Aizenman, Joshua, “Inflation, Tariffs, and Tax Enforcement Costs,” Journal of International Economic Integration (Autumn 1987), pp. 12-28.
Auernheimer, Leonardo, “The Honest Government’s Guide to the Revenue from Money Creation,” Journal of Political Economy. Vol. 82 (Chicago, 1974), pp. 598-606.
Giavazzi, Francesco, and Alberto Giovannini, “Limiting Exchange Rate Flexibility: The European Monetary System,” unpublished manuscript (1988).
Gros, Daniel, “Seigniorage in the EC: The Implications of the EMS and Financial Market Integration,” unpublished manuscript (1988).
Guidotti, Pablo, and Carlos Végh, “The Optimal Inflation Tax when Money Reduces Transactions Costs: A Reconsideration,” unpublished manuscript (1988).
Guitián, Manuel, “The European Monetary System: A Balance Between Rules and Discretion,” Part I of Policy Coordination in the European Monetary System, Occasional Paper 61 (Washington: International Monetary Fund, 1988).
Kimbrough, Kent, “The Optimum Quantity of Money Rule in the Theory of Public Finance,” Journal of Monetary Economics. Vol. 18 (1986), pp. 277-284.
Lucas, Robert Jr., and Nancy Stokey, “Optimal Fiscal and Monetary Policy in an Economy without Capital,” Journal of Monetary Economics. Vol. 12 (1983). pp. 55-93.
Obstfeld, Maurice, and Alan Stockman, “Exchange Rate Dynamics,” in Handbook of International Economics. Vol. 2, ed. by Ronald Jones and Peter Kenen (Amsterdam: North Holland, 1985), pp. 917-997.
Russo, Massimo, and Giuseppe Tullio, “Monetary Coordination Within the European Monetary System: Is There a Rule?” Part II of Policy Coordination in the European Monetary System. Occasional Paper 61 (Washington: International Monetary Fund, 1988).
Végh, Carlos, “On the Effects of Currency Substitution on the Optimal Inflation tax and on the Response of the Current Account to Supply Shocks,” doctoral dissertation (University of Chicago, 1987).
Végh, Carlos, “Government Spending and Inflationary Finance: A Public Finance Approach,” Working Paper No. WP/88/98 (Washington: International Monetary Fund), forthcoming Staff Papers (1989).
Végh, Carlos, “The Optimal Inflation Tax in the Presence of Currency Substitution,” forthcoming Journal of Monetary Economics (1989).
The authors wish to acknowledge helpful comments from Joshua Aizenman, Klaus-Walter Riechel, and participants at a seminar in the Research Department. They retain responsibility, however, for any remaining errors.
Phelps (1973) pioneered the study of the optimal inflation tax within a public finance context. He reaches the conclusion that it is optimal to resort to a positive inflation tax. Kimbrough (1986) challenges Phelps’ result and concludes that, if money is modeled as reducing transaction costs (unlike including money in the utility function as in Phelps (1973)), it is not optimal to resort to inflationary finance. Guidotti and Végh (1988) argue that Kimbrough’s result depends critically on a particular assumption about the transactions technology and that Phelp’s (1973) result may still hold.
For the purposes of this paper, the inflation tax is defined as the nominal interest rate. This definition originates in Phelps (1973) and has been stressed by Auernheimer (1974). It is based on the argument that, by issuing nominal debt which bears no interest (namely, money), the government avoids paying the prevailing nominal interest rate. The consumer’s opportunity cost of holding money, thus accrues to the government. Hence, in what follows, the terms “inflation tax” and “nominal interest rate” will be used interchangeably.
Végh (1989) shows that, in the context of a small open economy, the presence of currency substitution also renders the optimal inflation tax positive. This is because a positive domestic nominal interest rate mitigates the distortion introduced into the economy by a positive foreign nominal interest rate.
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.
See Giavazzi and Giovannini (1988) for a discussion of the benefits that the members of the EMS place on a system of fixed exchange rates.
