A POSITIVE THEORY OF INFLATION AND INFLATION VARIANCE
Empirically, inflation and the variance of inflation are positively associated. This paper develops a model that provides a potential explanation for this relationship in terms of the incentives facing the policymaker in a "discretionary equilibrium." The model can also account for an empirical association between inflation and measures of real output instability. There is, however, no direct causal link whatever from the average rate of inflation to either the variance of inflation or that of real output.
The debate over the use rules or discretion in monetary policy has been central to macroeconomics for many years (e.g., Simons ; Lucas ; Buiter ). Recently Kydland and Prescott  and Barro and Gordon [1983a,b] have identified "discretion" as the absence of policy commitment in a game between policymakers and the public. They argued that discretionary policymaking will lead governments to create excessive inflation. A policy of low inflation is not consistent with incentives facing governments, and thus will not be believed by the private sector.
Barro and Gordon [1983a] argue that this positive theory of monetary policy can help to explain many features of the trend rate of inflation in modern economies: high and persistent rates of inflation, a positive relationship between inflation and unemployment, and the observed countercyclical behaviour of monetary authorities, among others.
These models are based on the premise that there are significant costs to a high but fully anticipated rate of inflation. Another feature of inflation in modern economics, however, is the well-documented fact that inflation and the variability of inflation are positively associated. This phenomenon has been widely observed over different countries at different times.(1) This has led researchers to question the feasibility of a steady and predictable positive rate of inflation. The finding suggests that high rates of inflation may reduce the ability to forecast future inflation rates. A high average inflation rate may add an unnecessary degree of uncertainty to individual decision making and lead to a misallocation of resources. Friedman  suggests that this may cause output instability and possibly raise the average unemployed rate. A related paper by Logue and Sweeney  establishes that there is a positive relationship between inflation and the variability of economic growth for industrial countries. Given this perspective, the welfare costs associated with inflation might be considerably higher than the traditional costs of anticipated inflation. This paper extends the Barro and Gordon [1983a] model of discretionary monetary policy to take account of the relationship between inflation and measures of inflation and output variability. The extension focussed on is to model an endogenous wage-indexing scheme in the labor market. In the discretionary equilibrium, wage setters not only form rational expectations of the future price level, but also choose an optimal degree of wage indexation. This extension to the basic model has the following properties of a discretionary equilibrium.
1. There is a positive association between the mean rate of inflation and the magnitude of real disturbances in the economy, as well as between the mean inflation rate and the degree of output instability in the economy.
2. In an economy where real disturbances are relatively important, there is a positive association between the mean rate of inflation and the variance of inflation.
The explanation behind these results is as follows. The lower is the degree of wage indexation, the greater is the incentive for monetary authorities to cause surprise inflation, and hence the higher is the mean rate of inflation in a discretionary equilibrium. But the degree of wage indexation is negatively related to the variance of real disturbances in an economy which is subject to both real and nominal disturbances. …