STANDARD REAL-TERMS MODELS

The shortest adjustment lag and the least scope for disequilibrium money are provided by the simple model, which specifies that desired money makes its full long-run response to the changes in income or interest rates induced by exogenous changes in money without lag. The Friedman (1959) instantaneous response of desired money to the relevant variables is, in a sense, a form of this unlagged model, except that the relevant income, and perhaps the interest rate, variables are “permanent” ones. The essence of the Friedman model is, in natural logarithms,

where

m	=	M − P
y	=	Y − P
$\mathit{\Delta }{\mathit{P}}_t^e$	=	inflation rate expected in period t
c ≥ 0; g > 0

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m	=	M − P
y	=	Y − P
$\mathit{\Delta }{\mathit{P}}_t^e$	=	inflation rate expected in period t
c ≥ 0; g > 0

Strictly speaking, application of the permanent-income approach requires that

m = M − P^perm

Friedman concedes the possibility of some lag in reallocating the portfolio of financial assets in response to a change in the interest rate. And the use of permanent income implies—in its adaptive-expectations formulations—the equivalent of a lag with respect to the observable current-income variable.

A little more lag is provided in the real-terms stock-adjustment models that have lags in the adjustment of money to real income, interest rates, and expected inflation but (as will be shown later) no lag with respect to the price level. Where these models use current income rather than the lagging permanent variable for real income, they may show shorter lags on balance than the Friedman model, although empirically the effect of shifting from permanent to current income may be simply an offsetting lengthening of the estimated value of the stock-adjustment lag (of γ in equation (4)). According to Bronfenbrenner and Mayer ((1960), p. 813), the real-terms model was introduced by Klein and Goldberger in 1955 (following Klein’s use of the nominal-terms variant in 1950). This model has continued to be used by some researchers, particularly some members of the Chicago school (see, for example, Frenkel (1977)).

The stock-adjustment models require use of long-run desired money

where

$m_t^{*}=M_t^{*}-P_t$
y	=	real income
r	=	interest rate

View Table

$m_t^{*}=M_t^{*}-P_t$
y	=	real income
r	=	interest rate

and an asterisk represents the long-run desired level of the variable. A fraction, γ, of the discrepancy between desired money and pre-existing actual money is eliminated by stock adjustment in each time period.

The two equations are solved to eliminate m*,

Equations (3), (4), and (5) imply adjustment of the amount of nominal money demanded without lag to a change in the price level—that is, same-quarter rebuilding of the real value of preexisting M, and of other nominal asset holdings, through the hoarding achievable by sufficient reduction of consumption relative to disposable income (as defined in the national income accounts). This adjustment is shown through the addition of P_t − P_t−1 (all variables still being in logs) to both sides of (4). This expresses the real-terms model in terms of the actual change in nominal money holdings

FURTHER LAG IN STANDARD NOMINAL-TERMS MODELS

Stock-adjustment models yielding the slower adjustment implied by allowing a lag in adjustment of money to changes in the price level have long been used. The reason for their use—the need to allow for a lag of money behind the price level because of the welfare loss caused by a consumption cut sufficient to rebuild assets without lag—has been presented by Goodhart and Crockett (1970), Goldfeld ((1973), p. 611; and (1976)), Johnson ((1976), pp. 267, 273–78), and Harberger ((1978), pp. 516–17). This longest-lagging model has continued to be used by the Bank of England as well as by the Federal Reserve Board (Enzler and others (1976)) for M₁ by the Federal Reserve Bank of New York (Hamburger (1977); Landy (1980)), and in the complete DRI econometric models (Eckstein and others (1974); Fair (1976)).

The nominal-terms formulation of the stock-adjustment-lag model uses (when unit long-run elasticity of demand for nominal money with respect to the price level can be assumed)

This implies application of the stock-adjustment lags that equations (4) and (5) use for the other variables determining m* to the price-level variable as well; the latter may be seen by separating the right side of equation (6) into $\left[m_t^{*}-m_{t-1}+({\mathit{P}}_t-P_{t-1}\right)]$. That yields

Comparison of the final coefficient in equation (4’), which is unity, with its counterpart (γ < 1) in equation (6’) shows that the equilibrium model formulated in real terms explains an unlagged rise in money holdings as predominantly a short-run desired rise and leaves too little of the actual rise in money to be explained as an undesired buffer-stock rise. However, when—as for developing countries having difficulties with inflation—the real-terms model includes an adaptively formed negative expected-inflation-rate elasticity of demand for money, that bias against finding disequilibrium money is removed. Instead, the −(1 − γ)ΔP_t correction of (4’) to yield (6’) is proxied—as Goldfeld ((1973), (1976)) pointed out—by a spuriously high expected-inflation-rate elasticity of demand and also by a sharply understated expectations-formation lag.

An intermediate position on the lag of money behind the price level has been presented in White (1978); in that paper, the zero adjustment lag is valid with respect to the transactions cash portion of money—which varies in proportion to the price level. Moreover, the zero lag tends to be valid where the price change is endogenous to efforts to get rid of excess cash already held; and for time deposits, the zero lag tends to be valid to the extent that the actual inflation rate is expected and that this expectation is reflected in the nominal interest rate. (This enlargement of the relevant γ reduces the component of the estimated expected inflation-rate elasticity in equations (4) and (4’) that is in reality merely a proxy for the missing −(1 − γ)ΔP_t, but this component should remain a major part of the estimated elasticity.)

