I. Introduction

Central bank independence has emerged at the forefront of political agendas around the world. A significant part of the impetus for increased central bank independence derives from the performance of the German economy under the Bundesbank, but it also comes from the recent theoretical and empirical literature which has highlighted the positive association between lower inflation and increased central bank independence. ^1/ Furthermore, the empirical results suggest that the improved inflation performance is not at the expense of lower output (see e.g., Alesina and Summers (1993), and Grilli, Masciandaro and Tabellini (1991)). That is, increased central bank independence is a free lunch.

The theoretical rationale for increased central bank independence has developed from the time consistency model of Barro and Gordon (1983a, b). However, that model and most of its successors examine the effect of increased central bank independence on inflation and output in isolation from the actions of other policymakers. ^2/ In effect, the central bank is assumed to be the only policymaker in the economy. However, monetary policy is not conducted in a vacuum, nor is the degree of central bank independence generally exogenous to other policy institutions.

The purpose of this paper is to explicitly include a separate fiscal authority and examine the interaction between the two authorities in determining the macroeconomic performance of the economy (that is, the levels and variability of inflation and output). The modelling framework used is based on that of Alesina and Tabellini (1987), and considers interactions among three agents: the fiscal authority (government), the central bank, and wage setters. The government’s budget financing constraint acts to link the decisions of the central bank and the government.

The paper highlights three factors which affect inflation and output in addition to the literature’s traditional definition of central bank independence (in terms of the central bank’s degree of inflation aversion).

Firstly, the preferences of the fiscal authority play a key role in determining the state of the economy. The central bank’s preferences no longer are the sole determining factor.

Secondly, the nature of the policy game affects the level of inflation and output. In contrast to the previous literature which has focussed on the Nash equilibrium of the policy game, this paper also examines the Stackelberg equilibria, which may be a more accurate depiction of the actual relationship between central banks and government. If the fiscal authority has the superior commitment technology (is the dominant player in the policy game), then the inflation rate is likely to be higher than if the two players move simultaneously (neither’s commitment is superior). If the central bank has the superior commitment technology, inflation may be higher or lower depending on the preferences of the fiscal authority.

Thirdly, the obligations to repay debt have an influence similar to that discussed in Sargent and Wallace (1981). If the central bank is responsible for some of the burden of debt repayment, then a lower bound is placed on its choice of the inflation rate.

These results contrast with the theoretical results that underpin the existing empirical literature. There, the adoption of the natural-rate framework and the Barro-Gordon time-consistency framework with only one policymaker guarantee that the central bank’s degree of inflation aversion is the only influence on inflation. This paper suggests that the different aspects of central bank independence described above could be distinguished when examining the relationship between central bank independence and inflation, and in particular the preferences of the government should be controlled for.

The model developed in this paper can also be solved for the optimal degree of inflation aversion for the central bank (that is, the weight on inflation in the central bank’s objective function). The optimal level depends on the preferences of the fiscal authority and of society. That is, the choice of central bank type may be a reflection of the underlying preferences of society. Increasing the inflation aversion of the central bank, whilst always guaranteeing an improved inflation performance, may make society worse off, depending on the relative weights in the objective functions of the fiscal authority and society.

The optimal degree of inflation aversion of the central bank is also shown to depend on the nature of the policy game. Thus efforts to reform the structure of the central bank should consider the relationship between the central bank and the government, and not solely the degree of inflation aversion of the central bank.

The following section presents the one period model and solves it to determine the equilibrium inflation rate and output level for the economy in a second-best world. Section III solves for the Nash equilibrium of the game. It also discusses the determination of the optimal degree of central bank inflation aversion in this framework and the factors which affect it. Section IV analyses the Stackelberg equilibria when the assumption of simultaneous policy action is removed. Section V introduces debt into a two period version of the model. Section VI concludes.

II. One Period Model

The model is adapted from that in Alesina and Tabellini (1987). It consists of a representative firm and a worker, and two policy institutions: a central bank that chooses the level of inflation, and a fiscal authority that sets distortionary taxes and government spending. In this one period version of the model there is no debt. Section V will introduce debt explicitly. While debt may be issued in the short run, in the long run, adjustment must be made to either taxes, government spending or seigniorage to maintain a stable debt/GDP ratio.

