Journal Issue

Optimal Taxation Policies in the EMS: A Two-Country Model of Public Finance

International Monetary Fund. Research Dept.
Published Date:
January 1990
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The Convergence of national policies within the European Monetary System (EMS) has received considerable attention over the years.1 The comprehensive financial integration within the EMS scheduled for 1992 has rendered the topic even more relevant in the minds of both researchers and policymakers. In particular, with reference to the implications of the EMS for national inflation rates, the discussion has focused on whether the system would impart an inflationary or a disinflationary bias. While some have argued that low-inflation countries would suffer from inflationary pressures from high-inflation countries, others have suggested that the opposite would take place. As pointed out by Guitián (1988), the evidence has been inconclusive, and it is therefore difficult to argue on a factual basis that the EMS has so far imparted either an inflationary or a disinflationary bias. Earlier work by Ungerer and others (1986), arguing that the EMS had been influential in reducing inflation among member countries, has recently been challenged by Collins (1988), who finds no evidence in support of the disinflationary bias hypothesis. Collins (1988) suggests that the disinflationary process that took place after 1979 in EMS member countries has not been significantly different from that which occurred in other industrial countries outside the EMS.

The issue of national inflation rates is in turn related to the fiscal policies of the individual countries, insofar as revenues from money creation may constitute an important percentage of government revenues.2 For some countries within the European Community (EC) (for instance, Italy, Spain, Portugal, and Greece), seigniorage accounts for between 6 percent and 12 percent of tax revenues.3 Furthermore, as suggested by Giavazzi and Giovannini (1989, p. 200), “differences in fiscal structures thus justify differences in the ‘optimal’ revenue from seigniorage. In all likelihood the ‘optimal’ inflation rate is not the same across Europe. …”

In view of the links between the convergence of national inflation rates, the revenues from money creation, and fiscal policies, it is important to provide a framework of analysis in which the essential features of these relationships can be isolated and analyzed in detail. Such a conceptual apparatus should in turn prove useful in the consideration of policy matters in which these issues may be involved but whose importance and implications may prove difficult to assess because of the presence of other macroeconomic problems (for instance, output effects of monetary policy).

To analyze these public finance issues, this paper extends to a two-country world the framework developed in Végh (1989a), in which the relative importance of seigniorage as a source of revenue results from high government spending coupled with inefficient tax administration systems that make it costly to rely solely on “conventional” taxes (that is, consumption or income taxes). It has long been recognized that a key feature that distinguishes the inflation tax from other, conventional, taxes is that the inflation tax is almost costless to collect. Aizenman (1987) incorporates this characteristic of the inflation tax into an optimal taxation problem by assuming that a consumption tax, which is the other tax available to the government besides the inflation tax, carries collection costs and concludes that the optimal tax is positive. The same result is obtained by Végh (1989a) in the context of a model in which money is introduced as reducing transaction costs, as in Kimbrough (1986).4 Moreover, Végh (1989a) shows that if the consumption tax carries constant marginal collection costs, the optimal inflation tax does not depend on government spending; whereas if marginal collection costs are increasing (that is, total collection costs are a convex function of revenues), the optimal inflation rate is an increasing and convex function of government spending.

Within the public finance framework just described, this paper investigates how the constraints imposed by a system like the EMS affect the optimal taxation structure that would prevail in the absence of those constraints. The first issue is the equalization across countries of nominal interest rates. Specifically, under flexible exchange rates, if collection costs and/or levels of government spending differed among individual countries, governments would optimally choose different taxation structures and, in particular, a different nominal interest rate.5 With an arrangement such as the EMS, exchange rates are supposed to remain fixed over the long haul, which imposes the constraint of a shared common nominal interest rate among its members. Two important questions arise: first, will the resulting common nominal interest rate be closer to that of the high-inflation country or to that of the low-inflation country (that is, will there be an inflationary or a disinflationary bias)? Second, how will levels and differences in government spending and the relative efficiency of the tax administration systems affect whether there is an inflationary or a disinflationary bias?

The second issue is the equalization across countries of consumption taxes. Given that the EMS contemplates the possibility of periodic realignments, and most likely still will after 1992, it follows that national inflation rates may differ across countries for a given period of time. This raises the question, which is also related to current discussions in the EMS, as to how the differential between national inflation rates would be affected by equating, say, consumption taxes across countries. Put differently, would such tax harmonization policies make it easier or more difficult to sustain fixed parities with only occasional realignments?

It is worth stressing at this point that the model does not explicitly incorporate whatever benefits may result from establishing a fixed exchange rate regime or from equalizing consumption taxes. The rationale for not doing so is twofold. First is the desire to maintain analytical tractability, since from an analytical point of view, the model is already quite complex without these additional features.6 Second, since there is no consensus on the advantages of fixed over flexible exchange rates or of tax harmonization, there is no obvious way of incorporating these potential benefits into the model.7 Therefore, this model should be viewed as a means of isolating and analyzing the costs associated with the types of constraints that the EMS may impose upon its members, while abstracting from the potential benefits. (Clearly, since we will be comparing solutions to an unconstrained optimization problem with solutions to a constrained optimization problem, in terms of welfare, the latter can, at most, be as good as the former.) Insofar as simulations of the model suggest, however, that the costs imposed by the constraints are negligible—as will be the case when a common nominal interest rate is required—the benefits of a system of fixed exchange rates, in terms, say, of more stable real exchange rates, could certainly be presumed to outweigh these costs.8

The paper proceeds as follows. Section I reviews the determination of the optimal inflation tax and its dependence on government spending and the efficiency of the tax administration system in each country under flexible exchange rates. This review provides the benchmark case against which the more complex two-country model with fixed exchange rates can be compared. Section II introduces the two-country model with fixed exchange rates and analyzes the consequences of imposing the constraint of nominal interest rate equalization across the two countries. It is shown that the common inflation tax is closer to that of the original high-inflation country. The inefficiency of the tax administration system is shown to play the crucial role, as opposed to that played by the different levels of government spending. The consumption taxes may either converge or diverge depending on the initial tax structure of each country. The effects on the revenues from money creation as a fraction of total revenues are also analyzed. Section III discusses the effects of the imposition of consumption tax equalization. The analysis suggests that national nominal interest rates would be subject to important changes as a result of the large changes in revenues produced by the equalization of the consumption tax rates due to the relative unimportance of seigniorage as a source of revenue. Section IV contains concluding remarks.

