Steering Interbank Rates under the Aggregate Liquidity Management Model

The aggregate liquidity management model gave us the following equation for what determines the interbank rate:

Equation A: i_t = i_B*(P) + i_D*(1-P)     

where i_t is the interbank rate, i_B and i_D are the expected standing facility rates at the end of the maintenance period, P is the probability of recourse to the borrowing facility, and (1-P) is the probability of recourse to the deposit facility.

I used Equation A to create the following table, which describes the central bank’s policy options for changing interest rates. This is not in Bindseil’s book, but it directly follows from Equation A, and I think it is a nice way to condense the equation’s implications. Each cell is the result of keeping constant, changing, or not controlling some combination of the variables in Equation A.

The columns represent the central bank’s options for controlling the standing facility rates i_B and i_D  The CB can either actively change them over some period of time, leave them constant, or not even provide them. The rows represent how the CB can impact the probability of recourse to the standing facilities, which is done through OMOs. Similarly, the CB can either actively change them over some period of time, keep them constant, or not intervene at all. Note that keeping P constant isn’t exactly analogous to keeping the standing facility rates constant. To keep the facility rates constant, the CB does not have to do anything more than leave them at some stated rate. In contrast, to keep P constant, the CB will have to be constantly responding to liquidity shocks and changes in the market’s perceived probability density function of recourse (see Appendix) via OMOs.

Below, I explain each policy option one-by-one. Before doing so, I’d like to note the middle cell, which reads “static rate.” I’ve greyed it out since this policy option actually isn’t a viable way for the central bank to change rates. If the CB keeps i_B, i_D, and P constant, then the interbank rate is therefore constant. As such, you can think of this option as what the CB does when it wants to stabilize rates. All the other options are ways for the central bank to change rates.

Symmetric Corridor

I’ll start by explaining the ‘symmetric corridor’ approach to steering rates, which is employed by the ECB (Bindseil’s central bank) among many other central banks, and is arguably the easiest to understand. The idea behind this approach is that the interbank rate will be the average of the standing facility rates, and if the central bank wants to alter the interbank rate, all it does is change the standing facility rates in parallel. Examining Equation A, we can see there are two key ingredients to making this happen:

1. Maintaining P = 50% at all times via OMOs
2. Set i_B and i_D such that the average of the two rates, i = (i_b+i_d)/2, is equal to the target rate.

Using our simple model of B – D = M – A, then to achieve (1), the central bank just needs to set M equal to expectations of A, assuming the probability density function of A is symmetric (see Appendix). Since we assume that in the short-run, A is exogenous and thus independent of the target rate (empirically a reasonable assumption), then all a rate change entails is changing rates, not quantities! Bindseil on the rates versus quantity debate: 

“Thus the volume of outstanding open market operations is not affected by a change in the stance of monetary policy, which is of course the opposite of what proponents of reserve position doctrine had in mind.”

Adding some balance, Bindseil also critiques people more likely to be on the rates side. He writes that even though “OMOs are not relevant to implementing a change of market rates under the symmetric corridor approach… [this] has nothing to do with the idea of ‘open mouth operations’ made popular by Guthrie and Wright (2000). To change market rates, it is indeed not enough for a central banker to open is or her mouth, but the central bank needs to effectively adjust rates of standing facility in relevant reserve maintenance period.” And I’d also add the central bank will need to continue to monitor A: if the density function of A changes away from being symmetric, this will require a change in the quantity M. As noted above, however, we wouldn't expect this to occur from the rate change itself.

Here’s a graphical representation of the symmetric corridor approach, which I take from this Fed paper. I’d recommend reading that paper, with the model presented here in mind. They use many of the same qualitative explanations as Bindseil, but with their own spin, and indeed state that they are also coming from the Poole (1968) lineage. I had read this paper before but didn’t completely understand it. Now with Bindseil’s models in mind (particularly the liquidity shock model), it’s quite clear .

Floor/Ceiling System

The floor/ceiling system is similar to the symmetric corridor system in the sense that P is kept constant and the interbank rate depends only on i_B and i_D. The main difference is that P is now pegged to either 0% or 100%, such that the interbank rate will be either i_B or i_D. Monetary policy in the U.S. currently is a floor system. Banks are flush with so many excess reserves that the probability of recourse to the deposit facility is virtually 100%.  As such, the interbank rate is near the interest rate on deposits at the central bank’s deposit facility (it differs a bit due to some market and institutional irregularities that aren’t important here). Here is an illustration from the aforementioned Fed paper:

Note that there is now a range of quantity M that can drive the interbank rate to floor, in a sense “divorcing money from monetary policy,” as that paper states. This is different from the symmetric corridor, where there is a particular value M that needs to be set for P to equal 50%. I would argue, however, that the symmetric corridor approach also divorces money from monetary policy, in the sense that a range of rates can be achieved with the same quantity M. This was explained above, with Bindseil using it as argument against monetarist-style thinking.

