# On the Price of Money and Monetary Policy

It has become commonplace recently to discuss quantitative easing in the context of a comparison between the rates of return on T-bills with the interest rate paid on excess reserves. Money, however, is defined vaguely and the comparison of reserves with T-bills is a limiting case considering the scope of open market purchases conducted by the Federal Reserve in recent years. In all of the discussion, however, there is a neglected aspect of analysis and that aspect is in regards to the price of money.

Initially, it might seem odd to think about the “price of money.” Goods are priced in terms of money. So what is meant by the price of money? Often times, people think of the price of money as simply the reciprocal of the price of the good. In other words, if a banana costs 50 cents, then the price of a dollar is two bananas. Others see the price of hold money as an opportunity cost. In other words, by holding money, I am giving up some amount of rate of return. Thus, “the” interest rate is often considered the price of money. The interest rate, however, is not the price of money. The interest rate is the price of credit. So what is a meaningful definition of the price of money? Fortunately, the literature on monetary aggregation provides an answer to this question that is actually based on economic theory.

To define the price of money, we first need to define what we mean by money. Money consists of a lot of different things. Currency is money, a checking account or a savings account is money, and some have argued that due to things like repurchase agreements, even T-bills can be considered money. So if all these things can be considered money, how can we begin to define the price of money. As it turns out, each different type of money has its own price and every definition of a monetary aggregate has a corresponding price index.

Before getting to this, let’s first take a detour through monetary theory.

Traditional courses on monetary theory often start with a discussion about fiat money. Why would anybody hold fiat currency? It is clearly dominated in rate of return. Thus, shouldn’t people hold something else, like capital? Monetary theory has a lot of different answers to this question. For example, currency is assumed to be more liquid than other assets (i.e. there are lower transaction costs associated with using currency than other assets) or individuals value the constant (zero) rate of return in comparison to a stochastic (perhaps negative) rate of return, etc. Regardless of the reason, the general theme is that there are characteristics that currency has and that other assets do not have. Those characteristics create a non-pecuniary yield.

This is not only true of a comparison of say currency and capital, but also true of a comparison of currency with other types of things that we often consider “money”, such as a checking account or savings account, or a certificate of deposit. While these other forms of money might bear interest, some places refuse to accept checks, getting money out of a savings account might require a trip to the bank, withdrawing money from a certificate of deposit requires a transaction fee, etc. Thus, there is a trade-off between money and non-money, but there is also a trade-off between different forms of money. Less liquid forms of money yield higher rates of return, but the transactions costs associated with spending that money are higher.

These characteristics of different types of money are important. The reason that they are important is because they highlight the fact that different types of money and different types of assets more generally are imperfect substitutes for one another, a characteristic that is important when thinking about monetary policy. In addition, consider the counterfactual. If all different types of money were perfect substitutes, then individuals would only hold the money asset with the highest rate of return.

So what does this have to do with the price of money?

When we think about money, it is important to think about money in the way that we think about durable goods. Money provides a flow of services over time. As a result, the proper way to think about the price of money is to think about money in terms of its user cost. As Barnett (1978) derived, the real user cost of a given monetary asset i at time t is given as

$u_{it} = {{R_t - r_{it}}\over{1 + R_t}}$

where $u_{it}$ is the user cost of asset i at time t, $R_t$ is some benchmark rate of return, and $r_{it}$ is the rate of return of asset i. Thus, the user cost of holding a given type of money is the discounted present value of the opportunity cost of holding that asset rather than the benchmark asset that doesn’t provide any sort of monetary services. It is important to note that this captures the features of money describe above. An asset that is more liquid will have a lower rate of return and therefore a higher user cost. Nonetheless, individuals will be willing to hold assets with different user costs because the assets are imperfectly substitutable. The price of a monetary aggregate is then given by the share-weighted average of each of the components in a given monetary aggregate.

So why is this important for monetary policy?

A lot of the analysis of quantitative easing focuses on the fact that the Fed is now swapping an interest-bearing asset for another interest-bearing asset. From the perspective of a bank, reserves are more liquid than T-bills since banks can use reserves to settle payments, but not (directly) using T-bills. Thus, consider how monetary policy ordinarily works according to what Ben Bernanke refers to as the portfolio channel of monetary transmission. Suppose that we begin in equilibrium. A bank is holding a given amount of reserves and a given amount of T-bills. The Federal Reserve then purchases T-bills, reducing the supply of T-bills and the increasing the supply of reserves. Assuming that the bank was content with its allocation, it then decides to re-allocate its portfolio (i.e. get rid of the reserves by purchasing other stuff). This re-allocation then has real effects on the economy.

Some have argued that with the Federal Reserve paying interest on reserves, however, banks have no incentive to do this. In other words, the bank receiving the reserves actually gets a marginal increase in liquidity without sacrificing the rate of return. Thus, there is no reason to re-allocate and no corresponding real effects. However, this ignores the fact that quantitative easing has taken a variety of forms. Not all rounds of quantitative easing has entailed buying T-bills. Nevertheless, some have claimed that buying 10-year Treasury bonds instead of T-bills has no effect other than to change the slope of the yield curve.

Regardless of whether the critics of quantitative easing have been correct in the context of the argument above, there is one thing that hasn’t been discussed: the price of money. What effect do large scale purchases of MBS have on the price of money? Is the price of money more sensitive to the purchases of long term bonds or mortgage-backed securities? The counter-argument to the portfolio view espoused by Bernanke suggests quantities don’t matter because relative prices adjust without any corresponding real effects. However, even if we take that view as true, then it must be the case the price of money is changing. This would seem to matter since shocks to the price of money have been shown to have significant effects on real output.

Anyway, just some food for thought.