Inflationary Expectations, Taxes, and the Demand for Money in the United States

In his excellent article on the demand for money, Goldfeld cited Harry Johnson to the effect that the lack of “American evidence that the expected rate of change of prices enters the demand for money … [was] something of a puzzle” (Goldfeld (1973), p. 608). Goldfeld described his own empirical results as “a mixed bag” (ibid., p. 613) and concluded that “even at the theoretical level,” the question of “whether inflationary expectations have an independent role to play in the demand-for-money function” is controversial (ibid., p. 607). Studies dealing with developing economies, however, have generally found that inflationary expectations possess more explanatory power than institutionally rigid nominal interest rates in basic money demand functions. Furthermore, some recent studies for the United States have used both inflationary expectations and the rate of interest in the demand-for-money equation. These studies have not provided sufficient theoretical justification for doing so.

Abstract

In his excellent article on the demand for money, Goldfeld cited Harry Johnson to the effect that the lack of “American evidence that the expected rate of change of prices enters the demand for money … [was] something of a puzzle” (Goldfeld (1973), p. 608). Goldfeld described his own empirical results as “a mixed bag” (ibid., p. 613) and concluded that “even at the theoretical level,” the question of “whether inflationary expectations have an independent role to play in the demand-for-money function” is controversial (ibid., p. 607). Studies dealing with developing economies, however, have generally found that inflationary expectations possess more explanatory power than institutionally rigid nominal interest rates in basic money demand functions. Furthermore, some recent studies for the United States have used both inflationary expectations and the rate of interest in the demand-for-money equation. These studies have not provided sufficient theoretical justification for doing so.

In his excellent article on the demand for money, Goldfeld cited Harry Johnson to the effect that the lack of “American evidence that the expected rate of change of prices enters the demand for money … [was] something of a puzzle” (Goldfeld (1973), p. 608). Goldfeld described his own empirical results as “a mixed bag” (ibid., p. 613) and concluded that “even at the theoretical level,” the question of “whether inflationary expectations have an independent role to play in the demand-for-money function” is controversial (ibid., p. 607). Studies dealing with developing economies, however, have generally found that inflationary expectations possess more explanatory power than institutionally rigid nominal interest rates in basic money demand functions. Furthermore, some recent studies for the United States have used both inflationary expectations and the rate of interest in the demand-for-money equation. These studies have not provided sufficient theoretical justification for doing so.

This paper deals with the role of inflationary expectations from a theoretical and empirical point of view. It contains four sections. Section I presents a theoretical justification for introducing inflationary expectations as an independent variable in the demand-for-money function. The argument is based upon the necessity of explicitly taking into account the effect of taxation on the rate of return, an effect that has been ignored by previous studies. Section II presents some simple empirical tests.1 Section III outlines an alternative model, subjects it to testing, and presents the new empirical results. Section IV draws some conclusions.

I. Theory

Assume that an economy is growing at a steady pace and that the price level is not expected to change. For such an economy, it is widely agreed that the demand for money, m, can be represented by the function

m=f(r,y)(1)

where r and y denote, respectively, the interest rate and the income level. As the price level is constant, r and y, as well as m, represent both nominal and real values. In this case, the rate of interest reflects fully the opportunity cost of holding money.

Next, assume that although the economy is still growing at a steady pace, the price level is no longer stable but instead is increasing (and is expected to continue increasing) at an annual rate π. Does this require a modification of equation (1)? Or should π be included among the independent variables that affect m? The basic arguments against this inclusion would seem to be two: (1) the Fisherian hypothesis about the behavior of nominal interest rates during inflationary situations, and (2) the Keynesian assumption that money as an asset is substituted only for financial assets (“bonds”) and not for real assets.

If R denotes the nominal interest rate and r the real rate, Fisher’s hypothesis states that

Rt=rt+bπt

or, in a stricter version,

Rt=r+πt(2)

which implies that r is constant and that changes in π are fully reflected in R. When the strict version of the Fisherian hypothesis holds, the nominal rate of interest incorporates fully the expected rate of inflation. Furthermore, if interest income is not taxed, an individual who lends money at a nominal rate R receives a real return equal to the real rate r, which, under the assumed conditions, will always be positive and constant.2 This implies that R always exceeds π by the amount of the real rate. Therefore, financial assets that pay a nominal return equal to R will be preferred over assets that pay an implicit nominal return equal to π. The latter can be called consumption goods and would also include durables and non-income-yielding real assets such as works of art and jewelry. In such a situation, the real rate of return on equity will, at the margin, tend to be equal to the expected real rate of interest (r = R - π); consequently, there will not be any preference for real assets over financial assets. The demand for money will be limited to the amount needed for current transactions; temporary excesses over that amount would lead to the purchase of interest-bearing financial assets (bonds) or income-yielding real assets (equity) and not to increases in the holdings of “consumption goods.” The reason for this is that the purchase of the latter would be associated with an opportunity cost equal to the expected real rate of interest. Furthermore, if one still followed the traditional Keynesian assumption, even the substitution between money and income-yielding real assets (equity) would not take place, so that only financial assets would be purchased.