As long as we are dealing with stationary equilibria (i.e., 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 consumer’s problem is the one put forward by Kimbrough (1986), which can also be found in Guidotti and Végh (1988) and Végh (1989). The introduction of increasing marginal collection costs for the consumption tax into the government’s optimal taxation problem follows Végh (1989).
The foreign consumer holds only foreign money and the traded bond; namely, there is no currency substitution.
It should be clear that, given the non-negativity constraint on the nominal interest rate, the consumer would never choose X>XS so that the constraint on the range of 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 transactions costs are not zero when v’(Xs)=0, the optimal inflation tax is positive, as will become clear below.
If the primal approach to optimal taxation is used (Atkinson and Stiglitz (1972)), as in 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 simply 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 (1985)). Therefore, the economy is always in the steady state where r=∂*=∂ 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 a general ϕ(θC), as shown in Végh (1988).
It should be pointed out that the slope of the iso-revenue curve is [(cqqθΓ+cΓθ)/(cqqIΓ+cΓI)] rather than (Γθ/ΓI). But, an optimum, it can be verified that (qθ/qI) = [(cqqθΓ+cΓθ)/(cqqIΓ+cΓI)] can be rewritten as (Γθ/ΓI). 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.
The main point of Guidotti and Végh (1988) also follows immediately from (9) by setting k=0. If v[X(0)]>0, it is easy to check that the solution to (9) is some positive I (recall that ∂X/∂I<0). Money being an intermediate good, therefore, does not ensure, by itself, that it is optimal to follow the optimum quantity of money rule. For the purposes of this paper, however, the assumption v[X(0)]=0 will be maintained in order to concentrate on tax harmonization problems.
Note that since I is increasing in i, it does not make any difference, qualitatively speaking, whether one works with I or i. Analytically, it proves more convenient to work with 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.
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 Germany. (The source for the seigniorage figures is Gros (1988); government revenue figures are based on the EC Commission services.)
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.
Naturally, since potential benefits of having fixed exchange rates in the EMS (as discussed, for instance, by Giavazzi and Giovannini (1988)) have not been incorporated into the model, it is always welfare-reducing to fix exchange rates. These costs, however, will be present even if some benefits were taken into account. The way to think of the present model is as providing a conceptualization and an illustration of the costs that might be involved in unifying monetary policies. The model does not address the cost-benefit issue of fixing exchange rates.
Végh (1988) shows for different values of k that, given this specification of the model, the share of revenues from the inflation tax in total revenues is always a decreasing function of government spending. Obviously, this implies that the share of revenues from the consumption tax increases as government spending rises.
Again, the analysis begs the question of why would the foreign country willingly engage in equalization of consumption taxes, to begin with. As has been indicated in the Introduction, 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.
There is a third case where the iso-revenue of the foreign country lies above that of the domestic country, as is the case in Figure VI but now the domestic country has a lower consumption tax. As the reader can readily check, the result of equalizing the consumption tax would be convergence of the nominal interest rates and, unlike the case of Figure VII and VIII, there would be no reversal. Simulations suggest, however, that this initial equilibrium is very unlikely to take place because the country with the highest level of public spending usually has the highest consumption tax so that this case can be ruled out. Intuitively, the reason for the implausibility of this initial equilibrium lies in the fact that since the revenues from the consumption tax account for over 90 percent of total revenues (this should be interpreted, in thinking about the EMS, as revenues from sources other than the inflation tax), a higher level of public spending requires a higher consumption tax in order to finance it.
It should be clear that both an increase in g or k have to shift the iso-revenue upward; namely, the new iso-revenue cannot cross the old one. Suppose k increases while g remains constant, if both iso-revenues were to intersect it would mean that at the intersection point the same revenue is being raised in spite of the higher collection costs which is not possible. Suppose g rises while k remains unchanged, if both iso-revenue curves intersected it would mean that, at the intersection point, the taxes would yield too much revenue for the old level of g or too little for the new level of g.