loss of monetary discretion in a simple dynamic policy game

Journal of Economic Dynamics and Control 18 (1994) 763-779. North-Holland

Loss of monetary discretion in a simple dynamic policy game

Henrik Jensen* University of Aarhus, DK-8000 Aarhus C, Denmark

Received July 1992, final version received February 1993

We analyze a simple policy game featuring monetary credibility problems, and argue that loss of monetary discretion is not advantageous. Two elements form the basis of our analysis. Firstly, we endogenize the source of credibility problems, and secondly, we consider a dynamic framework where credibility problems are not time-invariant. By doing this we are able to demonstrate that credibility problems are temporary, and in steady state, the government has removed these through sound policies. A binding policy rule will only serve as an obstacle towards this steady state.

Key words: Monetary policy games; Credibility; Inflation bias; Rules vs discretion; Seigniorage JEL classijicaiion: E52; E61; E63

1. Introduction

Recently, inflation has been explained as a result of the monetary authority’s lack of credibility with private agents [Kydland and Prescott (1977), Calvo (1978), Barro and Gordon (1983a, b)].’ As private agents - with access to only nominal contracting - correctly foresee future policy incentives, any attempt to stimulate activity through monetary expansions is futile in equilibrium. The only consequence is an unwelcome inflation bias. The main prescription of this theory is therefore that policymakers should give up monetary discretion.

Indeed, it seems that voluntary loss of monetary discretion has been the policy of several European countries in the 80s where these ‘borrowed’ credibility from

Correspondence IO: Henrik Jensen, Danish Economic Council, Kampmannsgade 1, DK-1604 Copenhagen V, Denmark.

*I am grateful for helpful discussions with Torben M. Andersen, Morten 0. Ravn, and Jan R. Sorensen. Furthermore, I wish to thank three anonymous referees for many valuable suggestions and comments on an earlier version of this paper. The responsibility of errors and omissions, however, is solely my own.

‘See Blackburn and Christensen (1989) and Persson and Tabelhni (1990) for recent surveys of the literature.

0165-1889/94/$07.00 0 1994-Elsevier Science B.V. All rights reserved

764 H. Jensen, Monetary discretion in a dynamic policy game

the German Bundesbank by pegging to the Deutsche Mark; [cf. Giavazzi and Pagan0 (1988), Giavazzi and Giovannini (1989)]. This observation, together with the upcoming plans for monetary unification of Europe [cf. Delors (1989) and Treaty on European Union (1992) (a.k.a. the Maastricht agreement)] _ whereby countries irrevocably renounce monetary discretion - suggests that the policy recommendation of the rudimentary credibility approach to inflation has gained widespread acceptance [see Brociner and Levine (1992) for a recent survey on European monetary unification and credibility issues].

Inasmuch as the implementation of a certain policy is not necessarily optimal by definition, examination of its consequences is of on-going relevance. The main purpose of this paper is therefore to reconsider the conventional wisdom derived from the credibility approach. In fact, we oppose its policy prescription by the means of a simple theoretical example in the Barro and Gordon vein, and conclude that loss of monetary discretion is not advantageous. At a general level, our results illustrate that although a country immediately may obtain its desired rate of inflation by giving up monetary discretion, those distortions in the economy which generated the credibility problems, are still present. Deprived of its use of a policy instrument, the country will then in the longer run find it more difficult to remedy the distortions. The 1992 turmoil in the European Monetary System seems to indicate that several countries are now experiencing these difficulties.

More specific, two elements form the basis of our analysis. Firstly, in order to explain why credibility problems prevail, one must identify their source. The most popular explanation is that the natural rate of output is below the social optimum. This raises the question: why is output too low? The most widely cited reason is the presence of tax distortions [cf. Barro and Gordon (1983b)].’ But since taxes are there for a reason, the basic source of the credibility problem must be public expenditure motives. We therefore follow Alesina and Tabellini (1987) and model such motives, thereby endogenizing tax distortions and, in effect, credibility problems. With respect to the second element, note that over time, tax distortions are not constant: the evolution of public debt alters the need for tax revenues from period to period, and therefore credibility problems are not constant either. In consequence, we introduce a dynamic public budget constraint into the policy game. This is the main theoretical innovation of the paper. Through incorporation of these apparently unconventional elements ~ endogenous credibility problems and dynamic considerations - into the conventional (Barr0 and Gordon) model of inflation, we arrive at our opposing conclusion.