Society’s loss function or the loss function of a social planner is given by:

This loss function may be interpreted as reflecting the preferences of society or alternatively the average of the political parties. It is in contrast to the fiscal authority’s loss function in equation (3) below. The social planner desires to have inflation (π) as close as possible to the target level of zero, and to minimize the deviations of output (x) and government spending (g) from their target levels x^* (full employment) and g^* respectively. Whether zero is the appropriate inflation target is beyond the scope of this paper, but see the discussion in Lipsey (1990), Using a target of π different from zero does not alter the general conclusion. The targets x^* and g^* are those desirable in the presence of nondistortionary taxes, where g^* is the desired level of spending on public goods. s_π, s_x and s_g denote the weights that the social planner places on the various objectives. ^1/

The central bank has the following loss function, which it minimizes through its choice of inflation. ^2/ The central bank cares about deviations of inflation from its target level and deviations of output from its target x^*, but not about the level of government spending. This loss function is generally the only one considered in the Barro-Gordon style analysis.

The parameter μ=m_x/m_π denotes the relative weight the central bank places on output compared to inflation. It is often interpreted in the literature as the inverse of the degree of central bank independence. However, in the empirical literature, measures of central bank independence incorporate the financial linkages between the central bank and the government as well as μ. The framework in this paper allows these concepts to be distinguished so that the financial linkages reflect the nature of the game and the responsibility for debt, while μ solely reflects the weight on inflation in the central bank’s loss function.

This (standard) loss function is consistent: with the majority of central bank charters which explicitly include inflation and/or output in the objectives of the central bank, but do not refer to government spending. For example, the goal of the Reserve Bank of New Zealand is to “formulate and implement monetary policy directed to the economic objective of achieving and maintaining stability in the general level of prices” (Section VIII, Reserve Bank Act 1989). Before the reform in 1989, its objectives were to maximize economic welfare “having regard to the desirability of promoting the highest level of production and trade, and full employment, and of maintaining a stable internal price level” (Section VIII (2), Reserve Bank Act 1964).

The fiscal authority is assumed to have the same loss function as the social planner but with different weights (δ_π, δ_x and δ_g) that reflect either political business cycle considerations or the different weights of the different political parties.

The assumption is that δ_x/δ_π>μ. That is, the fiscal authority puts relatively more weight on output (less weight on inflation) than the central bank, as is observed in practice.

Distortionary taxes τ are levied on production and are the only form of taxation available to the government. ^1/ The fiscal authority chooses the level of distortionary taxes which enables it to fund government spending but creates a cost through the effect on output. An increase in taxation reduces output (which in equilibrium is always below target), thus increasing the loss.

Output X is produced by labor L and is subject to a white noise shock a_t:

Workers set the nominal wage w (in logs) to achieve a target real wage w^*. ^1/ They choose the nominal wage in advance of the actions of the two policymakers but knowing the objective functions of the policymakers. That is they minimize the objective function:

This implies that workers set a wage w_t = p_t^e + w^*.

The representative firm’s profit function is given by:

Solving for the firm’s labor demand, and assuming it can hire the labor it demands at the given nominal wage, gives (the log of) output:

where α=γ/(1-γ) and In(1-τ) has been approximated by -τ. For algebraic simplicity α will be set equal to one (that is, γ = 1/2).

Equation (7) illustrates the fact that the general problem of time inconsistency of monetary policy in Barro-Gordon models can be reduced to a lack of nondistortionary taxes, as pointed out by Fischer (1980) and Alesina and Tabellini (1987). If there were nondistortionary taxes, the fiscal authority could raise the revenue to enable it to subsidize employment to achieve its output target (which is assumed to differ from that determined in the labor market), while still financing its desired level of government spending. That is the government could provide a subsidy of τ=-w^*-x^*/α+logγ to achieve its employment target of x^*. This subsidy would also be funded by nondistortionary taxes. Output would now be:

Given that output (employment) would now be at the desired level x^*, there would be no incentive for the central bank to inflate. This is the first best outcome with output and government spending at their desired levels and with no inflation. In this model, the lack of (a sufficient level of) nondistortionary taxes means that the economy is operating in a second-best world.

As in Alesina and Tabellini (1987), the following assumptions are made. Money demand is given by M_t=P_tX’ where X’ is independent of the level of distortionary taxes τ. Thus π_t=m_t-m_t-1 The government financing constraint is G_t=τ_tP_tX_t+M_t-Mt- which when divided by nominal income gives g_t=τ+[(M_t-M_t-1)/M_t]X’/X_t. This approximates to:

That is, government spending can be financed only by taxes and seigniorage. Seigniorage is likely a nonlinear function of inflation, but for simplicity has been linearized here. ^1/ One can regard the seigniorage term as incorporating all the means by which the government can raise additional revenue through inflation, such as inflating away debt or bracket creep.

