Is Reserve Ratio Arithmetic More Pleasant?

Does it matter in a revenue-neutral setting if the government changes the inflation tax base or the inflation tax rate? We answer this question within the context of an overlapping generations model in which government bonds, capital, and cash reserves coexist. We consider experiments that parallel those studied in Sargent and Wallace's "unpleasant monetarist arithmetic;" the government uses seigniorage to service its debt, choosing between changing either the money growth rate (the inflation-tax rate) or the reserve requirement ratio (the inflation-tax base). In the former case, we obtain standard unpleasant arithmetic; in the long run, a permanent open market sale results in higher money growth, and higher long run inflation. Somewhat surprisingly, it turns out that for a given money growth rate, lower reserve requirements fund the government's interest expense. Associated with the lower reserve requirements is lower long-run inflation and higher welfare when compared to the money growth case. The broad message is that reserve-ratio arithmetic can be pleasant even when money growth arithmetic is not.