Krugman, Kaminska, and Waldman

There is an interesting debate taking place over the issue of whether we are in a new world, where monetary injections will no longer create inflation via a sort of “hot potato effect.”  Instead, base money and short term debt would become almost perfect substitutes.  Here’s Izabella Kaminska:

In this way, we agree with Waldman that the moment IOER created a preference for excess reserves over short-term debt assets or cash, was the moment excess reserves became a new type of safe asset security in their own right.

Excess reserves became the equivalent of state debt. But, very importantly, a state debt taken with the intention of never being spent, but rather for the purpose of creating safe assets instead.

Fed exit

And herein lies the differentiation point. If and when the Fed decides to exit unconventional policy, it will be obliged to re-associate opportunity costs with excess reserves. As rates go up, the spread between between the Fed Fund rate and the rate on excess reserves will only widen.

At this point the huge amount of excess liquidity sitting on reserve would either end up chasing any positive-yielding safe security in town or flood directly into the real economy. And both scenarios carry risks. In the former scenario, the crowding out of safe assets could once again lead to repo rates falling well below the Fed Funds rate, rendering central bank rate-hiking policy useless. In the latter scenario, the economy could face the real risk of run-away inflation.

To counteract these effects, the central bank would need to drain excess liquidity more quickly than the liquidity can flow into either alternative option. But what took four years to dish out could take a little while to reabsorb.

But there are other problems associated with unwinding such a huge position on the market, too. Especially if you view this as tantamount to either “spending” the money borrowed, or paying it off.

Consequently Waldman’s argument is essentially: why bother if you don’t have to? Let the excess reserves, just like state debt, roll on:

“Why go to the trouble of unwinding the existing surfeit of base money, which might be disruptive, when doing so solves no pressing problem?”

And since not moving quickly enough poses too great a risk, the alternative would be committing to IOER as a long-term rate-steering alternative instead.

As Waldman sums up:

“If the Fed adopts the floor system permanently, then the Fed will always “sterilize” the impact of a perpetual excess of base money by paying its target interest rate on reserves. As Krugman says, this prevents reserves from being equivalent to currency and amounts to a form of government borrowing. So, we agree: under the floor system, there is little difference between base money and short-term debt, at any targeted interest rate! Printing money and issuing debt are distinct only when there is an opportunity cost to holding base money rather than debt. If Krugman wants to define the existence of such a cost as “non-liquidity trap conditions”, fine. But, if that’s the definition, I expect we’ll be in liquidity trap conditions for a very long time! By Krugman’s definition, a floor system is an eternal liquidity trap.”

Krugman, for now, remains unconvinced.

I sympathize with Krugman’s view, albeit probably for slightly different reasons.  In his newest post Waldman says Krugman misinterpreted his argument.  So perhaps they aren’t that far apart.  But I still have reservations about where Waldman is going with his argument:

1.  I’ve already shown that the zero lower bound on the stock of excess reserves means that large increases in the price level would require a larger monetary base, if only to boost the currency stock.  So the quantity of money still matters, even with IOER.

2.  Waldman suggests that the Fed is not indifferent to the size of the currency stock.  Kaminska points out that a large stock of ERs might be beneficial, especially during financial crises.  So let’s consider the case where the Fed prefers to have banks hold ERs equal to 5% of GDP, roughly the size of the currency stock during normal times.  This implies that the base will be about 10% of GDP.  Obviously in that case the size of NGDP would be determined in ordinary quantity theoretic fashion.  Every extra dollar of base money has a hot potato effect, and boosts NGDP by $10 in the long run.  You might wonder how this occurs, when banks can freely exchange unwanted ERs for short term T-bills.  The key is that the Fed will adjust the IOER as needed to keep the level of ERs close to 5% of GDP.  If that seems like cheating, consider that Waldman made a very similar argument; that any Treasury injection of currency would be sterilized by the Fed, in order to maintain their macroeconomic objectives:

But Waldman definitely does not at all believe that 2(b) and (3) are equivalent when the interest rate is positive. He’s not sure where he implied that, but he must have done, and is grateful for the opportunity to disimply it. An expansion of the currency unopposed either by offsetting asset sales or paying interest on reserves would have the simple effect of preventing the Fed from maintaining its target rate. That would mean the Fed could not use interest rate policy to manage inflation or NGDP.