I. The Two-Country Model Under Flexible Exchange Rates

This section considers the optimal taxation policies for each individual country in a two-country model under flexible rates. Although the results of this section can be found in Végh (1989a), they are derived here by recourse to the dual approach to optimal taxation (as opposed to the primal approach), and different graphical representations are used.9 This way of presenting the results provides a convenient framework for understanding the results that obtain in the two-country model with fixed exchange rates (Section II) and the two-country model where the constraint of equal consumption taxes is imposed (Section III). Since the structure of the model can be found elsewhere, the presentation, while self-contained, will be brief. Both countries will be assumed to be identical; therefore, only the domestic country will be introduced. The variables pertaining to the foreign country will be denoted by an asterisk.

For simplicity, it will be assumed that this is a one-good world. This good is produced under a technology that exhibits constant returns to scale, given by

where y denotes units of the good, n stands for labor input, and units have been defined in such a way that producing one unit of the good requires one unit of labor. Labor is taken to be the numeraire.

The domestic consumer holds two assets: domestic money and an internationally traded bond whose rate of return is r.10 The consumer holds money in order to reduce transaction costs in the form of “shopping” time. Specifically, the time that the consumer devotes to transacting is given by

where s, c, and θ denote shopping time, consumption, and the consumption tax rate, respectively. We refer to Xt ≡ mt/[ct(1 + θt,)] (where m denotes real cash balances) as “relative money balances.” Equation (2) indicates that additional relative money balances bring about positive but diminishing reductions in shopping time for a given expenditure on consumption. When the level of relative money balances reaches Xs, the gains from holding money are exhausted.11 It will be assumed that when that level of relative money balances is achieved, transaction costs are zero (that is, v(Xs) = 0). 12 Assuming that the consumer is endowed with one unit of time in every period, the time constraint that he or she faces is

where h denotes leisure. The consumer’s optimization problem can now be formally stated as

subject to


is the interest rate discount factor; d0 ≡ 1, and β is the constant subjective discount factor; U(c, h), the instantaneous utility function, is twice continuously differentiable, with positive and diminishing marginal utilities; s is given by equation (2); and It ≡ [it/(1+it)] is the inflation tax, where i is the nominal interest rate. The consumer can be viewed as following a two-stage optimization process because real money balances enter the maximization problem only through the budget constraint. In the first stage, then, the consumer chooses an optimal amount of real money balances, which yields –v’(Xt) = It as the first-order condition. This optimality condition says that the consumer equates the benefit in terms of reduced shopping time of holding an additional unit of money to its opportunity cost. Solving for Xt (that is, Xt = X(It)) and substituting it into (4) yields the following budget constraint:


Note that q can be thought of as the “effective” price of consumption, as opposed to the market price, which equals (1 + θ). For our purposes, however, it is best to think of (q – 1) as the distortion introduced into the consumer’s leisure/consumption choice as a result of the presence of distortionary taxation. Clearly, if both taxes were zero (that is, It = θt = 0), then there would be no distortion; namely, q would equal unity. The consumer can now be viewed as maximizing over {ct, ht}t=0 his or her utility function, subject to equation (5). In addition to (5), the other two first-order conditions can be combined to yield (where a subscript i on a function denotes the partial derivative with respect to the ith argument)

whereby the consumer equates the marginal rate of substitution between consumption and leisure to its relative price. It can be shown that, given that government spending will be assumed to be constant over time, the optimal taxation structure will also be constant over time; that is, θt, = θ and It= I for all t. 13 Given that the consumer balances his or her budget in every period, and taking into account equation (7), it follows that c = c(q) and h = h(q), where (∂c/∂q) < 0 and (∂h/∂q) ≷ 0. Substituting these optimal choices into the utility function yields the indirect utility function V(q) ≡ U[c(q), h(q)], where (∂V/∂q) < 0.

The optimal taxation problem facing the domestic government is to maximize V(q) over {θ, I} or—which amounts to the same thing since V(q) is decreasing in q—to minimize q, subject to the constraint that its budget be balanced in every period. Formally, the government minimizes q subject to

where g denotes the constant level of government spending, and Tc) ≡ φ((θc)θc represents the collection costs associated with collecting revenue by way of the consumption tax as a function of gross revenues. For simplicity, it will be assumed that φ(θc) = kθc, where k is a nonnegative parameter.14 Thus, Tc) = kc)2, so that the collection costs schedule is a convex function (for k > 0): ∂T/∂c) = 2kθc> 0 and ∂T2/∂(θc)2 = 2k > 0. With this particular functional form taken into account, equation (8) can be rewritten for analytical convenience as g = cГ(θ, I), where Г (θ, I) ≡ (1 – kθc)θ + IX(1 + θ) (recall that c = c[q (θ, I)]). In addition to (8), the first-order conditions for this minimization problem can be combined to yield qθ/q1 = Γθ1, which can be rewritten as

