Chapter

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

Editor(s):
Vito Tanzi
Published Date:
June 1984
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In his excellent article on the demand for money, Goldfeld cites 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 describes his own empirical results as a “mixed bag” (ibid., p. 613) and concludes 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, but 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 on the necessity of explicitly taking into account the effect of taxation on the rate of return, an effect that has been ignored in previous studies. Section II presents some simple empirical tests.1Section III outlines an alternative model to be subjected 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

where r and y denote, respectively the rate of interest and the level of income. 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, while the economy is still growing at a steady pace, the price level is no longer stable but 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: (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 is the nominal rate of interest and r is the real rate of interest, Fisher’s hypothesis states that

or, in a stricter version,

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 assumed not to be 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, is always positive and constant.2 This implies that R always exceeds π by the amount of the real rate. Therefore, investment of money balances in financial assets that pay a nominal return equal to R will be preferred over investment in assets that are expected to pay an implicit nominal return equal to π. The latter can be called consumption goods and 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, at the margin, tends to be equal to the expected real rate of interest (r = R – π); consequently, there is no bias toward the preference for real over financial assets. The demand for money is limited to the amount needed for current transactions; temporary excesses over that amount lead to the purchase of interest-bearing financial assets (bonds) or income-yielding real assets (equity) rather than to increases in the holdings of “consumption goods.” The reason for this is that the purchase of such assets is associated with an opportunity cost equal to the expected real rate of interest. Furthermore, if one still follows 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 real 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 amount remaining after income taxes are paid. Assuming that this individual’s marginal tax rate, expressed as a fraction, is T, his after-tax interest rate would be reduced to RT where

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

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

Consider the rate of return to the individual, 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 whose 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 expects 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 considerably less than that shown above, especially since the total nominal increase in the value of the asset would be taxable. On the other hand, should he buy consumption goods, whose value is assumed to increase at the rate of inflation, he receives 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, 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.

As the rate of inflation rises, the relative importance of r in determining nominal income falls. Furthermore, the importance of r is also reduced by the tax because the higher T is, the lower r (1 – T) is. In recent years the U.S. income tax has been progressive, with a marginal rate reaching 70 percent. This means that, once π became positive and significant, the expected net-of-tax return on financial assets soon fell below the return on the holding of consumption goods that (ignoring storage and other costs) is assumed to be equal to the rate of inflation. Thus, for many individuals (and at times for most),

A vivid numerical illustration of this point is provided in 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 rate of inflation plus 2.

Table 1.Effect of Taxes on Yields(In percent)
Assumed

Inflation Rates
After-Tax Rates of Interest
Trπ1π2π3R1(1-T)R2(1-T)R3(1-T)
0.002510207.012.022.0
0.102510206.310.819.8
0.302510204.98.415.4
0.402510204.27.213.2
0.502510203.56.011.0
0.702510202.13.66.6

As the average tax rate on interest income in the United States has been estimated at between 0.30 and 0.40 during the 1970s,6 the most significant row in the table may be the one corresponding to T = 0.40. This row indicates that, even at an inflation rate of 5 percent, 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 percent 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 percent (not an unusually high rate) would receive a net-of-tax rate of return of only 6 percent when the rate of inflation is 10 percent and of only 11 percent when the rate of inflation is 20 percent. 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. But this implies that, in the determination of the demand-for-money function, inflationary expectations become increasingly more important than nominal rates of interest and cannot, therefore, be ignored as determinants of that demand.

In conclusion, there seems to be ample theoretical justification for rewriting the demand for money function as

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

The previous discussion is based on the assumption that the basic Fisherian hypothesis, stated as equation (2), holds. If (as was the case through much of the period studied in this paper) institutional reasons (such as usury laws) or inertia prevent the nominal rate of interest from increasing by as much as it is assumed to have increased under the Fisherian hypothesis, then the relative importance of π (as compared with R) in the demand-for-money equation would rise.7 The greater the constraints on R, the greater is the significance of π.

