Tuesday, September 17, 2013

Woodford's forward guidance—why not use forward contracts instead?

...once the supply of reserves is sufficient to drive the short-term riskless rate to zero..., there is no reason to expect further increases in the supply of reserves to increase aggregate demand any further... Once banks are no longer foregoing any otherwise available pecuniary return in order to hold reserves, there is no reason to believe that reserves continue to supply any liquidity services at the margin; and if they do not, the Modigliani-Miller reasoning applies once again to open market operations that increase the supply of reserves, just as in the model of Wallace.
-Michael Woodford, 2012.  

On a whim, I wrote an email to Michael Woodford last week. Woodford, a macroeconomist at Colombia University, is the authour of Interest and Prices (pdf), an important contribution to modern monetary policy. I'll be the first to admit that I haven't been able to work my way through his book—too few words and too many equations. But I have read two excellent papers by him. The first is Monetary Policy Without Money, which I'll touch on in another post, and the second is a well-known paper that he presented at Jackson Hole in 2012 entitled Methods of Policy Accommodation at the Interest-Rate Lower Bound. If you're interested in monetary policy and you haven't read it yet, you really should.

My email, affixed below, had to do with the above quote from his second paper:
Dear Professor Woodford,

I have read your paper Methods of Policy Accommodation at the Interest-Rate Lower Bound several times and it has taught me quite a bit.

One question:

In Section 3.1 (Effects of Targeted Asset Purchases in Theory), you point out that once the supply of reserves is sufficiently plentiful, banks no longer forgo a pecuniary return that would otherwise be provided by reserves (ie a marginal convenience yield). This is the point at which the overnight interest rate hits the lower bound, additional reserve additions are irrelevant, and the Modigliani-Miller result applies.

It seems to me that the overnight rate doesn't shadow the general convenience yield on reserves per se, but rather it shadows the 24-hour convenience yield on reserves. Just like there is a term structure to bonds, there is a term structure to the convenience yield on reserves. In addition to a 24-hour convenience yield, there is a 1 week, 1 month, 1 year yield, each point allowing us to construct a convenience yield curve.

Although the overnight yield may be zero, convenience yields further down the convenience yield curve may still positive. Banks hold reserves not only to enjoy their overnight convenience, but also to enjoy expected flows of future convenience. This would seem to imply that the present discounted value of future flows of convenience can be positive even when the overnight convenience yield is zero.

Which would indicate that even when we are at the lower bound for overnight rates, purchases are not necessarily subject to the Wallace irrelevance critique insofar as they specifically target positive yields further down the convenience yield curve. If purchases today can reduce convenience yields tomorrow, the present discounted value of future flows of convenience will be reduced. Overnight purchases won't suffice since they only target overnight convenience yields. Open-ended outright purchases might not work if there is no commitment to avoid unwinding these purchases in the future. Perhaps long term repo operations that target the distant end of the convenience yield will be most effective in avoiding the irrelevance criticism. Repos precommit a central bank to avoid unwinding at a future point in time, thereby reducing future convenience yields and, as a corollary, the present value of total convenience flows.

Does that make any sense? I am curious what your thoughts on this are.


JP Koning
Frequent readers will notice that my letter was just a summing up of my three recent posts on the convenience yield.* If you've already read those three posts and reached your quota, don't bother reading further, since much of what I'm going to write follows in that general theme.

Surprisingly, Woodford got back to me. I'm not going to publish his response, but in brief he doesn't think that there should be a convenience yield curve. Woodford told me that he thinks reserves are an overnight asset, not a long-term asset like, say, Treasury bills, and an overnight asset doesn't supply a convenience yield for longer than 24 hours.

I agree with Woodford that the convenience yield supplied by a short-lived asset is negligible. No one holds a stock of ripe avocados because they might serve as convenient medium of exchange 30 days from now.

But reserves aren't avocados. They are infinitely-lived instruments that can be perpetually held without the necessity of paying storage fees. This means that even when overnight yields have hit 0% (as indicated by an overnight fed funds rate of zero) reserves still supply current reserve-owners with a positively-valued marginal convenience yield over longer time frames than the 24-hour window. The implication of this is that although central banks may no longer be capable of manipulating the 24-hour convenience yield lower, they may be still be able to conduct targeted financial transactions, or balance-sheet policy, that change distant parts of the convenience yield curve. This gives a central bank plenty of traction at the zero lower bound. After all, a reduction in the future convenience flows thrown off by reserves will reduce the present value of all convenience flows. The expected return on reserves having been reduced, reserves will be spent away in the present and this will stimulate today's inflation and/or real activity.