In order to provide an informal understanding of the nature of our results, note that explicit consideration of public expenditures and their finance

ZAnother common justification is union power in the wage formation process. We comment on this aspect in the conclusion.

H. Jensen, Monetary discretion in a dynamic policy game 165

provides an unavoidable link to another common approach to inflation, namely that of considering inflation as a tax rate [Phelps (1972)]. Under this interpretation, inflation has the desirable property that it constitutes an additional source of revenue for the government. The government in our model thus faces a dynamic optimal taxation problem where it chooses sequences of distortionary taxes, inflation rates, and debt positions. Although tax distortions in a given period create suboptimal output, and hence a credibility problem, the associated inflation bias constitutes a positive externality for public finance. We are able to show that in the solution to the optimal taxation problem, credibility problems are temporary. In steady state the government has removed such problems through sound policies: over time it brings down the stock of debt, which ultimately obliterates the scope for distorting taxes, and ~ equivalently ~ credibility problems with associated incentives to stimulate the economy through monetary expansions.

Within this model we then assess the desirability of losing monetary discretion. As we portray a small open economy, we imagine this loss to be achieved by joining a fixed exchange rate system, which once and for all fixes the inflation rate at the government’s preferred rate, zero. ’ This results in complete loss of seigniorage, which reduces public expenditures and puts all burden of taxation upon distortionary taxes, resulting in lower output. Although inflation in each period will be at the government’s preferred rate, the losses in terms of output and expenditures will dominate, no matter how the governement weights these outcomes. Even though the government manages to steer the economy to the same steady state as under monetary discretion, a binding policy rule, like joining a fixed exchange rate system, only serves as an obstacle towards this steady state. At a more general level, our example thus suggests that a policy of voluntary giving up monetary discretion (as seen in Europe, cf. above) can be explained by an inability to deal with long-run distortions. Attempts are therefore made to offset such inabilities through short-run benefits obtained by policy rules. Such attempts may, however, turn out to be counter- productive.

The paper is organized as follows. Section 2 sets up the model, and solves it for discretionary policymaking. Then section 3 examines the case of a fixed inflation rule, and compares it to the outcomes of section 2. Section 4 summarizes, and an appendix contains a derivation.

‘Hence, we consider the implementation of a rule in the strict sense of the word, not, e.g., a scenario of commitment wherein the government either credibly renounces output considerations [cf. Rogoff (1985), Jensen (1992)] or assumes the role of Stackelberg leadership [cf. Alesina and Tabellini (1987), Bryson, Jensen, and VanHoose (1993)].


2. The model and discretionary policymaking

The structure of the model is as follows. In the beginning of each period, one-period nominal wage contracts are signed. Subsequently, the government conducts monetary and fiscal policies in the attempt of attaining target values for output, public expenditures, and inflation. Finally, firms produce goods according to the resulting aggregate output schedule.

The model does not allow for stochastic disturbances. Note that whenever a credibility problem in policymaking is present, Buiter (1981) has shown that there is a trade-off between flexibility and credibility: a fixed policy rule will solve the credibility problem, but leave the policymaker without the needed flexibility to accommodate disturbances. 4 In comparison with a stochastic framework, it is thus harder to challenge the desirability of fixed rules within a deterministic setting. Adding disturbances to the model would therefore make the case for discretionary monetary policymaking stronger, for reasons familiar in the literature. So in order to sharpen the analysis, we leave out disturbances.