This paper concentrates on the demand for money rather than on the choice between financial and real assets, but the analysis is also relevant to that choice. When the expected inflation rate is rising, individuals not only move out of money and into real goods, but they also move out of financial assets and into real goods. They do this for the reasons set forth above. Thus, because of these moves, bond prices fall while real asset prices (especially those of assets in limited or inelastic supplies) rise. In time, a new equilibrium is established, with less real money and higher nominal interest rates. On the other hand, a fall in the expected rate of inflation not only leads to an increase in the demand for money but also to a shift away from real goods and into financial assets. In this case, the higher demand for bonds increases bond prices and thus forces down the rate of interest. In a more complete analysis than that given here, it would be necessary to take these shifts into account.

II. PRELIMINARY TESTS

In order to test for the effects of inflationary expectations on the demand for money, a measure of those expectations is needed. One measure is provided by the Livingston series, as reworked by Carlson (1977). 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 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 expectation hypotheses suggested by Turnovsky and Frenkel—are also used and are referred to as extrapolative, adaptive, Frenkel, and distributed.8 The period covered in the tests is June 1964–December 1978, using semiannual observations and taking 1964 as the initial year because there was little inflation before that period. December 1978 is the latest period for which the data were available when this paper was written.

Preliminary tests involved the estimation of the following equations:

where m and y are money (M1) and income in 1972 prices, R is the rate of interest 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 four other entries in the first column refer to the series derived by the combination of that series with actual data of price level changes specified by various expectation hypotheses.

Table 2.Demand-for-Money Equations, 1964–78
Inflationary

Expectation Used
ConstantRπIn yIn m–1R¯2H
(6) Observed–0.4002–0.5417+ 0.0284+ 0.89600.8440.860
(0.47)(1.95)(0.73)(6.08)**
(7a) Observed–0.2549–1.250+ 0.1412+ 0.87400.9010.144
(0.69)(5.44)**(4.37)**(14.37)**
(7b) Distributed–0.1205–1.1791+ 0.1273+ 0.86680.9040.533
(0.35)(5.62)**(4.36)**(14.52)**
(7c) Adaptive–0.0029–1.0406+ 0.1130+ 0.86270.9020.479
(0.008)(5.49)**(4.09)**(14.27)**
(7d) Extrapolative–0.0752–1.1838+ 0.1313+ 0.82580.8900.758
(0.21)(4.95)**(3.93)**(12.89)**
(7e) Frenkel–0.3205–1.2951+ 0.1508+ 0.87420.900–0.132
(0.85)(5.43)**(4.44)**(14.35)**
(8a) Observed–0.4571–0.2392–1.1331+ 0.1369+ 0.91840.9020.026
(1.14)(1.21)(4.58)**(4.25)**(13.03)**
(8b) Distributed–0.4206–0.3055–1.0681+ 0.1271+ 0.92450.9110.567
(1.10)(1.67)(5.01)**(4.50)**(13.75)**
(8c) Adaptive–0.3570–0.3387–0.9425+ 0.1155+ 0.92730.9110.475
(0.94)(1.87)(5.01)**(4.38)**(13.81)**
(8d) Extrapolative–0.3577–0.3940–1.0718+ 0.1344+ 0.90450.9040.554
(0.91)(2.13)*(4.66)**(4.29)**(12.85)**
(8e) Frenkel–0.4866–0.2117–1.1798+ 0.1451+ 0.91330.901–0.179
(1.19)(1.05)(4.50)**(4.23)**(12.82)**
Note: One asterisk indicates significance at the 5 percent level; two asterisks indicate significance at the 1 percent 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.
Note: One asterisk indicates significance at the 5 percent level; two asterisks indicate significance at the 1 percent 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 may be summarized briefly:

  • (1) The comparison of equation (6) with equations (7a) through (7e) indicates that equations with inflationary expectations in place of the rate of interest have greater explanatory power. The R¯2 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 in equations (8a) through (8e), the rate of interest and inflationary expectations are jointly used in the same equations. However, in these equations the t-values for the inflationary expectations variables remain highly significant while those for the rate of interest 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 rate of interest than when they do not. This implies a long adjustment lag.