QE—what Woodford refers to as balance sheet policy—is a fairly blunt tool when it comes to reducing distance convenience yields.** This is because a one-time expansion of the central bank's balance sheet can be easily reversed at a future point in time by sucking reserves back in. Financial markets may therefore view QE as fleeting. If so, distant convenience yields will not budge much and, as a result, inflation and real activity will remain unaffected.

Rather than engaging in crude QE when the overnight rate hits zero, a central bank might enter into a more focused form of balance sheet expansion. Five-year repos, for instance, may be sufficient to ensure that excess reserves stay in the system for an extended period of time. Even more effective would be a policy of entering into forward contracts with banks. These transactions would commit the central bank to purchasing assets at various points in the future, thereby ensuring a series of large balance sheets down the road.

For instance, if the Bank of Canada faced the ZLB and wanted to reduce the future convenience yield on reserves after, say, 2015, it could contract with commercial banks to purchase assets at various dates in 2016, 2017, and 2018. It would enter into as many of these forward contracts as necessary to guarantee today a sufficiently large supply of reserves tomorrow. Unlike crude QE, forward contracts are irreversible. The permanency of these transactions should be sufficient to reduce the future convenience yield on reserves, thereby diminishing their expected return in the present and stimulating current spending.

A policy of using forward contracts to reduce the distant convenience yield on reserves could be a substitute for Woodford's verbal forward guidance. Rather than specifying in words the future time path of interest rates, the central bank need only add a sufficient amount of forward contracts to its balance sheet in order to ensure that it hits its targets (an inflation target, a nominal GDP target, whatever). The upshot is that balance-sheet policy needn't die at the zero-lower bound. Concrete actions that guarantee to alter the size of a central bank's future balance sheets and convenience yields can be just as effective as Woodford's carefully crafted wording.

In any case, I'm not holding my breath for Woodford to get back to me on that, he's a busy guy.

*Interestingly, Woodford uses the term convenience yield in his paper, too.
** Miles Kimball has equated balance sheet policy at the ZLB to using a massive fan to move the economy.


  1. First – that’s awesome Woodford got back to you.

    Second, I admittedly need to read closely your previous posts and more closely this one, as I don’t 100% get it yet. But let me know how far off this is:

    If banks would expect a payoff to holding reserves at some point down the road (i.e., longer than 24 hrs), should that not show up in the overnight rate? For example, if I think I’ll have a payoff 30 days from now of 1%, would I not roll over the loan for 30 days at an overnight interest rate no greater than [(1.01)^(1/30)-1] or whatever the correct math is? If I have this right, then if we observe overnight rates to be 0%, that would imply that banks judge the convenience yield across the entire term structure to be worth 0.

    To continue, you seem to be suggesting that the Fed can still have traction at the ZLB by playing with the longer term convenience yield. But by the above (again assuming I’m doing this right), it seems like it all gets wrapped into the one overnight interest rate at the end of the day (no pun intended). If you’re at the ZLB, it’s telling you future discounted payoffs are zero as well. Nothing else can be done.

    What am I missing?

    1. "If banks would expect a payoff to holding reserves at some point down the road (i.e., longer than 24 hrs), should that not show up in the overnight rate?"

      Not necessarily. The current overnight rate, say the federal funds rate, only compensates reserve lenders for forgoing the convenience of reserves over the *immediate* 24-hour period. It doesn't serve as an accurate indicator of what the market expects to be compensated over ensuing 24-hour periods (ie. 24 hours from now until 48 hours from now, 48 hours from now until 72 hours from now, etc). Planning to roll over a series of overnight loans at today's 0% overnight rate isn't a viable strategy since there is no guarantee that the current overnight rate will prevail the next night, or the night after, or the night after.