We consider a small open economy in a world of purchasing power parity. Fixing the foreign price level at 1, domestic prices then equal the nominal exchange rate, and inflation and exchange rate depreciation is the same thing. At any time t, production is undertaken by competitive firms whose revenues are taxed by the tax rate zt. Assuming a Cob&Douglas technology and labour as the only variable input, period-by-period profit maximization implies that aggregate output is given by

Yt = 4Pt - w - 4, a>o, vt,

where y,, pt, and w, are log of output, prices, and nominal wages, respectively [and where ln(1 - 7,) has been approximated by - z,]. We assume that wage setters sign contracts with the aim of achieving some real wage target. For simplicity, and with no loss of generality, (log of) this target value is set equal to zero.5 The wage setting rule is thereby given by w, = E(p, 1 I,_ 1 >, where E { pt 1 I, _ 1 > is the wage setters’ rational expectations about the price level at the time they sign contracts, conditional upon their information set I,_ 1. This set includes all structural variables and government preferences, but it does not include the policy choices of period t. Hence, the wage setters’ decision is, basically, their prediction. Letting 71, = pt - pt- 1 denote the inflation rate, we apply this wage setting rule to the aggregate output expression above, which then becomes

yt = 471, - E{nt I I,- I} - z,), Vt > (1)

4This point is also made by Barro (1983).

‘As in Canzoneri (1985), for example, wage setters’ utility can be represented by uw, = - (w, - p,)2.


where E { rc, 1 I, _ 1 } is the inflation rate expected by the wage setters. Note that (1) is a familar Lucas supply function augmented by tax distortions. Higher taxes lower output since they distort firms’ labour demand decisions downwards, and surprise inflation increases output since this erodes the real wage.

The dynamic link in this model is the government’s budget constraint. The government finances public expenditures and payments on debt through tax revenues, seigniorage, and new debt (of one-period maturity). Letting d, denote the ratio of debt to output, gt the ratio of expenditures to output, r > 1 one plus the interest rate on debt, the government’s dynamic budget constraint can be approximated by

c-4

The derivation of (2) is carried out in the appendix. The interest rate is constant and exogenously given. For a large open economy, an endogenous interest rate would be adequate, but debt dynamics would become nonlinear and less tractable. A fixed interest rate, however, is consistent with our small open economy assumption, and subsumes that the government conducts its loan activities on an international market for debt. It also removes any incentives to erode the real value of debt through inflation: any inflation is matched by an equivalent depreciation. Therefore our analysis is simplified by focusing exclusively on the credibility problem arising from the government’s incentive to increase output through surprise inflation; cf. below.6

The government lives forever and is for simplicity considered an entity simultaneously performing monetary and fiscal policy.’ The government has preferences defined over output, public expenditures, and inflation, and when performing policy it seeks to maximize ~~=O/?f~t(y,, gl, rcJ, the infinite discounted sum of per-period utility functions, with 0 < /I < 1 being the discount factor, and

being the per-period utility function. This corresponds to the one introduced by Alesina and Tabellini (1987). At any point of time, the government dislikes any deviation in (log of) output from zero, which we assume to be full employment output. Note that, by virtue of the wage setting rule, this is equilibrium output

‘On the issue of credibility problems in relation to nominal debt, see, e.g., Bohn (1991) and Persson, Persson, and Svensson (1987).

‘Hence, we neglect potential consequences of divergent policy objectives of, e.g., central banks and fiscal authorities [cf. Alesina and Tabellini (1987), Tabelhni (1986)] and/or conflicts between present and future governments [cf. Persson and Svensson (1989)].


absent any tax distortions; cf. (1). The wage setting rule thus corresponds to the market clearing wage in a nondistorted economy. Hence, without tax distortions there is no conflict between the government and wage setters. When distortions are present, however, the government would prefer real wages to be lower in order to counteract the inefficiencies caused by taxes. Moreover, the government dislikes any public expenditure deviations, defined as the diver- gence of the public expenditure ratio from some target ratio S > 0; i.e., the government prefers a positive level of public expenditures. One motivation for the inclusion of public expenditures in the utility function is that it reflects citizens’ utility from various forms of government spending (on, say, public services, education, health programmes, social security, etc.). Finally, the government dislikes any price movements. This could, for example, reflect the direct costs of changing prices (menu costs and shoe-leather costs), or indicate the government’s concern with the income distribution of the economy.8

