The inflation tax Laffer curve

As a general rule, tax revenues do not increase proportionally with the tax rate. The reason is that individuals tend to escape taxation, shrinking the tax base. The inflation tax is not an exception: when the inflation rate increases, people try to get rid of money (the tax base erodes), and this weighs negatively on the inflation tax revenue.

To see this formally, consider together the equations describing the inflation tax and the money demand (25):

12 A textbook example of seigniorage without inflation tax is what happened in the US along the 1960s.

At that time, the dollar became an international currency, being demanded all over the world to settle import and export payments in an expanding global economy. This means that the world’ demand for dollars was increasing. The huge increase in demand for dollars allowed the Federal Reserve to print enormous amounts of money without creating extra inflationary pressures in the US economy. Some calculations suggest that the seigniorage revenues raised by the Federal Reserve at that time were the enough to pay the cost of the Vietnam war.

 

ITax m i Y m r^ ^ Y^ (30)

In light of (30), when the inflation rate increases, there is a direct positive impact on revenues through a “tax rate” effect; however, the money demand (the “tax base”) decreases, so that the overall impact on revenue is uncertain.

Figure 8 illustrates this. Suppose that initially the inflation rate is equal to ₀. The corresponding inflation tax revenue is ₀m₀, described by the shaded area in grey (note that the inflation rate is equal to ₀  i₀ r). Now assume that the central banks unexpectedly increased the rate of money growth, once-and for-all, causing the inflation rate to jump to

1. In that case, the new money market equilibrium will move to point 1, with a higher nominal interest rate and a lower demand for real money balances. Suppose that the move from 0 to 1 (driven by a jump in the price level, P) was instantaneous.

In point 1, the tax rate (inflation) is higher than in point 0, but the tax base (money demand) is lower. The inflation tax revenue ₁m₁ (shaded area) may be higher or lower than before, depending on the balance between these two effects.

Figure 8. Inflation tax rate and inflation tax base i

(M/P) (M^S/P)₀

i₀= r+π₀ i₁= r+π₁

(M^S/P)₁

) , (Y i m 0

1

m₀ m₁

r

Figure 9: Inflation tax Laffer curve

Inflation tax

A

π^* Inflation (π) m

I_Tax

The relation between inflation tax and inflation implied by equation (30) is described in figure 9. The figure shows that, when the inflation rate is low, increasing the inflation rate increases the inflation tax revenue. Beyond a certain point however (A in the figure), the inflation tax revenue becomes a negative function of the inflation rate. Equation (30) describes the “Inflation-Tax Laffer curve”. Like in the case of a monopolist, the maximum revenue (point A), corresponds to the point where the elasticity of money demand in respect to inflation is equal to one (see Box 9 for an illustrative example).

The inflation tax-Laffer curve resembles the tale of the goose that laid the golden eggs: if you explore the resource with moderation, setting an inflation rate that is not too high, this will come along with high demand for your currency, and high seigniorage revenues, today and in the future. But if you are tempted to obtain too much revenue today, confidence on your currency will erode, and people will try to get rid of it. In the limit, you may end up with a worthless printing press.

It should be noted that the inflation rate that maximizes the inflation tax is not, in general, the inflation rate that maximizes the overall government revenue. The reason is that inflation erodes the real value of tax payments. Tax revenues are collected with a time lag after the corresponding income is generated. When inflation is high, it erodes the real value of tax proceeds too fast. Because of this effect, the inflation rate that maximizes the overall

government revenue is less than the inflation rate that maximizes the seigniorage revenues alone. This proposition is known as the Olivera-Tanzi effect¹³¹⁴. The Olivera-Tanxi effect has an important policy implication: when inflation reaches extremely high levels so that revenues from formal taxation become negligible, the government becomes addicted to inflation, in a vicious cycle.

Box 9. The maximum seigniorage revenue

To find out the inflation rate corresponding to point A in figure 9, let’s consider a particular functional form for the money demand:

 

m i Y e^{ }Y . (25a)

Replacing this in (30) and maximizing, in respect to the inflation rate, we obtain:

^r  ^r  0

ITax

e ^{ }Y e ^{ }Y



   

   



Implying:

* 1

 ^ (31)

Box 6. On the optimal rate of inflation

Milton Friedman argued that the optimal inflation rate should be negative, equal to symmetric of the real interest rate r. The reason is that money is costless to produce, so its

13 Olivera, Julio H. 1967. “Money, Prices and Fiscal Lags: A Note on the Dynamics of Inflation.”

Banca Nazionale del Lavoro Quarterly Review 20 (September): 258-67. Tanzi, Vitto. 1988. “Lags in Tax Collection and the Case for Inflationary Finance: Theory with Simulations.” In Fiscal Policy, Stabilization, and Growth in Developing Countries, edited by Mario I. Blejer and Ke-young Chu. Washington, D.C.: International Monetary Fund.

14 Also note that the inflation rate than maximizes the government revenue has nothing to do with optimality: the optimal inflation rate shall be one that maximizes a society’ welfare. Maximizing the government revenue is not, in general, a social goal (see discussion in Box 10).

opportunity cost (the nominal interest rate) should be equal to zero. Setting i r   0, we obtain the Friedman optimal inflation rate.

The Friedman conclusion was later questioned by Edmund Phelps¹⁵. The author argued that while inflation is distortionary, other taxes are distortionary too. Thus, the government should not neglect a priori any available form of taxation. The optimal inflation tax shall be obtained as the solution of a complex problem where the distortionary effects of all sources of government revenue are taken into account. The ideal tax structure would be the one maximising the difference between the total benefits of public provision and the total costs caused by the overall tax system, implying that the marginal costs of all forms of taxations should be equalized¹⁶.

Among the economic profession, there is today a wide consensus that the optimal inflation rate is positive. In a world with price stickiness, some positive inflation is essential to “grease the wheels” of the price mechanism and avoid the risk of deflationary traps. Still, inflation must remain low, because inflation is highly distortionary.