The Optimal Inflation Tax in the Presence of Imperfect Deposit – Currency Substitution

During the last decades, technological innovation has generated a major transformation in payment systems, stimulating a widespread use of different forms of electronic money and increasing substitutability between deposits and currency in transactions. A big advantage of deposits is that, unlike currency, they can pay nominal interest on the average balance at a very low cost. As a result, in most developed countries an increasing number of people chose debit cards to make transactions. Despite the huge impact that these cards have had on everyday life, little is known about their consequences for the optimal conduct of monetary policy. This paper contributes to the literature on optimal monetary and fiscal policy by analyzing how the presence of imperfect deposit-currency substitution affects inflationary taxation in a public finance framework. The paper presents a model where financial intermediaries supply deposits that can be used to buy goods and services. In order to produce deposits, financial intermediaries must incur a cost. It is shown that if this cost is zero, the optimal inflation tax is zero. However, in the more realistic case in which this cost is positive, the optimal inflation tax is positive whenever there are revenue needs. Furthermore, the higher the cost of producing deposits, the higher is the optimal inflation tax. These results suggest that central banks in countries with less productive financial intermediaries (implying a higher cost of producing deposits), should optimally choose to have higher inflation rates.