Carr and Darby ((1980), p. 5) defend the zero price-level lag of the real-terms model on pragmatic grounds. They apparently accept the proposition that the shrinkage of the real value of assets caused by rising prices will be reversed only gradually through extra savings. But they argued that the target amount of rebuilding of cash assets is the much larger one associated with _tΔP^perm rather than ΔP_t. If ${}_t\mathrm{\Delta }{P}^{\mathit{perm}}\cong 1/\stackrel{\wedge }{\gamma }\mathrm{\Delta }{\mathit{P}}_t$, approximately all of the shrinkage in real assets owing to ΔP_t would be made good without lag, even though only the fraction $\stackrel{\wedge }{\gamma }$ of the relevant shrinkage—the increase in size of the expected future shrinkage (_tΔP^perm)—is made good. In actuality, less than $\stackrel{\wedge }{\gamma }$ of the relevant shrinkage will be made good without lag (because the disutility from stock disequilibrium here is an expected future one that has a reduced present value); therefore, the shrinkage (_tΔP^perm) must be larger than $1/\stackrel{\wedge }{\gamma }\mathrm{\Delta }{P}_t$.

Since Carr and Darby believe that γ is usually 0.1 at most, it follows that they must be able to justify _tΔP^perm/ΔP_t > 10 at a minimum. Moreover, the information underlying _tΔP^perm is merely the next quarter’s expected inflation rate $\left({}_t\mathrm{\Delta }{P}_{t+1}^e\right)$, and the latter varies by only, say, ½ of ΔP_t.^l It follows, therefore, that money holders must be willing to extrapolate the newly expected next-quarter inflation rate for a minimum of more than 19 more quarters to arrive at Carr and Darby’s _tΔP^perm. And they must be willing to give full weight to that imaginative extrapolation in determining the needed reduction of current consumption. That is prima facie implausible; and, as indicated in the discussion of the same analysis by White ((1978), pp. 573, 597), the conditions for even the > 10 to > 12 quarters of extrapolation required for more plausible values for $\stackrel{\wedge }{\gamma }$ seem difficult to satisfy in the only-moderately-inflationary developed countries considered by Carr and Darby.²

This inference is supported by a test made by the Federal Reserve Board for M₁ in a period of moderate price rises. Addition to the real-terms model of a polynomial distributed-lag price elasticity of demand for real balances yielded a reduction of real money holdings in the same quarter by the greater part of the percentage increase in current prices, with rebuilding of real holdings beginning in the second month following the price increase (Farr and others (1978), pp. 103, 104). Comparable findings for a polynomial lag of the price level were reached by Dickson and Starleaf ((1972), p. 1039). The Hafer and Hein (1980) finding that the nominal-terms model fit better than the real-terms model also supports this conclusion.

On balance, some lag in the adjustment of money to the price level should exist. The customary real-terms models, which exclude that lag, therefore explain what could in reality be disequilibrium money. Conversely, the customary nominal-terms models, which impose a price-level-adjustment lag that is as long as the other adjustment lags, understate the initial desired change in money and leave part of it to be explained by a disequilibrium money term.

STARLEAF (1970)

The frequent citations of Starleaf (1970) overlook the fact that the author merely claimed that his equilibrium $\stackrel{\wedge }{\gamma }$ values did not permit the rejection of the hypothesis of the disequilibrium values he had hoped for (Starleaf (1970), p. 757). Worse still, Dickson and Starleaf ((1972), p. 1036) accepted their equilibrium regression results—supplied money equaled demanded money, which was a function of polynomial distributed lags of income, interest rates, and the price level.

ARTIS AND LEWIS (1976)

The widely cited Artis and Lewis (1976) econometric evidence on the United Kingdom tests a variety of disequilibrium-term variables for possible addition to conventional money-demand functions, including the difference between actual and desired changes in money and credit rationing variables thought to be promising measures of exogenous changes in money. The basic observation period of 30 quarters was dominated by endogenous money supply, with supply responding to changes—including stochastic changes—in money demand because of the central bank’s desire to smooth interest rates. Therefore, the estimated regression coefficients overstated the effects of exogenous or excess changes in money, and only the changes in the coefficient produced by two successive additions of merely a few quarters of changes in the money supply that were more nearly exogenous served as usable evidence.

Although they were interpreted as supporting disequilibrium money, the results of this difficult test seem erratic and not very conclusive (Artis and Lewis (1976), pp. 152, 158, 165).

A second kind of test, based on the reasoning that the gradual dishoarding of an initial, undesired acquisition of cash would exert only a gradual, accumulating pressure on the market interest rate (Artis and Lewis (1976), equations (4.1) and (4.7) on pp. 167 and 169, respectively) also received only very limited econometric support (p. 172). And a test carried out with U. S. data (Laidler (1979), pp. 31–32) led to the conclusion that the model was unacceptable. In any case, as will be shown in the discussion of Figure 1 (see Section V), the initial small dishoarding of the undesired cash would depress the interest rate not incompletely but rather by roughly the full amount consistent with long-run equilibrium because it encounters a comparably small part of the long-run interest elasticity of demand in the money market.³ By assuming that the long-run interest elasticity applied without lag, Artis and Lewis suppressed the increase in demanded money that accompanied the increasing supply of dishoarded cash.

CARR AND DARBY ((1978), (1980))

Carr and Darby (1978) introduced the rational monetarist approach to disequilibrium money demand modeling by adding to the real-terms stock adjustment model (equations (3) and (4) in this paper) a fraction of the excess of the current quarter’s actual change in nominal money over the change that had been rationally expected for the current quarter on the basis of the autoregressive elements in the time series of current and past money growth, $+w(\mathrm{\Delta }{M}_t-\mathrm{\Delta }{M}_t^e)=+\mathrm{w\Delta }{M}_t^u$.

The previously expected part of the actual change in money $\left(\mathrm{\Delta }{M}_t^e\right)$ was not considered as a cause of disequilibrium because the rational monetarist approach assumes that $\mathrm{\Delta }{P}_t=\mathrm{\Delta }{M}_t^e\mathrm{—a}$ relationship challenged in Section V—and because the real-terms formulation was used for the equilibrium part of the model, so that desired money changed without lag by the same percentage as the price level. Given the evidence of the need for some lag with respect to the price level that was presented earlier, this constitutes a misspecification that imparts a negative bias to the tests for disequilibrium money.

