The Long-Run Neutrality of Money

Our analysis so far has been based on the simplifying assumption that real income and the price level are exogenously given. For this reason, the only variable that could adjust to equilibrate the money market was the nominal interest rate.

Beyond the very short run, the price level also adjusts. We can see the direction of this adjustment by rearranging the equilibrium condition in the money market and solving (12.5) with respect to the price level:

Equation (12.6) indicates that the price level depends on the money supply and the two factors that determine the demand for money (i.e., aggregate real income and the nominal interest rate).

The price level can rise if there is an increase in the money supply, a decline in real income, an increase in the nominal interest rate, or some other extraneous factor that autonomously reduces the demand for money.

To explain inflation in the long run (i.e., continuous increases in the price level), the focus has to be on continuous increases in the money supply. As we saw in chapter 7, in the process of balanced growth, real incomes grow at a steady rate, while real interest rates are stabilized. Nominal interest rates are equal to the real interest rate plus expected inflation. Thus, in a steady state with constant inflation, the nominal interest rate is also constant.

Expressed differently, in the steady state, aggregate real income and the real interest rate are on their balanced growth paths. With constant inflation, nominal interest rates are also constant. Thus, the factors affecting the demand for money are given, and the level of the money supply determines the price level without affecting the evolution of real variables.

The proportional long-run relationship between the money supply and the price level has been analyzed since the sixteenth century, on the basis of the quantity theory of money, according to which the quantity of money demanded is proportional to the volume of transactions (aggregate real income) and the price level. Among the first who analyzed the relationship between the money supply and the price level was Copernicus, who, in a memorandum of 1517, used the quantity theory to explain the large increase in the price level in the early sixteenth century, following the import of gold and silver, used in the coinage of money, from the New World. The quantity theory of money has since been refined by many analysts and economists, such as Hume [1752] and Mill [1848], as an explanation of the determination of the price level.

Algebraically, the quantity theory of money took two alternative forms (see Humphrey [1984]). First, the form of the equation of exchange, MV = PY, where V is the velocity of money (Newcomb [1885], Fisher [1911]). Alternatively, according to the Cambridge School, it took the form of a money demand function, M = kPY, where k is the percentage of income held in the form of money (Pigou [1917], Keynes [1923]). After World War II, the quantity theory of money was restated by Milton Friedman and formed the basis of monetarism.⁷

To support the long-run neutrality of money, we should be able to prove that the money supply does not affect real output or real interest rates in the long run. This is both an empirical and a theoretical matter.

The evidence (including that presented in figures 1.12 and 1.13 in chapter 1) generally supports the long-run neutrality of money.

In addition, the long-run neutrality of money applies to all theoretically consistent general equilibrium models with flexible prices. The determinants of the level of equilibrium real income and other real variables are the available resources; technology; preferences; the functioning of markets; and the economic institutions that determine total factor productivity, the productivity of specific factors, and the efficiency of economic exchange.

In dynamic general equilibrium models, such as the ones examined in chapter 7, we must distinguish between the neutrality and the superneutrality of money. The neutrality of money refers to the effects of a one-off change in the money supply, and the super neutrality of money refers to the effects of a change in the rate of growth of the money supply.

The neutrality of money applies to all dynamic general economic equilibrium models with flexible prices. However, as we saw in chapter 7, the growth rate of the money supply affects inflation and long-term nominal interest rates, and it thus affects real money demand.

In a representative household model, the growth rate of the money supply does not affect any other real variable apart from real money balances. Consequently, it could be argued that the superneutrality of money applies to representative household models. This is the case of the Sidrauski [1967] model analyzed in chapter 7. In overlapping generations (OLG) models, the superneutrality of money does not apply, as the growth rate of the money supply affects savings and the accumulation of capital, and thus all other real variables on the steady growth path. This is the case with the Weil [1987b, 1991] model, also analyzed in chapter 7. Yet, as we saw for the dynamic simulations of the Blanchard-Weil model, even in OLG models, deviations from the superneutrality of money are not significant for output growth and the evolution of other real variables.