where c = c[q(θ,I)]. It is optimal to equate the marginal rate of substitution between the two taxes along a utility indifference curve to the marginal rate of transformation per unit of consumption along an isorevenue curve.15 If the consumption tax carries no collection costs (that is, k = 0), it is easy to verify (given that v[X(0)] = 0) that I = 0 is the solution to equation (9), so that all public spending is financed with the consumption tax; this is Kimbrough’s (1986) result. When k > 0, two aspects of the solution are worth noting. First, I = 0 is no longer a solution to (9). Second, the optimal I, depends on the level of government spending, because the presence of c in (9) implies that (9) no longer implicitly defines a reduced form for . In other words, equation (8) and, thus, g influence . In the general case where k ≥ 0, equations (8) and (9) implicitly define I° = I°(g, k) and θ° = θ°(g, k), where I(g> 0,0) = 0, I(g > 0,k > 0) > 0, [∂I°(g, k > 0)/∂g] >0, and [∂I°(g >0, k)/∂k] >0. The foreign country faces an identical problem, which determines the optimal taxes (I*, θ*). Given that the good produced in both countries is the same, the law of one price holds; namely 1 + Π = (1 + ê)(1 + Π*), where Π and Π* denote the domestic and foreign rates of inflation, and e is the rate of depreciation of the exchange rate (units of domestic currency per unit of foreign currency). Using the Fisher conditions, 1 + i = (1 + Π)/β and 1 + i* = (1 + Π*)/β, it follows that ê = (i – i*)/(1 + i*) (recall that β = β*).

It is useful at this stage to put some quantitative content into the solution of the optimal taxation problem of both countries under flexible exchange rates in order to establish a numerical benchmark against which the results in the next two sections—which are derived from the imposition of the constraints I = I* and θ = θ*—can be assessed.

For the purposes of obtaining numerical solutions, the utility function will be assumed to take the form U(c, h) = log(c) + log(h). This implies that h is always equal to one half. The function v(X) is assumed to be quadratic; namely v(X) = X2– a X + d, where a = 0.6 and d = 0.09.16 Since this numerical exercise will roughly replicate actual inflation rates, we will identify the domestic country with the Federal Republic of Germany (the low-inflation country) and the foreign country with Italy (the high-inflation country) and take their average government spending during 1986–88 as the values for g and g*. The value of k is chosen so as to generate the observed inflation rate.17 Thus, in the case of Germany, with g = 0.225 (45 percent of gross domestic product (GDP))18 and k = 0.023, i° = 0.6 percent, and the revenues from money creation as a fraction of total revenues are equal to 0.4 percent. For Italy, with g* = 0.25 (50 percent of GDP) and k* = 0.23, = 6.7 percent, and the revenues from money creation equal 3.3 percent of total revenues.19 Given that the differences in government spending are rather small, the model explains the different inflation rates based on the relative efficiency of the tax structures. By doing so, the model puts explicit analytical content into expressions such as “differences in fiscal structures” as used, for instance, by Giavazzi and Giovannini (1989, p. 200).

It has been shown here that, under flexible exchange rates, the optimal inflation tax in Germany and Italy would differ. The next section looks at the effects on the taxation structures of a common inflation rate, which is necessary to sustain fixed parities (with no realignments possible).

II. The Two-Country Model with a Common Inflation Tax

It is hard to disagree with the premise that if capital controls are completely eliminated by 1992 the sustainability of the EMS will depend crucially on the convergence of monetary policies. If there is divergence between monetary policies, and hence divergent inflation rates, any anticipated realignment will deplete the reserves of the devaluing country if it cannot resort to capital controls to keep the necessary amount of reserves to defend the postdevaluation parity. Hence, unless capital controls were available in case of speculative attacks, as has been the case in the past, the EMS could not survive unless member countries were willing to endure huge interest rate differentials when a realignment was expected (see Wyplosz (1987) and Giavazzi and Giovannini (1989)),

In this section the scenario of the convergence of monetary policies is addressed. It will be assumed that a fixed exchange rate is established between the two countries of the previous section and that the monetary authorities optimally choose a common inflation tax (that is, they coordinate their monetary policies).20 We are mainly interested in finding out how this common optimal inflation tax compares to the optimal inflation taxes under flexible rates; that is, whether the common inflation tax will be closer to the inflation tax in the country with the high inflation tax or to that in the country with the low inflation tax.

The consumer in each of the two countries behaves exactly in the same way as before, since nothing has changed as far as he or she is concerned. As before, consumers of each country are assumed to be identical as regards their preferences and utility discount factors. The transaction-technology functions v(X) and v*(X*) are also assumed to be identical (and will be denoted by v(X)); this enables one to isolate the effects of different levels of government spending and of different levels of efficiency in the tax collection system (that is, k ≠ k*). Therefore, the consumer’s problem remains unchanged and will not be repeated here. Suffice it to say that from the optimization problem of both consumers, V(q) and V(q*) result, where q ≡ (1 + θ)[1 + v(Xw) + IWXW] and q* = (1 + θ*)[1 + v(XW) + IWXW]. Variables that, in view of the constraints imposed on the problem, have to be the same in both countries will be denoted by the superscript “w.” Thus, relative money balances will be the same in both countries, since both representative consumers face a common interest rate, Iw, and the transaction technology is the same. The governments of the two countries, giving equal weight to their representative consumer, coordinate their monetary policies so as to choose a common inflation tax. Formally, they face the following optimization problem:

subject to

In addition to equations (10) and (11), the optimality condition for this problem is:

It is important to note that the terms in brackets on both sides of equation (12) would be zero if the constraint that I = I* = Iw were not binding, because optimality requires that these terms be zero in the flexible exchange rate case. For convenience, these terms are denoted by D and D*, respectively. (The notation “D” stands for “deviation,” because as long as D or D* is different from zero, there is a deviation from the unconstrained optimal taxation structure.) To begin the analysis, consider the simplest case in which k = k* = 0. As indicated in the previous section, the optimal inflation tax is zero independently of the level of g. This being the case, one can guess that the solution now involves Iw = 0, which implies that D =D* = 0. It follows from equations (10) and (11) that θ = (g/c) and θ* = (g*/c*). The joint solution coincides with the solution under flexible exchange rates. In other words, having the same inflation tax implies no welfare cost, since it would have been the same to begin with; formally, this result follows from D = D* = 0.