The single-equation M₁ regressions derived for the United States using quarterly observations for 1951–71 yielded w = ½—that is, half of the previously unexpected or currently unperceived ΔM_t, went into (came out of) buffer stocks of off-demand-curve money. But the extremely low $\stackrel{\wedge }{\gamma }$ values of 0.03 and 0.05 (which imply, respectively, that eight years and nearly five years, are required for the elimination of five eighths of a discrepancy between $m_t^{*}$ and m_t−1) obviously divert too much of the initial change in money away from what is a plausibly high amount of on-demand-curve initial stock adjustment (see Section IV). In any case, the authors reserved judgment, pending re-estimation with simultaneous-equation techniques; an upward biasing of ŵ was possible because of the endogenous (interest-rate-smoothing) money supply process noted previously (see Carr and Darby (1978), pp. 10, 11). Laidler ((1979), p. 39) found the risk that money changes were simply being regressed on what should have been left as an error term to be even greater than the authors had pointed out.

Simultaneous-equation techniques have since been applied by Carr and Darby (1980), for an observation period extending into 1976, to eight developed countries. The extremely low $\stackrel{\wedge }{\gamma }\mathrm{s}$ and other unacceptable parameter values continue. The U. S. regression is startling, in that the regression coefficient of m_t on m_t−1 is 1.00 (t = 37) (Carr and Darby (1980), p. 16), so that $\stackrel{\wedge }{\gamma }=0$ (see the coefficient of m_t−1 in equation (5) in Section II) and there is no stock-adjustment process. That means that Δm_t, is a function of the level of the interest rate and of the two change variables, transitory income and $\mathrm{\Delta }{M}_t^u$. The high, significant coefficient of $\mathrm{\Delta }{M}_t^u(ŵ=0.63)$ could not be taken seriously even if the equation otherwise merited retention; most of unexpected money is supposed to go partly into the buffer stock and partly into the money market, where it affects the interest rate. That means $\mathrm{\Delta }{M}_t^u$ must be acting—whether partly or completely—as a proxy for the interest-rate-change variable that ought to have been included among the variables explaining Δm_t.⁴

The reasons for the failure of this approach to testing for disequilibrium money may lie in the widely discussed “downshift” of the U.S. demand-for-money function in the mid-1970s (which Hafer and Hein (1980), (1981) found severely depressed $\stackrel{\wedge }{\gamma }$ if it was not handled appropriately),⁵ in the use of the misspecified real-terms formulation, and in a number of serious problems caused by the choice of the rational monetarist formulation.

PASTORE (1975)

One more piece of evidence for disequilibrium money that is often cited concerns inflationary developing countries. For Brazil in the 1950s and 1960s, Pastore (1975) used the real-terms model of equations (3) and (4) plus a disequilibrium money term consisting not of Carr and Darby’s $+w(\mathrm{\Delta }{M}_t-\mathrm{\Delta }{M}_t^e)$ but rather $+w(\mathrm{\Delta }{M}_t-\mathrm{\Delta }{M}_t^{*})$. This was done to represent the fraction of the excess of the actual rate of growth of nominal cash balances over the “rate of growth of desired nominal cash balances” that had to go into buffer stocks (Pastore (1975), p. 490). But once the partial stock-adjustment concept (equation (4)) has been accepted, the change in long-run desired M(ΔM*) is irrelevant. The short-run desired change in m given by equation (4) is the relevant expression. Replacement of Pastore’s $-w\Delta M_t^{*}$ by the correct $-\mathrm{w\gamma }(M_t^{*}-M_{t-1})$ means (accepting the nominal-terms model or assuming prices fixed, for simplicity of exposition):

Here, the ŵ provided by Pastore is simply an artifact of the misspecification.⁸

The Brazilian data looked very promising for demonstrating disequilibrium money because, despite the country’s experience with very high inflation, it was observed that real money balances rose in the first period (probably a quarterly period) in which nominal money growth accelerated. But, as will be discussed in Section V, much or perhaps most of that initial rise may have been the spurious product of downward biasing of rises in the price indexes. And it is no surprise that a disequilibrium, off-demand-curve explanation would have to be used to explain departures from a demand function that did not even exist.

CONTRARY ECONOMETRIC EVIDENCE

In contrast to this succession of failures to demonstrate disequilibrium money econometrically, there is the recent finding made by Hafer and Hein ((1980), p. 35), using an improved estimating technique, of so good a fit of the nominal-terms model to the U.S. data that room does not seem to be left for an economically significant amount of disequilibrium money.

PRESUMPTION OF DISEQUILIBRIUM UNDER THE FRIEDMAN-SCHWARTZ MODEL

An early demonstration of a logical case for disequilibrium money that is often cited turns out to be irrelevant because it concerns a model with one inflexible independent variable. Walters ((1965), pp. 547, 549) found that the Friedman and Schwartz equilibrium money-demand function ought not to be satisfied at all times simply because it specified money demand as solely a function of $Y_t^{\mathit{perm}}$. That meant that demand equalled supply only if (variables in percentages) ΔY_t,/ΔM_t exceeded unity by a substantial amount and if, with ΔM_t+1 = 0, 0 > ΔY_t+1/ΔY_t > − 1.

PRESUMPTION OF OFF-DEMAND-CURVE HOLDINGS BECAUSE PORTFOLIO IS ALWAYS REBALANCED WITH A LAG

Artis and Lewis ((1976), p. 168) provide the most persuasive logical explanation for disequilibrium money (also touched on by Starleaf (1970), p. 749). Just as the partial stock adjustment of the equilibrium models specifies that an excess of actual over desired cash holdings created by a rise in interest rates will be only gradually eliminated, so undesired acquisitions of new cash must also be eliminated only with a lag. But the conventional model provides neither for a partial adjustment to eliminate such undesired acquisitions nor for the retention of what is not initially eliminated. It must, therefore, yield initial deviations from the demand curve that have the same sign as the initial change in M.