The ceiling system is something I came up with - or at least I haven't seen it explicitly discussed elsewhere (see comment section below. Also, Bindseil notes that this approach was practiced by the German Reichsbank from 1876 until at least 1914). Theoretically, you could make it certain that banks would end up short of reserves at the end of the maintenance period, such that the interbank rate equals the borrowing rate. I am not sure if this has ever been implemented, but it seems theoretically possible.

Asymmetric Corridor

I am actually not sure if “asymmetric corridor” is a widely accepted term, but I’ll proceed with the following definition: there is a fixed spread between the interbank rate and borrowing facility rate, but the deposit facility rate stays constant. An example of this was the U.S. prior to the 2008, where discount window loans were some fixed spread above the target interbank rate, but there were no interest on reserves (i_D was fixed at 0%). As such, the distance between the floor and target rate would change if the central bank changed its target rate. Here’s a graphical illustration of this, although the linkage between the target rate and the ceiling is not made explicit:

In order to change the interest rate under this system (again assuming the ceiling is tied to the target rate), all variables in Equation A would have to change. For instance, suppose the target interbank rate was 5% and the spread to i_B was 1%. In this case, i_t = 5%, i_D=0%, i_B=6%. Examining Equation A, then then P would have to equal 5/6 to achieve the target rate of 5% (6%*5/6 + 0%*1/6 = 5%). Suppose the CB then changed the target rate to 4%, such that i_B would now equal 5%. In this case, to achieve that target, P would have to be equal to 4/5 (5%*4/5 + 0*1/5 = 4%). To change P from 5/6 to 4/5 requires the Fed to alter liquidity conditions in the market by changing the quantity M via OMOs (presumably by soaking up a bit of reserves to make them a bit more scarce).

Other Theoretical Systems

One could imagine a variety of other theoretical systems by mixing and matching the various combinations in the table.

Suppose the standing facility rates were held constant but P was allowed to be manipulated through OMOs. If the borrowing rate was detached from the interbank rate, in contrast to the example above, then rate changes could be achieved by just varying P through OMOs and leaving the standing facility rates constant. This would be a pure quantity-oriented approach to rate changes, assuming that the corridor would be wide enough for the central bank to enact a range of rate changes. You can refer to any of the above graphs to imagine this, whereby the bank would be changing quantity to move rates along the demand curve.

Another theoretical approach would be to set P at some value other than 50% (which pegs rates at the corresponding position within a given corridor), and rate changes could be implemented by changing the floor and ceiling. This would be similar to the symmetric corridor approach, except that P would not equal 50%. The added challenge here is that the central bank has to be more in tune with the actual shape of the probability density function to get M such that P will equal 30%. With the symmetric approach, the central bank just cares if the distribution is roughly symmetric through time, allowing it to set M equal to expected A. Here, it’s more complicated since the higher order moments of the density function constantly matter for the central bank to attain the proper value of M.

Here’s a pure rates oriented approach. Suppose the central bank doesn’t conduct OMOs at all, and thus doesn’t exert influence on P. The CB could still control i by setting i_B and i_D to the proper levels given the market’s perceived value of P without OMOs.

Bounded Volatility

If the central bank left the standing rates constant but didn’t intervene in markets with OMOs, then P would fluctuate based solely on market conditions. As a result, i would fluctuate within the corridor set by the standing facilities.

?

I’ve labeled instances where the central bank does not provide a standing facility with a question mark. What I had in mind initially was that the CB does not offer a borrowing facility, thus abandoning their ‘lender of last resort role.’ As such, the central bank is not placing a ceiling on rates, which greatly increases the potential for high volatility and bank failures. A passage from Bindseil’s book applies here:

“This is in line with Bagehot’s (1873: 58) early insight regarding the inherent instability of money markets to the effect that only the central bank could limit the implied volatility of rates, for instance by offering standing facilities...”

One big question mark exists, however, which is that we need to define what happens at the end of the maintenance period if a bank does not have sufficient reserves. If the rule is that the bank gets shut down, then rates indeed would likely be highly volatile. But this seems like a ridiculous hypothetical to me. More plausible is that there’d be some sort of costly penalty instead. But in that case, we’re essentially back to a borrowing facility, which really is just a penalty.

All this is to say that the right column may not be a very useful construct if we’re thinking about a central bank in the first place. But it’s interesting in the sense that, at least for me, it drives home the message that the ‘lender of last resort’ function is a fundamentally core feature of central banking – practically inseparable. I can almost imagine a central bank that doesn’t conduct OMOs more easily than one that doesn’t provide standing facilities. Perhaps more on this in a future post on rates versus quantities.