Now we turn to the question of optimal policymaking within the model. At time t, the government takes nominal wages, i.e., inflation expectations, and the state variable, d,, as given. When it performs its optimal taxation problem, its control variables are assumed to be the inflation rate, the tax rate, and its debt position in the next period. The Bellman equation, or value function, associated with its maximization problem is therefore

v(4)= max (-C~l~:+~2(~r-9)2+71:l+~v(d,+l)}, VtrO, rr,nt.dt+ I

(4)

subject to (1) and (2). The necessary first-order conditions for maximum are

I*l@.?J, - P2CYt - S) = 0, vtro, (54

- Play, - P2(91- 4) - 71, = 0, vt20, (5b)

- 112(gt - a + Bv’(d,+ 1) = 0, vt20. (5c)

Eq. (5a) states that whenever public expenditures are too low, the per-period marginal gain from raising taxes, in terms of higher expenditures, must be offset by the marginal loss, in terms of lower output. Eq. (5b) states that inflation is set so as to equate its marginal gain, in terms of expenditures and output (remember that inflation expectations are taken as given), with its marginal loss, in terms of inflation itself. Finally, eq. (5~) shows that the current marginal gain from raising next period’s debt position, in terms of higher current expenditures, must be

8Although the quadratic formulation of(3) is rather restrictive, it may be viewed as a second-order Taylor approximation to a more general utility function.


offset by the (discounted) future value loss it creates, in terms of constraining future policy.

Because d, + I is considered a control variable, the transition equation for d f+ 1 does not include the state at t, and therefore Benveniste and Scheinkman’s (1979) formula yields j?v’(d,+,) = j?p2r(g,+l - S). I.e., given that the next period’s expenditures are below target, carrying more debt over to the next period constitutes a value loss in terms of reduced potential for public expenditures. Of course, the higher I, the higher is this loss, and the higher 8, the higher is the current valuation of such a loss. Inserting this back into (SC) and using that, ex post, E{~c,IZ,_~} = Z, in this deterministic model, eqs. (5aH5c) are rear- ranged so as to yield the following open-loop Nash equilibrium characterization (formally, focus on open-loop equilibria makes the application of dynamic programming techniques inappropriate; we, however, apply them for exposi- tional purposes):

2, = -::;r,bt - S) =- y, = ‘(St - g), vt20, PlH

Vt20, (W

B(st+1 - $7) = 1 (St - S) i’ vt20. (64

Eq. (6a) demonstrates that in a period where expenditures are below target, taxes are positive, as the government then has the incentive to raise revenues by conventional tax measures. The more the government is concerned with expenditures relatively to output, i.e., the higher pLz/pl, the stronger is this incentive and, hence, the higher is taxes. As an immediate consequence, the lower is output, since output in equilibrium (where inflation expectations are validated) is exclusively determined by the tax rate; cf. (1).

Also, by (6b), when expenditures are below target, inflation is positive, partly because the government has incentives to raise revenue through seigniorage. Another part of inflation is attributable to the government’s incentive to raise output [which is too low due to tax distortions - cf. (6a)] by surprising wage setters. However, as wage setters are rational, they set expectations (that is, sign contracts) sufficiently high so as to pre-empt this incentive. As a result, the game situation between wage setters and the government caused by suboptimal output due to tax distortions, results in a Nash equilibrium characterized by inefficiently high inflation in comparison to a situation where the government could credibly renounce its desire to surprise wage setters. This is the well- known credibility problem as described by Kydland and Prescott (1977) and Barro and Gordon (1983a, b). Note that inflation in this model is primarily


a consequence of the government’s expenditure concern, pL2 > 0. If p2 = 0, there would be no inflation: there would be no need for seigniorage revenues, and as taxes would also be zero, output would be at its desired value, and the incentives to surprise wage setters would vanish.

The government never specializes completely in any revenue-generating instrument. Only in the extreme case, where inflation is immaterial to the government (i.e., p1 and ,LL~ become very large), would seigniorage be the only source of revenue, and only in the case where output did not matter (i.e., ,ul would be very small) would taxes be the only source. Otherwise, the solution to the optimal taxation problem is characterized by a mix of the two instruments.