      "But by the above (again assuming I’m doing this right), it seems like it all gets wrapped into the one overnight interest rate at the end of the day (no pun intended). If you’re at the ZLB, it’s telling you future discounted payoffs are zero as well. "

      Think about lending out a book, say War & Peace. By lending it out overnight, you're foregoing consuming it for 24 hours. You may have plenty of books on the go at the moment, so no big deal -- you'll be willing to lend it for free overnight (say the borrower is 100% trustworthy). But that doesn't mean that you value War & Peace's lifetime flow of future consumption claims at 0. At some point in time, you may know that you'll want to read it again. Maybe you expect your current book supply will eventually dwindle a month from now, at which point reading War & Peace will be necessary to fill your reading quota. Maybe reading War & Peace satisfies a very specific need that you don't expect to arise in the immediate future, but you'll probably want it in the distant future. In any case, you'll reveal these preferences in the longer term lending market. Although you may be willing to lend overnight at 0%, the price of foregoing these very real future consumption claims means that you'll need a better rate in the longer term rental market.

    2. Right - of course. Thanks for clarifying. Will have to think about this more then.

    3. ATR - It's a work in progress so I very much appreciate the criticism.

  2. JP, nice! I agree w/ ATR on his 1st point, and I'm interested to see you answer the 2nd point. Want to know what Woodford thinks? Just ask him. Nice. Who would have thought? Well I hope Woodford gets back to you on your follow up question too. And I like this contract idea... much better than vague promises. As Cullen Roche has said, Bruce Lee kicks Chuck Norris' behind because “saying is not enough, you must do.” Cullen actually provided a clip this time to back that up (bottom of post):


    ... actual a still from that clip would make an excellent graphic for a future post... maybe the part where Lee pulls Norris' chest hair out?:

  3. JP, regarding the contracts: Like you say, it's a more powerful move in that it's not reversible, but what if conditions change and it looks like NGDP is going to be above the target level? What can be done to neutralize these contracts? And if it's known that something can be done to neutralize the contracts, are they really more powerful than forward guidance words from the CB?

    1. I don't think they're necessarily more powerful. The two options are equivalents, or substitutes. Forward guidance can be pulled, just like an existing portfolio of forward contracts can be neutralized in the future by entering into new forward contracts that do the reverse of the existing contracts.

      Both, however, are probably more effective than raw QE.

  4. Hi JP,

    Very interesting post and certainly very timely given what our corner of the blogosphere has been debating lately.

    My 2 cents:

    First, I think it's not the forward convenience yield that we want to lower, it's forward nominal interest rates. I recognize that they happen to be the same with interest on cash at 0% and low IO(E)R, but still, if convenience yield went to 2% while nominal interest rates stayed at 0%, we'd be just fine so I think it's clearer to speak in terms of nominal rates.

    Second, there is no trade the Fed can do to commit itself to future size of base, future convenience yield, or future nominal rates. Every trade can be unwound, or some opposite trade can be entered into.

    For instance, the Fed could do $3tn of 2 year reverse repo bringing the base to $6tn and 1 year from now execute $5tn of 1 year repo bringing the base down to $1tn. The market knows this and therefore won't give much importance to excess base.

    When the Fed executes these scary long-term/risky QE trades, it's a signal, much like the size of a peacock's tail is a signal that is otherwise useless. However, unlike peacocks, central bankers can speak and give forward guidance which is precisely what Woodford is advocating for.

    Of course they could default on their guidance at the cost of their credibility, and maybe there's some legal apparatus that could be used to cement the commitment and "tie themselves to the mast". But simple trades cannot be the solution to this problem because they can be unwound or reversed.


    1. Hi DOB, thanks for stopping by. You bring up some good points about reversibility that I'm currently mulling over. In the meantime, a few comments:

      "...if convenience yield went to 2% while nominal interest rates stayed at 0%"

      The nominal overnight rate is entirely a function of the overnight convenience yield (keeping IOR out of the picture). So if a central bank suddenly increases the marginal convenience yield on reserves (say by sucking in most of outstanding reserves), the overnight rate won't stay at 0%. It'll spike up.

      "...so I think it's clearer to speak in terms of nominal rates."

      We can always choose to speak in terms of overnight interest rates instead of convenience yields. It definitely streamlines the conversation. But I don't think we should lose track of the fact that a central banker is manipulating the underlying convenience yield in order to conduct monetary policy.

