Tuesday, 22 April 2014

"Asymmetric Redeemability" in Woodford's Cashless Economy

I've had a few exchanges recently on the question of what gives the central bank the ability to set interest rates, including on Nick Rowe's most recent post.

The discussion prompted me to read Woodford's paper Monetary Policy in the Information Economy in which he discusses various possible implications of improvements in the efficiency of the use of monetary base.  The paper includes an excellent analysis of the operation of a corridor system and the role of rates and quantities in such a system.

Woodford also considers how the central bank might set rates in a world where its liabilities had no useful function beyond any interest rate paid on them.  Normally, central bank liabilities have other uses.  Currency has a convenience value; reserves are used in clearing.  Woodford wants us to think about what might happen if currency became obsolete and where clearing had became so efficient that reserves were no longer needed (assuming also that there are no mandatory reserve requirements).

He explains how this might work through an arrangement whereby there is a small aggregate positive balance held by commercial banks with the central bank.  The central bank would decide what rate to pay on this balance and Woodford shows how this would then force all commercial banks to base their rates around this benchmark.  The balances that commercial banks hold with the central bank in this system are functioning just like any other interbank balance.  They have no longer have any special role in clearing.

Woodford says[1]:

"Why should the central bank play any special role in determining which of these outcomes should actually occur, if it does not possess any monopoly power as the unique supplier of some crucial  service?  The answer is that the unit of account in a purely fiat system is defined in terms of the liabilities of the central bank."

I don't actually like the idea that the dollar is defined by central bank liabilities.  We can certainly make various observations about the relationship between liabilities of the central bank and those of commercial entities, including about the legal and commercial obligations over the rate at which liabilities get exchanged.  But there isn't anything beyond that.  There isn't anything additional to those relationships that constitutes defining the dollar (and I'm not sure those relationships themselves actually constitute defining the dollar), so I don't really like the introduction of this concept.

That said, Woodford goes on to specify one of the most important of such relationships.  This is (from above) that "[a] financial contract that promises to deliver a certain number of U.S. dollars at a specified future date is promising payment in terms of Federal Reserve notes or clearing balances at the Fed...".  The important points here are that, if another party (bank or non-bank) holds a balance at Bank A, a) it can require Bank A to deliver obligations of the Fed as settlement; and b) it is entitled to receive such obligations at par (dollar for dollar).

It is worth noting that as a commercial matter, banks also undertake to settle by delivery of claims on other banks.  If I have money with Bank A, I can ask Bank A to pay into may account at Bank B.  This is economically equivalent to Bank A depositing money with Bank B and then transferring title to that deposit to me.  However, once Bank A has committed to delivering Fed obligations at par, it is no more onerous to also undertake to similarly deliver claims on other banks.

In order for the central bank to be able to set rates, is it sufficient that other banks commit to an either-way exchange of central bank liabilities for their own liabilities?  In fact, whilst this is critical, slightly more is needed. 

To see this we need to understand what the equivalent provision would mean if applied to the central bank.  Let's imagine that everything is in equilibrium with interest rates at 5% and the central bank then decides to lower its deposit rate to 4%.  At this point, anyone (bank or non-bank) holding deposits with the central bank would (if they could) require the central bank to settle that deposit by delivery of a claim on another bank (paying 5%).  In Woodford's scenario, this would rapidly lead to all of the outstanding central bank liabilities being extinguished, whereupon the rate on them would be meaningless. 

It is therefore critical that the central bank does not undertake to redeem its deposit liabilities by delivering claims on other banks.  If a commercial bank wishes to reduce its balance with central bank, it must do so by lending the excess out.  This is what forces the rates of all the other banks into line.

The fact that the central bank will not redeem its deposit liabilities in this way, when the commercial banks must do so is what Nick Rowe calls "asymmetric redeemability".  In one form or another, it is essential to a central bank's ability to set interest rates.  Normally, we do not notice it, because things like currency are by their very nature irredeemable and so it seems odd to even frame the question that way.  In Woodford's hypothetical scenario, where balances with the central bank are otherwise no different from all other interbank balances, it's easier to see.

