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Inflation and Real Interest Author(s): Robert Mundell Source: Journal of Political Economy, Vol. 71, No. 3 (Jun., 1963), pp. 280-283 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1828985 Accessed: 02-11-2016 11:25 UTC

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INFLATION AND REAL INTEREST

ROBERT MUNDELL

International Monetary Fund

I. INADEQUACIES OF FISHER'S THEORY

THE theory of interest under inflation needs further investigation. Irving

Fisher's analysis, which concluded that the money rate of interest rises by the antici- pated rate of inflation or falls by the antici- pated rate of deflation, was subjected to at- tack by Keynes: "The mistake lies in sup- posing that it is the rate of interest on which prospective changes in the value of money will directly react, instead of the marginal efficiency of a given stock of capital."' Fisher himself seems to have had misgivings about the empirical reliability of his explana- tion and presented evidence suggesting that the adjustment of money interest was only partial, concluding:

When the cost of living is not stable, the rate of interest takes the appreciation and deprecia- tion into account to some extent, but only slightly, and, in general, indirectly. That is, when prices are rising, the rate of interest tends to be high but not so high as it should be to compensate for the rise; and when prices are falling, the rate of interest tends to be low, but not so low as it should be to compensate for the fall.2

Later he showed that the real rate of interest was much more variable than the money rate and conjectured that:

Men are unable or unwilling to adjust at all accurately and promptly the money interest rates to changed price levels.... The erratic behavior of real interest is evidently a trick played on the money market by the "money illusion" when contracts are made in unstable money.3

Thus Fisher found verification for a theory of partial adjustment of money interest to

I General Theory, p. 143.

2 The Theory of Interest (New York, 1930), p. 43.

3 Ibid., p. 415.

inflation and deflation but none for his own theory of complete adjustment under fore- sight. And to attribute the discrepancy be- tween theory and reality solely to lack of foresight is to raise doubts about the nature of the evidence that would be required to reject the theory.

The theory presented in this paper is more consistent with Fisher's empirical ob- servations than his own theory, for it shows that anticipated inflation or deflation is likely to raise (lower) the money rate of in- terest by less than the rate of inflation (de- flation) itself. It is also consistent with Keynes's theoretical criticism of Fisher, yet paradoxically retains the concept of an equilibrium interest rate uninfluenced by unanticipated once-for-all changes in the quantity of money.

II. INFLATION AND THE DISCREPANCY

BETWEEN REAL AND MONEY

INTEREST RATES

To analyze the problem I shall utilize the apparatus invented by Lloyd Metzler in his celebrated article, "Wealth, Saving, and the Rate of Interest."4 It is assumed that wages and prices are flexible, that full employment is continuously maintained, and that the share of profits in full employment income is constant. Wealth is assumed to be held in money and shares, the real value of the latter being real profits capitalized at the going real interest rate. It is further assumed that real investment depends on the real in- terest rate and real saving on real balances and that wealth-holders divide their assets between money and securities in a propor- tion which depends on the money rate of interest.

Under these conditions the equilibrium

I Journal of Political Economy, LIX (April, 1951), 93-116.

280

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INFLATION AND REAL INTEREST 281

interest rate is determined by the intersec- tion of two schedules, in some respect analo- gous to the Hicksian LM and IS curves (see Fig. 1). The IS schedule plots the locus of pairs of values of real interest rates and real money balances along which saving is equal to investment. Its slope is positive because an increase in the real interest rate lowers investment, causing a deflationary gap, while an increase in real balances lowers sav-

'S

i I

41)

-n&o i 0 ~ro

0

Real Money Balances

Fio. 1

ing, causing a compensating inflationary gap. Thus, an increase in the real interest rate would have to be associated with an in- crease in real balances5 in order to maintain equality between real saving and real invest- ment. Points above and to the left of IS would be points of deflationary pressure and points below and to the right of IS would be points of inflationary pressure.