The only obvious important case of undesired cash acquisition—apart from the unrealistic textbook example, the Great Depression proposal to “drop money from airplanes”—seems to be a high propensity to save cash temporarily out of transitory income, reflecting income recipients’ inability to make immediate adjustments in consumption or in wealth portfolios. But proponents of disequilibrium money include current transitory (or total) income in the argument of short-run money demand in the equilibrium portion of their models and, therefore, cannot rely on such income to create disequilibrium.

MONETARY DISEQUILIBRIUM COUNTERPART OF DISEQUILIBRIA IN THE GOODS MARKET

A view widely held in the early 1970s was that macroeconomic changes in demand for output in the United States met producer resistance to changing either prices or output by enough in the short run to permit customers to stay on their demand curves. Tucker (1971) provides an excellent demonstration of how the initial changes in money associated with such frustrated changes in macroeconomic demand must be converted into temporarily undesired holdings. However, as Brunner ((1971), pp. 552, 563) warned, the price data used reflected the understatement by the wholesale, and to some extent the consumer, price index of the actual flexibility of prices; and even the corrective measures of the 1970s found some continued reliance on “list” prices and some difficulty in securing transactions prices that were adequately adjusted for cyclical fluctuations in the price discounts offered by manufacturers (United States, Council on Wage and Price Stability (1977), pp. V-ll–V-13 and V-17). And, given even limited validity for the insights of the rational expectations school, there would not be significant amounts of price disequilibrium of this sort. From another point of view, a supporter of disequilibrium (Jonson (1976), p. 510) concedes that goods disequilibrium tends to be unimportant in open economies, since the elastic supply of imports substitutes for rationed domestic products; and, to some extent, the short-run inflexibility of output will be compensated for by the use of inventories as buffer stocks.

Even if purchase plans were frustrated to a significant extent, holdings of excess borrowed cash need not exist. It is impossible for such holdings to exist under the overdraft loan system used in many countries, which automatically applies demand deposits to the repayment of outstanding loans; and in other countries, the flexibility of bank loan terms to maturity and the frequency with which scheduled loan repayments, renewals, or additional loans are made—not to mention the possibilities offered by their money markets for placement of surplus cash—would preclude observation of much of the supposedly undesired money.⁹

INSUFFICIENT FLEXIBILITY OF SHORT-TERM INTEREST RATE TO PERMIT UNLAGGED CLEARING OF MONEY MARKET

Carr and Darby ((1978), p. 6, from Darby (1976), pp. 314-15) offered the quite plausible prima facie case for the existence of disequilibrium money holdings that prices and real income would change in the same quarter by only a small fraction of the percentage change in M that reflected $\mathrm{\Delta }{M}_t^u$. In conjunction with “the low [unlagged] interest elasticity of money [demand] in most estimates, the implied interest rate fluctuations [for maintaining equilibrium money] are nothing less than incredible.” These investigators argued that the equilibrium model could be defended only if the endogenous adjustment of the short-term interest rate could absorb without lag most of an unexpected change in money of 1 per cent per quarter (a 4 per cent annual rate of unexpected change in money). They first required $\raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$ of the change to be accounted for by the interest rate but then in 1980 apparently reduced that to $\raisebox{1ex}{$810$}\!\left/ \!\raisebox{-1ex}{$$}\right.$ by accepting the rational monetarist hypothesis, $\mathrm{\Delta }{y}_t=\mathrm{\Delta }{M}_t^u,$ in conjunction with an unlagged real income elasticity of demand for M of 0.1 that was said to be “typically” estimated when the long-run elasticity was unity (Carr and Darby (1980), p. 4).

Addition of a claim that the “typically” estimated unlagged interest elasticity was a tiny −0.01 then led to the conclusion that an “implausibly large” 80 per cent unlagged adjustment of the interest rate was required to vindicate the equilibrium model. In actuality, these are completely untypical, implausibly low values for $\stackrel{\wedge }{\gamma }$ and the interest elasticity. The 0.01 interest elasticity is substantially below their own estimates (Carr and Darby (1978), p. 10; (1980), p. 16), and a survey of the other readily available models also shows much higher single-equation elasticities and elasticities that are typically three times as large (as 0.01) under the simultaneous-equation approach that these authors themselves prefer.¹⁰ In addition, the testing of the equilibrium model against as much as a 1 per cent quarterly $\mathrm{\Delta }{M}_t^u$ is discredited by the facts that: (i) the two extremes among Carr and Darby’s 82 quarterly observations for M₁ were merely 1.0 per cent and 1.2 per cent (these also being the largest (1.9 per cent) and the fourth largest (1.1 per cent) among 90 observations in the more up-to-date observation period of Sheffrin ((1979), p. 12); (ii) both of these extreme values are exaggerations of the relevant concept of unexpected money;¹¹ and (iii) only 4 of the 80 other observations were between 0.60 per cent and 0.93 per cent. Finally, Carr and Darby reached the 0.01 interest elasticity under the assumption of a semi-log interest-demand relationship and the initial condition given by the average interest rate found over their period of observation—a now antique 4⅓ per cent. That means that for the 1980s, the pertinent elasticity would be at least twice their figure, so that the market-clearing percentage of interest rate adjustment would be further reduced by 50 per cent or more.

In sum, while the preceding points may not suffice to prove that the interest rate equates supply and demand without lag, they are sufficient to demolish the prima facie case offered against such equilibration.

