Evan Soltas on optimal control theory

Evan Soltas has a very interesting new post suggesting how the Fed could better achieve its targets:

How would it do that, exactly? Here is where I come in with my recommendations. What the Fed has tried to do with forward guidance over the last year is plot the possible paths of the policy rate conditional on economic scenarios, but the way they’ve been doing it is kludgey when you think about it. We’ve been talking about asset purchases and signaling future policy — and signaling is imperfect! — so much that we’ve forgotten that there is a way to do this more directly.

My recommendation is that the Fed should target federal funds rate futures, eurodollar futures, overnight indexed swap (OIS) rates, or an appropriate proxy for the expectation of future interbank lending rates. (Whatever the specific contract form, I’ll call them fed funds futures going forward.) The reason why it ought to do this: There’s nothing clearer than just talking about the actual course of policy directly.

Here’s how this would work. The FOMC concludes its next full meeting in mid-December. In the summary of economic projections, the Fed should report what fed funds futures prices it believes to be warranted given the midpoint of the central-tendency projection over some five-year curve. It should also report the fed funds futures prices warranted conditional upon upward or downward deviations in economic data from the midpoint of the central-tendency projection. In other words: If we get ugly or nice surprises, how does the Fed plan on changing plans?

Before commenting, let me say that my math is somewhere between rusty and non-existent, so I may use the wrong terminology.  My main concern with this proposal is the difficulty of estimating the optimal path of the fed funds rate.  The proposal seems to assume that the lower the expected future fed funds rate, the more expansionary the policy.  But that can’t always be true, as the interest rate path that would produce Zimbabwean hyperinflation is likely higher than the current path, at least for 2015 and 2016.  So the relationship between expected 2016 interest rates and expected 2016 NGDP may not be monotonic, and thus there could be multiple equilibria.

I will concede that the relationship may be monotonic over the range relevant to current policymaking (although that’s less certain than most would assume), but nonetheless this thought experiment shows the difficulty of estimating the appropriate path of rates; the Wicksellian equilibrium rate changes as the expected growth rate of NGDP changes.  So while Evan’s plan might well be a big improvement over current policy, it is still not optimal.

In contrast, there is no multiple equilibria problem with NGDP futures targeting. Under that sort of regime the market for NGDP futures becomes the de facto FOMC.  This is the step that almost all elite macroeconomists (with the exception of John Cochrane) refuse to take.  There’s an endless search for the optimal path of the policy instrument, but very little soul-searching as to whether policymakers should even be in the business of forecasting the relationship between various instrument settings and future expected aggregate demand.  In other areas of economics we’d almost automatically view that as something that markets do better.  Why not in macro?

PS.  Here’s another way of making the same point.  Evan discusses the case where the market doesn’t find the future path to be credible.  But what he overlooks is that the lack of credibility can come from two sources; either a lack of trust that the Fed will persevere in its attempts to hit its nominal targets, or else markets may have confidence in those targets, but disagree as to whether the central bank’s estimate of the appropriate target path is actually the correct one. I believe that the second problem is dominant in Britain right now. Markets believe Carney is committed to faster NGDP growth, they simply don’t think he can hold rates low for as long as he claims, even if he hits the (implicit) NGDP target.

HT:  Saturos



20 Responses to “Evan Soltas on optimal control theory”

  1. Gravatar of John John
    28. September 2013 at 06:57

    “In other areas of economics we’d almost automatically view that as something that markets do better. Why not in macro?”

    Careful about applying this argument logically. It might lead you to conclude that there should be no federal reserve, no government police, no government roads, no government military, no government healthcare, no government at all. After all, no one has really elaborated good reasons why markets couldn’t do these things better. They just repeat tired arguments about light houses and collective action/public goods that haven’t changed from John Stuart Mill in 1820. It’s worth noting that at the time Mill used lighthouses as the seminal example of a public good and 75% percent of lighthouses in England were privately run at that time.

  2. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    28. September 2013 at 07:24

    John, ever hear the terms, ‘non-rival- and ‘non-excludable’ in consumption?

    Maybe the MM boys should produce a video, along the lines of this;


    Not the specifics in it–which are wrong in several things–but, the ease of exposition.

