"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.

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

Eggertsson & Mehrotra and SFC Models

I'm very interested in the new paper from Gaudi Eggertsson and Neil Mehrotra (E&M) on secular stagnation.  What they have done is to adapt a simple overlapping generations model like Samuelson's consumption-loan model so that the financial asset is represented by a corresponding liability of other agents in the model.  This is very similar to something I myself posted on recently, but whereas I used land purchase as the motivation for private borrowing, they have households borrowing to finance consumption ahead of earning income.

I have reservations about some of the things they have done in this paper but, on the whole, I like it.  I think this sort of approach with differentiated borrowers and lenders is key to understanding the dynamic role of debt.

Other are less impressed.  Amongst various criticisms (some of with which I'd agree), Unlearning Economics dislikes the apparent omission of banks and believes that a stock-flow consistent (SFC) model would be preferable.  I find this quite interesting, because as far as I can see there are no stock-flow inconsistencies in their model and I can imagine a simple SFC model with banks that would be structurally identical to what E&M have produced.  So, I thought it would be useful to recast E&M's basic model in some more heterodox language. 

E&M don't talk about banks.  However, there is an important structural element in there where I think that banks fit the story quite well.  They are vague on the story, which is OK because it doesn't have to involve banks - it's a more general point.  But I'm going to use banks in my description.  (Note that, as a result, some of my variable names do not correspond to theirs)

So, in this model households live for three periods, then they die and are replaced by new households.  They consume in each period, but only work and earn in the middle period.  They therefore need to borrow to fund consumption in the first period and to save to pay for consumption in the second period.  Borrowing takes the form of loans from banks and savings take the form of bank deposits. 

The balance sheet at the end of each period, after the old have spent their savings, is as follows:

	Young	Middle Aged	Old	Banks
Loans	- L			L
Deposits		M		- M

In each period a number of things are going on.  The young are borrowing from banks to fund consumption spending.  The old are funding their spending by drawing down their deposits (together with interest).  The middle aged are earning wages*, spending on consumption and repaying with interest the loans they incurred when young.  As they are spending less than they earn, they are also accruing deposit balances.  Banks are assumed to pay the same rate of interest on deposits as they charge on loans.  All this is shown below:

And more formally, in a flow of funds matrix.

	Young	Middle Aged	Old	Banks
Wages		W
Loan interest		- Lt-1 . rt-1		Lt-1 . rt-1
Deposit interest			Mt-1 . rt-1	- Mt-1 . rt-1
Consumption	-Cy	-Cm	-Co
Loans	L	- Lt-1		- ( L - Lt-1 )
Deposits		- M	Mt-1	M - Mt-1

Every row and column here sums to zero, providing a budget constraint for each cohort.  These correspond to equations (1), (2) and (3) of E&M.

The spending behaviour of the young and old is dictated by their budget constraints.  The middle-aged have to choose between how much to spend and how much to save.  E&M derive this decision from some assumptions about household utility functions, but it turns out that middle-aged consumption can be given by:

                C^m = α₁ . ( W  -   L_t-1 . r_t-1 )  -  α₂ . L_t-1              with α₁ = α₂

Interestingly, the current interest rate doesn't factor into this, because with the utility function E&M use, the income effect and the substitution effect cancel out.  The equation for aggregate consumption (taking into account that L = M) is then of the form:

                C = α₁ . W  +  α₃ . M_t-1 . r_t-1   +  α₄ . M_t-1  +  L        

This looks very similar to the sort of function you might see in a standard SFC model, and indeed it does generate steady state stock-flow ratios. 

It is a critical feature of this model that banks make independent lending decisions.  In other words, the decision by middle-aged about how much to save is not the same as the decision about how much is loaned to the young.  So we need a separate way of determining how much banks want to lend.

We could do this by modelling profit-maximising banks and things like asymmetric information, but is not really warranted by the model and is probably unrealistic anyway.  The best approach I think, which is the one taken by E&M, is to put it down to what can best be described as animal spirits.  The level of bank lending is therefore treated as exogenous.

Although the lending decision and the saving decision are independent, the accounting dictates that loans and deposits will be equal.  The actual amount of deposits that the middle-aged accumulate is determined by the extent of lending.  For a given interest rate, it is the level of consumption spending that has to change to ensure that they are saving as they intend.

E&M want to use the model to explain secular stagnation.  I would agree with Unlearning Economics that there it doesn't have enough going on to do that.  I also think that the way the interest rate is working within this model is unusual and they should say more about that.  However, I believe that the basic model they have constructed here involves very much the sort of approach that I think is needed to address this issue.

Even though they do not use the same language, their model actually incorporates features, like stock-flow consistency and the direction of causation between lending and saving, that are key elements of a post-Keynesian approach.  There is more than enough disagreement between economists on methodology, so it's nice when seemingly different approaches are in fact quite similar.

[edited for a typo in the FoF matrix spotted by dsquared]

* In E&M's basic model, the middle-aged just get an endowment, but since this must equal total consumption, I've just tied it in to income from production.