IMMEDIATE ELIMINATION OF CASH DISEQUILIBRIUM THROUGH ENDOGENOUS INTEREST RATE

The argument against the existence of off-demand-curve money seems to be made truly conclusive by the argument presented earlier (in White (1978), p. 574) that the costs of stock adjustment, and hence stock-adjustment lags, are bypassed when the immediate effort to make a partial stock adjustment induces changes in variables in the argument of the money-demand function in the equilibrating direction. When an induced rise in the price level—or a drop in the interest rate—converts some of the undesired cash still passively held into a desired holding, the amount of conversion taking place immediately is that associated with the high long-run demand elasticity because none of these passive holdings had to go through a transaction.

In addition, the amount of induced change in the interest rate tends to be just enough to convert all the excess cash into on-demand-curve holdings. The fraction γ’ of the excess cash holdings is dumped on the money market in the initial period and depresses the interest rate to the point where the rise in desired cash along the interest-demand curve with its comparably low zero-lagged interest elasticity—γ times the long-run elasticity (−c)—enlarges demand by the amount being offered.

Defining the initial forced acquisition of cash as ΔM_exogt, the two same-quarter adjustments of cash holding are (variables in logs):

To the extent that γ’ ≅ γ, the observed change in the interest rate is exactly enough to convert all of the supposedly excess cash into equilibrium, on-(long-run)-demand-curve holdings, so that ΔM/Δr = −c. Since good statistical results are obtained using the standard stock-adjustment models—which assume that all the variables determining money demand take effect with a single lag (that associated with γ)—this implies that γ’ approximates γ. In particular, if a rise in interest rates causes the public to offer on the money market without lag only the fraction γ of its newly created excess cash holdings (of the excess implied by its long-run interest-demand curve), then it is reasonable to assume that the fraction offered of the excess cash acquired through exogenous or unexpected changes in money supply would also be γ.¹²

The same result is shown graphically in Figure 1. There, of the initial excess rise in M that is equal to ac, ab is immediately offered on the money market (ab/ac = γ). Similarly, the ratio of the zero-lagged elasticity to the long-run elasticity of demand for money is also γ, so that the observed change in unlagged desired money also equals ab. In short, the change in the interest rate induced by the interaction of the unlagged dishoarding of surplus cash and the unlagged interest elasticity of demand for cash exactly equals the induced change in the interest rate that would (and, as was stated previously, does) convert all the excess cash into long-run desired cash.

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INTEREST AND EXPECTED INFLATION RATE EFFECTS ON INVENTORY INVESTMENT AS LIMITS TO EQUILIBRATION VIA THE INTEREST RATE

Analysis based on exogenous or unexpected money

Insofar as ΔM_exogt is paid into circulation through the financing of current expenditures such as investment, budget deficits, and an export surplus, it immediately raises prices and/or real income. Insofar as these changes imply a rise in desired transactions cash balances, the full long-run elasticity of demand applies in the short run. At full employment with flexible prices, prices would rise in proportion to the quarter’s ΔM_exogt ÷ Y|4 or—if one adopts the apparently standard implicit assumption in monetarist work that M approximates Y|4—by ΔM_exogt/M_t−1.

ΔMexogt	=	ac = undesired rise in M
γΔMexogt	=	ab = portion of undesired rise in M immediately offered on money market
rt	=	market-clearing interest rate that would immediately absorb offered funds and that also would be the long-run equilibrium interest rate found if all of γΔMexogt were offered on the money market and the long-run interest demand, L1, were effective
Ls	=	zero-lagged interest demand for M, with the elasticity equal to γ times the elasticity of L1
DI.rs	=	zero-lagged interest demand curve for investment; de = gh

View Table

ΔMexogt	=	ac = undesired rise in M
γΔMexogt	=	ab = portion of undesired rise in M immediately offered on money market
rt	=	market-clearing interest rate that would immediately absorb offered funds and that also would be the long-run equilibrium interest rate found if all of γΔMexogt were offered on the money market and the long-run interest demand, L1, were effective
Ls	=	zero-lagged interest demand for M, with the elasticity equal to γ times the elasticity of L1
DI.rs	=	zero-lagged interest demand curve for investment; de = gh

In quarter t + 1, the intersection of L_s with r_t moves to the right of b by γbc. If the fact that long-run equilibrium has already been reached is ignored, an additional excess holding of M of γbc is also offered on the money market, so that the interest rate continues at r_t (D_I.rs is assumed to be zero).

(The rational-expectations result for expected ΔM is exactly this.)

The part of the exogenous changes in money that is absorbed in unlagged desired nominal money in these ways is to be excluded from ΔM_exogt when the (potentially) disequilibrium holdings are measured. The ΔM_exogt of Figure 1 is therefore to be understood as net of the collaterally related unlagged rises in desired money. (“Collaterally” is used because the price or income rise and the money rise are both the reflections of the same rise in expenditure on goods.) But there may be further “endogenous” effects on the price level or real income that will account for part of that net ΔM_exogt. Thus, even though the same-quarter interest elasticity of demand for investment (and of the supply of savings) is close to zero, and only a very moderate adjustment of the interest rate is now seen to be necessary (r_{t − 1} to r_t), that adjustment would elicit some reaction from inventory investors, which is reflected in the curve D_I.rs in Figure 1. The presence of such a nonzero investment elasticity implies an additional source of demand for funds on the money market besides the short-run liquidity-preference demand, L_s, considered in the preceding section. Horizontal summation of the two demands yields a decline in the interest rate, because of the dishoarded γΔM_exogt, only as far as $r_t^{\prime }\mathrm{.}$ At that interest rate, it appears that a reduced, but nonzero amount of disequilibrium money, km, would survive. Approximately all the excess cash initially dumped on the money market, ab = fh, would still be absorbed into short-run desired money. Absorption of fg would be accounted for by the short-run liquidity demand, and gh would be absorbed because, to simplify, the extra spending of gh during the quarter raises prices by gh/¼Y_{t − 1} ≅ gh/M_{t − 1}. That rise in prices raises both long-run and short-run desired nominal balances in the same proportion to prevent real balances from falling.¹³ Hence, L₁ shifts right from k toward m by the fraction gh/M_t−1 to k’. Thus, the inventory investment constraint on the adjustment of the interest rate permits only a markedly reduced k’m of the excess money holdings to survive as disequilibrium money.

