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, compared with the money-growth case. The broad message is that reserve-ratio arithmetic can be pleasant even when money-growth arithmetic is not.