This paper examines the interplay between monetary and fiscal policies in an inflation-targeting framework. In this vein, the paper asks the following question: can an inflation target induce an independent central bank to provide the optimal rate of inflation, resulting in optimal seigniorage, taxes, public spending, and output? Does this also lead to optimal stabilization of aggregate supply shocks? The answer to the first question is yes, while the answer to the second is no, and the paper shows why.
These issues have been analyzed in various ways. First, a strand of literature has focused on the interaction between monetary policy and the private sector, and thus on the credibility/flexibility trade-off.  This approach, however, fails to take into account the impact of monetary policy on public finances. Second, other authors have employed a deterministic framework to explicitly model the interaction between monetary and fiscal policy. This approach has the weakness of disregarding the implications of aggregate supply shocks.  Finally, the inflation-target literature aims at resolving the time inconsistency problem of monetary policy but tends to overlook the fact that inflation targets could be used as a way of providing the optimal level of seigniorage (see, for example, Svensson, 1995). The aim here is to merge these ideas to derive implications for the optimal policy mix and the optimal policy response to a supply shock. 
The paper extends the work by Beetsma and Bovenberg (1997) by allowing for an aggregate supply shock and by investigating the merits of inflation targets for public finances when the government interacts with an independent central bank. Beetsma and Bovenberg (1997), following along the lines of Alesina and Tabellini (1987), stress the importance of public debt and assume a constant ratio of real base money holdings to nondistortionary output, that is, the inverse of velocity.  Within this framework, they analyze the implications of alternative institutional arrangements--centralization versus decentralization, Nash versus Stackelberg--for society's welfare. Whichever arrangement is preferable depends on society's preferences for inflation, output, and public spending, as well as the structural parameters of the economy, such as real base money holdings and outstanding public debt.
This paper extends this analysis in several directions. First, it considers the link between monetary and fiscal policies in a stochastic model, that is, it includes an aggregate supply shock. Second, it provides intuition as to why it makes a difference whether the government faces a constrained optimization problem in which public spending is one of the arguments in the government's objective function, or whether public expenditure is given as a residual by substituting the budget constraint into the policymakers' objective functions. The implication of the constrained problem is that the central bank, when decentralizing its policies, does not automatically internalize the government's budget constraint. Thus it does not make a difference whether the bank cares about public spending, which is in contrast to the existing literature (e.g., Alesina and Tabellini, 1987; and Debelle and Fischer, l994).  The paper then shows how an inflation target can bring society closer to the second-best equilibrium by s erving as a substitute for the central bank's disregard for the government's budget constraint. The paper's final extension is to analyze an "extreme" interpretation of the Maastricht proposal of price stability as the main objective of the European Central Bank (ECB) on a national basis. Again, a positive inflation target has interesting implications for smoothing the government's financing requirement over the sources of finance, as well as for stabilization.
The analysis is formulated as a game involving the private sector, the monetary authority, and the fiscal authority. The main results can be summarized as follows. A social planner, when in charge of monetary and fiscal policy, can achieve only a second-best equilibrium, as lump-sum taxes are ruled out.  The social planner then has to use alternative sources of finance--distortionary taxes, seigniorage, and the shortfall of public expenditure from its desired target. The resulting second-best equilibrium involves optimal positive mean inflation. Therefore, depending on the tax base--that is, the size of real base money holdings--raising seigniorage revenues to some extent appears optimal, which is in contrast to the various zero inflation rules studied in the literature. Since discretionary policymaking is ruled out, the optimal positive inflation rate derives from optimal revenue considerations and not from a desire to raise output via surprise inflation. Aggregate supply shocks cause inflation, taxes, spending, and output to fluctuate (second best) optimally around their respective means.