The next step toward realism requires that the existence of income taxes be recognized.3 In today’s world, an individual who buys a financial asset bearing an interest rate equal to R does not retain the total interest income derived from the asset but only the portion of it that is left after paying income taxes. Assuming that an individual’s marginal tax rate, expressed as a fraction, is T his after-tax interest rate will be reduced to RT, where

RT=R(1T)(3)

If the Fisherian relationship is still assumed to hold, equation (3) can be rewritten as

RT=r(1T)+π(1T)(4)

Obviously, the higher is T, the lower RT will be compared with R.

Consider the rate of return that an individual gets, ceteris paribus, if, instead of buying a financial asset, he buys, first, an equity, and, second, consumption goods. As unrealized capital gains are not taxed, if this individual buys an equity for which nominal value is expected to increase at the rate of π and to pay an income (in the form of dividends, rent, etc.) equal to r, he will expect to receive a net-of-tax nominal rate of return equal to π + r (1 - T). However, should the capital gain be realized, or should the investor take into account the tax liability that he will face in the future when he sells the asset, the actual rate of return would be less than what has been shown, especially since the total nominal increase in the value of the asset would be taxable. But if the individual buys consumption goods, the value of which is assumed to increase at the rate of inflation, he will receive the full nominal rate of return equal to π, as the nominal increase in the value of the goods is not taxable.4

In summary, assuming that the Fisherian relationship holds, when, as in the United States, there is inflation and nominal incomes are taxed, the opportunity cost of holding money for an individual taxed at marginal rate T, measured in terms of forgone nominal yield, is5 [π (1 - T) + r (1 - T)] for financial assets, [π + r (1 - T)] for equities with unrealized capital gains, and π for consumption goods.

If nominal capital gains from holding equities were taxed at a rate T* (where T* < T), then the opportunity cost of holding money in terms of these equities would be π (1 - T*) + r (1 - T). For simplicity’s sake, I shall ignore this possibility.

As the rate of inflation rises, the relative importance of r in determining nominal income decreases. Furthermore, the importance of r is also reduced by the tax, since the higher T is, the lower is r (1 - T). The U.S. income tax is progressive with a marginal rate that, over the period analyzed in this paper, reached 70 per cent. This means that with it positive and significant, it was not unusual for the expected net-of-tax return to financial assets for individuals with high incomes to fall below the return on holdings of consumption goods that (ignoring storage and other costs) has been assumed to be equal to the inflation rate. Thus, at all times for many, and at some times for most, individuals

π(1T)+r(1T)=RT<π

A vivid numerical illustration of this point is provided by Table 1. The table assumes that the strict version of the Fisherian hypothesis holds and that the real rate of interest is constant and equal to 2. Therefore, in the absence of taxes, the nominal rate R would be equal to the inflation rate plus 2.

Table 1.

Effect of Taxes on Yields

(In per cent)

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As the average tax rate on interest income in the United States has been estimated to be around 0.40 during the past decade,6 the most significant row may be the one corresponding to T = 0.40. This row indicates that even at an inflation rate of 5 per cent, individuals subject to a marginal tax rate of 0.40 receive a measurably higher return from holding consumption goods than from purchasing financial assets paying 7 per cent interest. When inflation reaches higher levels, or when the tax rate is higher, the differentials become great indeed. For example, an individual with a marginal tax rate of 50 per cent (not an unusually high rate) would receive a net-of-tax rate of return of only 6 per cent when the rate of inflation was 10 per cent and of only 11 per cent when the rate of inflation was 20 per cent. As a consequence, for many individuals, the direct substitution of consumption goods for money becomes far more attractive than the substitution of financial assets for money.7 But this implies that in the determination of the demand-for-money function, inflationary expectations become increasingly important compared with nominal rates of interest and cannot, therefore, be left out of the determinants of that demand.