The last equation, (6c), is the Euler equation which expresses how expenditure deviations evolve over time in optimum. Given that expenditures are below target at t, then whenever /?r > 1, expenditures will be closer to target in the next period. This is because the present value loss of passing on debt to the next period, in terms of constraining future expenditure possibilities, more than outweighs the current gain. In other words, it is optimal to substitute future expenditures for current. As will be shown below, only in the case where fir > 1 is the equilibrium stable, so it will be assumed throughout.

In order to characterize the solution completely, we need to find the explicit solution for public expenditure deviations. This is accomplished through a com- bination of the Nash equilibrium characterization and the government’s budget constraint. In order to rule out the trivial strategy of infinite borrowing, however, we impose the following No-Ponzi-Game restriction upon the solution:

lim reTdT = 0. T-r,

(7)

Forwarding (2), using (6a) and (6b), and applying (7) we then obtain the government’s intertemporal budget constraint:

f r-j(gt + j - 4) + j=O

+G + f-4 = f r-j(zt+j + 7~,+~) j=O

= - f r-jy(g,+j -g), Vt 2 0, j=O

where

47, + 4 “J’ = d(g, - g)

= 2#u2 + + PlCf

quantifies the government’s willingness to substitute taxes (of either kind) for public expenditure deviations. Eq. (8) simply states that the present value of all


current and future public expenditures (here written in terms of expenditure deviations plus targets) plus today’s debt and interest payments must equal the present value of all current and future tax returns. Now, note that eq. (6~) can be forwarded so as to yield

St+j - g = fl-jr-j(g, - a), Vj 2 t, Vt 2 0, (9)

which gives any future deviations in public expenditures as a function of current deviations. Inserting (9) into (8) then gives us the expression for optimal expenditures as a function of the state, d,:

gt - CT = - (1 + y)fir’ r - 1 Br2-1 {Lg+rd,), VtTO, (10)

where the term in curly brackets is the present value of expenditure targets plus current value of debt. In order for the government’s intertemporal budget constraint to be satisfied, this amount must equal the present value of all current and future tax returns minus the present value of all current and future expenditure deviations. This equality then defines the feasible gt residually. Whenever the term in curly brackets is positive, the government must accept that public expenditures at t must be below target. Only if the government’s willingness to use taxes (of either kind) is unbounded, that is, if y -+ co, expenditures would be targeted perfectly. Also, in the border case where the government is extremely short-sighted (j3 + 0), expenditures would be targeted (this would also apply in the perverse case where the government should not repay debt at all, i.e., if r -+ 0). Only in the intermediate cases, however, an interesting dynamic trade-off exists, where the government in equilibrium accepts some deviation in expenditures from a, and, therefore, deviations in output and inflation from their respective target values.

Applying (10) together with (6a) and (6b) gives us equilibrium taxes, output, and inflation, and inserted into (2), we obtain the equilibrium evolution of debt as

(11)

As is immediate from (11) fir > 1 must hold in order to secure stability of the solution. Otherwise, debt as a fraction of output keeps growing over time.’

‘If a low value of B is loosely interpreted as ‘political instability’ (which in some sense is synonymous with short-sighted politicians), the model predicts a positive correlation between exploding debt (together with high inflation) and political instability. Such a correlation finds empirical support in Cukierman, Edwards, and Tabellini (1992) and Grilli, Masciandaro, and Tabellini (1991).

772 H. Jensen. Monetary discretion in a dynamic policy game

Remark that y, i.e., the government’s willingness to use taxes, does not play a role in the determination of the optimal path of debt. Consider a high value of y. This implies that an expenditure deviation has a large effect on next period’s debt, as taxes and inflation will be large; cf. (6a) and (6b). But note that, at the same time, a high value of y implies a low value of expenditure deviation; cf. (10). These effects cancel out, leaving the debt path unaltered. From (ll), it follows immediately that the steady state value of debt is