  3. Gravatar of Saturos Saturos
    28. September 2013 at 07:38

    Evan Soltas for Fed Chair. #Soltas2014

  4. Gravatar of Saturos Saturos
    28. September 2013 at 07:39

    John, actually even David Friedman admits that anarcho-capitalism has trouble with national defense, and that it’s only like 60% certain that completely private law would work…

  5. Gravatar of Evan Soltas Evan Soltas
    28. September 2013 at 09:12


    Thanks for the discussion. I know we agree that the end goal of monetary policy should be stabilizing expected and actual nominal growth over the medium run. I also have no objection to the creation of an NGDP futures market; it’s compatible with my suggestion above in guiding monetary policy paths. Where I think we might diverge, or have a misunderstanding, is on the policy instrument at the mechanical level.

    My understanding is that you think the Fed’s actual instrument should be expanding or contracting the monetary base in order to push NGDP futures up and down. My instrument is the monetary base in the present, but interbank overnight swap rates for the future, because trying to manipulate a single policy instrument to control some intertemporal trend in NGDP may have Tinbergen-style problems (i.e. too few instruments relative to objectives). As time passes, eventually the central bank follows through on its fed funds futures contracts by changing the monetary base.

    Another reason is that I just don’t think markets care about the monetary base, or feel it’s that informative about the stance of policy. However, markets plainly do care about marginal changes in expected future interbank lending rates, as seen by my series of posts in the early summer. In the end I think markets understand how my instrument should steer nominal growth more clearly than they do for yours. If the Fed were to say “the fed funds futures contract dated January 2016 implies, given the Fed’s economic projections, a fed funds rate 100 basis points above the Fed’s intended course of policy,” the futures contract prices would change, and that would bring down longer-term rates just as effectively as asset purchases, given the way that the sum of short rates becomes a long rate.

  6. Gravatar of Max Max
    28. September 2013 at 09:49

    Knowing the interest rate path pins the price of long term bonds, but it tells you little or nothing about the economy. It doesn’t tell you whether you should be optimistic or pessimistic. So the only benefit is less speculative trading in the bond market, maybe.

    (That’s not to say that such a program wouldn’t have an effect. Certainly people would say, “the Fed is much more dovish than we thought” and revise up their estimates of inflation and GDP. But the perceived attitudes of the people at the Fed are what makes the program work, not the program itself. Just like QE…)

  7. Gravatar of John John
    28. September 2013 at 10:14


    Here’s an exposition on national defense without the government (I’m not sure I like the term anarcho-capitalism because there is no anarchy).


    Historically, standing armies are incredibly ineffective fighting forces compared with guerilla fighters anyway. Think of how many armies have marched directly into cannon or machine gun fire? Nation states are simply god awful at waging war. It’s not difficult at all for me to imagine a private company able to do a much better job at it even without the massive resources a nationstate can bring to bear.

    I think it’s easy to make the case that private defense could do a much better job. At least 90% of wars are needless or unwise anyway and they couldn’t happen without governments.

  8. Gravatar of ssumner ssumner
    28. September 2013 at 10:17

    John, I promise to be careful.

    Evan, Unfortunately the terminology here is not well defined, which can cause misunderstandings. My proposal does not contemplate replacing the fed funds rate with the monetary base as a policy instrument. Rather the fed funds rate is replaced with NGDP futures as an intermediate target. Even when central banks use the fed funds rate as an intermediate target (as prior to 2008), they continue to use the monetary base as a tool for achieving that target. So my proposal does not contemplate giving the base any more prominence than under fed funds targeting.

    As far as what markets focus on, that depends on the fed policy. Back in the old days markets cared about gold flows, as those had a direct impact on the base. Even today the base matters to market participants, as we saw in the strong market reaction to QE. But on the other hand I agree that if the Fed uses the fed funds rate as a policy signal, and if the base is endogenous in the short run, then base changes are of little interest to markets.

    In a 1995 paper I did discuss the possibility of multiple targets, to overcome the credibility problem. The idea is that the Fed would peg the price of 12 month forward NGDP contracts, and use that market to determined the base (and fed funds rate) and then simultaneously peg longer term NGDP futures prices to add policy credibility. I no longer view credibility as being a serious problem, so I haven’t discussed that proposal in a long time.

    As far as future expected changes in the fed funds rate, I agree that markets care more about that variable than they do about the current setting of the base. But I think that’s because markets care about the future path of policy than the current setting, however defined. I’d add that I believe they care more about the future path of NGDP, than either the future path of fed funds rates or the future path of the base.

    Max, I agree, except I’d say “sort of like QE.”