In conclusion, far from being a controversial issue, there seems to be ample theoretical justification for rewriting the demand-for-money function as

mt=f(Rt,πt,yt,)(5)

with the understanding that, under inflationary conditions, y and π will be important variables with well-specified signs (positive for y and negative for π), while the importance of R will no longer be obvious. This conclusion implies that leaving π out of the equation introduces an upward bias in the coefficient of R. Therefore, that coefficient should decrease when π is added.

The previous theoretical discussion has assumed that the strict version of the Fisherian hypothesis, which was stated in equation (2), holds. However, in the real world, that strict version of Fisher’s theory may not hold, and the market interest rate may adjust by less or more than the expected inflation rate. Theoretical8 and institutional arguments9 have been advanced to make a case that the interest rate will adjust by less than the inflation rate; and theoretical arguments have been advanced that it will adjust by more.10 There is now overwhelming empirical evidence that in the United States over the period covered by this paper (1964–78), the nominal interest rate adjusted by less than expected inflation. This implies that the relative importance of π (compared with R) in the demand-for-money equation was even greater than has been previously described in this paper. In the post-1978 period, however, the nominal interest rate increased by more than the expected inflation rate. This implies that, in this latter period, the interest rate became more important as a determinant of the demand for money than it had been in the previous period. As a consequence, the conclusions reached in this paper may have to be qualified when they are applied to the post-1978 period. Elsewhere, I have argued that this recent change is due to the loss of fiscal illusion on the part of lenders.11

II. Preliminary Tests

In order to test for the effects of inflationary expectations on the demand for money, one needs a measure of those expectations. One such measure is provided by the Livingston series as reworked by Carlson.12 This series of “observed” inflationary expectations is used in this paper. It provides a direct measure over six-month periods. However, an observed price expectations variable may contain various types of errors that could make it differ from the true, unobservable price expectations variable. Therefore, several alternative price expectations variables have been derived by the combined use of observed data and actual (known) price changes. These derived series—which incorporate expectations hypotheses suggested by Turnovsky and Frenkel—will also be used and will be referred to as extrapolative, adaptive, Frenkel, and distributed.13 The period covered in the tests will be June 1964-December 1978. 1964 was taken as the initial year, as there was little inflation before then. December 1978 is the latest period for which the needed data were available when this paper was written. All the data are measured semiannually.

Preliminary tests involved the estimation of the following equations:

lnm=a0+a1R+a2lny+a3lnm1(6)
lnm=b0+b1π+b2lny+b3lnm1(7)
lnm=c0+c1R+c2π+c3lny+c4lnm1(8)

where m and y denote, respectively, money (M1) and income in 1972 prices; R denotes the interest rate on six-month Treasury bills, and π is the measure of inflationary expectations. The estimations are made in logarithmic form for m and y.

Table 2 shows the results. The first column identifies the series used for the inflationary expectation. “Observed” refers to the direct use of the Livingston-Carlson series, while the other four entries in the first column refer to the series derived by the combination of the Livingston-Carlson series with actual data on price level changes specified by various expectation hypotheses.

Table 2.

Demand-for-Money Equations, 1964–7811

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One asterisk indicates significance at 5 per cent level; two asterisks indicate significance at 1 per cent level. Numbers in parentheses are t-values. A first-order Cochrane-Orcutt correction is employed in equation (6). The values of the H-statistic are within the acceptable range.

The results for the short-run demand for money can be summarized briefly as follows:

(1) The comparison of equation (6) with equations (7a) through (7e) indicates that equations with inflationary expectations in place of the interest rate have greater explanatory power. The R2 is raised substantially when the rate of interest (R) is replaced by the variable measuring inflationary expectations (π); furthermore, the t-values for π are sharply higher than those for R.

(2) There is little difference among the five series of inflationary expectations. The directly observed series performs about as well as the other derived series.

(3) Little is gained in terms of explanatory power when, as is done in equations (8a) through (8e), the rate of interest and inflationary expectations are jointly used in the same equation. However, in these equations, the t-values for the inflationary expectations variables remain highly significant while those for the interest rate are, for the most part, not significant. Furthermore, the coefficient of R falls sharply when π is added.

(4) The coefficients for the lagged dependent variable are somewhat higher when the equations contain the interest rate than when they do not. This implies a long adjustment lag.