In steady state, debt is negative, meaning that the government has become a net creditor. Inserted into (10) this gives steady state expenditures as

and, in consequence, steady state taxes, output, and inflation as

In words, the government builds up reserves over time, so as to finance public expenditures through interest revenues, which makes any other taxation unnec- essary. Output, therefore, will be at its desired value, and the incentive to surprise wage setters vanishes. The (Barr0 and Gordon) credibility problem is removed, and inflation is zero in equilibrium. Only on the path towards steady state will there be distortions. If, e.g., initial debt is above the steady state, the government will have to finance part of public expenditures by conventional taxation and seigniorage in order to pay off some of the debt. It will then experience credibility problems vis-a-vis wage setters, who recognize the government’s incentives to raise output (through surprise inflation) which is too low due to tax distortions. But as time proceeds, debt is reduced, and eventually the government becomes a net creditor, which enables it to reduce taxes and seigniorage completely and, in consequence, alleviate its credibility problems vis-a-vis the wage setters.

An equivalent point is made by Obstfeld (1991) in a model of the Calvo (1978) vein. There, the government has a credibility problem vis-a-vis consumers, in the sense that it has an incentive to tax (by inflation) real cash holdings in order to finance public expenditures. This causes consumers to hold an inefficiently low amount of real cash. As time goes on, however, the government builds up reserves, making this incentive weaker and, in effect, affecting consumers’ real cash holdings in the right direction.

For later reference, when we are going to evaluate the desirability of various policy regimes, we derive the expression for the value function under monetary

H. Jensen, Monetary discretion in a dynamic policy game

discretion. Using (6a) and (6b) together with (4), we arrive at

‘tdt) = - f fljO(g*+j - g)‘, .i=O

113

(12)

where

@_ _ dud*) P2

d(g, - g)2 = ” ~ + 1 + ‘t/L2 PIU2

denotes the impact on equilibrium per-period utility of a deviation in public expenditures. To find the explicit form of v(d,), we then first use that eq. (9) shows how to express any future deviations in expenditures in terms of current deviations. Secondly, we apply that (10) gives current expenditures as a function of debt. Combining (9), (lo), and (12) thereby yields

v(dt) = - O/jr2 _ 1 (1 + )))/3.2 -K{ pr2-- (-&“+‘q (13)

As long as debt is different from its steady state value, the government experien- ces a loss, due to the ensuing dynamic adjustment towards steady state which is characterized by tax distortions and credibility problems. The higher a value of y, the lower is this dynamic loss. This is because the government then is willing to ‘bite the bullet’, in terms of using its tax instruments so as to obtain smaller public expenditure deviations. This has the consequence that on the path towards steady state, expenditures are closer to target in each and every period the higher y is. However, a higher value of 0 makes the loss larger,” as any per-period loss due to expenditure deviations has stronger adverse consequences for the government’s utility.

As any path characterized by tax distortions features the well-known Barro and Gordon credibility problem of the government vis-a-vis the wage setters, it is of interest to analyze whether the government will gain from adhering to an institutional arrangement where it gives up monetary sovereignty. The analysis of this question is the object of the following section.

3. Loss of monetary discretion

Now we consider whether a strategy of giving up one’s discretionary powers in fact is advantageous within the model presented in the previous section. We

“Note, however, that y and 0 cannot move independently, as they both depend on the same utility weights.


assume that the government pegs its currency to a perfectly stable currency.” This fixes the inflation rate once and for all at the government’s preferred rate, zero. We therefore have that

q=o, vt20. (14)

The Bellman equation then becomes

WJ = max ( - CPIY: + p2(gt - S121 + BW,+,)} , Vt 2 0, (15) dr+ ,.*t

subject to (l), (2), and (14). The necessary first-order conditions for maximum are

P1EYt - P2(Sr - S) = 0 9 Vt20, (164

-~Ul(gt-g)+BOl(dt+l)=O, Vt20. (16b)

As before, PM+ A = Pp2r(g,+ 1 - S). Inserting this in (16b) and using that E(rc, 1 I,_ i> = 0, eqs. (16a)-(16b) yield the following equilibrium characterization:

P(St+1 - S) = 1 (St-S) I’