    2. I think we're on the same page.

      Operationally, the Fed
      (1) increases base, in order to
      (2) reduce convenience yield, and since IOR is 0%, this also
      (3) reduces nominal interest rates, which in turns
      (4) props up the price level (if everything is held constant)

      Sumner and the monetarists focus on (1).
      You've put the spotlight on (2).
      I (and Woodford and a lot of others) like to look at (3) because it's the only part necessary to achieve (4):
      - if we do (3) without (1) and (2) (by keeping IOR some fixed spread away from CoF), we get (4) all the same. However,
      - if we do (1) and (2) without doing (3) (again, by moving IOR and CoF), then we do not get (4)

      Therefore, (3) is what's critical even though (1) and (2) are important parts of the monetary mechanics.

    3. Cost of Funds, from DOB's write up:

      "[Update: Article previously said "Cost of Funds" instead of "lending rate" but that was confusing as Fed Funds is often referred to as the cost of funds. As Max pointed out, Fed Funds wouldn't fit here so I changed it to the "lending rate" which you can think of as the rate at which money is lent into existence by the Fed (either an explicit rate if via repos, or implicit if via asset purchases). Loosely speaking, it's the Treasury GC repo rate.]"

    4. CoF = Cost of Funds which is commonly understood to be Fedfunds, but I really mean the rate at which money is lent into existence by the Fed (against government bond collateral).

      Fedfunds and my definition of CoF only diverge by the Fedfunds/GC Repo basis (small). They can diverge more if the monetary base is zero but that would mostly occur in theoretical exercises.

    5. No prob. DOB, Nick Rowe has a simple story up about apples, bananas, interest rates and New Keynesian models to explain what's wrong with them (the NK models that is, not the apples). I think you should check it out:


      I'd love to see your response.

    6. "if we do (1) and (2) without doing (3) (again, by moving IOR and CoF), then we do not get (4)"

      Ok, let's work out our similarities and differences. Let's start with a normal central banking environment in which the overnight is x% above IOR (In Canada it's 0.255). When I think about the monetary expansion process, by doing (1) and (2), a central bank will simultaneously cause both (3) [specifically a decline in the overnight rate, or fed funds rate] and (4), a rise in prices. (3) occurs simultaneously with (4) -- (3) doesn't cause (4).

      Only when the overnight rate has fallen to the level of IOR will (1) no longer change (2), and therefore will not change (3) or (4). At this point the only way to increase prices (4) is to reduce (3) -- specifically via a reduction in IOR. We've now arrived at a pure Woodfordian interest rates only world in which IOR is the lever. But until we get to point at which the overnight rate has fallen to IOR, (1) and (2) will be sufficient to directly cause (4).

      [However even when the overnight rate has fallen to IOR, (1) might still change (2) in that it reduces future expected convenience yields, and via that route increases (4) in the present. That's where I was going with this post].

      What do you think?

    7. I think I agree with everything you're saying except for the part where (2) causes (4) directly without needing (3).

      Let me illustrate with 2 scenarios where the central bank uses CoF and IOR as policy instruments:

      Starting Point:
      - CoF = 4%
      - IOR = 2%
      - (Convenience Yield = 4% - 2% = 2%)

      Everything in equilibrium, price-level stable.

      Scenario A: (2) but not (3)
      - CoF = 7%
      - IOR = 5%
      - (CY unchanged at 2%)

      In this case convenience yield is unchanged but monetary conditions were massively tightened. Putting aside future expectations issues, price level should be dropping drop.

      Monetary base expected to remain roughly stable.

      Scenario B: (3) but not (2)
      - CoF unchanged at 4%
      - IOR = -9%
      - (CY up to 13%)

      In this scenario, CoF, i.e. the nominal return on assets is unchanged, but the convenience yield was dramatically increased. No notable impact on the price-level should be observed.

      Nominal assets still yield the same: 4%
      Money still yields the same, though the breakdown is changed:
      - Was previously 2% pecuniary + 2% non-pecuniary = 4% total nominal return
      - Now -9% pecuniary + 13% non-pecuniary = 4% total

      There are fewer people who think non-pecuniary return of money exceeds 13% (than 4%) and for that reason, monetary base will be much smaller.