[1] It was this section, quoted by PeterN in a comment on Nick Rowe's post, that prompted me to read this paper.


  1. From a Functional Finance/MMT perspective, the dollar is defined in terms of taxing power. I am unfamiliar with Institutionalism, but I think they would add in the web of private sector obligations that are defined in money terms. Without those liability structures, small currencies would probably disappear.

    And it seems that Woodford's analysis is way more complicated than it needs to be (I glanced at it quickly). The fact that the central bank can set interest rates if they pay intest on reserves seems a straightforward arbitrage relationship for the banking sector, since the private sector banks can only reallocate those assets amongst themselves.

  2. Yes, I think that there might be various ways of defining the dollar. It's more a question of the approach you want take, rather than it being an objective fact. That's why I don't think it helps to bring it in - I don't think it explains anything.

    I wasn't attempting here to cover everything Woodford was saying; just how it relates to this asymmetry point. In some senses, I agree that it is simple; in others, perhaps not. After all, one of his main points - about the unimportance of quantities - is not straightforward and certainly not generally agreed upon.

    1. Upon further reflection, I realise that I was thinking of "defined" in a broad sense, as in "the value of the currency is operationally defined by the taxing authority of the state". In the sense of a narrow technical definition, I accept that the currency can be defined as a central bank liability - it's a definition in terms of a unit of account. (I blame the broken iPad commenting interface to Blogger. It's nearly impossible to review or edit what I write.)

      What I was reacting to was the notion that this being associated solely with the central bank. The unit of account has also to be tied to the taxing authority; e.g. the currency is a unit of account for taxes.

      For example, the Bank of Canada could define a new unit of account, the "Polozoon". The Polozoon could be supported with a payments infrastructure similar to that of the Canadian dollar. But nobody would be interested in it, other than note and coin collectors (if banknotes were created.) Since the Polozoon would not be tied into taxation liability network, it would have no economic function, no matter what rate of interest the Bank paid on Polozoon balances.

      Private sector entities could also try to create new units of account - e.g., bitcoin. But since every transaction has to be re-denominated into the local currency for tax purposes, and taxes have to be remitted in local currency, there's not much chance it will be adopted for domestic legal transactions.

      Since all banks' liabilities are denominated in the same unit of account. I am unsure about the notion of redeemability. If I did some work for the Bank of Canada, their payment would end up deposited in my commercial bank account. As far as I am concerned, their legal obligation to me was discharged in form of a deposit at a commercial bank.

    2. I think you potentially could define the dollar a number of ways, but my point was that it doesn't really help the explanation of why the central bank can set rates. You need to look at the actual operational mechanics, in particular who agrees to exchange what and in what manner. If someone wants to say that that is what constitutes defining the dollar, the fine, but it doesn't help to just say the dollar is defined in terms of central bank liabilities. To me that just begs the question.

      So, my preference would be to forget the idea of defining the dollar and just stick to the question of who can set rates and why they can do so and no-one else. And I think you'd agree that it is the central bank, rather than the taxing authority, that sets rates.

      That said, I agree with you that the question of why the dollar has value and is widely used is a much wider one. In my view, the value derives from the demand for dollars from people who must obtain them to cover liabilities falling due. On the back of this demand, others will hold dollar denominated debt as store of value. Bitcoin might also be a store of value, but without the end game of the demand from those with debts to settle it is far more fragile. Clearly, a material part of the liabilities people need to meet with dollars are their tax liabilities, which gives the taxing authority a strong position in this game.

      What people choose as the unit of account follows from this. Given the existing extensive network of dollar denominated claims, including crucially as you say the need to pay taxes in dollars, it could hardly be anything else.