But that is precisely why Krugman is a bit unhelpful when he concludes, “Short-term debt and currency are still not at all the same thing, and this is what matters.” It does not matter, once the Fed’s reaction function is taken into account. The Fed will do what it needs to do to retain control of its core macroeconomic lever. Its ability to pay interest on reserves means it has the power to offset a hypothetical issue of currency by the Treasury, regardless of its size. Krugman is right to argue that, above the zero bound, an “unsterilized” currency issue would be different from debt, that it would put downward pressure on interest rates and upward pressure on inflation. But that is precisely why it is inconceivable that the Fed would ever allow such a currency issue to go unsterilized! In a world where it is certain that the Fed will either pay IOR or sell assets in response, we can consider issuance of currency by the Treasury fully equivalent to issuing debt.

[BTW,  Scott Sumner is a bit puzzled as to why Waldman refers to himself in the third person.  :)]

3.  Waldman’s strongest case would be that the Fed wants banks to hold very large amounts of ERs, but doesn’t much care how large as a share of GDP.  In that case we can assume the Fed uses IOER to make sure the level of ERs adjusts passively to offset any shocks to currency supply or demand, keeping NGDP on target.

I don’t think anyone disputes that, over a fairly wide range of the money supply, IOER can be used as the exclusive central bank monetary policy tool, with changes in the quantity of base money having no immediate impact on the economy.  After all, the price level is simply the inverse of the value of base money.  Obviously the value of base money can be altered via changes in either base supply (OMOs) or demand (IOER).

But I find it unlikely that the Fed would become completely indifferent over the share of GDP held as ERs, at least when rates are positive.  So I expect they’ll continue to do monetary policy via both supply and demand techniques.  Most importantly, even if T-bills become almost perfect substitutes for ERs, it will not allow fiscal policy to impact the price level.  It’s inconceivable to me that the Fed would allow this to happen.  They’ll simply adjust the IOER (downward) until they have traction, until they can do whatever it takes to change the amount of currency in circulation, and hence the price level.  (Again, I’m assuming normal times with positive interest rates–I think the strongest Keynesian argument is that “normal” may become increasingly unusual during the 21st century.)

There is another issue that tends to (wrongly) get lumped in with this debate—does pre-2008 monetary policy involve changes in the base, or the fed funds target?  And in that case I’d argue strongly for the quantity of money approach, even though in the ultra-short run (prior to 2008) the Fed targeted the fed funds rate and the base was endogenous.  However over more extended periods of time the fed funds target was adjusted so that the base would grow at levels compatible with 2% inflation.  If and when the Fed shifts to IOER targeting, I’d expect this to continue—money will be endogenous in the ultra-short run, and endogenous exogenous over the long run.

Where things may differ is the medium run.  No question that IOER allows the Fed to keep the stock of base money endogenous for a much longer period of time than fed funds targeting alone.  That’s because under fed funds targeting with no IOER the level of excess reserves is generally close to zero (at positive interest rates).  In that case control of the currency stock is a necessary and sufficient condition for price level control, not just in the long run, but even in the medium run.  With positive IOER you now have a high level of ERs, and by adjusting the rate of return on ERs you can stabilize inflation without changing the monetary base for a fairly extended period of time.



23 Responses to “Krugman, Kaminska, and Waldman”

  1. Gravatar of c8to c8to
    17. January 2013 at 15:58

    this leads me to my slightly off topic question:

    what does scott sumner think the main real effect of boosting the money supply is.

    off the top of my head i can think of:

    lowers real wages (in the instance of inflation) so hiring unemployment drops and second round effects (output might increase &c.)

    animal spirits: people just want to hold more money (simple first round demand) and if more money is issued they can hold more, are less worried and can spend while still having a high nominal bank account for no real reason (wealth effect)

    some actual shortage of currency available to people like if there was not enough money (you posted previously about the groups who hold large $100 bill hoardings, and maybe theres just not enough currency for the rest of us to do normal transactions) think about the limit case, there was only $1 note we all had to share for all our transactions (ridiculous but one gets the point)

    related to the above, some bizarre shortage of M2 and banks holding onto large swathes of money because of IOR that they don’t make loans out into the system or something. (related to your posts about base has grown but its attenuated by having IOR, so no money is actually getting “out”)

    some other force.