Suppose now that k = 0, and k* > 0. From the previous section we know that under flexible exchange rates Io = 0 and (I*)o > 0. It can be readily verified that Iw = 0 is not a solution because equation (12) does not hold: the left-hand-side is zero, whereas the right-hand-side is negative.21 We can already assert, therefore, that Iw> 0. Furthermore, at an optimum, D> 0 and D* < 0. Figure 1 illustrates and clarifies the interpretation of the solution. (In all the figures that follow, a subscript “0” denotes the initial equilibrium and a subscript “1” refers to the final equilibrium.) The curves labeled g and g* represent isorevenue curves; namely, the locus of points (θ, I) and (θ*, I*) where revenues are constant. The curves labeled q0, q1

represent isodistortion curves; that is, the locus of points along which the distortions (q - 1) and (q* – 1) remain constant. As we move downward (that is, for a given I or I*), the level of the distortion decreases and, hence, welfare increases. Consider the optimal taxation structure of the domestic country (k = 0), which is given by point E0 where the isorevenue curve g is tangent to the isodistortion schedule q0. The optimal taxation structure of the foreign country (k* > 0) is given by point
where the schedule g* is tangent to q*0. Because k* > 0, I*0 is positive. Suppose now that the constraint of a common nominal interest rate in both countries is imposed. With the help of Figure 1 and taking into account equation (12), it follows that the optimal r lies somewhere between I0 and
. To see why, consider the initial situation in the domestic country. Since government spending remains unchanged, any movement toward the new optimum will imply moving along the isorevenue curve g. This implies that at the new optimum, the isodistortion curve is steeper (in absolute value) than the isorevenue curve as exemplified by point Ex (where qx is steeper than g). Therefore, in equation (12) D > 0; it thus follows that D* < 0, which implies that in the foreign country there is a leftward movement along the isorevenue g* because D* cannot be negative to the right of
. Intuitively, the collection costs for the two countries as a whole will be less than for the high-collection-costs country, since the total will involve, roughly speaking, some sort of average of the two individual collection-costs schedules. The same is true of the level of government spending. The costs, in terms of welfare, of convergent monetary policies are illustrated in Figure 1 by the fact that the new optima for both countries, E1 and
, lie on higher isodistortion curves than the initial optima at E0 and
under flexible exchange rates.22 In Figure 1, it is seen that the optimal consumption taxes tend to converge; namely, the difference between θ1 and
is less than that between θ0 and
. As can be readily verified with the use of Figure 1, however, this need not always be the case. If the low-inflation country has the lowest consumption tax at the initial optimum, then the consumption taxes will diverge as a result of the imposition of a common nominal interest rate.

Figure 1.Optimal Taxation Policies Under Flexible and Fixed Exchange Rates

Proceeding with the numerical exercise initiated in the previous section, we now compute the common nominal interest rate if the Federal Republic of Germany and Italy were to agree on jointly setting monetary policy. Recall that for Germany the optimal inflation was 0.6 percent, and for Italy it was 6.7 percent. Under the same parameter values, iw turns out to be 4.2 percent. The ratio iw/(i + i*) ≡ α can be viewed as an indicator of whether the imposition of a common nominal interest rate induces an inflationary or disinflationary bias to the system. A value of a greater than 0.5 would indicate that there is an inflationary bias. In this particular case, α = 0.572, which implies that the common inflation rate is higher than the average of the initial inflation rates. Welfare costs appear to be quite small under the present specification. Since leisure remains constant, the change in welfare depends exclusively on the change in consumption. Consumption in Germany falls by 0.029 percent and, in Italy, by 0.016 percent. As one would have expected, since the common optimal nominal interest rate is closer to that of Italy, the fall in consumption in Italy is less than that in Germany, but is nonetheless negligible in both cases. Therefore, the numerical analysis suggests that the costs of unifying monetary policies are almost nonexistent in this context. The reason is that since the revenues from the inflation tax are not important, the constraint of a common inflation tax in the two countries imposes only minor restrictions on the optimal fiscal structures. For the same reason, one can already anticipate that the constraint of equal consumption taxes (the issue to be addressed in the next section) will impose major restrictions on the optimal fiscal structures.

In order to interpret the inflationary bias induced by the unification of monetary policies, it is useful to think of the government’s problem as follows. Using equation (10), one can solve for θ as a function of I, g, and k, and substitute it into q(0,7) in the objective function V(q). Analogously, one can solve for θ* from equation (11) and substitute it into V(q*). Thus, the problem faced by policymakers is transformed into an unconstrained optimization problem by substituting the constraints into the objective. The new objective is thus V[q(I;k, g)] + V[q(I*; k*, g*)], so that the only choice variables are I and I*. The loss function is defined as follows: L(I;g, k) ≡ V[q(I°;g, k] – V[q(I;g, k)]. This loss function measures the loss, in terms of utility, of choosing an I other than the optimal one. Obviously, it reaches a minimum of zero when I = . Under flexible exchange rates, the government can thus be viewed as minimizing L (I;g, k) by choosing I, the optimum choice being I0 as illustrated in Figure 2.