III. Nash Equilibrium

This section analyzes the Nash equilibrium where the central bank chooses π_t and the government τ_t, taking expectations and each other’s actions as given, after the workers have chosen the wage. Expectations are formed rationally. Note that the reaction function of the monetary authority does not internalize the government budget constraint, and correspondingly the monetary authority’s role as a source of seigniorage revenue. The reaction functions of the two authorities are:

Monetary:

Fiscal:

These equations imply:

The key result is that, in contrast to the existing literature, inflation and output depend not only on the central bank’s weight on output, but also on the fiscal authority’s weights. They also depend on the parameters x^*, g^* and w^* which reflect the institutional and political structure of the economy. This suggests that empirical estimates of the relationship between central bank independence and inflation should also control for the fiscal authority’s parameters and other institutional parameters such as the output and spending goals.

The average level of inflation is given by:

It depends positively on the central bank’s weight on output, μ. This is the standard time consistency problem: the more weight the central bank places on output, the greater the incentive to create surprise inflation. Since this is perceived by the workers, in equilibrium, there is higher inflation but no gain in output except through the seigniorage channel (see below). When the central bank’s weight on output is zero (μ = 0), then equilibrium inflation is zero. In that case, the loss function is like that of the Reserve Bank of New Zealand, where the focus is formally only on price stability.

As long as the central bank places any weight on output (μ>0), the output and expenditure targets, x^* and g^*, and the workers’ real wage target w^* influence average inflation. In such cases, inflation depends positively on the spending target g^*: an increase in the target increases distortionary taxation on the margin thus reducing output and hence increasing the incentive to inflate. Inflation also depends positively on output and wages, as a higher output (employment) target and/or a higher real wage target increase the desire to inflate. It depends negatively on the ratio of the fiscal authority’s weights (δ_x/δ_g). An increased weight on the government spending target relative to the output target means that the level of distortionary taxes is increased on the margin, thus reducing output and increasing the incentive of the central bank to inflate. Table 1 summarizes the influence of the parameters on the economy.

Table 1:

Effects of Changing the Parameters on the Economy

Table 1:

Effects of Changing the Parameters on the Economy

	†μ	†δx	†δg	†x*	†g*	†w*
Inflation	↑	↓	↑	↑	↑	↑
Output deviation (x-x*)	↑	↑	↓	↓	↓	↓
Govt spending deviation (g-g*)	↑	↓	↑	↓	↓	↓

View Table

Table 1:

Effects of Changing the Parameters on the Economy

	†μ	†δx	†δg	†x*	†g*	†w*
Inflation	↑	↓	↑	↑	↑	↑
Output deviation (x-x*)	↑	↑	↓	↓	↓	↓
Govt spending deviation (g-g*)	↑	↓	↑	↓	↓	↓

The average level of output and government spending fall short of their respective targets, reflecting the tradeoff at the margin the fiscal authority faces between spending and output. The difference between realized and targeted output is decreasing in μ, and decreasing in δ_x/δ_g. An increase in μ means that the central bank places more weight on the output objective, thus inflating the economy more. This has no direct effect on output as inflation expectations also adjust. However, increased inflation has an indirect effect on output through the corresponding increase in seigniorage revenue, which reduces the need for distortionary taxation, thus increasing output. As mentioned above, this effect is not internalized by the central bank.

The preferences of all the policymakers also affect the variances of inflation and output. The variance of inflation is given by:

It depends positively on μ and negatively on δ_x/δ_g, while the variance of output depends negatively on μ and δ_x/δ_g:

The increase in the variance of output when the inflation aversion of the central bank is increased reflects the tradeoff between flexibility and commitment highlighted by Rogoff (1985) and Lohmann (1992). When central bank independence is increased to reduce the time consistency problem, the willingness to respond to output shocks is decreased.

The general presumption in the literature is that the decline in inflation as a result of increasing central bank independence must always decrease the value of the loss function (except in terms of the loss of flexibility discussed above). However, this relies on the specification of the loss function solely in terms of the central bank’s objectives. Here, although the inflation rate is clearly zero when the central bank is fully independent, society is not necessarily better off in this case. The expected loss in each period is:

The first part of this term is increasing in μ; however, the second part is decreasing in μ, because whilst more central bank independence reduces the level and variance of inflation, it also decreases output and government spending.