Vt20. (17’4

These equations are identical to the ones under monetary discretion, (6a) and (6~). That is, the incentives to have positive taxes when public expenditures are too low, and in that case let expenditures rise in the next period, are the same as under monetary discretion. This, of course, does not mean that the solutions for taxes and expenditures are the same. The difference is that the inflation rate is now exogenously fixed by (14), and this has consequences for the determination of public expenditures and, therefore, taxes. As before, public expenditures follow residually from the budget constraint. Ruling out Ponzi games by (7) and using (17a), the intertemporal budget constraint under a zero inflation rule

“As noted by Canzoneri and Henderson (1988), one may ask whether pegging one’s currency is more credible than maintaining a stable price level. This question is ignored here, and it is assumed that the government gains access to a commitment technology which allows a credible peg.

H. Jensen, Monetary discretion in a dynamic policy game 71s

5 '-j(gt+j - $7) + j=O

-JJj + rd, = f r-jz,+j j=O

(18)

= -fr-jy*(gl+j-g), Vt20, j=O

where

is - dzt P2 =-

4s, - s) PIN"

Vt>O,

quantifies the government’s willingness to substitute taxes for public expenditure deviations under a monetary rule. The only difference between (8) and (18) is this willingness. More specific, y > 9, which means that under a zero inflation rule, the government’s willingness to use taxes is obviously reduced, since it is deprived of using inflation as a tax instrument.

Applying (9), we then find optimal expenditures from (18) as

g1 - a= -(I '*'-' {$,+rd,}, Qt20. + 9)p.Z (19)

This has the same form as (lo), and again the only difference is the term i. As the government’s willingness to use taxes under a zero inflation rule is smaller than under discretion, it follows that public expenditure deviations, for any debt position, are larger than under discretion. If, e.g., the term in curly brackets is positive, expenditures are too low, and lower than under discretion.

Using (2) and (19) together with (17a) gives us the optimal path of debt:

d ffl Qt20.

As was the case with the path of debt under discretion, the term 9 has no effect, and therefore the path of debt is the same under rules and discretion.12

In order to assess the desirability of losing monetary discretion, we derive the explicit form of the value function (15). It is found to be

12This is attributable to the fixed interest rate assumption which accounts for identical Euler equations under the two alternative regimes; cf. (6~) and (17b).

116

where

H. Jensen, Monetary discretion in a dynamic policy game

represents the impact on equilibrium per-period utility of any deviation in public expenditures when inflation is determined by (14). In comparison with discretion we have that 0 > 6, i.e., any deviation in public expenditures has a more adverse effect on per-period utility under discretion. This is because such deviations are accompanied by price movements [cf. (6b)], due to credibility problems and seigniorage motives, which, by definition, are absent under the rule given by (14).

Having derived (20), we are in a position where we can compare the desirability of losing monetary discretion in any state, i.e., given any value of debt. We find:

Proposition. For any d,, we have that v(d,) 2 v*(d,), and only ifd, = - g/(r - l), we have v(d,) = O(d,) ( = 0).

Proof A comparison between (13) and (20) immediately reveals that the value functions v(d,) and O(d,) are identical, and equal to zero, whenever d, = - g/(r - 1). Furthermore, for all other d,, this comparison reveals that

0 s v(d,)gf(d,) o ~ ~

(1 + &l + 9)2.

Inserting the values of 0, 6, y, 9 then readily shows that v(d,) > C(d,). W

No matter what the debt position of the government is, it is not advantageous to give up monetary discretion. And only when debt has reached its steady state value, is the government indifferent between the two regime forms.

The intuition behind the result is as follows. In a situation where debt is off steady state, the target value of public expenditures is unattainable; cf. (10) and (19). Under a monetary rule, the government’s willingness to ‘bite the bullet’ and accept taxes (conventional taxes as well as inflation taxes) in order to reduce expenditure deviations is forced to be more faint in comparison with a situation where it has discretionary powers; cf. that 3 < y. Hence, public expenditure deviations will, in each and every period, be larger when the government loses discretion. Output deviations will be larger; cf. (6a) and (17a).