    Which of these do you think is the strongest? or what combination…

    that is if we shifted to nominal targetting (well just thought of another, the sheer act of the fed saying we will hit the target just instantly changes people expectations (an animal spirits one without needing to do anything) what would be the main driver? i guess it falls into expectations and monetary effects, with inflation a second if that results from the monetary injections.

  2. Gravatar of flow5 flow5
    17. January 2013 at 16:32

    The Mayan prophecy fulfilled.

  3. Gravatar of Doug M Doug M
    17. January 2013 at 17:49

    I am puzzling over why the Fed wants banks to hold excess reservers. I even go so far as to say why does the Fed tollarate bank holding excess reserves.

    If the fed buy T-bills and the money that the fed creates sits in the bank as excess reserves, as I see it no money has really been created.

    If you can get 25 bps and 26 bps on a 2-year note there is no incentive to take risk.

    It seems to me that the Fed should be charging banks to hold excess reserves.

  4. Gravatar of Doug M Doug M
    17. January 2013 at 17:50

    If you can get 25 bps and 26 bps on a 2-year note there is no incentive to take risk.

    Ugh… If a bank can get 25 bps interest on reserves or 26 bps on a 2 year note….

  5. Gravatar of ssumner ssumner
    17. January 2013 at 20:01

    Yikes, I should have proofread that post.

  6. Gravatar of Don Don
    17. January 2013 at 20:39

    Do the claims of “runaway inflation” account for currency operations by other central banks? I would think that large inflation here would be negated by other central banks, since they don’t want to be at trade disavantage. Inflation is a boogeyman.

  7. Gravatar of Benjamin Cole Benjamin Cole
    17. January 2013 at 20:45

    Here’s my take: How can it be, in a democracy, even our best experts are guessing at what our most important macroeconomic policy-making institution is doing?

    Do you think we voters, who also live in this economy and make it work, might be clued into what the Fed is doing, and plans to do?

    Crickey, you mean to tell me no one knows (outside the Fed) why the Fed is paying IOER?

    How have we gotten to a point (and I know it was worse before) that secret meetings are held by the FOMC, and it is considered “okay” for the Fed too be, variously, oblique, coy, or forthright (sort of).

    Why doesn’t someone at the Fed say what they are doing in regards to IOER? State the case clearly? They want IOER to be at a level that banks have plenty of capital?

    Of course, this state of affairs (Fed opacity) reflects the weakness of our media, but many bloggers are asking these questions, and—incredibly—have no opportunity to directly ask these questions of the Fed and get clear answers.

    My guess is inflation is dead for a long time, and interest rates will be squishy. However, since we cannot get a clear answer from the Fed what they plan to do, who knows?

    Soi, we may be facing 20 years of zero bound, perm-gloom ala Japan–and the Fed is acting with opacity? Yes, at least now we get some targets–the 6.5 percent unemployment, the 2.5 percent inflation.

    But I think the public deserves clarity, transparency, accountability.

  8. Gravatar of Rien Huizer Rien Huizer
    18. January 2013 at 01:11


    Democracies of various types (ranging from the rotating single party dictatorship in the Westminster system to the highly fragmented proportional representation systems in some European countries) have discovered that “Central Bank independence” (with varying levels of (a) independence, (b) opacity and (c) discretion is a useful way of achieving policy stability, especially regarding variables that can cause trauma to markets and to the democratic system as such.

    The US sits somewhere in the middle of several scales: US democracy is not easily captured by extremists and populist minorities (alas the present situation seems to contradict this) as would be possible in first past the post Westminsterism (but there the safeguards reside outside the constitutional core) or highly fragmented ones (just look at Greece or Belgium) respectively.
    The US monetary authority is not extremely independent (much less than the ECB), has high levels of discretion plus an ambiguous target (a minority position among OECD countries) and tends to keep markets guessing maybe more than necessary.

    So far, US institutions like the Fed and the Supreme Court have done a decent job at reducing the policy volatility that may result from the sort of volatility bias inherent in political systems based on rotation of power, maybe more so than the pairing of executive and legislative powers that tends to produce periods of inaction (gridlock) or hurried activity but rarely well considered good government

  9. Gravatar of Benjamin Cole Benjamin Cole
    18. January 2013 at 01:49

    Rien Huizer:

    Yeah, I know, I know.

