Despite growing interest in competitive payments systems and the continuing progress of bank deregulation, relatively little is known about the macroeconomic implications of completely unregulated or 'free' banking. Its advocates view free banking, where competing banks freely issue monetary liabilities redeemable in base money,1 as a means for 'depoliticising' the money stock by replacing public holdings of government money with private bank money while limiting changes in the monetary base. Such a programme begs many crucial questions. How would the (unregulated) stock of bank money be determined? Would free banking enhance or reduce macroeconomic stability compared to regulated banking? What implications would free banking have for the proper conduct of monetary policy? Lawrence H. White (i 984, ch. I) employs a model of a free banking system to answer some of these questions. However, because it concerns free banklng as practised in Scotland in the nineteenth century, White's model assumes an open economy operating in an international gold standard, where the price level is given and there is no such thing as monetary policy in its modern sense. Were free banking to reemerge today, it would probably be based, not on a gold standard, but on irredeemable paper ('fiat') base money issued by a former or extant central bank. Under this form of free banking, the price level is no longer given, and conventional monetary policy questions remain relevant. In particular, would free banking on a fiat standard simplify or complicate the control of nominal variables, including the price level and nominal income? Would it be easier or more difficult to adhere to a simple monetary rule? What would happen if the stock of base money were frozen as a means for ruling out discretion altogether? Answers to such questions require an analysis of determinants of the money stock in a closed free banking system with a centrally-determined stock of base money. Here I offer some preliminary answers based upon Carl Christ's (i 989) formal interpretation of Selgin (I988). The features of free banking stressed here because they bear most on questions of monetary control include (i) the freedom of banks to issue notes as well as deposits, where banknotes are a more