In the Carr and Darby, rational monetarist context, the extra money involved in the disequilibrium question was previously unanticipated and therefore is currently ignored as a macroeconomic value. Therefore, the rational economic agent has no reason to hoard goods in anticipation of a corresponding rise in prices, and the same marked reduction of scope for disequilibrium money applies fully.

MODELING LONG-RUN INTEREST ELASTICITY FOR EQUILIBRATING CHANGES IN INTEREST RATE

The discussion in the preceding section has indicated that the unlagged equilibration of money holdings by the endogenous adjustment of interest rates and of income need not be complete. But the analysis has left intact the view that whatever amount of such equilibrating adjustment does occur retains the powerful equilibrating influence of the high long-run elasticity rather than the weak influence of the low short-run elasticity. That is the situation where the change is brought about by the partial disposal of surplus cash in the current period to acquire bonds or the disposal of bonds equal to a part of the current shortfall of actual below desired cash holdings. (Changes in interest rates owing to current open market operations carried out by the consolidated money and banking system and by foreigners should retain the low, unlagged interest elasticity; the public presumably is moving voluntarily on its short-run interest-demand function when it accepts the others’ offers to buy or sell bonds. Hence, the equilibrium model is fully satisfied despite the lowness of the unlagged interest elasticity.)

Formally, correction of equation (6) is made by addition of an adjustment term:

where $M_t^{*}=a+{\mathit{by}}_t-{\mathit{cr}}_t+P_t\mathrm{.}$

Since Δr_endog in equation (8) by definition excludes the initial changes in r that are caused by broadly defined open market operations or by changes in the supply of credit to would-be goods buyers, some difficulty will exist in the use of (8).¹⁵ However, it is not unlikely that, in practice, equation (8) can be disregarded; equation (6) remains valid for the two sources of Δr just described while—as argued in the next section—the only other channels of change in money are, in practice, those in which demand/supply equilibrium tends to be achieved without the need for significant equilibrating interest rate movements.

IMMEDIATELY DESIRED CHARACTER OF MONEY PLACED IN CIRCULATION THROUGH LIKELY CHANNELS

Setting aside the nondisequilibrating open market changes in money and the misleading illustrative “airdrop money,” the observed changes in money fall into two main classes that can be shown to be largely nondisequilibrating: (i) changes in money that finance a changed rate of payments to the factors of production; and (ii) the much larger changes in idle holdings that the recipients of the payments desire to make gradually after the given rise in their incomes and the initial rise in their transactions cash holdings.

Insofar as the potentially disequilibrating changes in money must create equal changes in, for example, households’ money incomes for their pay periods, the observed money increases must equal the increase in household income.¹⁶ And, since that money is gradually disbursed by the households until they receive their next wage payments, the initially desired transactions balance jumps by the full amount, and the average desired transactions balance for the period jumps by one half that amount.¹⁷ Thus, one half of this main source of supposedly disequilibrating M is fully desired.¹⁸ And it can be shown that the other half that, on average, is not desired tends either to disappear from circulation or to be converted into desired business transactions balances.¹⁹

Transactions cash balances are obviously a small fraction of the observed (changes in) M. Given a two-week interval between income payments, the traditional simplified assumptions yield desired transactions cash averaging only $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$52$}\right.$ of annual income—a small fraction of total money holdings.

But, in addition to the unlagged rise in transactions cash, a given one-step rise in income implies a string of additional rises in desired money holdings, those reflecting the gradual stock-adjustment process of raising idle money holdings by a multiple of the rise in pay-period income to their long-run desired level by means of an increased propensity to save. (If there were a steady-state growth path, this would mean that total money was rising in proportion to current income—the transactions-cash part was rising in response to the current rise in income, and the much larger “idle”-cash part was rising as a function of a moving average of past rises in income.) These rises in money holdings may seem like ideal candidates for undesired money because they are uncorrelated with current income—that is, they have no observable effect on current income. But that is because they are the counterpart of a voluntarily increased propensity to save out of current income. Hence, just as the current increases in transactions cash are ineligible for undesired buffer-stock status, so also are these larger additions to current holdings. The country’s money growth target policy, which accommodates this fairly stable moving-average trend growth in currently desired money, will thus be comparable to the accommodating, or endogenous, money supply policy of the 1960s, which is classed by the disequilibrium modelers as not eligible to create disequilibrium money.²⁰

Because of the increasing financial sophistication that has permitted households enough flexibility in timing their payments for consumer expenditures so that most payments can take place immediately after receipt of an income payment, the working assumption stated previously that half of the money increase is quickly absorbed in transactions cash may understate the scope for disequilibrium money. This presumably means a reduction of the ratio of household transactions cash to income that was assumed previously. But, for reasons like those just given, it should also mean a reduced ratio of the rise in observable money supply to the rise in income. (A large part of the cash wages is immediately paid back, directly or indirectly, to the enterprises or to the banks that finance the credit cards and so tends to disappear from circulation.) Moreover, the factors providing for increased household efficiency in use of transactions cash have also tended to increase the cost of holding excess balances and to reduce or eliminate the transactions costs involved in disposing of excess balances. Increasing household use of personal overdraft accounts, bank credit cards, and the similar retail store charge cards has led a substantial proportion of households to be in debt on account of these means of financing consumer purchases.²¹ Such debts often require partial payment every month, and there is no transactions cost at all in adding the current holding of surplus cash to the monthly payment, while a very high interest rate is “earned” on that disposal of the new surplus cash. The increased efficiency in use of transactions cash is thus accompanied by increased efficiency in placement of surplus cash.