Consequently, if the central bank were to commit to zero inflation (set μ=0), while inflation would be at its optimum level of zero, output and government spending would fall short of the optimal level. Again, whether society is better off or not depends on its relative weights on the three objectives. As Beetsma and Bovenberg (1995) point out, imposing another distortion in a second best world does not necessarily improve welfare.

It should be noted that the model above does not allow for any direct distortionary effects of inflation. Taxes are the only distortion present. Hence the conclusion that a decline in inflation may increase the loss function may be overstated if higher inflation has a distortionary effect on output. For instance, inflation may have a negative impact on productivity so that the productivity shock a_t may be a function of inflation (see, e.g., Howitt in Lipsey (1990), and Selody (1990)).

IV. Stackelberg Equilibria

Thus far, the policymakers have moved simultaneously. This has been the convention in the literature. The Nash structure may be appropriate if we think that the two authorities have full knowledge of each other’s actions and reaction functions developed over a long history of playing the policy game. An alternative concept of central bank independence is the degree to which the central bank accommodates the fiscal authority’s actions.

In this section the effect on the equilibrium inflation outcomes, the optimal degree of inflation aversion and the welfare implications of these Stackelberg equilibria will be examined. Alternatively, the Stackelberg equilibria can be interpreted as reflecting the strength of the commitment technology available to the two authorities.

If the fiscal authority has the better commitment technology, it can credibly commit itself to a particular policy program regardless of the central bank’s actions, and thus acts as the leader in the game. Examples of commitment mechanisms include projections of fiscal policy stated in the government’s budget statements or legislation such as the Gramm-Rudman Act in the United States.

The assumption of a dominant fiscal authority yields the following average inflation rate:

This structure implies that the fiscal authority chooses the level of government spending and the central bank chooses the means of finance, that is the split between seigniorage and distortionary taxation. However, unlike the Nash solution, the fiscal authority takes into account the reaction function of the central bank to the fiscal authority’s choice of the level of government spending. This equilibrium may be a more appropriate description of fiscal-monetary interactions in practice than the Nash equilibrium.

Alternatively, if the central bank has the superior commitment technology, then the average inflation rate is:

Its superior commitment could result because it is separated from the government and its independence is supported by legislation similar to that in New Zealand. Another example of a commitment mechanism for the central bank is the adoption of inflation target bands such as in Canada and New Zealand.

When the monetary authority leads, it internalizes the budget constraint and thus takes account of the role of inflation as a source of seigniorage revenue. Note that the monetary authority does not care directly about government spending. However, increased seigniorage revenue reduces distortionary taxation on the margin which in turn increases output closer to its desired level.

We would expect the inflation rate to be higher when the fiscal authority leads than in the Nash equilibrium, and to be lower than in the Nash equilibrium when the central bank leads.

Since the fiscal authority is likely to place more weight on output relative to inflation (δ_x/δ_π) than the central bank (μ), we expect π_F>π_N.

Inflation is lower when the central bank commits than in the Nash solution, when the fiscal authority’s weight on output exceeds its weight on spending. An increase in the fiscal authority’s weight on output causes it to raise less distortionary tax revenue on the margin due to the adverse effect on output. As a result there is less incentive for the central bank to create surprise inflation and output is closer to target, resulting in less equilibrium inflation.

Thus the nature of the policy game, in terms of the commitment technology available to the two participants, has a significant effect on the inflationary outcome, in addition to the weights of the policymakers.

Society’s expected losses under the two different scenarios can be calculated. When the central bank leads the expected loss is:

When the fiscal authority leads the expected loss is:

We could next ask whether it is better, from the viewpoint of society, for the central bank to be the Stackelberg leader. Comparing the expected value of the social loss function when the central bank is the Stackelberg leader with its value at the Nash equilibrium, we find that although inflation is smaller when the central bank leads if condition (25) is satisfied, output and government spending fall further below target, thus increasing the loss. The net outcome in terms of welfare depends on both the social weights and the weights of the two authorities.

For small values of s_g, society is always better off in the Nash equilibrium than if the fiscal authority leads provided condition (24) holds; that is, provided the central bank is more inflation averse than the fiscal authority. ^1/ Thus independence of the central bank, in the sense that it is not required to finance a pre-determined deficit, is desirable in this model.

If the central bank is exceptionally weak, the fiscal authority may be able to force it to finance a pre-specified deficit. In this fiscal domination equilibrium, the fiscal authority in effect sets τ and π, and the central bank is a cipher. In this case, the inflation rate is higher than in the Nash equilibrium, and social welfare is lower, except for unusual parameter values. This means that the Stackelberg equilibrium in which the central bank leads is preferable to fiscal domination.