12.5.1 Monetary Growth, Inflation, and Nominal Interest Rates in the Long Run

In the same way that a permanent increase in the money supply causes a long-run increase in the price level by the same proportion, monetary growth (in the form of continuous increases in the money supply that exceed the long-run growth rate of output), causes continuous price inflation. Inflation in the long run is determined by the difference between the long-run growth rate of the money supply and the long-run growth rate of money demand, which is equal to the long-run growth rate of output.

where π is inflation, μ the growth rate of the money supply, and g + n the growth rate of output and demand for real money balances, assumed exogenous. This relation is derived by taking the growth rates of prices, money, and output in the money market equilibrium condition (12.5), assuming a unitary elasticity of money demand with respect to real output, an exogenous rate of technical progress and population growth, a constant growth rate of the money supply, and a constant long-run nominal interest rate. These assumption are all compatible with the long-run growth monetary models of chapter 7.

The positive one-to-one relation between monetary growth and inflation implied by the above relation is related to the neutrality of money. A high growth rate of the money supply by the central bank results in long-run inflation without affecting either the growth rate of output or real interest rates.

However, long-run inflation affects the level of nominal interest rates, as investors in bonds and other interest-yielding nominal securities seek to be compensated for the loss in the real value of their assets through inflation. Thus, in an economy with nonzero long-run inflation, nominal interest rates are determined by the Fisher equation, which states that the nominal interest rate is equal to the real rate of return on capital, plus expected inflation. As we saw in chapters 2 and 7, the Fisher equation takes the form

where r is the equilibrium real interest rate, equal to the real rate of return on capital.

As there is a one-to-one relationship between long-run monetary growth and inflation, so there is a one-to-one relationship between long-run inflation and nominal interest rates in the Fisher equation.

12.5.2 The Welfare Cost of Inflation

Economies with high inflation will tend to have high nominal interest rates. High nominal interest rates will result in a reduction in money demand. Thus, such economies will be associated with lower real money balances in the long run. This will result in a loss of consumer surplus from the use of money, which is the welfare cost of inflation.

The welfare cost of inflation was analyzed in chapter 7 with the help of figure 7.1. A higher long-run inflation rate causes nominal interest rates to rise. This reduces money demand and real money balances in the long run, and it creates a welfare cost in the form of loss of consumer surplus. Essentially, in high-inflation economies, households and firms hold smaller quantities of money for their transactions, because of the higher opportunity cost of holding money implied by higher inflation. This forces them to make more transactions to convert interest-yielding assets into money, and thus implies a welfare cost in the form of higher transactions costs.

We shall return to this issue when we discuss high inflation and hyperinflation in section 12.9.1.

12.5.3 The Long-Run Neutrality of Money and Monetary Reforms

An alternative way to think about the neutrality of money is to consider the impact of a very radical change in the money supply. Such radical changes take place in times of monetary reforms. Such historical examples exist, which suggest that, after a monetary reform, the price level adjusts immediately to the new monetary standard.

For example, in May 1954, a radical monetary reform took place in postwar Greece. A new drachma was created, which amounted to 1,000 old drachmas. Essentially this reform was equivalent to a direct reduction in the money supply to one thousandth of the old money supply.

Similar monetary reforms involving the redefinition of the value of a national currency have taken place in the European economies that were affected by hyperinflation in the 1920s, and more recently in many other countries. Mexico redefined the peso in January 1993 by creating a new peso, equal to 1,000 old pesos. The price level fell to one thousandth of the old price level. Turkey redefined the lira in January 2005 by creating a new turkish lira, equal to 1,000,000 old liras, and the price level fell to one millionth of the previous price level. Argentina and Brazil have also gone through a number of such monetary reforms. The creation of the euro was also a monetary reform of this nature, as the euro replaced national currencies of different denominations, causing immediate changes in the price level related to the conversion rates to the new currency for all countries that adopted the euro.

Gradual increases in the money supply in the long run have effects similar to such monetary reforms. The tripling of the money supply over a decade has the same long-run effects as a monetary reform in which a currency unit is replaced with three units of a new currency.

Thus, although a short-term change in the money supply can cause equilibrating changes in nominal interest rates, in the longer term, what adjusts to equilibrate the money market is the price level. Nominal interest rates return to their long-run equilibrium value, determined by the real interest rate plus expected long-run inflation, as suggested by the Fisher equation.

12.6