The policy outcome under the assumption that a benevolent policymaker is in charge of monetary and fiscal policy serves as a benchmark case. Once policies are decentralized, that is, monetary policy is delegated to an independent but committed central bank, both financing and stabilization are distorted. Since the central bank does not optimize subject to the government's budget constraint and therefore ignores the social value of seigniorage, the entire financing requirement has to be met by the fiscal authority. The central bank does not provide any seigniorage revenues, either through budgetary considerations, or through a desire to boost output closer to its target through surprise inflation. Therefore, the fiscal authority has to rely to a greater extent on taxes--causing output to move further away from its desired target--and a larger expenditure gap. In terms of stabilization, inflation/seigniorage fluctuates less, while output and spending vary more. As a result, the social loss in this scenario is larger than under centralization. The way out of this dilemma is to impose a non-state-contingent inflation target on the central bank. The appealing feature of this target is that it provides the optimal level of expected seigniorage. This result highlights that any output effect in the targeting regime derives from lower taxation, since the amount of taxes necessary to finance a given financing requirement depends on the level of seigniorage provided by the central bank. The optimal inflation target is allowed to vary, depending on the base for the inflation tax. At the limit, where real base money holdings tend to zero, the seigniorage motive vanishes and the optimal inflation target becomes zero. In terms of society's loss, this solution--in which the central bank is independent but subject to an optimal inflation target--dominates the arrangement in which the independent central bank has no inflation target, but is still inferior to the centralized case. The last scenario is one in which controlling inflation is the sole objective of the central bank. While the model's inflation target ensures that the means of inflation/seigniorage, output taxes, and spending are at their second-best level, the central bank does not stabilize supply shocks at all, leaving the entire burden of smoothing the supply shock to the fiscal authority. Regarding the social loss, this solution is inferior to the centralized setting and the decentralized setting with the inflation target. Whether this extreme form of central bank independence is preferable to a central bank that cares about output but is not subject to an optimal inflation target depends on the significance of supply shocks.
The remainder of the paper is organized as follows. Section I sets up the basic model. Section II considers the social planner's problem as a benchmark case. Section III explores the decentralized setting and the implications of inflation targets. Section IV analyzes an "extreme" form of the Maastricht proposal for monetary policy--a framework in which the central bank only cares about inflation. Section V concludes the paper and gives some ideas of how to extend our model. The appendices provide derivations in support of our findings.
I. The Setup
The model has three players, namely, the private sector (represented by a trade union), the monetary authority (central bank), and the fiscal authority (government).  The trade union seeks to minimize deviations of the real wage rate from a particular target. For convenience and without loss of generality, this real wage target is normalized to zero. Thus, trade unions set the log of the nominal wage rate equal to the expected price level, that is, w = [p.sup.e]. To give the monetary and fiscal authorities an incentive to engage in surprise inflation, nominal wage contracts are assumed to be signed before the policies are selected. Our model is stochastic rather than deterministic, in contrast to Beetsma and Bovenberg (1997) and Alesina and Tabellini (1987). Thus, we allow for the possibility that the economy can be hit by shocks. Given these assumptions, normalized output, y, is given by 
y = [pi] - [[pi].sup.e] - [tau] + [varepsilon], (1)
where y is the log of real output; [pi] and [[pi].sup.e] denote the actual and expected rate of inflation, respectively; [tau] is the tax rate on output; and [epsilon] is an aggregate supply shock, distributed normally with zero mean and variance [[[sigma].sup.2].sub.[epsilon]]. From equation (1), it follows that in a rational expectations equilibrium, where [E.sub.t-1]([[pi].sub.t]) = [[[pi].sup.e].sub.t], the long-run expected output level, denoted by the unconditional mean E(y), is equal to -[tau]. To achieve E(y) = 0, one has to remove the distortions arising from output taxation. The model also allows for nontax distortions, which are measured by [y.sup.*] [greater than] 0.  Note that [y.sup.*] represents the first-best level of output in the absence of any distortion. Hence the first-best output level [y.sup.*] can be achieved only by removing both the tax and the nontax distortions. The natural way to achieve the first best and to remove these distortions would be to subsidize output by setting [y.sup.*] = -[tau], whereby the negative tax represents the subsidy on output. This results in E(y) = …