In both Stackelberg equilibria, one can solve for the degree of inflation aversion that minimizes the expected losses in equations (26) and (27). The solution when the fiscal authority leads is not analytically tractable but when the monetary authority leads the solution is given by:

The optimal degree of inflation aversion of the central bank varies with the structure of the institutions (reflected in the nature of the policy game). Consequently, in endeavoring to reform the central bank, attention should be paid not only to the inflation aversion of the central bank but also its interaction with the other institutions in the economy. Simply legislating a more inflation averse central bank may not necessarily improve welfare in this model. Once again, this conclusion depends on there being no other costs of inflation besides those modelled here.

V. Two Period Model

This section extends the model to two periods to allow the introduction of government debt. It shows that the inflation outcome depends on the assumption as to which authority is forced to repay the debt.

The fiscal authority is now assumed to be able to finance part of its spending by issuing debt. The model below is a two period game where all debt must be repaid in the second period. The burden of repaying debt is assumed to be such that the central bank must repay a proportion β and the government the remainder.

When β=1, the model is similar to that of the unpleasant monetarist arithmetic of Sargent and Wallace (1981): all the debt is inflated away in the second period. When β=0, the burden of debt repayment falls solely on the fiscal authority, β can be seen as incorporating the costs of reforming the central bank or of placing pressure on it to inflate away the debt.

The authorities maximize the two period version of equations (2) and (3) subject to the following financing constraints:

Where d denotes the debt to GDP ratio and the gross interest rate R is assumed to be constant.

This game is solved sequentially with the central bank and government choosing inflation and taxation respectively in the second period taking each other’s actions and the level of debt as given. Then the first period problem is solved where the government chooses d and τ₁, and the central bank chooses π₁.

This yields the following solution:

where K₁=δ_x+δ_g+δ_gμ and K₂=R/K₁(δ_πδ_gμ²+δ_xδ_g(μ-1)+δ_x²), θ_F is the discount factor of the government, and π_N is the inflation rate from section III.

For positive debt in the first period θ_FK₂<δ_x is required. In this case, the use of debt in the first period reduces the need for seigniorage and the need to inflate. Assuming no corner solutions, this results in a lower inflation rate in period one, but a higher inflation rate in period two.

Finally, if enough debt is issued in the first period such that the central bank is constrained to set second period inflation above its optimum, then it is possible that the solution is at a corner where π₂=β d.

The model in this section highlights the role of the three differing aspects of central bank independence discussed in this paper. Firstly, there is the weight on output in the objective function μ which was examined in Section III. Secondly, there is the nature of the game within each period, that is whether the fiscal authority or the central bank has the superior commitment mechanism, which was examined in Section IV. (Only the Nash solution is shown above.) Thirdly, there is the financial relationship in the form of responsibility for the debt burden in the second period. ^1/ All of these three features have a significant effect on the inflation and output performance of the economy. Empirical estimation of the effect of central bank independence on economic performance could thus control for all three features independently and determine the relative influence of each.

VI. Conclusion

The paper has shown that the introduction of another policymaker, the fiscal authority, into the Barro-Gordon time consistency model modifies the standard results. In particular, inflation and output have been shown to be a function of the objectives of the fiscal authority, the nature of the policy game (commitment technology), and the nature of debt repayment obligations, in addition to the standard influence of the objectives of the central bank. The model has isolated and highlighted the way in which these different aspects of central bank independence affect economic performance.

In particular, it was shown that if the central bank has the stronger commitment technology, then it is possible that there will be a superior outcome than if the fiscal authority is the leader. Furthermore, it may be in the government’s best interests to grant the central bank this stronger commitment technology depending on the preferences of society.

The observed negative relationship between central bank independence and inflation may be a reflection of the underlying preferences of the economy in question. Those economies with a strong anti-inflation preference are likely to have already instituted an independent central bank with strong anti-inflationary tendencies. Other economies with higher inflation may have elected to institute a central bank whose preferences are more in keeping with their lower weights on inflation. To argue that such economies would benefit from having a more independent central bank requires there to be other negative effects of higher inflation on output than those which are modelled here, perhaps through the effect of inflation on productivity growth. Consequently, increasing the inflation aversion of the central bank without consideration of the existing institutional structure and the preferences of society, may not necessarily result in a free lunch.