III. Alternative Model

In Section I, a theoretical argument was made for the inclusion of inflationary expectations among the arguments of the demand for money. Therefore, as equation (5) indicated, it was concluded that the demand for money should be written as

mt=f(Rt,πt,yt,)(5)

The results in Table 2 indicated, however, that, empirically, not much was gained by putting both π and R in the same equation. The R2s were hardly affected. Furthermore, the use of both R and π in the equation raises the problem of multicollinearity, since Rt =ft). Elsewhere (see Tanzi (1980)) it has been shown that

R=rt+πt+f(yty¯t)(9)

where r denotes the real interest rate; π and R have the same meanings they had previously; and yt and yt denote, respectively, real actual and potential incomes. This equation indicates that in the absence of changes in economic activity (yt = yt) and expected inflation (π = 0), the nominal rate of interest will equal the real rate and will be constant. If πt>0 and yt = yt then the nominal rate of interest will increase pari passu with the rate of inflation. If ytyt, then the real rate will be affected, since, empirically, it appears that the coefficient of π, is close to 1 (see Tanzi (1980)). The empirical relationship between the rate of interest and its determinants is shown in Table 3.14

Table 3.

Interest Rate Equations, 1964–781

(Equation (9))

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One asterisk indicates significance at 5 per cent level; two asterisks indicate significance at 1 per cent level. Numbers in parentheses are t-values. A first-order Cochrane-Orcutt correction is employed.

Let us call the difference between yt and yt the gap and denote it by Gt. Then

yt=Gt+y¯t(10)

Combining equations (5), (9), and (10), the demand-for-money equation can be restated as

mt=f(πt,Gt,y¯t)(11)

Equation (11) states that the demand for money is a function of (1) potential income, (2) the difference between actual and potential income, and (3) inflationary expectations. The replacement of actual income with potential income is particularly significant, as it introduces a true scale variable not distorted by cyclical fluctuations.15 Therefore, the elasticity of the demand for money with respect to income can be estimated in a more meaningful way. Obviously, in the absence of cyclical fluctuations, the gap would disappear, so that the elasticity with respect to actual income would be identical to the elasticity with respect to potential income. Also, should inflationary expectations be reduced to zero when the gap is also zero, the relevant opportunity cost of holding money would be the real interest rate. In this case, the real interest rate would be constant; therefore, it would no longer play a role in the determination of changes in the demand for money. These would then depend exclusively on changes in a scale variable—namely, income.

Let us restate the model to be tested. From equation (5), let

lnmt*=α0+α1lnyt+α2Rt+α3πt+εt(12)

where

  • mt* = long-run demand for real money balances

  • yt = real (actual) income

  • Rt = nominal interest rate

  • πt = expected inflation rate

εt= error term

α 1 > 0 α2, α3 < 0

From equation (9),

Rt=β0+β1πt+β2lnGt+ut(13)

where β1 > 0, β2 < 0, and ut = error term

lnGt=lnytlny¯t(14)

Substituting equations (13) and (14) into equation (12) yields

lnmt*=γ0+γ1lnGt+γ2lny¯t+γ3πt+wt

where

γ0=α0+α2β0γ1=α1+α2β2γ2=α1γ3=α2β1+α3ωt=α2u1+ɛt

Let us assume that

lnmtlnmt1=θ(lnmt*lnmt1)(16)

where θ,0 < θ < 1, is a coefficient of proportionality that measures the speed at which the demand for money adjusts to its long-term desired level, mt*. Then, after making due substitutions,

θlnmt*=θγ0+θγ1lnGt+θγ2lnγ¯t+θγ3πt+θωt

Therefore, the short-run equation for the demand for money can be written as

lnmt=φ0+φ1lnmt1+φ2lnGt+φ3lny¯t+φ4πt+υt(17)

where

φ0=θ(α0+α2β0)φ1=(1θ)φ2=θ(α1+α2β2)φ3=θ(α1)φ4=θ(α2β1+α3)

Table 4 shows the regression equations corresponding to equation (17). These new equations, which correspond to the short-run demand for money obtained using the alternative model suggested in this paper, are clearly superior to those obtained using the traditional model with actual income and interest rate variables (see equation (6) in Table 2). Furthermore, in terms of explanatory power, they are comparable to those equations in Table 2 that use the inflationary expectation variable instead of the interest rate variable (see equations (7a)-(7e) in Table 2).

Table 4.

New Demand-for-Money Equations, 1964–781

(Equation 17)

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One asterisk indicates significance at 5 per cent level; two asterisks indicate significance at 1 per cent level. Numbers in parentheses are t-values. The values of the H-statistic are within the acceptable range.