    Still, there is every indication the globe’s central banks have become ossified, as exactly as any student of organization theory would predict. “Public independent agency” and “ossified” are probably synonyms.

    The fact the ECB is even less democratic than the Fed makes my point for me: They can follow policies they like, not what voters need. And the Ferd now is more expansionary than the ECB.

    BTW, there is a sinister observation to be made: Staffers at central banks are not entrepreneurs. They get paychecks. If you believe people act in their self-interest, then it would behoove central bank staffers to generate all sorts of studies on the evils of inflation, and perhaps even seek deflation. Think the Bank of Japan.

    BoJ staffers have not only been getting step or seniority raises, but deflation bonuses too.

    I could refer you to a Friedman tape in which he says the Fed has failed miserably, and repeatedly and that was before the 2008 bust.

    Did the Fed react properly to the 2008 bust?

    I say no, and I say they reacted so slowly as they were ossified, self-exalted in their inflation-fighting glory, and not making a living in the real economy like voters. And not fearful of getting tossed out for doing a bad job.

    Every organization seeks to be comfortable. It is wonderful not to have to make a living in the raw competitive private markets, or to answer to irksome voters and their representatives.

    But is it working anymore?

    PS I am not a legal scholar, but the Supreme Court of late seems overtly, expressly political, and horribly ossified. It might be better to chuck them out too, and have the whole 9 stand for re-election every four years, as long as they really did adhere to a Constitution.

    The only problem with determining whether the Supreme Court is adhering to the Constitution is that only the Supreme Court can make that determination….

  10. Gravatar of interfluidity » A confederacy of dorks interfluidity » A confederacy of dorks
    18. January 2013 at 03:12

    […] Kaminska, Josh Hendrickson, Merijn Knibbe, Ashwin Parameswaran, Cullen Roche, Nick Rowe, Scott Sumner, and Stephen Williamson are all dorks, albeit of a more articulate variety. I say the most […]

  11. Gravatar of JN JN
    18. January 2013 at 05:13


    Two points…

    1. Does paying interest on excess reserves really controls the monetary base?
    -> Let’s assume the economy recovers, rates go up quite a lot, and therefore the opportunity cost of holding reserves becomes too high and banks start lending out those reserves. -> As a result, the Fed increases its IOER to 2% to control the outflow of ER.
    -> Well, if we take the current $1400bn of ER, that’s $28bn to pay as interest, which then are added to the current ER. If this is new money created by the Fed (is it?), then the monetary base is expanded by $28bn, which is already A LOT higher than pre-crisis ER levels.
    -> If banks judge sufficient their ER at their previous level, they will then lend out those $28bn, which through fractional reserves increase the money supply by a lot more.
    -> In order to increase the incentive to retain higher ER, the Fed then increases again the IOER, and so on.

    Would the short-term pressure on lending interest rate by increasing money supply be enough to reduce the opportunity cost? Not certain.
    On the contrary, the margin between lending rates and IOER might not reduce enough before inflation (or asset bubbles) kicks in and actually start pushing up nominal lending rates.

    2. Following Benjamin, I am also questioning the political ramifications of those IOER. Can the public really accept that banks earn “risk-free” income just by leaving their cash at the Fed instead of putting it to work in the real economy?
    And the situation is even worse if the money paid out as interest isn’t actually “created” by the Fed, but funded through tax or anything else.

  12. Gravatar of Rien Huizer Rien Huizer
    18. January 2013 at 06:12

    Benjamin Cohen,

    My sympathies. I am spending my retirement partly playing Golf (capital intended) and racking my brains about government an public policy. Monetary policy is part of that and Scott’s prescriptions are attractive for people who live under a regime where the gvt is supposed to care about the business cycle (in the sense of caring about unemployment etc not only about avoiding irreparable damage to institutions which I believe every responsible get should do). So I suppose that the US monetary authority, with its wide discretion, cloak of opacity and sympathetic politicians (they like a fall guy when they see one) could do with a more rational approach to policy, ie MM, although I am still in the dark as to what precisely the Fed should do. But Targeting NGDP is unquestionably the best policy under the complex mandate, only how to do it avoiding incentive problems etc is as yet a mystery to me.