Figure 2.Determination of Optimal Inflation Tax Using Loss Functions

The vertical axis in Figure 2 measures L(I; g, k) and L*(I*; g*, k*); and the horizontal axis measures I and I*. Under flexible exchange rates, the optimum inflation taxes are I0 and

, where the loss, in terms of welfare, is reduced to zero. The shape of the loss functions should be intuitively clear. As we move either leftward or rightward from the optimal inflation tax, there is a welfare loss due to a suboptimal choice of I, which causes the distortion—and, hence, the welfare loss—to rise at an increasing rate. When the constraint of a common optimal inflation tax is imposed, the optimal I—that is, Iw—takes place where the slope (in absolute value) of both loss functions is the same: it is optimal, at the margin, to equate the welfare loss of the representative consumer in each country.

Figure 3 illustrates how a change in the levels of government spending affects the optimal common inflation tax. Figure 3 assumes that g* increases, whereas g decreases. Since k and k* remain unchanged, it follows from the analysis of the previous section that the optimal inflation tax in the domestic country under flexible exchange rates decreases (in Figure 3, I1 < I0), whereas the opposite is true in the foreign country (in Figure 3,

). The common optimal inflation tax increases from I0w to I1w. It can be seen that the effect of the smaller g (g1 < go) is to shift the loss function of the domestic country to the left, whereas the higher g* (
) shifts the loss function of the foreign country to the right. Given these shifts, it follows that at the initial common optimal inflation tax, the slope of L* is higher (in absolute value) than that of L and, since as one moves to the right of
the slope of L* decreases (in absolute value) while that of L increases, the new optimal common optimal inflation tax is greater than the initial one.

Figure 3.Effects of a Higher Difference in Levels of Public Spending on the Common Optimal Inflation Tax

Tables 1 through 3 present numerical simulations of the model that illustrate the effects of different levels of government spending on the inflationary bias.23 The effect on the importance of seigniorage as a source of revenue is also investigated. The computations in Tables 1 and 2 use the values of k obtained in Section I. The differential between the levels of government spending is widened from 0 to 20 points of GDP (recall that GDP in both countries equals one half), so that this exercise can be interpreted as suggesting how different levels of government spending in both countries would affect the common optimal inflation tax. Tables 1 assumes that the level of government spending in the foreign country (the one with high collection costs) increases, and that of the domestic country (the one with low collection costs) decreases. 2 undertakes the opposite exercise. An inspection of both tables reveals the following. First, when government spending is the same in the two countries, there is always an inflationary bias. In other words, the fact that one country has higher increasing marginal collection costs than the other is sufficient, given equal levels of government spending, to yield a common optimal nominal interest rate that is closer to that of the high-inflation country, as indicated by the value of 0.548 for a in the first row of both tables. Second, given this initial value of a, if government spending increases in the high-collection-costs country and decreases in the low-collection-costs country, the inflationary bias rises accordingly. As Table 1 shows, for instance, if the difference in government spending were 0.06 (equivalent to 12 percent of GDP), α = 0.608.

Table 1.Effects of Increasing Government Spending in High-Collection-Costs Country and Decreasing It in Low-Collection-Costs Country
0 = 24 – 240.5483.896.440.662.173.342.170.40
2 = 25 – 230.5684.176.710.632.223.322.410.40
4 = 26 – 220.5884.466.980.602.263.292.670.41
6 = 27 – 210.6084.777.260.582.313.272.970.41
8 = 28 – 200.6305.097.530.552.353.253.290.41
10 = 29 – 190.6515.427.810.522.403.233.660.41
Note: All figures, except for g, g*, and α are in percentage terms. The values of g and g* are multiplied by 100 to save space. Seigniorage levels are denoted by S and S*.
Note: All figures, except for g, g*, and α are in percentage terms. The values of g and g* are multiplied by 100 to save space. Seigniorage levels are denoted by S and S*.

If, however, as suggested by Table 2, the spread in the levels of government spending arises because of an increase in the low-collection-costs country and a decrease in the high-collection-costs country, the inflationary bias decreases and even turns into a disinflationary bias (namely, α < 0.5) for a difference of 0.06 (12 percent of GDP), in which case α = 0.492. The simulation thus suggests that given the values of k derived in Section I—which yielded inflation rates of roughly the same order of magnitude as those observed in Germany and Italy—an inflationary bias is more likely to be the outcome of a unification of monetary policy, because for the opposite to happen, the low-collection-costs country should have a considerably higher level of government spending than the high-collection-costs country.

Table 2.Effects of Increasing Government Spending in Low-Collection-Costs Country and Decreasing It in High-Collection-Costs Country
0 = 24 – 240.5483.896.440.662.173.342.170.40
2 = 25 – 230.5283.626.160.692.133.361.960.40
4 = 26 – 220.5113.375.890.712.083.391.760.40
6 = 27 – 210.4923.135.620.742.043.411.590.40
8 = 28 – 200.4752.915.350.772.003.441.430.40
10 = 29 – 190.4592.705.080.801.973.461.290.40
Note: All figures, except for g, g*, and α are in percentage terms. The values of g and g* are multiplied by 100 to save space. Seigniorage levels are denoted by S and S*.
Note: All figures, except for g, g*, and α are in percentage terms. The values of g and g* are multiplied by 100 to save space. Seigniorage levels are denoted by S and S*.

Table 3 shows the effects of an increasing spread between levels of government spending in both countries on the inflationary bias for a common value of k. The purpose of this exercise is to isolate the effects of an increasing spread between levels of government spending on the inflationary bias. The figures in Table 3 clearly suggest that different levels of government spending hardly influence the inflationary bias. Even a substantial spread of 0.10 (20 percent of GDP)—an extreme situation—yields α = 0.524. The overall conclusion resulting from the numerical exercises is that what really matters for the inflationary bias is the difference in the values of k; namely, the relative efficiency of the tax administration system in both countries. The differences in the values of k impart an inflationary bias to the system. Differences in levels of government spending matter as long as the values of k differ to begin with; otherwise, they have little effect, and the common optimal nominal interest rate is very close to the average of the two optimal nominal interest rates under flexible exchange rates.