      That said, because it yields the same as any other asset class (risk-adjusted), the money market is in equilibrium and the price-level should not be impacted.

      In the language of (1)/(2)/(3)/(4), (1) and (2) aren't necessary for (3), and don't directly cause (4). (3) alone is what matters for (4).

      If you fix IOR = 0%, then (2) and (3) are artificially bound together but it's still (3) that matters.

      In other words, Woodfordian mechanics works even when there are monetary frictions and base is non-zero.

    8. Interesting. You seem to view the convenience yield as a residual -- you back it out via the accounting identity cy = CoF - IOR.

      I view the convenience yield as the root cause of the overnight rate.

      Say a central bank sets IOR at 2% and the overnight rate (the fed funds rate) is currently at 4%. The central bank steadily buys stocks or corporate bonds outright in the open market with reserves. What happens to the convenience yield? the overnight rate? the price level?

      Or say that the central bank can't legally pay interest on reserves. It injects reserves into the economy by purchasing gold outright at market prices. It doesn't announce an intermediate overnight interest rate target -- it lets rates float according to the whims of the market. And it says that it wants to target 3% CPI. There are no interest rates in this scenario, so can the Fed exercise monetary policy? How?

    9. "Say a central bank sets IOR at 2% and the overnight rate (the fed funds rate) is currently at 4%. The central bank steadily buys stocks or corporate bonds outright in the open market with reserves."

      (caveat: everything else held equal, ignore future expectations issues)
      "What happens to the convenience yield?" => it goes down
      "the overnight rate?" => goes down by same amount since IOR is kept constant.
      "the price level?" => goes up


      "There are no interest rates in this scenario, so can the Fed exercise monetary policy? How?"

      There is an interest rate, it's just that the CB targets something else and lets it float in the market.

      When the nominal rate wanders north of the Wicksellian natural rate plus inflation, prices will fall. When it happens to be on the other side, prices will rise.

      The Wicksellian rate is unobservable, difficult to estimate and perpetually on the move. So whether the CB keeps its stock of gold, or the price of gold, nominal interest rates or even the quantity of base money constant in-between (sufficiently frequent) meetings is not important to a first order. (There are other, lower order issues, that make me prefer interest rate targeting).

      What matters is that at each meeting, it moves its intermediate target in a way that keeps the risk-adjusted return on nominal assets in line with what it estimates the Wicksellian rate will be for the coming period. And that the market expects it do the same at every meeting in the future.

      With competent central bankers and the same CPI target, the market nominal rate under gold-price targeting will end up being close to what it would have been had the CB targeted rates directly.

    10. ""the overnight rate?" => goes down by same amount since IOR is kept constant."

      I agree that the overnight rate goes down along with the convenience yield. Why do you think the overnight rate go down? What drives the process?

      "There is an interest rate, it's just that the CB targets something else and lets it float in the market.... What matters is that at each meeting, it moves its intermediate target in a way that keeps the risk-adjusted return on nominal assets in line with what it estimates the Wicksellian rate will be for the coming period."

      But the way I structured my original hypothetical was without an intermediate target. The central bank passively buys and sells gold and tries to hit a final inflation target. Nor does it set a gold price ( sort of like how the Fed doesn't set a bond price when it does QE). Can this central bank influence the price level or not? and if so, how?

      Put differently, can this central bank reduce the return on reserves below the idealized Wicksellian return in order to get prices moving higher? How so?

    11. "I agree that the overnight rate goes down along with the convenience yield. Why do you think the overnight rate go down? What drives the process?"

      There's no "transmission mechanism" between convenience yield and overnight rate. The convenience yield is defined as overnight minus IOR. So when convenience yield moves, and IOR doesn't overnight rate moves by definition.

      "But the way I structured my original hypothetical was without an intermediate target."

      The meeting-to-meeting Gold target is just a practical consideration because Bernanke can't crank his models and rub his beard every 5 seconds to estimate his policy actions. He periodically runs his calculations and boils down his result into a simpler intermediate target which he hands over to the OMO desks and which any monkey trader should be able to hit.

      But assuming the OMO trader is infinitely smart, there is no need for an intermediate target.