In contrast with these disadvantages of adhering to a monetary rule, is, of course, the advantage of a lower loss for any given expenditure deviation, due to the fact that inflation is at the government’s target value in every period; cf. that

H. Jensen. Monetary discretion in a dynamic policy game 711

6 < 0. This advantage, however, cannot offset the formerly mentioned disadvantages ~ not even in the case where the inflation rate under monetary discretion is excessively high. To understand this, note that such a case would be attributable to very high governmental weights on output and expenditure targets.’ 3 Therefore, the disadvantage of losing monetary discretion, in terms of lower expenditures and output, would have a very strong negative impact in terms of government utility. In addition, the gain of reducing inflation is decreasing with inflation, while the losses of lowering output and expenditures are increasing; cf. the concavity of the utility function.

4. Concluding remarks

We have demonstrated that letting the government bind itself to an inflation rate, which in fact is identical to its preferred rate, is not advantageous within this model. This applies in spite of the fact that, outside the steady state, the model features a monetary credibility problem leading to the well-known (Barr0 and Gordon) inflation bias. Our analysis is carried out within a dynamic context, where the emphasis is on optimal taxation issues. This provides an explicit, and endogenous, justification for credibility problems. These are shown to be temporary, and our main result holds for any debt position apart from the steady state. Although debt dynamics is left unchanged by a regime shift, each period towards the steady state is characterized by a less efficient outcome under rules than discretion. Basically the reason is that without monetary discretion, the disadvantage caused by loss of freedom in the taxation problem more than outweighs the credibility gains. It is interesting to note that the ‘net disadvantage’ of losing monetary discretion [measured as the difference in value functions, v(d,) - v*(d,)] therefore is larger the more debt diverges from steady state, as this means more periods of inoptimal taxation.

To follow up on the implications of the results for monetary policies in Europe, we note that the model lends support to the claims of, e.g., Giavazzi (1989) and Dornbusch (1988) who consider the difficulties some southern Euro- pean countries will face when they give up monetary discretion in accordance with the upcoming plans for monetary unification of Europe.14 As these countries rely on seigniorage as a means of public finance, adherence to the zero inflation rule envisioned in these plans necessitates a shift towards distortionary taxation, with ensuing employment problems.’ 5

r3Combining (10) with (6b) immediately reveals that A, is an increasing function of g1 and p2.

14Grilli, Masciandaro, and Tabellini (1991) argue that the seigniorage part of revenue for these countries are declining. The question then, of course, is whether this is a deliberate optimal policy choice or a natural consequence of their closer association with the (low-inflation) EMS system.

“Also, there may be collection costs associated with conventional taxation which supports this argument further.


In our model credibility problems have exclusively been due to tax distortions. One could also imagine that the natural rate of output was socially inoptimal due to monopoly union powers in the wage formation process. We conjecture, however, that our results would carry through under such a specification as well. If, e.g., the union demanded a real wage above zero, the optimal dynamic taxation problem would lead to a steady state wherein interest payments would not only finance the desired public expenditure ratio as in this model, but also provide a wage subsidy to the union in excess of the market wage. Then firms would produce the socially optimal output. The main issue is that it is optimal for the government in the long run to alleviate distortions, of any kind, by the appropriate debt management policy.

Appendix: Derivation of (2)

Assuming that D, is the nominal value of debt denominated in foreign currency at the beginning of period t, the budget constraint is

&D f+l = rE,D, + f’,G - d’,Y, -CM, - M,-I), (A.11

where E, is the nominal exchange rate (domestic price of foreign currency), G, is public expenditures, P, is the price level, Y, is output, and M, is money supply. Dividing by nominal income, P,Y,, and remembering that purchasing power parity, P, = E, (with foreign prices normalized by one), is assumed to apply, (A. 1) reduces to

D f+l D, G -~r-+---_z,- Mt-ME-1

K y, yt ply* (A4

Assuming that money market equilibrium is characterized by the conventional quantity theory specification (with velocity equal to one), P, Y, = Mt, the last term of (A.2) illustrates the money growth rate, which we approximate by rc,. Then (A.2) is the same as (2) [note, however, the slight abuse of notation as d ,+1 = D,+l/Yt and d, = WYJ.

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