Macroeconomic implications of the government budget identity : the case of a predetermined fiscal deficit and a pure nominal interest rate peg

Abstract

We consider the restrictions that the government budget identity places in an economy with rational expectations and, in particular, the case in which the fiscal authorities predetermine the conventional government deficit and the monetary authorities peg the nominal interest rate. With the assumption of rational expectations, an undesirable aspect of a nominal interest rate peg is the indeterminacy of the price level when prices are flexible and the indeterminacy of the inflation rate when prices are sticky. We solve the indeterminacies by considering the government budget identity and the fact that changes in the nominal money stock take place through open market operations. When prices are flexible, the price level is unique as long as the path of the lump sum flow taxes is independent of the path of the government debt. If the authorities try to set the price level in addition to the nominal interest rate, the system will be overdetermined, making a policy of setting both a level and a rate inconsistent. This causes Sargent and Wallace's (1981) unpleasant arithmetic. The unpleasant arithmetic will not appear if the authorities indirectly, via a nominal interest rate peg, set the rate of change of prices. Nevertheless, when the lump sum flow taxes adjust to finance all or part of the interest on the debt, the equilibrium price level is indeterminate. In contrast to the conventional wisdom of monetary economics, we show that an increase in the nominal interest rate results in a decrease in the price level for plausible parameter and initial values. In an economy with sticky prices, we show that the equilibrium inflation rate is unique as long as lump sum flow taxes are independent of the burden of the debt. Our determinacy result is achieved without government debt providing liquidity services, contrary to recent determinacy results in the literature. Finally, in an experiment with plausible parameter values for the United States, we found that an increase in the nominal interest rate is welfare decreasing and contractionary, replicating an earlier experiment where an increase in the bonds to money ratio is achieved through other means.