Table 3.Effects of Increasing Differences in Government Spending for a Common Value of k (k = 0.1265)
0 = 24 – 240.5003.583.583.582.
2 = 25 – 230.5013.583.733.431.942.002.102.02
4 = 26 – 220.5023.603.883.281.872.002.212.03
6 = 27 – 210.5083.644.033.131.811.992.342.04
8 = 28 – 200.5153.694.182.981.771.982.482.05
10 = 29 – 190.5243.754.332.821.741.972.652.06
Note: All figures, except for g, g*, and a are in percentage terms. The values of g and g* are multiplied by 100 to save space. Seigniorage levels are denoted by S and S*.
Note: All figures, except for g, g*, and a are in percentage terms. The values of g and g* are multiplied by 100 to save space. Seigniorage levels are denoted by S and S*.

As can be seen from the figures for individual S/g and S*/g*, the relative importance of revenues from seigniorage in terms of total revenues under flexible rates is a decreasing function of government spending, even when the optimal inflation tax is an increasing function of government spending. For example, in Table 1, as g* increases, the share of seigniorage in total revenues declines from 3.34 percent to 3.23 percent, while at the same time the optimal nominal interest rate increases from 6.44 percent to 7.81 percent. It is interesting, however, that in both Tables 1 and 2, the restriction imposed by having a common inflation tax reverses this result. In Table 1, as iw increases the share of revenues from the inflation tax increases in both countries, as can be seen from the figures for EMS S/g and S*/g*, even though g* is increasing while g is decreasing. Similarly, in Table 2 the share of revenues from seigniorage falls as iw declines, independently of what is happening to g and g*. Therefore, the two-country model of optimal taxation under fixed exchange rates reverses, under the same specification, the relationship between government spending and the seigniorage in total revenues obtained in one-country models or, which amounts to the same thing, for two-country models under flexible exchange rates.

III. The Two-Country Model with a Common Consumption Tax

There is an ongoing discussion in the context of the general liberalization measures contemplated for 1992 in the EMS concerning the harmonization of tax rates across countries. The consequences that these tax measures could have for national inflation rates is not usually at the center of policy discussions, but these effects deserve at the least to be looked at, in order to determine whether they might be important. The reason that the effects of tax harmonization could have important implications is that if such measures tended to increase the spread between national inflation rates, the need for periodic realignments would increase. Given the impossibility of resorting to capital controls at the time of a devaluation crisis, large changes in domestic interest rates would be needed to prevent a flight from the weaker currency. This section examines the impact of tax harmonization (which, for the purposes of this paper, is taken to mean consumption tax equalization) on national inflation rates.24

From the consumer’s maximization presented in Section I, V(q) and V(q*) result, where q ≡ (1 + θw)[1 + v (X) + IX] and q*=(1 + θw) [1 + v(X*) + I*X*]. Note that, unlike the case studied in Section II, the nominal interest rates may be different, whereas the consumption tax, denoted by θw, is the same in both countries. The optimization problem jointly faced by both governments is given by

subject to

In addition to equations (13) and (14), the optimality condition for this problem is

As was the case in Section II, the terms in brackets, denoted by D and D*, respectively, would be zero if the constraint θ = θ* = θw were not binding, because optimality, under flexible exchange rates, requires that D =D* = 0. When the constraint I = I* = Iw was imposed in Section II, the solution was Iw = 0, when k = k* = 0. It is interesting to note that this solution no longer holds when the constraint θ = θ* = θw is imposed. It can be readily verified that even when k = k* = 0, it is not optimal for both I and I* to be equal to zero. If this were the case, then condition (15) would hold (because D = D* = 0), but equations (13) and (14) would imply that unless g = g*, the system is inconsistent, because if I = I* =0, then c = c*, so that g = θw c and g* = θwc* cannot hold simultaneously. A graphical analysis of the optimal solution leads to the conclusion that a corner solution takes place (namely, condition (15) holds as an inequality), as illustrated by Figure 4, where for simplicity only the isorevenue curves have been drawn. Points E0 and

denote the optimal taxation policies of the domestic and foreign country, respectively, under flexible exchange rates. Due to the nonnegativity constraint on the nominal interest rate, it follows that the common consumption tax, θw has to be at, or below, point
. It should be clear that θw cannot be below θ*0, because the welfare of both representative consumers would decrease by moving beyond E*1 along g* and moving beyond point E1 along g. Therefore, the optimum θw is equal to θ*0. The optimal taxation structure of the foreign country thus remains at
(that is,
), whereas that of the domestic country is at point E1. Imposing the constraint of an equal consumption tax brings about two interesting results. First, the optimal taxation structure of the foreign country does not change. Second, even in the absence of collection costs, the domestic country finds it optimal to resort to inflationary financing. Naturally, all the cost of equalizing consumption taxes is borne by the domestic country.25 This case also provides a clear example of how the equalization of consumption taxes may cause national inflation rates to diverge, given that in the initial situation they were both zero, thus not only producing a higher average inflation rate but also making it more difficult to sustain fixed parities.26

Figure 4.Effects of Equalizing Consumption Taxes on Inflation Taxes When I0 = = 0

It is of interest to simulate the model for the cases of Italy and the Federal Republic of Germany (see Section II) to see what would be the effects on the national inflation rates of equalizing the consumption tax. Figure 5 illustrates this case. The initial equilibrium of Germany is at point E0 with a very low inflation rate and a lower consumption tax rate as well. Point

represents the initial equilibrium of Italy. If the constraint of equal consumption taxes is imposed, the simulations show that a corner solution occurs at point E1 for Germany. This means that the inflation rate in Germany would fall to zero (in spite of its positive value of k), while that in Italy would increase to point
from point
. Therefore, given the specification of the model and the initial equilibrium that roughly reproduces the German and Italian fiscal structures, the optimal outcome is for Germany to achieve a zero inflation tax and for Italy to increase its inflation tax, so that a divergence of national inflation rates would result. The reasoning leading to the optimal consumption tax, θw, is as follows. If the nonnegativity constraint on the nominal interest rates were not imposed, the simulations indicate that the optimal θw would lie between the intersection of both isorevenue curves on the Y-axis. The best the authorities can do, given the nonnegativity constraint, is to choose point θw. Clearly, the costs borne by Germany would be less than those borne by Italy, since the unconstrained optimal tax structure of Germany has a nominal interest rate of only 0.6 percent (that is, practically zero) to begin with.