      Here's how to think about OMOs in the world you're describing: decompose an open-market gold purchase as follows:
      (1) Fed purchases Gold future (no reserve impact)
      (2) Fed lends money (the notional amount of the Gold future) into the market (it happens to be against Gold collateral, but that doesn't matter all that much)

      If we ignore the distortionary effects that (1) has on the Gold market, and to a lesser extent on every other market, then the job of the OMO trader is to use the effect of (2) and do just the right amount of OMOs in order to get the nominal rate where it needs to be vs the Wicksellian rate.

      The nominal rate nowhere figures explicitly on anything tangible that the OMO trader does (and neither does the Wicksellian natural rate), but they're there, under the hood, in the decision process.

      "Put differently, can this central bank reduce the return on reserves below the idealized Wicksellian return in order to get prices moving higher? How so?"

      Return on cash and reserves could be moved around in order to stabilize the amount of Gold held by the CB and therefore reduce the distortionary effects of the (1) part of the OMO. You may also need to lower it at the zero bound, just like when there is no Gold involved.

      In short, the Gold part introduces distortions due to the (1) part of the trade but doesn't otherwise change much since (2) is still there.

      Does that make sense?

    12. "There's no "transmission mechanism" between convenience yield and overnight rate. The convenience yield is defined as overnight minus IOR."

      Your answer confirms my earlier point about accounting identities. I think we're saying different things. You're making a point about an accounting identity, specifically Fed funds - IOR = convenience yield. I'm interested in the equilibrium condition. Nick Rowe gives a good explanation of the difference between the two in the comments section of the linked post.

      "Does that make sense?"

      Your (1) and (2) are confusing me. Say the central bank only buys and sells gold *outright*, not via repos. It doesn't lend reserves into existence. It doesn't set the gold price nor any intermediate target. In 125 words or less, can this central bank influence the price level or not? and if so, how?

    13. "Say the central bank only buys and sells gold *outright*, not via repos."

      Yes, that is what I've been talking about: an outright purchase is functionally identical to a purchase in derivatives form + a (collateralized) loan. In fact, in finance-speak we often say that buying something in derivatives form is buying it "unfunded", i.e. the counterparty is virtually loaning the funds for you to buy the asset.

      So yes, that central bank can control the price-level because of the implicit loan in any asset purchase. The other part of the asset purchase (the transfer of risk from the derivatives part) is just an unnecessary distortion in the market for gold (or whatever other underlier) but it shouldn't prevent the CB from achieving its price-level target.

      Will read Nick's article tomorrow and come back.

    14. I read Nick's quantity theory story carefully and it is fully translatable in an interest rates based framework. The same conclusions are reached.

      (Mind you there are a few "explosive paths" in his story which wouldn't be time consistent, but I assume that's just to keep things simple)

      I even agree that a small bit of conditional taxation is a good way to rule out the "infinite inflation" equilibrium, i.e. to jumpstart the machine if it's completely off.

      I still think the interest rates story view is more elegant and intuitive, especially in its handling of IOR and at the zero-bound.

      Also I find it unnecessary to talk much about taxes/govt spending for the purpose of valuing money because when the government borrows to spend, the effect on equilibrium interest rates is identical than when you and I borrow to spend (except for size of course). In both cases, it pushes real interest rates up. And for a given inflation target, that pushes nominal interest rates up too. So it's ok to think of the government as "just another monetary player".

      So to get back to what we were talking about, I fail to see how Nick's post is in contradiction with anything I wrote.

    15. Oops. I wanted you to read Rowe's post not because of the actual substance of the post, but because of the bits on reasoning in terms of accounting identities versus an equilibrium condition. You're reasoning in terms of the former, me in the former (at least with respect to fed funds - IOR = convenience yield). Glasner and Krugman have also written good posts on this distinction.

      As for the rest, we'll go with your loan/futures setup. Say the central bank is only allowed to borrow gold/buy futures at the going market lease rate. In other words, it makes no effort to guide or set the gold lease rate. There is no IOR. Does monetary policy work or not?

    16. Hmmm there's been posts about the difference between accounting identities and equilibrium conditions but I didn't recognize this one as one of them.

      In any case, I don't think CY = CoF - IOR is either. It's an identity but not an accounting one.