III. ALTERNATIVE MODEL

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

The results in Table 2 indicate, however, that, empirically, very little is gained by putting both π and R in the same equation. The R¯2s are scarcely affected. Furthermore, the use of both R and π in the equation raises the problem of multicollinearity because Rt = ft). Elsewhere (Tanzi (1980)) it has been shown that

where r is the real rate of interest, π and R have the same meaning as they had above, and yt and y¯t represent, respectively, real actual and potential incomes. This equation indicates that, in the absence of changes in economic activity (yt=y¯t) and expected inflation (π = 0), the nominal rate of interest would equal the real rate and would be constant. If πt > 0 and yt=y¯t, then the nominal rate of interest will increase pari passu with the rate of inflation. If yty¯t, then the real rate is affected because, empirically, it appears that the coefficient of πt is close to unity (see Tanzi (1980)). The empirical relationship between the rate of interest and its determinants is shown in Table 3.9

Table 3.Interest Rate Equations, 1964–78

(Equation (9))

Inflationary

Expectation Used
ConstantπIn G
Observed+ 0.0275+ 0.8480+ 0.3280R¯2 = 0.714
(3.77)**(5.12)**(3.01)**D-W = 1.640
Distributed+ 0.0286+ 0.8265+ 0.3609R¯2 = 0.653
(3.91)**(4.64)**(3.01)**D-W = 1.717
Adaptive+ 0.0323+ 0.7252+ 0.3256R¯2 = 0.603
(4.91)**(4.63)**(2.76)*D-W = 1.786
Extrapolative+ 0.0278+ 0.8540+ 0.3873R¯2 = 0.624
(3.26)**(4.10)**(2.89)**D-W = 1.725
Frenkel+ 0.0272+ 0.8433+ 0.3215R¯2 = 0.718
(3.72)**(5.18)**(2.98)**D-W = 1.642
Note: One asterisk indicates significance at the 5 percent level; two asterisks indicate significance at the 1 percent level; numbers in parentheses are t-values. A first-order Cochrane-Orcutt correction is employed.
Note: One asterisk indicates significance at the 5 percent level; two asterisks indicate significance at the 1 percent level; numbers in parentheses are t-values. A first-order Cochrane-Orcutt correction is employed.

Let us call the difference between yt and y¯t the gap and define it by Gt. Then

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

Equation (11) states that the demand for money is a function of (1) potential income, (2) a measure of the difference between actual and potential income, and (3) inflationary expectations. The substitution of potential income for actual income is particularly significant because it introduces a true scale variable undistorted by cyclical fluctuations. 10 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 in such a way that the elasticity with respect to actual income would become identical to that with respect to potential income. Also, if inflationary expectations are reduced to zero when the gap is also zero, the relevant opportunity cost for holding money would be the real rate of interest. In this case, the real rate of interest 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

where

From equation (9),

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

Combining equations (13) and (14) with (12),

where

Let us assume that

where θ, which is 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,mi*. Then, after due substitutions,

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

where

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

Table 4.New Demand-for-Money Equations, 1964–78

(Equation (17))