Figure 5.Equalizing Consumption Taxes: Effects on the Inflation Taxes of the Federal Republic of Germany and Italy

Table 4 presents four sets of simulated outcomes that could result from an equalization of consumption tax when no corner solutions are involved. Each set shows the individual outcome and the optimal tax structure, after the constraint of equal consumption taxes has been imposed. The only new symbols are ic and (i*)c, which denote the optimal nominal interest rates of the constrained optima.27 The criteria for differentiation of the different cases are the existence of divergence or convergence of the initial inflation taxes (recall that I = i/(1 + i) and I* = i*/(1 + i*)) and the existence or absence of reversal (reversal means that the country with the lowest inflation tax initially ends up with the highest). In the first case—divergence of the initial inflation taxes with no reversal—both the consumption and the inflation tax are initially higher in the foreign country. These initial taxes could result, for instance, from k = k* and g* > g, but other parameter configurations could yield the same outcome as well. When the consumption tax is equalized at θw, i* increases, whereas i decreases, so that the difference between inflation rates rises. The second case—divergence with reversal—can arise when the domestic country has the lowest inflation tax but the highest consumption tax. This could result, for instance, from g > g* and k <k*. When the consumption tax is equalized, the initial order of magnitude of the inflation taxes is reversed; namely, the domestic country now has the higher inflation rate. The difference between the initial inflation rates can increase, as happens in the second case—divergence with reversal—but it could also decrease, as happens in the third case—convergence with reversal. In the last case—convergence with no reversal—the initial situation is the same as in the third case of convergence with reversal, but because the isorevenue curves intersect, the result of the consumption tax equalization is a convergence of the nominal interest rates. For the isorevenue curves to intersect it is necessary that the country with the highest level of government spending have the lowest level of k.28

Table 4.Equalization of Consumption Taxes: Possible Outcomes
Case I: Divergence with No Reversal
Case II: Divergence with Reversal
Case III: Convergence with Reversal
Case IV: Convergence with No Reversal
Note: The first two rows under each case show individual outcomes; the third row shows the optimal tax structure with the equal consumption tax constraint. All taxes are expressed in percentage terms; ic and (i*)c denote the optimal nominal interest rate of the constrained optima.
Note: The first two rows under each case show individual outcomes; the third row shows the optimal tax structure with the equal consumption tax constraint. All taxes are expressed in percentage terms; ic and (i*)c denote the optimal nominal interest rate of the constrained optima.

The predictions of the model of the likely consequences of an equalization of the consumption tax are highly sensitive to the parameter specification. In general, the nominal interest rates are highly sensitive to any change in parameters, making the occurrence of corner solutions quite common. The sensitivity of the nominal interest rates should not be surprising, given that revenues from seigniorage account for only a small fraction of total government revenues. This implies that large movements in nominal interest rates are needed to compensate for small changes in the consumption tax that cause a dramatic change in revenues.

It should be borne in mind that in attempting to use this theoretical framework in the context of the EMS, one should view the revenues from the consumption tax as fiscal revenues from any source other than the inflation tax. This interpretation implies that the experiment undertaken in this section is quite strong, in the sense that it would imply the equalization of all tax rates (value-added taxes, income taxes, and so forth) currently used in the EMS. The usefulness of conducting such an extreme experiment is that it suggests that dramatic changes could come about if the EMS began to move in the direction of a broadly based tax harmonization and that caution should be exercised in taking such steps. The key problem is that, given different revenue needs in different countries, the equalization of a wide range of taxes would provide little room for maneuver for those countries that need more or less revenue than the “average” country. These results should also be viewed as “food for thought” for both researchers and policymakers since they call attention to issues that otherwise might not have been raised.

IV. Conclusions

A two-country model of public finance has been used to analyze how different constraints that are likely to emerge from the liberalization process taking place in the EMS would affect the optimal way in which governments finance their spending. A two-country model of public finance was analyzed and simulated to gain further insights into the issues involved. When the constraint of a common nominal interest rate was imposed, it was shown that the costs were likely to be small, given reasonable parameter values for EMS countries. This model therefore suggests that policymakers need not worry about the possible fiscal consequences of the required convergence of monetary policies needed to avoid frequent exchange rate realignments.

The picture that emerges from the equalization of consumption taxes, however, is mixed. Depending on the initial parameter configuration, equalizing most conventional taxes could lead to divergences in the national inflation rates, which would make it more difficult to sustain fixed parities. This model thus suggests that caution and further study of the issue are warranted.


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Carlos A. Végh, an economist in the Research Department, was an economist in the European Department when this paper was written. He holds a Ph.D. from the University of Chicago.

Pablo E. Guidotti is an economist in the Research Department and holds a Ph.D. from the University of Chicago.

The authors are grateful to Joshua Aizenman, Torsten Persson, Klaus-Walter Riechel, and participants at a seminar in the Research Department for helpful comments.

See, for instance, Guitián (1988) and Russo and Tullio (1988) for a review.

