosley fits in this category.

    Antisumnerism: The view that the reason for the crash was a Hayek-esk business cycle caused by excessively easy money in the years leading up to the crash. This seems to be Arnold Kling’s view.
    To put it into language a macro-economist would understand, although Hayek would never use this language: what creates NGDP growth expectations is the ease of credit/money access. If the central bank prices it too cheaply, then that creates expectations of high NGDP growth. Later on when the growth doesn’t match expectations, we have a crash. The flip side of the coin, is that if the central bank makes the money even easier to match NGDP growth expectations we get runaway inflation.

  7. Gravatar of Philo Philo
    5. December 2009 at 18:51

    What do we social theorists *really* want? Let’s stipulate that the answer is: “social happiness.” (Never mind exactly what that is supposed to be.) Then the argument for targeting smooth growth in NGDP is that there has been observed a close correlation between the steadiness of NGDP growth and social happiness. Goodheart’s Law implies that once the authorities explicitly target smooth growth in NGDP, the correlation will evaporate, or at least be greatly reduced.

    But why take Goodheart’s Law seriously? It probably holds in some kinds of cases and not in others; in other words, it isn’t really a *law*.

  8. Gravatar of Philo Philo
    5. December 2009 at 18:54

    ‘Goodheart’? ‘Goodhart’? Ah, well!

  9. Gravatar of OGT OGT
    5. December 2009 at 19:22

    And if we accept most empirical evidence that EMH does not hold, whether do to reflexivity, cognitive biases, or limits to arbitrage, I assume that would only affect the NGDP futures targeting regime. Or is EMH more central to your monetary theory?

  10. Gravatar of bill woolsey bill woolsey
    6. December 2009 at 05:39

    Perhaps I never understood Goodhart’s Law, but I thought the key element of it was that even if some macroeconomic variable appeared to lead nominal expenditure, that once the central bank begins responding to it, then its future behavior will begin to be driven by what speculators expect the central bank to do.

    I certainly hope that nominal expenditures targeting will cause speculators to influence nominal expenditures in a way that will keep nominal expenditures growing at a slow stable rate.

    Much of Sumner’s discussion of how temporary changes in the quantity of money are offset by changes in velocity (or accomodated by changes in the demnad to hold money) is exactly this process. The temporary changes are temporary because they are inconsistent with the target (even if implicit) and so speculators offset the impacts that would occur. The point of an explicit target for nominal expenditure is to harness this speculation in the service of nominal expenditure stabilization. If the quantity of money is too low or too high temporarily, speculators should change their demand to hold money to offset this impact, leaving nominal expenditure on target.

    If there were index futures contracts, and the Fed began targeting their price, then it is probably correct that their market price would be driven by the Fed’s expected response, which would be to keep them on target. Bernanke at al pointed out this problem with the Fed targeting something like this. Those of us favoring index futures convertibility are very concerned with this issue.

    Of course, with index futures convertility, where the central bank buys and sells the contracts at the target price, of course the price would never deviate from target because of the Fed’s actions. They are buying and selling them at a fixed price. The information generated by the institution is in the positions speculators take on the contract rather than in changes in its price. (Scott’s point that there are no such contracts today and so targeting those contracts cannot impact their behavior is true but more than a bit too clever. Ha ha, Scott.)

    Actual positions on the contract will be due to disagreements among different speculators. Buyers will expect to profit from sellers. Sellers from buyers. They disagree on what will happen to nominal expenditures. And, yes, these expectations are conditional of an understanding that those on the other side of the market are causing expected nominal expenditure to deviate from target. And that your own position, against them, is pulling it back to target.

    If a representative agent is assumed, then this process makes no sense. There is only one speculator. He disagrees with himself? Goodhart’s law (as I understood it,) makes sense if “the market” is like one individual and the central bank is playing a game with them. It breaks down with index futures convertibility.

  11. Gravatar of Mattyoung Mattyoung
    6. December 2009 at 06:44

    Not Godharts’s Law, but pure laziness. It takes more work to get accurate NGDP numbers, and when we operate relatively smoothly, that data will be subject to a lot of proforma responses as firms are too lazy to collect nuanced data. Or alternatively, during rapid change there will be large firms that fraudulently report wrong NGDP numbers.