Table 4 has been estimated from a model that is conceptually different from the traditional one. In this model, (1) the interest rate has been replaced by its determinants, (2) inflationary expectation has been entered as a separate variable, and (3) a form of permanent income (potential income) has replaced actual income. This model allows a separation of the effects associated with a true scale variable (potential income) from those associated with cyclical fluctuations. The explanatory power of the model is quite substantial. Of particular relevance is its clear indication that the variable measuring inflationary expectations plays a dominant role in the determination of the demand for money.

IV. Concluding Remarks

After experiencing several years of inflation, we should all by now be aware that relationships that hold under stable conditions may not hold in an inflationary environment. However, in spite of this awareness, the pervasive influence of taxes on the selection of assets and the interaction of taxes with inflationary expectations in bringing about a fragmentation of the financial market is not yet fully understood. This paper has attempted to show how the desired asset compositions of economic agents and, consequently, the demand for money have been affected by taxes and by inflation. It has been shown that in this environment, given the nature of the tax system, inflationary expectations have come to play a far more powerful role than interest rates in determining the demand for money. The former’s inclusion among the determinants of demand for money should no longer be considered controversial. In this sense, it can be said that the influences on the demand for money in the United States have not been very different from those in other countries, including the developing countries. This conclusion vitiates the rule of thumb, attributed to Modigliani and supported by Dornbusch and Fischer in their macroeconomic textbook, on how “to decide whether the nominal interest rate or the expected rate of inflation should be included as determining the demand for money.” The rule of thumb states that “if the nominal interest rate exceeds the expected rate of inflation, the nominal interest rate should be thought of as the cost of holding money. If the expected inflation rate exceeds the nominal interest rate, think of the expected inflation rate as the cost of holding money.”16 When income taxes exist, even if the nominal interest rate exceeds inflationary expectations, the opportunity cost of holding money may often be better reflected by inflationary expectations than by the nominal return.

This paper has emphasized that in the United States in recent years, the net-of-tax rate of return on financial assets was often lower than the rate of expected inflation. It therefore became convenient for many people to get out of both money and financial assets and into real goods (gold, houses, etc.). More recently, the inflation rate has been falling, while market rates of interest, for a variety of reasons, have remained high. Given these circumstances, one would expect that individuals would switch out of real goods and into financial assets and, perhaps, money. These switches would help to bring down high interest rates.

The paper has concentrated on the demand for money. However, the analysis developed in Section I can also be applied to the choice between interest-bearing financial assets and real assets when inflationary expectations are changing. When inflation accelerates and the tax system is not changed, there will be a tendency to move out of (fully taxed) financial assets and into relatively untaxed real assets. This shift will contribute to a lowering of bond prices and to a raising of real asset prices. When inflation decelerates, the reverse will occur. These shifts have implications for the determination of the interest rate. They strengthen John Rutledge’s argument17 that the interest rate at any one time is not only determined by flow variables but also by switches in the public’s demand for existing assets. These switches do not change the volume of these assets but, by changing their values, affect their rates of return and, in the short run, the interest rate. These switches are often brought about by changes in inflationary expectations, but they may also be brought about by significant tax changes of the types that the United States has enacted recently.

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*

Mr. Tanzi, Director of the Fiscal Affairs Department, holds a doctorate in economics from Harvard University. He was formerly a professor and Chairman of the Economics Department at American University.

1

I shall stay within the established demand-for-money literature in order to test more accurately the main innovations in this paper. Areas of disagreement and current research effort are well surveyed in Laidler (1980).

2

However, the real rate may not, in fact, be constant (see Tanzi (1980)).

3

The role that income taxes may play in the demand for money has been largely ignored (see Tanzi (1979)).

4

Furthermore, even if these goods are eventually sold, with the result that some capital gain is realized, the sale does not generally create any tax liability.

5

I am assuming that equities and consumption goods are affected by the same rate of inflation π. If one were to assume differential rates, some modifications would need to be made in the analysis.

6

Calculated by the author from data in U.S. Internal Revenue Service, Statistics of Income: Individual Income Tax Returns (Washington, various issues).

7

It must, of course, be remembered that not all individuals are affected in the same way. For some, the marginal tax rate is low, so that, for them, financial assets remain more attractive than real assets. For them, the relevant opportunity cost of money holding remains the rate of interest.

9

See B. M. Friedman (1980) for a discussion of institutional and market factors behind less-than-complete Fisherian adjustment.

13

For details, see Tanzi (1980) and Lahiri (1976).

14

Note that in order to avoid difficulties with the logarithm of a negative number, a ratio specification of the gap is employed in the empirical analysis.

15

This approach is consistent with that of studies using permanent income as an explanatory variable. See Laidler (1977).