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 X_t ≡ m_t/[c_t(1 + θ_t,)] (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 X^s, 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(X^s) = 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

where

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 I_t ≡ [i_t/(1+i_t)] 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’(X_t) = I_t 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 X_t (that is, X_t = X(I_t)) and substituting it into (4) yields the following budget constraint:

where

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, I_t = θ_t = 0), then there would be no distortion; namely, q would equal unity. The consumer can now be viewed as maximizing over {c_t, h_t}_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, θ_t, = θ and I_t= 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 T(θc) ≡ 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, T(θc) = k(θc)², so that the collection costs schedule is a convex function (for k > 0): ∂T/∂(θc) = 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 q_θ/q₁ = Γ_θ/Γ₁, 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, 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 I°. In other words, equation (8) and, thus, g influence I°. 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(X^w) + I^WX^W] and q^* = (1 + θ^*)[1 + v(X_W) + I^WX^W]. 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, I^w, 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^* = I^w 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 I^w = 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 I^o = 0 and (I^*)^o > 0. It can be readily verified that I^w = 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 I^w> 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

and 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 E_x (where q_x 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.

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, i^w turns out to be 4.2 percent. The ratio i^w/(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 = 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.

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, I^w—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 I₀^w to I₁^w. It can be seen that the effect of the smaller g (g₁ < g_o) 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.

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.

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 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.

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 i^w 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 i^w 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 + θ^w)[1 + v (X) + IX] and q^*=(1 + θ^w) [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 θ^w, 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^* = θ^w were not binding, because optimality, under flexible exchange rates, requires that D =D^* = 0. When the constraint I = I^* = I^w was imposed in Section II, the solution was I^w = 0, when k = k^* = 0. It is interesting to note that this solution no longer holds when the constraint θ = θ^* = θ^w 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 = θ^w c and g^* = θ^w c^* 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, θ^w has to be at, or below, point . It should be clear that θ^w 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 θ^w 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

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, θ^w, is as follows. If the nonnegativity constraint on the nominal interest rates were not imposed, the simulations indicate that the optimal θ^w 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 θ^w. 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.

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 i^c 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 θ^w, 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

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.