    So what is the link to democracy/democratic paraphernalia? Democracy needs (as the ancient Greeks found out expensively) some form of scaffolding in order not to collapse/be perverted. In the US that may well need an opaque Fed; In Kiwiland, it may not. HOwever, imo the Fed could be much more communicative without limiting its policy space (important when you have discretion) but for some reason it is not. Which keeps a live a cottage industry of fed-watchers…

  13. Gravatar of Rien Huizer Rien Huizer
    18. January 2013 at 06:30


    The banks cannot lend all that much given current capitalisation, especially for banks subject to Basle III (The US has shot itself in the foot by allowing very large banks (Basle III subjects) to acquire high market shares – otherwise it would have had lots of market share in the hands of smaller banks only subject to US rules). Hence it is difficult to predict how much of that ER money is really available for a lending surge. My bet is that much of it is in the hands of the top ten. It depends how the manage their capital and lending may not be the most efficient way to do that. What will happen to those ER then is of course a very good question. Maybe useful to read Kazuo Ueda (JEP Vol 26 No 3 pp 177-202). Channels matter! The thing that made the Us different from everywhere else pre 2008 was the existence of an large shadow banking system (ie a system without formal supervision and capital requirements) Will that return? If so then yes there may be channels unaffected by bank capital rules. But otherwise, banbk capital constraints will impose transaction costs that may well make monetary expansion efforts less effective. In fisher terms: lover velocity for a given level of M, or a lower nominal M, despite Fed efforts to be Sumnerian.

  14. Gravatar of JN JN
    18. January 2013 at 06:55

    Rien Huizer,

    This is not entirely exact regarding capitalisation and Basel III. Banks could inject the new money into asset classes or customer types that require very low capital requirements. This is already what happened pre-crisis.

    Regarding the shadow banking sector, I personally don’t see it as a real threat. The shadow banking sector “transfers” money rather than “creates” money, unlike fractional reserve banks, limiting potentially destructive effects. But this is off-topic.

  15. Gravatar of dlr dlr
    18. January 2013 at 06:57

    Scott, I think in the last second of the next to last paragraph you meant to “exogenous over the long run.” Assuming I’m right, I think this is a funny typo, because it reflects maybe the key point of departure between you and the Woodford-style rate-centric view. I think the NK argument would be that even over the long run, money is most helpfully seen as endogenous for the same reasons you concede it might be somewhat endogenous over the medium run. I’m not actually how to best describe what underlies your view that the supply of base money relative to NGDP can be thought of as the *cause* of NGDP from a quantity theoretic perspective in the long run but not necessarily in the medium run when the Fed is manipulating demand via IOER.

    Sometimes you mention that a strict relationship is ultimately necessary to provide a nominal anchor. You like to ask, for example, why things cost 100X more in Japan than the US. I don’t find this a compelling reason to believe that the quantity of base money relative to NGDP ultimately determines NGDP. In my view, all you need for a nominal anchor is a starting point and a reaction function from an entity with influence over either supply OR demand. The starting point can be an accident of prior monetary regimes as long as some ultimate antecedent included a nominal anchor. The Yen/Dollar mystery can be seen as an accident of history as opposed to requiring a cause long run relationship between the monetary base and NGDP amid demand manipulation.

    The only genuine debate here is not Krugman versus Waldman which is all semantic except insofar as it is a prediction of how the Fed will implement an IOER policy in practice. The genuine debate is between Stephen Williamson and everyone else, since he plainly believes that changes in the monetary base are irrelevant *even if there is a spread between IOER and T-Bill rates.* This is essentially the MM argument or the Wallace neutrality argument. I am curious if there are other economists who also believe his perspective on this.

  16. Gravatar of ssumner ssumner
    18. January 2013 at 07:32

    C8to–I see the wage channel as strongest. Although I use W/GDP, not W/P.

    JN, The Fed would sterilize any effect of paying IOR on the base. So I don’t see that as a problem (although I oppose IOR for other reasons.)

    dlr, Thanks, I’ll correct the typo.

    I view the argument that OMOs don’t affect the price level at positive interest rates as being wildly at variance with the facts. I sometimes wonder if the proponents even know that during normal times 99% of the base is currency (including vault cash.) Do they really think that other assets are close substitutes? That defies common sense. Then you have evidence from market reactions to Fed policy changes. Then there is the evidence from the time path of base velocity and its determinants. And the other side has some abstract models with highly unrealistic assumptions. . . . and what else?