Wealth changes along IS by less than the change in real money balances since the real value of equities moves in inverse proportion to the real rate of interest; the wealth effect along IS is therefore less than the real balance effect, though it is still in the same direction.

The LM schedule gives the locus of pairs of money interest rates and real money bal- ances that is consistent with equilibrium in the money market. This schedule has a nega- tive slope because asset-holders divide their wealth between money and securities in a proportion that depends on the opportunity cost of holding money, which is the money rate of interest. Thus at high money rates of interest the demand for real balances is low,

and at low money interest rates the demand for real balances is high. Only along LM are people content to hold the existing stock of real money balances. Above LM there is excess liquidity and below LM there is de- ficient liquidity.

The IS and LM schedules intersect at Q, which determines the equilibrium interest rate, r = i0, and the equilibrium stock of real money balances, in. Only at Q is the de- sire to save equal to the incentive to invest, the demand for shares equal to the supply of shares, and the desire for real money bal- ances equal to the existing stock of real

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282 ROBERT MUNDELL

money balances. Q is the equilibrium at which the price level is constant and, there- fore, the equilibrium at which real and money interest rates are the same.

III. THIE FALL IN REAL INTEREST

UNDER INFLATION

Let us now consider the effects of antici- pated inflation on the equilibrium. Inflation creates a discrepancy between money inter- est rates and real interest rates equal to the rate of inflation. This discrepancy widens the difference between the nominal earnings of shares and the return on money because the rate of depreciation of money (the infla- tion rate) must be added to the real return on shares to get the total cost of holding money.6 Since the LM schedule is derived on the basis of a money rate of interest (as that measures the true cost of holding money), it follows that the LM schedule, as a function of the real rate of interest, shifts downward, at any given level of real balances, by the rate of the inflation. In the figure, for ex- ample, at the inflation rate RT the com- munity would wish to hold the stock of real

money balances ml only if the real interest rate were r1 and the nominal interest rate

were il, the difference being the rate of infla- tion RT. Thus, the entire schedule LM, which is fixed as a function of the money rate of interest, shifts downward, as a function of the real interest rate, by the rate of inflation.

Consider now the IS schedule. From any given point on the schedule an expected in- flation, at a given nominal rate of interest, will create a divergence between the produc- tivity of investment and the return on sav- ing equal to the inflation rate, for a dollar borrowed at a given money rate of interest will yield a normal real return plus the rate of appreciation in value of goods, which cor- responds to the rate of inflation itself. To

6 The following discussion of the demand for money under inflationary conditions has been helped by the works of Philip Cagan, "Monetary Dynamics

of IHyperinflation," in Studies in the Quantity Theory of Alooiev, ed. M. Friedmnan (Chicago, 1956), pp. 25- 117; and Martin Bailey, "Welfare Cost of Inflation- ary Finance," Journal of Political Economiy, LXVI

(1956).

maintain equality between saving and in- vestment at any given rate of inflation, the nominal interest rate must therefore rise by the rate of inflation. In the figure, for ex- ample, the point T on the IS schedule gives a pair of values of real interest rates and real money balances at which saving is equal to investment at a zero rate of inflation. But if the expected inflation rate were RT, a money interest rate of only rl would create a discrepancy between investment and saving. Only if the nominal interest rate were in- creased to ii would investment and saving be equal at the level of real balances, ml. The IS schedule therefore remains fixed, as a function of the real rate of interest, but is raised by the amount RT, as a function of the money rate of interest.

The ingredients of the solution are now established. If we interpret the ordinate of the figure as the real rate of interest it be- comes necessary to shift the LM schedule downward by the anticipated rate of the in- flation, while the IS curve is unaltered. If, on the other hand, the ordinate is taken to refer to the money rate of interest, the IS schedule must be shifted upward by the rate of the inflation, while the LM curve remains fixed. More simply, it is sufficient to take account of the discrepancy between the real rate of interest (for which the existing IS curve applies) and the money rate of inter- est (for which the existing LM schedule is appropriate), the discrepancy being the rate of the inflation.