  3. There's possibly a good short paper lurking inside the Woodson paper.

    Improved cash management by the banks is not really an issue. Banks need to hold
    Iiquid governmemt liabilities because it would be crazy to trust banks or the banking system in aggregate. If banks only hold private sector liabilities, they are vulnerable to a run on the system, such as we saw in 2008. Since these government liabilities are entwined with the banking system, the central bank always has the leverage to set the interest rate.

    1. I agree that it is sensible to require banks to hold high quality liquid assets, so even in the absence of material reserve holdings, they should be holding suitable amounts of government debt. When you say that the central bank always has the leverage to set the rate, I'm not sure if you mean even if there was "symmetric redeemability" on central bank liabilities.

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    3. The server for Nick Rowe's article was down, and so I did not see exactly what he meant about asymmetric redeemability. I had only looked at the Woodford article.

  4. I'm not following the adjustments in balance sheets implied by your last three paragraphs, but perhaps it's because I haven't been following the 'asymmetric redeemability' discussion.

    "Let's imagine that everything is in equilibrium with interest rates at 5% and the central bank then decides to lower its deposit rate to 4%."

    To be clear, what interest rate are we discussing? I would presume the rate on central bank reserves?

    "At this point, anyone (bank or non-bank) holding deposits with the central bank would (if they could) require the central bank to settle that deposit by delivery of a claim on another bank (paying 5%)."

    What do you mean by this? Bank A instructs the central bank to move its reserves from its central bank account to Bank B, where it receives Bank B deposits in return? So Bank A assets are now deposits at Bank B instead of deposits (reserves) at the commercial bank. But Bank B still holds the reserves at the central bank, no?

    1. Sorry, meant: "So Bank A assets are now deposits at Bank B instead of deposits (reserves) at the central bank."

    2. With rates at 5%, I am assuming that is the rate the central bank pays on balances held with it, and that the interbank rate is then also 5%. I'm then assuming that the central bank reduces its rate and considering whether the interbank rate follows.

      On the payments, I mean that the central bank is required to pay into Bank B for Bank A's account, but not by transferring the reserve balances. So the Bank A's reserve balance is simply extinguished and the central bank either has to borrow from Bank B on Bank B's terms (or from any other bank) or sell assets. That is, Bank B is not required to accept the reserves in payment. So it's like the reserves were just a regular interbank balance.

      Of course this not what normally happens with reserves, which is why the reserves don't get extinguished and why they are not therefore like other interbank balances. Which is an essential part of the central bank's ability to set rates.

  5. Short comment. I am not really a fan of this irredeemability thing. Whatever looks like irredeemability is just an aspect of the fact that the government is typically the most creditworthy resident economic unit/borrower. In recent times Turkey had problems with its balance of payments and financial markets forced the hand of the central bank. That had nothing to with whether the central bank redeems or not.

    1. "I am not really a fan of this irredeemability thing."

      I take it you mean you don't like this way of analysing things, rather than that you think central bank liabilities should be redeemable. I don't know enough about the Turkey situation to say whether I think an asymmetric redeemability analysis would be appropriate. But I'm not sure that comparing relative creditworthiness alone is enough to address the question of how it is that the central bank can set rates.

      I'd also say that I'm not sure there are many real operational consequences of all this. I just find it useful as a way of helping expand my perspective on the relationship between things.

    2. I am not saying it should be redeemable but that the the high creditworthiness of the government is what makes look some liabilities as "irredeemable", rather than the other way round. These liabilities which are supposedly irredeemable are not truly irredeemable first in the sense that they cannot be issued in high amounts without there being a demand for it.

      The reason I mentioned Turkey is that the power of the government does not allow it to set interest rate unilaterally under all circumstances. In general it can set the short term rates and in one sense it is exogenous that it is set but endogenous in another sense that it depends on market conditions, although needn't be market determined.

      In a formal way, all I can say is that if one writes a model with Tobin's asset allocation included, one can see that short interest rates can be chosen under reasonable circumstances and so on but all this needs to be qualified. So the question of interest rate setting really has less to do with "irredeemability".