Drazen (1988) reports that for the period 1979–86, the share of seigniorage in tax revenues was 6.2 percent for Italy, 5.9 percent for Spain, 9.1 percent for Greece, and 11.9 percent for Portugal.

Extensions and evaluations of Kimbrough’s (1986) contribution include Faig (1988), Guidotti and Végh (1988), Végh (1989b), and Woodford (1989). The study of the optimal inflation tax in a public finance context was pioneered by Phelps (1973).

Since the model abstracts from capital accumulation, the real interest rate equals the common rate of time preference. Setting the nominal interest rate is thus equivalent to choosing the inflation rate.

The reason for the analytical complexity is that the exercises undertaken in this paper lead to third-best optima. These third-best optima result from the imposition of constraints on the initial second-best world economy’s equilibrium.

Canzoneri and Rogers (1988) assume that using multiple currencies is costly. In this way, they incorporate an explicit benefit associated with adopting a single currency for the EMS.

See Giavazzi and Giovannini (1989) for a discussion of the benefits that the members of the EMS perceive to result from a system of fixed exchange rates.

As long as we are dealing with stationary equilibria (that is, the system is always at the steady state), the results obtained for a closed economy, a small open economy under flexible exchange rates, or large economies operating under flexible rates are the same.

The foreign consumer holds only foreign money and the traded bond; that is, there is no currency substitution.

It should be clear that, given the nonnegativity constraint on the nominal interest rate, the consumer would never choose X > Xs, so that the constraint on the domain of v(X) does not imply any loss of generality.

As pointed out by Guidotti and Végh (1988), this assumption is critical in obtaining the result that the optimal inflation tax is zero in the absence of collection costs. If transaction costs are not zero when v’(Xs) = 0, the optimal inflation tax is positive. The assumption that transaction costs are eliminated when X = Xs allows us to motivate the use of the inflation tax based only on the presence of collection costs associated with the consumption tax.

If the primal approach to optimal taxation is used (Atkinson and Stiglitz (1972)), as in Kimbrough (1986) and Végh (1987), it follows immediately that if the exogenous variables are constant over time, the optimal social choices of (c, h, m) are constant over time. For this optimal social allocation to be the outcome of a competitive equilibrium, (I, θ) have to remain constant over time. The intuition is that constant expenditures across time are optimally financed from contemporaneous taxes, because it is optimal to smooth tax distortions over time (see, for instance, Lucas and Stokey (1983)). Therefore, the economy is always in the steady state where 1/(1 + r) = β = β*, and will adjust instantaneously to unanticipated changes in the exogenous parameters (Obstfeld and Stockman (1985)). Accordingly, in what follows the analysis will be conducted in the steady state and time subscripts will be dropped for notational simplicity.

The key results that obtain with this particular specification extend to any φ (θc), such that Tc) is a convex function, as shown in Végh (1989a).

It should be pointed out that the slope of the isorevenue curve is [(cq qθ Γ + cΓθ)/[(cq q1Γ + cΓ1)] rather than (ΓθI). But, at an optimum, it can be verified that (qθ/qI) = [(cq qθ Γ +cΓI)] can be rewritten as (qθ/qI = (ΓθI). This is because the negative effect on revenues of q that results from an increase in θ, relative to that which results from an increase in I, is proportional to the relative distortion introduced by both taxes.

This specification of the model has been previously used by Végh (1987, 1989a). It implies that the demand for relative money balances is linear in I.

For simplicity, the real interest rate is assumed small enough so that the nominal interest rate can be identified with the inflation rate. Due to the highly abstract nature of the model, the specific numbers generated by the model throughout the paper should be viewed as illustrations rather than actual predictions.

For simplicity, GDP is defined gross of transactions costs.

The actual figures (average for 1985–87) for revenues from money creation as a fraction of total revenues are 3.0 percent for Italy and 1.33 percent for the Federal Republic of Germany (see Gros (1989)).

An alternative possibility, not pursued here, is to focus on noncooperative solutions (see van der Ploeg (1988), and Casella and Feinstein (1988)).

Note that at an optimum the denominators on both sides of equation (12) are positive. This follows from the first-order conditions. It should also be clear that no corner solution can be involved in this case, because if Iw = , then D = 0 but D* < 0, and if Iw = (I*)°, then D* =0 but D > 0.

Naturally, since potential benefits of fixed exchange rates in the EMS (as discussed, for instance, by Giavazzi and Giovannini (1989)) have not been incorporated into the model, fixing exchange rates will always reduce welfare. These costs, however, would be present even if some benefits were taken into account. The present model should be seen as providing an illustration of the costs that might be involved in unifying monetary policies; it does not address the cost-benefit issue of fixing exchange rates.

It is worth noting that these exercises represent comparative statics around a third-best optimum.

In the present context, consumption tax harmonization implies the harmonization of all taxes other than the inflation tax. Although this assumption makes this experiment rather extreme, it provides a useful benchmark (see the discussion below).

Again, the analysis begs the question of why the foreign country would willingly engage in equalization of consumption taxes to begin with. As was indicated earlier, however, the analysis abstracts from the potential benefits of tax harmonization.

It is not the case, however, that a corner solution necessarily implies the divergence of the nominal interest rates when one or both of the countries have positive values of k, as the reader can easily verify graphically.

As the reader will see from Table 4, the values of g and g* have to be quite close to avoid the corner solutions that have already been discussed. Because of the importance of the revenues from the consumption tax in terms of total fiscal revenues, any difference between levels of public spending that requires a substantially different consumption tax is likely to lead to a corner solution, because the country whose consumption tax increases generates too much revenue; if a negative inflation tax were allowed, this revenue would be handed back to the public. Table 4 reports results for i and i*, but the same results would hold for I and I*.

A more detailed graphical analysis of the cases presented in Table 4 may be found in Végh and Guidotti (1989).

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