      The equilibrium condition is that for a given CY, there will be a certain quantity of base demanded by the market. As the monopoly supplier, the central bank will supply that quantity. (In fact they fiddle with the quantity until they achieve a certain CY).

      "There is no IOR. Does monetary policy work or not?"

      Well "no IOR" really means "IOR = 0%". Monetary policy works fine, except you'll run into trouble at the zero-bound, just like when there is no Gold involved.

      (Gold might add slight complication to the usual framework as now the convenience yield includes the cost of safe storage for Gold, but I don't think it fundamentally changes much)

      What's your view?

  5. Seems odd that he would dismiss it so quickly. How can he believe in the power of expectations and the signaling of the CB balance sheet, and then not believe in a futures contract and the reversal (opposite short/long) of that contract using the CB balance sheet? Maybe he thinks borrowing overnight is such a small interest payment, but of course you can use leverage to cover several days, or the the contract itself could be term 30-180 like one of the term repo programs during 2009-10.

  6. Instead of targeting reserves why doesnt the central bank target broad money? The rates on broad money are nowhere near 0. Broad money is much more relevant to the overall economy than base.

  7. Nice series of posts. But I disagree that is makes sense to attempt to target future convenience yields with things like forward contracts with banks. I think this is easy to see if we imagine the Fed entering a bunch of these contracts to purchase assets over 5 years, and then velocity suddenly spikes due to some sunspot. Inflation and NGDP start to increase above the Fed's target. What does it do about its forward commitments? Easy. It nullifies their overall impact on convenience yields by tightening monetary policy (selling assets or raising IOR) more than it otherwise would have. But if the Fed can easily reverse the effects of its forward contracts on convenience yields when it "should" it can also do so when merely thinks it should, and thus is committing to nothing in particular.

    I would go even further to say that your suggestion isn't "really" targeting future convenience yields with forward contract any more than a mere explicit promise to do so or a Wallace Neutrality stifled purchase of 10YR treasuries. All of them are merely ways to attempt to establish institutional credibility that an entity which still retains complete discretion will in fact take the net actions required to make reserves sufficiently available relative to its nominal target. You are free to argue that somehow these forward contracts are a more credible indicia of commitment than other methods (an ALL CAPS Fed statement, say), but I think the issue turns on what is perceived to be most binding and not on whether the Fed is "directly" targeting future convenience yields.

    1. Hi dlr,

      Thinking about this a bit more, I'm inclined to think of the forward contracting strategy not as directly "targeting" some future path or level of convenience yields on reserves, but reducing them to as far as necessary in order to hit a nominal GDP target (or some other target) in the present. To do so, the central bank would only have to enter as many contracts as necessary for it to start moving present NGDP.

      But now I'm inclined to think that QE and forward contracts are much more similar strategies then I originally thought -- they both work by sufficiently "attacking" future convenience yields in order to hit current NGDP. (Perhaps the forward contract strategy would require less commitment of space on the its balance sheet than QE?)

      Whereas QE and contracts reduce the future path for the convenience yield to whatever level is necessary in order too hit the target, forward guidance commits to a very specific path for the convenience yield (or, alternatively, a specific path for IOR, insofar as IOR happens to be the policy instrument going forward).

  8. I saw your tweet on ANCAP, so I was wondering: what do you envision as base money in a free banking system (completely free, not a fiat base)? Gold or something else?

    I saw a Bill Woolsey post with ideas about free banking. To me, the "Black-Fama-Hall" proposal (commodity bundle dollar definition + indirect redeemability into gold) seems most workable. Any thoughts?


    1. I haven't picked a side which means I'm open to being swayed by all sides of the debate. It seems to me that the ideal base money is the one that the market settles upon, whatever that happens to be.

  9. Below, I try to translate your thoughts into Woodford’s model of the interbank rate, which I go over in detail here (http://macromoneymarkets.blogspot.com/2013/12/michael-woodfords-individual-liquidity.html). I either partially succeed in demonstrating why Woodford didn’t quite go along with what you’re suggesting, and/or fail to capture what you were suggesting. I am not sure. I’m not yet familiar enough with the other Woodford papers you post here, so that doesn’t help.