    Once the fast change comes, then the Fed is stuck with data that is not up to date. My opinion is that hidden information will always make the central banker about 6 months late, there is a noise floor that cannot be avoided. Even Selgin cannot generate a complete solution.

  12. Gravatar of ssumner ssumner
    6. December 2009 at 07:44

    Doc Merlin, No the ultimate goals of policy are stable growth and stable prices. Because NGDP picks up both goals, it better describes the goal of monetary policy than RGDP alone. Could the relationship between NGDP and RGDP change after you begin targeting NGDP? I suppose that is possible, but that would equally be a problem for monetary regimes that tried to target NGDP via intermediate targets. Remember, even money supply and interest rate targeting are aimed at NGDP, not RGDP.

    Patrick, That’s right. And that term would then describe me. I’d become a reactionary defending my ideas against upstarts with even better plans.

    Rob, Thanks for the question.

    jean, Good point. But in principle we’d want to target whatever best fit the social welfare function. As you say, prices plus output gaps might fit better than NGDP. But also as you say, output gaps are hard to measure. Hence I prefer NGDP.

    Doc Merlin; You said;

    “Disestablishmentsumnerism: The idea that the Fed should be abolished, but also that money should be backed by NGDP future convertibility. Bill Woosley fits in this category.”

    No, that would be “Disestablishmentsumnerianism” Then there is disestablishsumnerism, which would refer to people who want me dead.

    Philo, That’s true, but isn’t that also true of whatever we try to achieve in life. You are a philosopher—haven’t most of the great philosopher’s pointed out that after people get what they think they want they are never satisfied, they always want something more.

    OGT, Only the futures version would be affected. But I would claim that even if EMH doesn’t hold exactly, it’s a good enough approximation that if we peg NGDP futures at plus 5%, the Ratex optimal forecast for next years NGDP will be in the plus 4% to 6% range. And that is good enough for macro stability.

    Bill, I’m not really sure what explains Goodhart’s Law. I’ve always thought of it in terms of the Lucas critique. So expectations may play a role. Another issue is the difference between a variable than is endogenous (not being targeted) and exogenous (being targeted.)

    You said:

    “(Scott’s point that there are no such contracts today and so targeting those contracts cannot impact their behavior is true but more than a bit too clever. Ha ha, Scott.)”

    I know it sounds like a too clever by half argument, but I think I am right. This isn’t Goodhart’s law, because there is no relationship to change. I think what you did is note that this thought experiment raises a different issue, the circularity problem. And also that the circularity problem can be best addressed with index futures convertibility. And I agree with all that. But I think the problem that you describe as being fixed by index futures convertibility is better described as the circularity problem, not Goodharts’s law.

    I do find Goodhart’s Law to be a bit confusing, and am not quite sure what drives it. Here’ one idea that I forgot to mention in the post. New regimes may be tried out when policy is doing very poorly under the old regime. But those periods (1933, or 1979) are also periods when velocity is very unstable because of all the problems in the economy. So perhaps in the long run velocity would not be any more unstable merely because you moved from interest rate to money supply targeting.

    Mattyoung, Good point, but some of this can be reduced by targeting not the initial GDP estimate, but the later revised number, which is presumably more accurate.

  13. Gravatar of David Heigham David Heigham
    6. December 2009 at 08:57

    We are getting potentially quite prestigious: ssumner is an ‘contradisestalishmnetsumnerianist’. Since I judge that, given the intellectually stimulating nature of sumnerianism, it is contrary to the interest of sumnerianism as a movement to debate the question of whether it is an established creed or not, I must be an ‘anticontradisestablishmentsumnerianist’

    Goodhart’s Law should have been called the Goodhart Rule – like the Taylor Rule. Its’ theoretical backing is dubious and debatable; but it sure as hell describes how official targetting of a statistical variable does a pratfall into its own aspiring intentions. I continue to judge that the Chinese have targetted NGDP to assess the performance of their regional and provincial authorities (for reasons that are Marxist, and probably irrelevant to the debate here); and am waiting to find out what the pratfall is.