    3. Yes, I agree that the monetary authority might be constrained in how it sets rates if it is trying to achieve other objectives. On the whole those objectives will dictate how it sets rates. However, I think that when we say here that the central bank has the power to set rates, it is more a question of whether or not the interbank rates will track the rate set by the central bank on its own liabilities.

      Whilst I find the standard Tobinesque asset allocation approach very useful, as you know, I don't think it can deal with this question. In this instance, in particular, we are considering a case where the central bank is able to control the interbank rate, even though its liabilities are negligible.

    4. I think it can be done although it may become complicated on paper. This can be done by switching the amounts of bond sales between bills and bonds etc. Will try sometime.

      The case of negligible liabilities can be addressed by taking limits on reserve requirements and cash holding preferences hopefully.

      The reason I mention creditworthiness is because the asset allocation parameters can be thought of as being dependent on creditworthiness, so other debtors may have to pay more to raise funds they need.

      Also consider the case where official creditors can redeem liabilities. This can actually be seen more via using asset allocation models, so redeemability has less to it. It is like it is an effect not cause.

    5. I've read this several times, but I'm afraid I don't think I quite see what you're saying.

      I think if you were using Tobin here, you'd have to set out a matrix with the central bank and commercial banks each holding some form of balance with the other. You might also need to disaggregate the commercial banks, or at least represent them as unconsolidated so you could include interbank balances.

      You would then want to consider the behavioural relationships. Clearly there must be some difference here between the central bank and any commercial bank, so then it's a question of understanding what that difference means. In particular does it amount to the same thing as this asymmetric redeemability? I think it must.

  6. Nick: I think I am with you here.

    "I don't actually like the idea that the dollar is defined by central bank liabilities."

    I didn't like that bit either. I think it is asymmetric redeemability that does the defining.

    1. Put it this way: I don't see Woodford saying anything that contradicts the idea of asymmetric redeemability being what defines the dollar and giving the central bank its power. And if I squint a bit, I can interpret him as implicitly assuming asymmetric redeemability.

      Trouble is, AR only works if there does exist some central bank liability for which commercial bank liabilities can be redeemed.

    2. Yes - I think he is implicitly assuming AR, but then I think most people implicitly assume AR, which is perhaps why they find it hard to see why it matters.

      I agree it only works if there is actually some central bank liability. The same applies to Woodford's basic point as well really. There has to be a central bank interest rate and you can't have an interest rate on nothing. (Which reminds of the striker's banner: "2% of nothing is nothing. We want 4%.")

      So the central bank liabilities can be very small, but not nothing. Practically, I think it simply needs to be big enough for people to bother about. If total reserves were $10 and the central bank cut the rate by 1%, no-one would bother doing anything about it.

    3. "So the central bank liabilities can be very small, but not nothing."

      Does this amount to a multiplier of some kind then? (akin to the infamous "money multiplier")

    4. In a sense. What is the minimum amount you need to have in a bank deposit account to be bothered to move it if the rate was cut to 1% below that of other banks? How does that minimum amount relate to your net financial worth? It's probably true that the bigger the latter the bigger the former, so there's some kind of multiplier there. Whether that's a useful relationship is another matter, but then some people would say the same about the money multiplier.

    5. Maybe, it's not a question of how big or small the monetary base actually is, but how big or small it could be, if the central bank decided? (including negative values??) I'm not sure.

    6. Nick; "...but then I think most people implicitly assume AR, which is perhaps why they find it hard to see why it matters."


    7. The whole AR analysis should work even if you are considering a system where the central bank was operating through a "negative" monetary base, but I'd have to think about it to work it all out. I'm not sure "redeemability" would be the appropriate term.

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  10. Nick Edmonds, I updated my interactive version of your last simulation (I kept the old one beneath it). Now I have more plots, six iterations per time step, all the parameters are available for editing, and the solution itself fits on a single page. If you were to download it and unhide all the rows and columns though, it would not be so pretty. The autoscaling on the plots sometimes has a problem: I blame the hidden rows.


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