  9. Gravatar of Lorenzo from Oz Lorenzo from Oz
    28. September 2013 at 13:07

    John: It’s worth noting that at the time Mill used lighthouses as the seminal example of a public good and 75% percent of lighthouses in England were privately run at that time. “The Lighthouse in Economics” by Ronald Coase is a favourite trouble-making article.

    I defend the proposition that Coase was the most important C20th economist here:
    If you think that too large a claim, go through the list of Nobel Memorial Laureates and work out for how many of them their seminal work was based on Coase’s insights. Now, try and find another C20th economist who has more such examples.

  10. Gravatar of BC BC
    28. September 2013 at 14:11

    Scott, Tyler Cowen just posted a link on Marginal Revolution to a note on declining nominal income expectations: [http://www.federalreserve.gov/econresdata/notes/feds/2013/why-have-americans-income-expectations-declined-so-sharply/].

    This would seem to be a smoking gun that Fed policy has been too tight. Given the low nominal income growth expectations shown in Figs. 1-2b, if we had a NGDP futures market, wouldn’t these graphs suggest that market participants would be net selling, rather than buying, NGDP-bonds to the Fed? In turn, what does that suggest that the Fed should be doing now with respect to tapering?

  11. Gravatar of benjamin cole benjamin cole
    28. September 2013 at 16:50

    NGDP targeting, or other transparent rules-based monetary policies are fine—as long as they are not too restrictive (central banker’s disease) and subject to oversight by democratic institutions.
    I fear central bankers setting up a form of mechanized monetary asphyxiation, gloating over the results, for which they now absolve themselves of responsibility.

  12. Gravatar of Mark A. Sadowski Mark A. Sadowski
    28. September 2013 at 17:00

    Here’s a Chicago Fed paper on the same subject:

    Expected income growth and the Great Recession
    Eric French, Taylor Kelley, and An Qi


    Plus David Beckworth did posts in April and May on this topic.

  13. Gravatar of John John
    28. September 2013 at 17:12


    It seems like most free market economists who assume markets work better in most areas never put the skepticism they have have about welfare, trade barriers, or monetary policy to work against things like government provision of roads, defense, or money production in general. It isn’t surprising that the government wants to control things like roads, money, education, or the military. What is interesting is that so few people ever call them out on it and are content to uncritically accept and regurgitate (bad) 200 year old arguments about lighthouses to their undergraduate students.

    People are so contentious about everything in economics except claims about the government needing to control all of the most critical areas of the economy.

  14. Gravatar of TESC TESC
    28. September 2013 at 18:34

    Dr. Sumner, I have questions about the NGDP futures market. Do I just ask here or do I go to a post related to it?

  15. Gravatar of Mike Mike
    28. September 2013 at 18:40

    “My main concern with this proposal is the difficulty of estimating the optimal path of the fed funds rate. The proposal seems to assume that the lower the expected future fed funds rate, the more expansionary the policy.”

    Maybe quantity of broad money targeting is optimal. For any given interest rate you could have the supply of money grow at any rate therefore targeting the interest rate may be inappropriate. Also targeting broader money is correct because most of the money in the economy is broad not just base.

  16. Gravatar of Benjamin Cole Benjamin Cole
    28. September 2013 at 22:29

    Thanks Mark S. Why not you start blogging…

  17. Gravatar of ssumner ssumner
    29. September 2013 at 05:36

    Lorenzo, Excellent post.

    BC, Maybe, but I distrust those sorts of polls. I focus on market prices.

    John, I’m certainly very skeptical of the government’s role in the areas you cite. I’d prefer the private provisions of roads and schools, and a much smaller military. I also propose that the markets determine the quantity of money and the level of interest rates.

    But perhaps I am the exception.

    TESC, First see if it is answered in the article I linked to. If not, you can ask here.

    Mike, I much prefer NGDP targeting to broad money targeting.

  18. Gravatar of Mike Mike
    29. September 2013 at 07:38

    “Mike, I much prefer NGDP targeting to broad money targeting.”

    Broad money targeting would be the mechanism by which policy is conducted. The point of targeting broad money interest rates or quantity is to achieve inflation targeting or NGDPLT.

  19. Gravatar of TESC TESC
    29. September 2013 at 08:09

    Sumners ,


  20. Gravatar of ssumner ssumner
    30. September 2013 at 05:41

    Mike, I think NGDP futures would be a much better mechanism. If they don’t exist, I’d prefer using other forecasts.

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