As the monetarist assumptions are relaxed, the proxies for the demand for US dollars and supply of US dollars changes. For example, the Fed controls the monetary base to the decimal point. In turn, the monetary base has two uses. The dollars can be used as either currency or reserves. In formal terms, the two are perfect substitutes in supply. This also means that the Fed does not control how the private sector allocates the base between bank reserves and currency in circulation. This also means that the Fed does not completely control the money multiplier and that, in turn, means that the multiplier can change and potentially offset undesired changes in the monetary base or amplify desired changes in the base. In principle, this makes the narrower aggregate a better proxy for money controlled by the Fed. However, that ignores the organization of the monetary system. Under a price rule, the open market operations are determined by the underlying inflation rate relative to the target rate. The point of all of this is that, if the broader aggregate is endogenous (as we are arguing here), they cannot cause inflation. In fact, the reverse is true. Another insight produced by this analysis is that the broader the aggregate the greater the explanatory power.

One point that we need to make here is that for many of the countries in the world, the financial system and the banking system are not as developed and deep as in the United States; therefore in these countries, the flexibility of the money multiplier may be limited. In simple terms, the central banks may have a better control of the domestic monetary aggregates. But this does not mean that foreign central banks have complete control of the quantity of money circulating in these economies.

The traditional models assume that under a floating exchange rate system only local residents use the local money. Implicitly, this assumption assumes that there are legal tender provisions that prevent the use of foreign monies in the local economy. This means that the currencies are not substitutes of each other in the domestic transaction. In technical terms, the monetarist assumes the elasticity of substitution across currencies to be zero. However, we know that foreign currencies circulate and are accepted in many economies of the world, and if the holding of these currencies respond to changes in the relative inflation, we can interpret that as evidence of currency substitution. Viewed from this perspective, it is clear that the case where local residents only hold the local currency is one where the elasticity of substitution is zero.

At the other end of the spectrum, we have the perfect substitutability case. This would be the case under a fixed exchange rate system. The convertibility assures that one country’s currency is a good as another. The more general case is when the currencies are imperfect substitutes for each other. In that case, the changes in the income in the rest of the world and the rest of the world’s money supply will affect the global demand for US dollars. The parallel here is that of the broader monetary aggregates, currency in circulation and demand deposits are not perfect substitutes in demand. They have slightly different characteristics and or transaction costs associated with their use.

Once the substitution effects among currencies are considered, it is obvious that the local central bank does not control the quantity of money circulating in the economy. This means that the rest of the world’s demand for dollars depends on how stable a monetary policy the local central bank runs. Changes in expectations and the actual domestic inflation rate induce the foreign economies to alter their demand for dollars to use in domestic transactions. While each individual country’s change may be insignificant relative to the US economy, collectively they may not be. Hence the rest of the world’s demand for US dollars to be used in local transactions could have an impact on the US monetary equilibrium, and thus the US inflation rate.

This line of reasoning produces alternative specifications for the estimation of the US inflation rate. They depend critically on the degree of substitutability, at one end of the spectrum if the different currencies are perfect or high substitutes. One specification is based on the world demand for dollars, as opposed to the US demand for dollars. The former assumes a high degree of substitutability among the currencies, be it demand and or supply through a fixed exchange rate system. The narrower aggregate based solely on local money assumes that there is no substitutability among the currencies. This gives rise to three possible specifications for the demand for dollars. One is to calculate the world income in US dollars, another possibility is to break down the world aggregates into their United States and rest of the world components and the third and final one is to consider only the US aggregates.

The second column of Table 30.1 estimates a different specification that considers the possibility of some substitution effects on the demand for various currencies. If that is the case, the growth in the rest of the world’s monetary aggregates and real GDP should have an impact on the U.S. equilibrium. The signs for the domestic M3 growth rate are the opposite of what we expected. However, the signs for the domestic real GDP growth and the foreign real GDP growth are negative. The results are consistent with the view that the higher real GDP growth rate here and abroad increases the demand for money and thereby produces a lower inflation rate. While our interpretation is interesting, the results are not statistically significant at the usual confidence levels.

The third column is the most ambitious one. It assumes that there is one world money market and that the US inflation rate is determined by the world money supply measured in dollars and the world real GDP growth. Here we get some incremental good news. The world real GDP growth has a negative and statistically significant impact on the US inflation rate. The coefficient for M3 is positive as expected. However, as before, the coefficient for M3 is not statistically significant.

Are these results disappointing? Not to us. They are consistent with the view that M3 is mostly endogenously determined and as a result of interest rate paid at the margin on M3, the aggregate is indexed against inflation and unaffected by it. If that is the case there is no reason to expect that M3 would have any significant relationship to the inflation rate. This discussion suggests that we need to focus on an aggregate under the potential control of the monetary authorities, such as the monetary base. Although not reported, the results using the monetary base instead of M3 are even less significant.

Yet to the extent that the Fed’s knowledge is not perfect, unanticipated increases in real GDP would lead to too little money chasing too many goods, which means a decline in the underlying inflation rate. Eventually the price rule would accommodate. But that is not all that the Fed has to anticipate. The rest of the world’s real GDP growth rate will affect the worldwide demand for money and to some extent the US dollar. Easy monetary policy in the rest of the world would also lead to a higher worldwide inflation rate if there is currency substitution. A floating exchange rate system does not insulate the economy from external monetary shocks. Especially if locals use the foreign currency in domestic transactions. The changing inflation rate differentials will alter the demand for the different currencies and that in turn will affect the inflation rates. This we define as currency substitution on the demand side. Also, if the rest of the world central banks watch the foreign exchange value of their currency, the substitution effects will be reduced and the broad global monetary aggregates would then be a very good proxy for the relevant monetary aggregate to focus on. In the extreme case of a fixed exchange rate, the central bank will make the currencies perfect substitutes on the supply side. Either way, the substitutability argument suggests that the global money supply may be an important indicator and or explanatory variable.