The inflation itself is generated by mone-

tary expansion in excess of growth. The rate of excess monetary expansion is equal to the rate of inflation, RT. The real rate of inter-

est falls7 from r0 to ri, while the money rate

I The change in the rate of interest that results from the anticipation of inflation is a "permanent" change in the sense defined in my "Public Debt, Corporate Income Taxes and the Rate of Interest," Journal of Political Economy, LXVIII (December, 1960), 625 n. Recently Metzler's model has been sub- jected to further investigation, extension, and criti- cism (see George Horwich, "Real Assets and the Theory of Interest," Journal of Political Economy, LXX [April, 19621, 157-70; for references and a criti- cism of the monetary dynamics inherent in the sys-

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INFLATION AND REAL INTEREST 283

of interest rises from i0 to i1. Real money balances are reduced from mn to m1 as a consequence of the shift in expectations, and real investment and real saving are both higher than in the inflationless equilibrium. The shaded area measures the depreciation of existing money balances.8

IV. CONCLUSION

I have argued that the money rate of in- terest rises by less than the rate of inflation and therefore that the real rate of interest falls during inflation.9 The conclusion is

tern), but despite objections it seems to me that Metzler's system retains its essential utility, espe- cially for "comparative statics" purposes.

8 If the new money issued were spent by the gov- ernment on goods, the IS schedule would shift up- ward, whereas if it were spent on securities the LA! schedule would shift downward: the rise in money interest will be greater than that shown in the dia- gram in the former case and smaller in the latter in- stance. The textual treatment has avoided these complications by postulating (implicitly) changes in the money supply unaccompanied by any physical quid pro quo to the government, a procedure that is probably justifiable for purposes of isolating the theoretical effects of pure inflation, even though it be lacking in institutional foundation.

I Charles Kennedy, in his "Inflation and the Bond Rate" Oxford Economic Papers (October, 1960), pp. 269-74, interprets the "Keynesian" solu- tion as an unchanged bond price, an interpretation that does not seem to me to take account of the word "directly" in the passage I have quoted in the intro- duction. I have tried to show that the change in money interest can be interpreted as being due to a shift in the marginal efficiency schedule as a function of money interest, or as a shift in liquidity preference as a function of real interest, the former being the solution Keynes presumably had in mind.

based on the fact that inflation reduces real money balances and that the resulting de- cline in wealth stimulates increased sav- ing.'0 Real conditions in the economy are altered by the purely monetary phenome- non. The evils or benefits of inflation cannot be attributed solely to the failure of the community to anticipate it."

Foreseeable fluctuations in the rate of inflation can thus have very real effects on economic activity. When prices are expected to rise, the money rate of interest rises by less than the rate of inflation giving im- petus to an investment boom and an ac- celeration of growth. Conversely, when a rise in prices is expected to end, there occurs a stock market slump, a rise in the real rate of interest, and a deceleration of growth.

10 Although the analysis has concentrated on the division of wealth between money and equities, it can also be expected to apply to an economy in which wealth is held in other forms. Arbitrage will bring relative earnings of bonds in line with the money rate of interest (under the conditions of cer- tainty implied in the theoretical analysis) and "cost- of-living" bonds (an instrument used in many coun- tries accustomed to inflation) will yield a nominal return equal to the real rate of interest plus the rate of inflation. Similarly, foreign exchange will yield a return equal to the rate of inflation, as the domestic exchange rate depreciates, though the initial stock adjustment is complicated by the highly liquid at- tributes of foreign exchange, which imply that the flight from domestic money will be partly into for- eign exchange.

11 Cf. A. P. Lerner, "The Inflationary Process- Some Theoretical Aspects," Review of Economics and Statistics, August, 1949; reprinted in Essays in Eco- nomic Analysis (London, 1953): "What is harmful about inflation is not the rise in prices but the failure to anticipate and offset them" (Essays, p. 330).

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