  17. Gravatar of Tyler Joyner Tyler Joyner
    18. January 2013 at 08:08

    For some reason I can’t submit comments with links in them, but there’s an article titled “Abe’s challenge” on the Foreignpolicy website you might enjoy, Scott.

    Here’s an excerpt:

    “… the new government has more or less merged fiscal and monetary policy by essentially bringing enormous political pressure to bear to force the Bank of Japan to achieve a 2 percent inflation rate through aggressive quantitative easing (QE) measures.”

  18. Gravatar of StatsGuy StatsGuy
    18. January 2013 at 08:25

    That is not the real question – the real question is whether we’re in a new world where the demand to save has permanently increased, such that the stock of money can be increased (to meet that demand) with the likelihood that the debt (or, nearly equivalently, currency) will never be called in at the aggregate level (e.g. we can print money to finance spending, and essentially never pay it back because the demand to hold the money will continuously increase).

    BTW, how is Krugman’s argument different? DeLong has been making the “exchange one zero-rate asset for another” argument since 2009?

    When, I wonder, will people start to engage the question about the expectation of permanency? I think they’re scared of touching it, because seignorage is such a dirty word.

  19. Gravatar of Tyler Joyner Tyler Joyner
    18. January 2013 at 08:33

    StatsGuy: Talk of new worlds and permanent changes in human behavior opens one up to making bad judgments, in my opinion.

    Presenting “can we continue to finance spending with debt and never experience any negative effects?” as a valid question is a pretty serious leap down the rabbit hole.

    What happened to “there’s no such thing as a free lunch”? It’s one thing to say lunch is the worth the price, quite another to call it free.

  20. Gravatar of vasja vasja
    18. January 2013 at 08:50

    Dear Scot,

    My question relates to C8to’s question. If the wage channel is the strongest then how effective is the monetary policy’s “wage transmission channel”, in the crisis? I understand that in normal times lower real wages give incentives for companies to hire, but would they also decide to hire in a situation when there is huge lack of demand? Considering that production (and therefore hiring) is currently demand determined more competitive wages can not help much if the demand is constant. Shouldn’t we be more focused on getting the demand up? I don’t mean through fiscal stimulus, that is only temporary, but through affecting consumer expectations rather.

    Thank you!

  21. Gravatar of ssumner ssumner
    18. January 2013 at 14:39

    Thanks Tyler.

    Statsguy, I’ve talked a lot about how very low rates are the new normal—but I still haven’t accepted the fact that we are so stupid that near-zero rates are here forever. But maybe someday I’ll have to bite the bullet and admit “Yes, we are that stupid.” If I lived in Osaka I probably would have already bit the bullet.

    Vasja, You are mixing two issues, how does NGDP get increased, and how do increases in NGDP create jobs? The wage channel explains the second, you are right that you first need more demand–that’s the first part.

  22. Gravatar of Rien Huizer Rien Huizer
    19. January 2013 at 07:15


    “This is not entirely exact regarding capitalisation and Basel III. Banks could inject the new money into asset classes or customer types that require very low capital requirements. This is already what happened pre-crisis.”

    Yes of course but those asset classes are not necessarily the right channel to reduce borrowing costs for borrowers with weak bargaining positions. That was execactly the problem in Japan. The ones that got credit did not need it and the ones that needed it, went out of business or shrunk. It is possible that with the very high Basle III requirements that the major banks will be subject to (not very different from what rating agencies imposed on asset based lenders in the late 1990s)there will be an evolution of lending on purely commercial terms. However, the literature about purely commercial lending (ie not backed by implicit gvt guarantees and without access to a got supported banking system) indicates that such entities have very high degrees of pro-cyclicality (ie prone not to survive a crisis without substantial pro-active portfolio management) I wonder how such entities (shadow banking commercial/residential lenders) can get airborne in the current environment. Anyway, the future will tell.

  23. Gravatar of RebelEconomist RebelEconomist
    20. January 2013 at 01:46

    @Benjamin, if only you could be a fly on the wall of a central bank! There as many inflationists in central banks as anywhere else – which is one thing that has gone wrong with monetary policy if you ask me. Central bankers tend to benefit disproportionately from inflation, being income poor and property rich, and their pensions are generally index-linked. The BoE pension fund is infamous for being abnormally long of index-linked gilts.

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