    I trust we will continue to steer away from ‘output gap’ targetting in any form. An ex-ante output gap estimate is always highly conditional. It is interesting that the UK Treasury uses (used?) an estimated output gap to guide their fiscal policy. Over-estimating that gap for some years lead them into entering the present crisis with a large fiscal deficit. More fundamentally, if trend ex-ante output gap as we usually estimate it was a constraint, the performance of the US economy which overwhelmed the Axis in the years 1943-45 could not have occurred.

  14. Gravatar of Doc Merlin Doc Merlin
    6. December 2009 at 13:33

    In a functioning free market if someone asks in a way to take advantage of an inefficiency, the inefficiency goes away. In a semi-centrally planned market (like the market for US currency) inefficiencies are created every time the central planner takes an action. The market then tries to gain profit from the planner’s action, both by trying to expect that action, and by trying to beat everyone else to the market in responding to the action. Thus when the central planner tries to manipulate the market the market responds by trying undo the inefficient parts of the manipulation.

    Anyway, I don’t think markets are actually efficient; I think they are efficiency seeking. If they were actually efficient you couldn’t make any money trading. (Before someone brings up Beta strategies and economic growth, I want to point out that the stock market share’s value has been growing at a much higher rate than the economy as whole over its lifetime.)

    Anyway, Goodhart’s law is naturally what would happen when you have a policy-seeking market manipulator interacting with an efficiency-seeking market.

  15. Gravatar of ssumner ssumner
    7. December 2009 at 12:43

    David, I’ve always thought that NGDP was a better way of getting at the concerns of output gap proponents. It doesn’t require any difficult estimation, and leaves the price level somewhat anchored.

    And yes, that’s a very long word you created.

    Doc Merlin, Surely the market response plays a role, but it is still difficult to pin down what is going on.

  16. Gravatar of What does “harm” mean? Or, the importance of baselines | Morton and George What does “harm” mean? Or, the importance of baselines | Morton and George
    11. May 2011 at 08:41

    […] system? Or maybe just compared with alternative policy decisions the Fed could have made, like targeting NGDP or strictly following the Taylor […]

  17. Gravatar of Pete Pete
    27. October 2011 at 10:47

    “There is no possibility of the relationship between NGDP futures prices and actual future NGDP breaking down, because NGDP futures contracts do not exist””thus there is no relationship to breakdown.”

    If there are no NGDP futures contracts, how can there be prices for them?

  18. Gravatar of Scott Sumner Scott Sumner
    29. October 2011 at 05:44

    Pete, The Fed will create them.

  19. Gravatar of fred smalkin fred smalkin
    12. January 2012 at 07:23

    I’m coming to this a little late, but it seems to me that if the fed uses rules based on NGDP futures, then parties would have the incentive to tie nominal payments to some derivative of NGDP futures in order to hedge inflation risk. If everyone does that, then NGDP futures become dependent on fed policy, and there’s a short-circuit. Is there something I’m missing or getting wrong?

  20. Gravatar of ssumner ssumner
    12. January 2012 at 13:15

    Fred, You might want to google my post entitled “spot the flaw in NGDP futures targeting.”

  21. Gravatar of fred fred
    19. January 2012 at 17:44

    Thanks for the reply, Professor!

    I read the post you referenced as well as your 2006 article about circularity. I understood it to say that with your proposal there’s no circularity as between the Fed and NGDP futures traders, but what about between futures traders and other contracting parties? In terms of your model I think what I mean is that where V(t+1) = S(t) + aM(t) + e(t+1), if economic actors anticipate inflation as being a function of Vf(t+1), then the term S(t) would be a function of Vf(t+1), introducing a circularity. But I fear I may misunderstand the role and meaning of S(t). Could you comment? Thanks!

  22. Gravatar of ssumner ssumner
    20. January 2012 at 07:56

    fred, I’m afraid I don’t recall that paper very well. I’d suggest you check out my paper in Contributions to macroeconomics from 2006, which is entitled “Let a Thousand Models Bloom.” I think it’s easier to follow that proposal.

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