Deflation and the Optimum Quantity of Money

Years ago, Milton Friedman argued that deflation--a falling price level--is optimal because it is necessary to make make the real rate of return on money equal to its opportunity cost. In Less Than Zero, George Selgin appeals to that argument in support of the productivity norm--a rate of deflation equal to the growth rate of productivity.

The argument can be seen using the Fisher effect of expected inflation on nominal interest rates. In equilibrium, the nominal interest rate is equal to the real interest rate plus the expected inflation rate. Other things being equal, a decrease in the expected inflation rate reduces the nominal interest rate.

The opportunity cost of holding money (at least one of them) is the difference between the interest rate on nonmonetary assets, like bonds, and the interest rate that can be earned on money. Suppose the nominal interest rate on money is fixed at zero and the equilibrium real interest rate on nonmonetary assets is greater than zero. Then a decrease in the nominal interest on nonmonetary assets shrinks the difference with the nominal interest rate on money and reduces the opportunity cost of holding money. Since expected deflation further reduces nominal interest rates below the real interest rate, expected deflation should further close the gap.

Why would anyone hold money with a zero nominal yield when nominal yields on other assets are greater than zero? Steve Horwitz, following Hutt, describes the services received from holding money as a liquidity yield. Each person adjusts the amount of money held so that his or her subjective liquidity yield equals the opportunity cost of holding money.

For example, suppose the equilibrium real interest rate is 3% and the expected inflation rate is 2%. The equilibrium nominal interest rate is 5%. The nominal interest rate on money is assumed to be 0%. The opportunity cost of holding money is 5%. Each person chooses to hold a quantity of money such that his or her subjective liquidity yield on money is 5%.

If the expected inflation rate is negative, say -1%, then the nominal interest rate is 2%. The opportunity cost of holding zero nominal interest money is 2%. Each individual increases the quantity of money held until their subjective liquidity yield is equal to 2% on the margin.

If the nominal interest rate on nonmonetary assets is driven to zero, then each person will demand an amount of money such that the subjective liquidity yield is driven to zero on the margin. The optimal quantity of money will meet the demand to hold zero-yield money at a point where the rate of deflation is equal to the equilibrium real interest rate, and the nominal interest rate on nonmonetary assets is equal to the zero nominal interest rate on money.

Given the example above, a deflation rate of 3% results in a nominal interest rate of 0% on nonmonetary assets. The opportunity cost of holding money is zero. People hold even more money, to a point where their subjective evaluation of liquidity is zero on the margin.

What is wrong with the argument? Under the existing monetary regime, most money earns interest. Using the MZM measure of the quantity of money, 90 percent takes the form of deposits and 10 percent the form of hand-to-hand currency. Deposits can and do pay explicit nominal interest rates.

The yields on deposits are typically less than those on nonmonetary assets, most obviously the yields on the earning assets that banks hold on their balance sheets. While there are many costs of financial intermediation, one cost is due to the creation of liquidity. Banks take earning assets that approximate the actual liquidity characteristics of productivity enhancing investments and transform them into more liquid deposits. This activity is risky, and the stockholders of banks require compensation for providing this service. Depending on the real interest rate generated by productivity enhancing investments and the real cost of providing intermediation services, the real yield on deposits that serve as money can be positive or negative.

For example, suppose the real interest rate on productivity enhancing investments is 3% at the margin. The cost of providing intermediation services, particularly the creation of liquidity, is 1%. The competitive real interest rate on deposits serving as money is 2%.

At first pass, the expected inflation rate has nothing to do with the opportunity cost of holding money. It will equal the cost of providing intermediation services. Each person will hold a quantity of money such that his or her subjective evaluation of the services provided, the liquidity yield, equals the cost of providing intermediation services. In the example, the liquidity yield will be 1%.

If the expected inflation rate is 2%, the nominal interest rate reflecting the real return on investment is 5% and the nominal interest rate on deposits that serve as money is 4%. The opportunity cost of holding money is 1%. Each person holds money such that the subjective liquidity yield is 1%, which is the cost to the banks of providing this liquidity.

If the expected deflation rate is 1%, then the nominal interest rate reflecting the real return on investment is 2%. The nominal yield on deposits serving as money is 1%. The opportunity cost of holding money remains 1%. There is no impact on the real quantity of money held or the liquidity yield on the margin. It remains equal to the real cost of providing intermediation services.

If the expected deflation rate is 3%, then the nominal interest rate reflecting the real return on investment is 0%. The interest rates on deposits is -1%. The opportunity cost of holding money remains 1%. People will hold a quantity of money such that they evaluate the liquidity services at 1%.

But then, there is currency. The government monopolizes the issue of hand-to-hand currency and pays zero nominal interest. The real yield is the negative of the inflation rate. This negative yield generates seignorage revenue from the monetary authority to the government. With a monetary authority organized on banking principles, the central bank can borrow at a negative real interest rate by issuing currency. With a 2% inflation target, the central bank borrows at a negative 2% real interest rate. Deflation creates a positive real yield on currency. The central bank borrows by issuing currency at a positive real interest rate.