    Woodford’s world:

    Woodford’s world looks something like this (to summarize the above post):

    Pretend each reserve maintenance period is one day. The central bank conducts an OMO at the beginning of the day, determining the probability banks end the day short or long reserves (relative to the reserve requirements) based on the probability distribution of end of day liquidity shocks to banks. Following the OMO, banks then trade reserves in the interbank market based on this information. After the interbank session, the liquidity shocks occur, and the day ends with banks seeking recourse to the central bank as appropriate. Say interest on reserves is 0% and the central bank’s lending rate is 1%.

    Each bank is trying to minimize its cost of holding reserves across each maintenance period – here, one day. (Actually, Bindseil puts it as ‘minimizing costs of refinancing’ when he reviews Woodford’s model, whereas Woodford puts it as ‘maximizing return on reserves’ - I think they’re analogous). The cost function for one maintenance period looks like: C(s) = is + P*ib + (1-P)*id, where i/ib/id correspond to the market/lending/deposit rates, respectively, and the P corresponds to the expected probability of ending the maintenance period short reserves (1-P is thus the probability ending long reserves). A bank will determine the proper quantity of reserves (s) it wants to hold based on the values of all other variables in the equation, and will trade for it in the interbank market. The market rate ‘i’ is determined by supply of reserves (set by the central bank in the morning via the OMO) needing to equal the demand for reserves arising from that function across all banks (see my post for the modeling of this). Thus, by controlling P and the aggregate quantity of reserves (both via adjustment of the size of OMOs), ib, and id, central banks can control the interbank rate i.

    My attempt to insert your terminology: Since I have assumed interest on reserves is 0%, then reserves have no pecuniary return. They can only have a convenience yield. Their convenience yield for each bank is determined by how they impact the aforementioned cost function. The interbank market will function until the convenience yield is zero, and it’s at this point that an equilibrium market rate ‘i’ is determined. (Sorry if I botched this. I think that’s what you mean when you use these terms.)

    1. (Continued from above)

      JP Koning’s World?

      If I try to work your thoughts into this model, perhaps what you’re thinking is that the aforementioned cost function should not just capture expected costs across the current maintenance period but rather costs across all maintenance periods going out into the future (theoretically forever). The cost function that includes maintenance periods going out into the future would look like the above plus the expression [is + P*ib + (1-P)*id] for each maintenance period captured (as well as discount factors to account for the time value of money), and each i/ib/id/P would be unique to each period.

      It is implicit in Woodford and Bindseil’s models that central banks and banks are only thinking about the current maintenance period when it comes to setting the current interbank rate. This makes controlling the interbank rate relatively easy. If instead the expected costs of future maintenance periods played a meaningful role in determining i, then we’d have to believe that for central banks to control the current interbank rate, it can also control expectations of relevant variables for each maintenance period going out into the future.

      But here’s the thing: the central bank is still operating with a target for i *in the current maintenance period.* Whether we imagine only the current maintenance period matters or all future ones do, the central bank is still going to set ib/id/P for the current period and set expectations for ib/id/P/i for all future periods such that it achieves the same i in the current period. Note that the central bank has to set uniform expectations for the value of ‘i’ in future periods for ‘i’ in the current period to settle where it wants it. In contrast, it doesn’t have to say anything about the value of ‘i’ it wants in the current period. The forces of supply and demand will do that for it.

      At the end of the day, we end up in the same place whether we include just the current period or the future. The market will trade reserves until it settles into equilibrium. If I have you correct, this is the same as saying markets will trade until the convenience yield on reserves is eliminated (whether that convenience yield takes into account just the current period or also all future ones). The central bank can control this equilibrium rate to the extent that it can control the aforementioned variables. The central bank’s life is easier if setting expectations for all that future stuff isn’t important for determining the current rate. But regardless, the goal is to end in the same place: achieve the same interbank rate i today.

    2. Ah, sorry. The basic cost function I wrote above is not correct. I accidentally fused Bindseil's aggregate liquidity model with Woodford's equations. In the correct equation, the variable 'P' does not appear as readily. However, it still plays the driving role behind the scenes, and so everything else I wrote should be fine. See my post for the correct equation if interested.

    3. Cool, I'll try and take a closer look at this after New Years. Busy with all sorts of family holiday events.