The preceding points not only make it unlikely that disequilibrium money exists but also make the concept a logical impossibility when, as is usually the case, new money is created for, or because of, immediate expenditure on output. The first of the two standard behavioral relationships—the unlagged enlargement of transactions cash in step with money income—implies that money expenditure is temporarily not increased as money income and prices rise. The second relationship—gradual restoration of the real value of other cash holdings—implies a sustained depression of money expenditure for consumption relative to increased money income and prices. But the supposedly passive, or forced, additional enlargement of cash holdings—the disequilibrium money buffer-stock reaction—initially requires further restriction of money consumption expenditure relative to increased money income and prices. Dependence on that illogical behavioral assumption makes disequilibrium money almost a logical impossibility.

DISEQUILIBRIUM MONEY IN HIGH-INFLATION DEVELOPING COUNTRIES

High-inflation countries seem the least likely to tolerate undesired real balances when the growth rate of nominal money accelerates. They should be most aware of the possibilities for increased loss of the real value of cash balances; and with financially unsophisticated economies usually involved, the extra money has to be paid into circulation primarily through simultaneous expenditure for goods and services in economies where prices are very responsive to increases in expenditure. This appears to be confirmed for Argentina by the finding of Blejer ((1978), p. 533) that in 1963–76, accelerated growth in nominal money relative to desired real money caused a slight rise in the same quarter’s free market interest rate because prices accelerated too quickly to permit any rise in real balances (except possibly in the initial month). However, as stated by Sjaastad ((1974), p. 129), “empirical work on Chile (Harberger 1963) and Argentina (Diz 1971)” has made “important contributions to the understanding of inflation in Latin America” by regressing the quarterly rate of price rise on current and lagged money growth rates. These studies found that prices move proportionally with money in the long run but that the coefficient on unlagged money growth is less than unity. The evidence for those two countries could be generalized to demonstrate a tendency for prices to lag behind money initially—for real money to rise initially—when money growth accelerates in high-inflation countries. This was interpreted as implying temporary holding of disequilibrium money (Sjaastad (1974), p. 129).

The Diz and Harberger studies plus one by Pastore (considered later) are cited also by Frenkel ((1975), p. 403, footnote 1) as having “documented” “the short-run rise in the real value of cash balances [in inflationary countries].”

Unfortunately, these broad conclusions were reached without reading a little further into the Harberger and Diz papers to where both explicitly state that the unit regression coefficient used to represent unlagged proportionality between prices and money was replaced by a coefficient of ½. To permit a sufficiently long distributed lag, the quarterly rate of price change was regressed on current and lagged semiannual rates of money growth (Harberger (1963), p. 224; Diz (1970), p. 113). And, in fact, for Chile’s consumer price index, the unlagged regression coefficients did approximate the zero-lag value of ½ provided only that one excludes the rent component, which Harberger ((1963), p. 238) states was often under official price ceilings and remained completely unchanged for 10- to 12-month periods despite the country’s high inflation rate and despite the fact that the ceilings were “widely evaded.” (Harberger also notes ((1963), p. 239) that some retail price controls were imposed some of the time, which creates further scope for the official consumer price index to understate the actual inflation rate.)

In Argentina, unlagged money showed two thirds of the proportional effect on the consumer price index. But the lagged money changes did not yield the expected catch-up of prices to money (Diz (1970), pp. 119–20). That suggests that the moderate initial increases in real balances were permanent ones—contrary to what the disequilibrium money explanation assumes—so that econometric problems, or the reluctance of retailers to admit to government price collectors the full amount of their price increases when those increases accelerated,²² or the positive correlation between real income and money growth rates cited by Blejer ((1978), p. 531),²³ should be the explanation. Disequilibrium money cannot be inferred from the moderate, but permanent lag of the inflation rate behind the money growth rate in Argentina.²⁴

Unfortunately, these reinterpretations cannot convert the Argentine and Chilean evidence into anything usable because the zero-lagged money change includes both a zero lag and a lag of one quarter.²⁵ Assuming that the serial correlation introduced by overlapping observations of the independent variable does not deprive the findings of meaning, they are consistent with anything between a zero lag and a lag of one quarter.

The Pastore (1975) study of Brazil found that in the first quarter of a period when there was an increased rate of money growth, the inflation rate increased only one third as much as money growth, approaching full proportionality only in the third quarter (Pastore (1975), p. 493). Apart from the problems with specification of the model’s disequilibrium term raised earlier, the observed initial rises in real money may be partly the consequence of the country’s extensive price controls—which may cause the price index to understate the actual price rise²⁶—and of neglect of the nominal interest-rate elasticity of demand for money—which could have accounted for some valid observations of initial rises in real money.²⁷

In addition, in Brazil and a number of other developing countries, the banks make a practice of obliging business borrowers to leave fairly large fractions of their bank loans as blocked compensating deposit balances (often 40 per cent of loans in the case of Brazil). Insofar as faster money growth is accompanied either by a rise in the ratio of business loans to total money supply or by banks’ attempting to restrict business demand for their shrinking loan-making capacity through increasing their deposit requirements, the faster money growth includes a rising amount of blocked, relative to usable, money. That change causes mismeasurement of the economically meaningful money supply for which approximate correction should be possible before econometric work begins.²⁸

There is a kind of initial rise in real money holdings that should be a desired one in developing countries that lack money markets, or market-clearing deposit interest rates, and that conduct monetary policy mainly through varying the availability of bank credit. Just as relaxation of the rationing of import licenses has been found to lead to excess acquisitions of licenses (or excess imports) because of the anticipation that the easing will be reversed (Baer (1965), p. 128), so businesses should overborrow and hold funds idle when credit rationing is eased. The latter behavior is illustrated by the U. S. Federal Reserve Board’s finding that fear of credit rationing was mainly responsible for a “burst of anticipatory [business] borrowing” from banks in the first quarter of 1980 (see “Monetary Policy Report to Congress,” Federal Reserve Bulletin, Vol. 66 (July 1980), p. 541). Of course, where free money or government-securities markets have developed, or where time deposits yielding significant interest can be acquired in the amount wanted, the excess money will tend either to be converted into desired money by the interest rate variable or to disappear from the M total that is defined to exclude those deposits.