The best way to understand the argument regarding the optimal quantity of money and deflation is that it is really about the optimal quantity of currency and deflation. With deflation, the real return on currency can be made equal to the real return on deposits. Rather than obtaining "liquidity" services from holding "money" in place of securities or other nonmonetary assets, people obtain more of the monetary services peculiar to currency rather than the more general "liquidity" services from money inclusive of deposits.

Again, suppose the real interest rate implied by productivity enhancing investments is 3% and the cost of providing liquidity services is 1% resulting in a 2% real interest rate on deposits. If the expected inflation rate is 2%, then the nominal interest rate reflecting productivity is 5%, the interest rate on deposits is 4% and the nominal interest rate on currency is 0%. The real interest rate on currency is -2%. Depositors will restrict currency use and perhaps substitute deposits until the subjective liquidity yield on currency is 4% greater than that on deposits.

If the expected inflation rate is reduced to -1%, then the nominal interest rate on productivity enhancing investments is 2%, the nominal interest rates on deposits is 1%, and the nominal interest rate on currency remains fixed at 0%. The opportunity cost of holding currency relative to deposits is 1%, and so the currency deposit ratio rises until the subjective liquidity yield on currency is 1% greater than the liquidity yield on deposits.

A 2% expected deflation rate would result in a nominal interest reflecting the real productivity of investment of 1%. The nominal interest rate on deposits is 0%, matching the 0% nominal interest rate on currency. The liquidity yield on currency relative to deposits would be zero.

Perhaps more deflation would be desirable. Following Friedman's approach, suppose that expected deflation is 3%. Then the nominal interest rate on productivity enhancing investments is 0%. The cost of intermediation is 1%, and so the nominal interest rate on deposits is -1%. The government is issuing currency with a 0% yield. Deposits shrink, perhaps to zero, or at least until other benefits, perhaps protection from theft, are valued at 1% on the margin. Of course, the provision of liquidity is no longer an issue for the banks, since they could simply hold vault cash, and so storage costs would be relevant. The central bank is providing liquidity services free of change.

Clearly, it is possible that expected deflation could go too far. Suppose the expected deflation rate is 4%. The nominal interest rate on productivity enhancing investments on the margin is negative 1%. The cost of intermediation is 1% but that is subsidized by government. The nominal interest rate on currency is 0% and the nominal interest rates on deposits is negative, but only reflecting storage costs.

There is no private benefit from funding productivity enhancing investments that provide a 3% real yield because, the 4% real return on currency is better. Fewer productivity enhancing investments are made, until the real return is 4% on the margin. That brings the nominal interest rate on those investments to zero, matching the zero nominal yield provided by currency.

Having the rate of deflation and zero nominal interest rate currency driving the allocation of resources between consumption and investment appears highly distortionary on its face. The result is the sort of liquidity trap frequently discussed these days--the zero nominal bound. It is difficult to see how any equilibrium is possible consistent with a stable expected deflation rate higher than the real equilibrium interest rate. Limiting deflation to the increase in productivity and the relationship between the equilibrium real interest rate and expected improvements in productivity should avoid this problem.

While the point of deflation is to increase the currency-deposit ratio so that people can obtain more benefits from using currency rather than deposits that can be used as money (or, more generally, from other uses of resources,) the scenario where the real yield on currency matches that on productivity enhancing investments is especially interesting. Currency is made superior to ordinary bank deposits, though presumably such deposits would be replaced by 100% reserve deposits.

Is that scenario desirable? If the central bank can provide liquidity services at no cost, then having private banks do so is a waste. On the other hand, it is difficult to see why anyone would want to hold any asset that provides the same return as currency but with reduced liquidity--things like certificates of deposits, long term bonds, or equities. And so, the equilibrium would appear to be for the monetary authority, organized as a central bank, to finance the entire capital stock, funded by the issue of hand-to-hand currency.

Considering that scenario for a moment, it becomes clear that the provision of liquidity services by the central bank is not always costless. At some point, having a centralized, politically-controlled bank direct the allocation of capital would be very costly. Competing banks issuing deposits that can be used as money to fund portfolios of assets that approximate the liquidity and risk characteristics of real productivity enhancing investment projects is probably the least bad option. The creation of liquidity through intermediation has real costs.

If there are outstanding short term government bonds, like T-bills, then the cost of having the central bank provide more liquidity services is presumably minimal. It can purchase the T-bills and issue additional currency. As long as the deflation rate implied by the productivity norm leaves the real rate of return on zero-nominal interest rate currency less than or equal to the competitive real interest rate on deposits, the productivity norm allows for a more efficient currency deposit ratio.

What are the public finance implications? Assuming the government is on the efficient side of the laffer curve for the inflation tax, shifts from a higher to a lower expected inflation rate reduces seniorage income. Futher, Selgin (like me,) favors free banking. Does the argument change when the issue of hand-to-hand currency is privatized? Watch for more posts on this topic.