Inflationary

Expectation Used
ConstantIn mt−1In GIny¯πR¯2H
Observed–0.0743+ 0.8572+ 0.2390+ 0.1275–1.0284
(0.18)(12.74)**(2.30)*(4.22)**(3.84)**0.9050.196
Distributed–0.0589+ 0.8610+ 0.1944+ 0.1225–1.0598
(0.15)(13.10)**(1.84)(4.40)**(4.08)**0.9090.437
Adaptive+ 0.0180+ 0.8588+ 0.1719+ 0.1128–0.9694
(0.05)(12.97)**(1.57)(4.26)**(3.99)**0.9070.492
Extrapolative+ 0.0502+ 0.8316+ 0.1693+ 0.1301–1.1272
(0.12)(12.17)**(1.41)(3.84)**(3.40)**0.8960.647
Frenkel–0.1004+ 0.8549+ 0.2562+ 0.1331–1.0382
(0.23)(12.74)**(2.50)*(4.23)**(3.84)**0.905–0.057
Note: One asterisk indicates significance at the 5 percent level; two asterisks indicate significance at the 1 percent level; numbers in parentheses are t-values. The values of the H-statistic are within the acceptable range.
Note: One asterisk indicates significance at the 5 percent level; two asterisks indicate significance at the 1 percent 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, everyone should 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 are not yet fully understood. This paper has attempted to show how the desired asset composition of economic agents—and consequently, the demand for money—has been affected by taxes and by inflation. It has shown that, in this environment, given the nature of the U.S. tax system, inflationary expectations have come to play a far more powerful role than interest rates.

The inclusion of inflationary expectations among the determinants of the demand for money can no longer be considered controversial. In this sense, it can be said that the influences on the U.S. demand for money are no longer 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, as to 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 is stated by Dornbusch and Fischer (1981, pp. 244–45): “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.” When income taxes exist, even if the nominal interest rate exceeds inflationary expectations, the opportunity cost of money may often be better reflected by inflationary expectations than by the nominal return.

References

    CarlsonJohn A.“A Study of Price Forecasts,”Annals of Economic and Social Measurement (New York) Vol. 6 (Winter1977) pp. 2752.

    DornbuschRudiger and StanleyFischerMacroeconomics (New York: McGraw-Hill2nd ed. 1981).

    FriedmanBenjamin .M.“Price Inflation, Portfolio Choice, and Nominal Interest Rates,”American Economic Review (Nashville Tennessee)Vol. 70 (March1980) pp. 3248.

    GoldfeldStephen M.“The Demand for Money Revisited” Brookings Papers on Economic Activity: III (1973) The Brookings Institution (Washington) pp. 577638.

    LahiriKajal“Inflationary Expectations: Their Formation and Interest Rate Effects,”American Economic Review (Nashville Tennessee)Vol. 66 (March1976) pp. 12431.

    LaidlerDavid E. W.The Demand for Money: Theories and Evidence (New York: Harper and Row2nd ed.1977).

    LaidlerDavid E. W.“The Demand for Money in the United States—Yet Again,”in On the State of Macro-economicsed. by KarlBrunner and Allan H.MeltzerCarnegie-Rochester Conference Series on Public PolicyVol. 12 (Amsterdam: North-Holland1980) pp. 21971.

    TanziVito“Income Taxes and the Demand for Money: A Quantitative Analysis,”Quarterly Review Banca Nazionale del Lavoro (Rome) Vol. 32 (March1979) pp. 5572.

    TanziVito“Inflationary Expectations, Economic Activity, Taxes, and Interest Rates,”American Economic Review (Nashville Tennessee)Vol. 70 (March1980) pp. 1221.

This study is based on the established literature in order to provide a better test of its principal innovations. Areas of disagreement and current research on the demand for money have been well surveyed by Laidler (1980, pp. 140–48).

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

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

Furthermore, even if these goods are eventually sold and some capital gain is realized, the sale does not generally create any tax liability. This is not true if the goods are held by corporations.

It is assumed 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.

Calculated by the author from data in U.S. Internal Revenue Service, Statistics of Income: Individual Income Tax Returns (Washington, annual issues). The data are available up to 1978. The average tax rate was probably higher after 1978 until the 1982 tax cut.

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

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

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.

This approach is consistent with that of studies using permanent income as an explanatory variable. See Laidler (1977, pp. 140–48).

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