Recently, there has been a great deal of discussion about paying interest on excess reserves and the corresponding implications for money and monetary policy. While much of this discussion has been interesting, it might be useful to consider the impact of the influence of paying interest on reserves in the context of an explicit macroeconomic model so that we might better understand the dynamics of the effects of such a policy. In addition, a model allows us to be explicit about the assumptions that we are making and also to keep are logic consistent. Fortunately, we do not need to start from scratch on this topic as Peter Ireland has written an excellent paper entitled, “The Macroeconomic Effects of Interest on Reserves.”
Before we discuss the impact of paying interest on reserves, it might be beneficial to talk about how this impacts the market for reserves using a straightforward supply and demand analysis, as Ireland does. Consider a simple supply and demand graph with the interest rate on the vertical axis and the quantity of reserves on the horizontal axis. Typically, in the market for reserves, the demand for reserves is a standard downward sloping demand curve. This is because a higher federal funds rate means that there is a higher opportunity cost of holding reserves rather than lending them to banks. If the Federal Reserve sets a target for the federal funds rate, the supply curve is horizontal at that interest rate. Where the supply curve intersects the demand curve is where one gets the unique quantity of reserves necessary to clear the market. One can therefore think of the Fed as providing the quantity of reserves necessary to maintain its interest rate target.
Now let’s suppose that the Fed starts paying interest on reserves. In this case, the supply curve remains the same (horizontal at the federal funds rate), but the demand curve changes. In particular, with demand curve for reserves is now downward-sloping for all rates above the interest rate on reserves. At the interest rate on reserves, the demand curve is horizontal. Why? Suppose that the federal funds rate is above the interest rate on reserves. In this case, an increase in the federal funds rate, holding the interest rate on reserves constant, causes a reduction in the demand for reserves. In other words, when the federal funds rate is above the interest rate on reserves, the opportunity cost of holding reserves is now the spread between the federal funds rate and the interest rate paid on reserves.
So why do people think that money doesn’t matter in this context? They think that money doesn’t matter because when the federal funds rate target is equal to the interest rate on reserves, the supply curve is horizontal at the same interest rate at which the demand curve is horizontal. This implies that there is a continuum of values for reserves that can be an equilibrium.
Unfortunately, this is where most of the debate stops in the blogosphere. Those who think that money is irrelevant point to this latter result and conclude that any quantity of base money is consistent with equilibrium and therefore the actual quantity doesn’t matter. However, as Ireland notes, this leaves many questions unanswered:
[The preceding analysis ignores] the effects that changes in output, including those brought about in the short run by monetary policy actions themselves, may have on the demand for reserves. And to the extent that changes in the interest rate paid on reserves get passed along to consumers through changes in retail deposit rates, and to the extent that those changes in deposit rates then set off portfolio rebalancing by households, additional effects that feed back into banks’ demand for reserves get ignored as well. One cannot tell from these graphs whether changes in the federal funds rate, holding the interest rate on reserves fixed either at zero or some positive rate, have different effects on output and inflation than changes in the federal funds rate that occur when the interest rate on reserves is moved in lockstep to maintain a constant spread between the two; if that spread between the federal funds rate and the interest rate on reserves acts as a tax on banking activity, those differences may be important too.
The point of developing a corresponding macroeconomic model is to fundamentally assess whether or not these hypothesized effects are of any significance. To do so, Ireland extends a New Keynesian model to have a banking system and a shopping time specification to motivate the use of a medium of exchange. Since this is a large scale model and this is a blog post, I will spare further details of the model and refer interested readers to the paper. However, I would like to discuss what Ireland finds as it relates to the discussion among econobloggers (there are more results that are of interest as well).
First, and perhaps most importantly for the blogosphere discussion, Ireland’s model demonstrates that even if they pay interest on reserves, the Fed still has to use open market operations to adjust the supply of bank reserves in order to change the price level. In other words, not only does the monetary base remain important, it is still necessary to pin down the price level. Second, there are important implications for how the Fed conducts open market operations. Specifically, in a world without interest on reserves, when the Fed raises its target for the federal funds rate it correspondingly reduces the supply of reserves. However, in Ireland’s model, the impulse response function for reserves following a change in monetary policy is just the opposite. In his model the central bank would have to increase bank reserves in response to a tightening of monetary policy as a result of an increase in the demand for reserves from banks, which in turn are caused by the portfolio reallocations of households. This is because a contractionary monetary policy causes a reduction in the user cost of deposits, which raises the demand for deposits and thereby the demand for reserves.
As noted above, there are other results of interest and I would encourage anyone who wants to have a serious discussion about interest on reserves to read the paper in its entirety. Nevertheless, just to summarize, the importance of Ireland’s paper is to present an explicit macroeconomic model that allows us to talk about the short-run and long-run behavior of the monetary base when the Fed pays interest on reserves. The implications of his model is that the monetary base is important in both the long- and short-run. In the short run, the Fed has to adjust the supply of bank reserves in accordance with their desired interest rate target. This response differs depending on whether interest is paid on reserves, but in either case, this behavior is necessary. In addition, and most importantly, the nominal stock of reserves is essential for influencing the price level in the long run. In other words, the monetary base is not irrelevant.
The Everyday Economist 
Ireland’s paper is quite well-executed, but the particular result you’re describing (and its apparent contradiction with blogospheric conventional wisdom) is due mainly to a particular modeling trick, plus some differences in interpretation, not any fundamental insight of the model.
In particular, in equation (29), we see that providing real deposit services requires a CES aggregate of labor and reserves. Since the elasticity of substitution here is above zero, if the Fed tried to push the IOR rate up until it equaled the market interest rate, it would have to inject *infinite* base money through OMOs. (Bank demand for reserves is a function of the spread, and in the absence of other costs would approach infinity as the spread approaches zero.) To avoid this, Ireland puts in an ad-hoc cost of managing reserves, so that the base is bounded even if IOR = FFR. (where by “FFR” I mean the market rate)
This means that as long as the Fed is trying to hit IOR = FFR, it will have to consciously adjust the quantity of base money in the banking system. If it keeps targeting a certain IOR but fails to adjust the quantity of base money in response to macroeconomic conditions, including the price level, then FFR will move away from the target in one direction or the other (could even go below IOR if there are too many reserves, due to the reserve management cost!), and eventually the situation will become untenable. (After all, in this model, FFR is really the key rate — it controls the cost of capital directly, whereas IOR only matters indirectly by affecting the cost of deposits, which have some small interaction with real decisionmaking.)
What people in the blogosphere, including me, have in mind is somewhat different. Generally I don’t think people view the ad-hoc “reserve management cost” as an important real-world issue rather than a modeling trick. Instead, they assume that the Fed can satiate the demand for reserves — suppose, for instance, that there are no reserve management costs, and reserves and labor are Leontief complements in (29). In that case, it could easily push a huge excess of reserves into the system, and then basically forget about open market operations for a while as it managed monetary policy exclusively through IOR.
For instance, right now the level of total reserves is over 10 times the level of required reserves. Barring some extraordinary substitution toward demand deposits by account holders, or extraordinary inflation, if the Fed keeps reserves at their current level, there will be massive excess reserves for *decades*, meaning we will have IOR=FFR. For a few decades, then, the Fed can manage monetary policy via IOR without bothering to care about the quantity of base money at all. This is entirely consistent with Ireland’s model.
Of course, eventually (sufficiently far down the line!) the Fed will always have to adjust base money to keep up with nominal growth. But as long as it makes an effort to keep the banking system satiated with reserves, which is very easy to do, active monetary base management is pretty much irrelevant, and monetary policy can be conducted exclusively using a floor system with IOR.
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