ERRONEOUS ADVOCACY OF EXPECTED INTEREST RATE

Since the actual interest rate changes for the most part in advance of the adaptively expected interest rate, use of the actual interest rate may cause false attribution of an initial disequilibrium change in money to the collinear actual interest variable. However, the Friedman tradition of using the adaptively expected interest rate variable can easily be shown to be logically incorrect.

First, the short term is usually considered the correct time period in which to judge the opportunity cost of money, and therefore the expected interest rate—usually that for the next quarter—is irrelevant. The actual interest rate is the known return available now, and if the expected rate for the next quarter is different from the current rate, the repayment of a current three-month loan at the predetermined price when it matures at the end of the quarter will permit the lender to obtain the expected interest rate when it becomes available.

Even if a long- or medium-term interest rate were thought to represent the relevant opportunity cost of holding cash, so that expectations did play a role, the slowly-adjusting expected long-term rate would be an inferior specification to the actual rate. In fact, a yield that is more volatile than the actual rate is easily shown to be the ideal: thus, a rise in the actual long-term rate leads to a smaller rise in the adaptively expected rate, so that the expected rate is lower than the current rate. But that means that the actual return will be the current rate plus an expected capital gain. As explained in Polak and White ((1955), p. 420) and Enzler and others ((1976), p. 268), the substitutability between long- and short-term securities tends to make the short-term interest rate track the sum of the interest yield plus expected capital gain/loss on long-term securities, so that (neglecting some distortions caused by portfolio inflexibilities) the actual short-term interest rate would be the preferred interest rate variable, even if the relevant opportunity cost were a long-term interest rate.²⁹

INTEREST RATE SHOCKS THAT SHIFT LIQUIDITY PREFERENCE

Darby ((1976), pp. 143–44) and Carr and Darby (1978) argue that disequilibrium money may be explained by unexpected rises in money being created mainly in the money market, where they cause unexpected drops in the interest rate and, hence, unexpected rises in security prices. That price rise “frustrates plans of some potential purchasers of securities. During the period in which they are reformulating their plans, their money holdings are temporarily increased. When they [belatedly] make purchases, other plans [plans of those not in touch with current events] are frustrated so that the process of adjustment is spread over time with the aggregate short-run money demand increased” (Carr and Darby (1978), p. 5). In effect, would-be bond buyers are temporarily “crowded out” by the central bank’s unanticipated buying of bonds, which forces bond prices up; would-be buyers hold more cash than they would have if the bond price rise had been foreseen.

This reasoning ignores the offsetting, presumably comparable reformulation of transactions plans in response to unexpected price changes by would-be bond sellers. The latter should also pause to reformulate plans and temporarily hold more bonds and less cash than they would have if the new level of bond prices had been foreseen.

A net shift in aggregate liquidity preference of the proposed sign could be justified if the stated delays needed to reformulate plans were interpreted as reflecting the expectations-formation lag referred to in the previous section—would-be buyers would delay buying because they would expect a reversal of the price rise just experienced, and would-be sellers would want to accelerate sales for the same reason. Here, both groups’ demands for money increase relative to what the reduced level of interest rates justified. But, while this rationalization of the liquidity preference shift (as reflecting an understatement of the relevant total change in yields) would be a logical one, it cannot be used by Carr and Darby. They employ a short-term interest rate; and, as described in the preceding section, that already corrects for the larger movement in the true yield on long-term securities.

BORROWING FROM BANKS IN ADVANCE OF NEED

The familiar argument that newly created money percolates only gradually through a succession of ill-informed financial markets and into the financing of purchases of goods and services has been reformulated by Brunner and Meltzer (as described in Laidler (1979), pp. 27–28) to make acquisition of money a complement to the acquisition of real assets, but with the money obtained in advance of the assets. The markets for real assets do not permit the highly efficient use of cash found in the financial asset markets. When credit and money are expanding in conjunction with an inventory or capital spending boom, the money will rise in advance of the rise in expenditure and in income. That constitutes a temporary shift in liquidity preference in the same direction as the current change in bank credit (relative to trend).

Institutional conditions seem to rule out a significant role for this kind of temporary excess money holding. As discussed earlier, there is the overdraft banking system, through which credit is obtained only at the moment of making an expenditure for goods; a similar arrangement under lines of credit, which permit a prearranged total to be borrowed intermittently in relatively small increments; the flexibility provided by the continuously maturing and continuously renewed fixed-term loans at short term; and certificates of deposit and other temporary money market placements that are available in case funds are borrowed before they are needed to finance expenditures.³⁰ Similar consequences flow from the practice of U. S. banks in financing construction of buildings by lending each month only the amount spent by the builder during the month. A major part of bank loans to small enterprises and households tends to be for financing a specific acquisition of assets at a specific date, with the loan being extended only on that date.

In short, financing of increased real expenditures with advance borrowings of temporarily idle cash is logically possible, but institutional conditions severely limit its importance. The estimated disequilibrium money term could just as well be a proxy for the equilibrium model’s error term as a proxy for this behavior relationship.