velocity and the growth of money in the united states, 1970–1985

DOUGLAS FISHER North Carolina State University

Raleigh, North Carolina

Af’OSTOLOS SERLETIS The University of Calgary

Calgary, Alberta Canada

Velocity and the Growth of Money in the United States, 7970- 7985*

In this paper we examine the determinants of recent velocity behavior in the United States in terms of two hypotheses previously advanced by Friedman. These refer to the effect on velocity of changes in the growth rate of money and in the (increased) variability of money following the 1979 revision in monetary policy operating procedures. Both hypotheses come through strongly over nine measures of velocity (based on simple sum, Divisia, and MQ measures of the money stock) and three sub-aggregates. The data are monthly, covering the period 1970 through mid- 1985.

1. Introduction In recent years there has been a resurgence of interest in the

determinants of the velocity of money in the United States-how- ever velocity is measured-primarily as the result of a rather sub- stantial decline in the velocity series, beginning in 1981 and con- tinuing, intermittently, since then. This apparent deviation is statistically unusual in that velocity generally had been growing for a considerable time prior to 1981. The debate that has arisen mostly concerns the rather abrupt decline in velocity, and quite a few spe- cific hypotheses regarding the determinants of velocity have evolved from this discussion. Among the propositions advanced, those most often cited involve the influence of structural changes in the financial sector, tax cuts, inflation (or expected inflation), changes in gov- ernment expenditures, changes in energy prices, and money growth.’ It is the last-named variable, along with its variability, that we wish to explore as an influence on velocity in this paper.

*We wish to thank Douglas K. Pearce and two referees for their helpful com- ments on an earlier draft of this paper. We are also grateful to David Banack for assistance in the computations.

‘See, especially, Hall and Noble (1987), Judd and Motley (1984), Tatom (1983), Taylor (1986), and Santoni (1987), for more on these and other suggested (and sometimes empirically supported) influences.

Journal of Macroeconomics, Summer 1989, Vol. 11, No. 3, pp. 323-332 323 Copyright 0 1989 by Louisiana State University Press 0164-0704/89/$1.50

Douglas Fisher and Apostolos Serletis

It is not difficult to imagine why money growth might influence the behavior of velocity, although in the final analysis the relationship is essentially empirical, For one thing, ceteris paribus, velocity will tend to fall during recessions and rise during expan- sions as a consequence of the income elasticity of money demand being less than unity. In addition, we might argue that since changes in the growth rate of money will have a lagged effect on real income (if a monetary-induced real cycle exists) velocity will decline in the early months of a monetary expansion and then recover. Sim- ilarly, a slowdown of monetary growth would be associated with a spurt in velocity followed by a subsequent readjustment.

For the effect of the variability of money growth, there are essentially two avenues of influence proposed, both by Friedman (1983). The first concerns the behavior of the demand for money (accommodated by money supply) and the second involves the behavior of real income itself. For the money demand effect, Fried- man argues that increased uncertainty in financial markets, due to the increased volatility of money after the 1979 change of policy- operating techniques in the United States, has produced both an increased demand for money for (essentially) precautionary pur- poses and, assuming the money supply process accommodates the pressure, a rise in money holding relative to nominal income. Friedman argues that the actual fall in the inflation rate in this period was actually greater than the decline in the rate of growth of the money stock. This he attributes “not to a pre-announced slow- ing of monetary growth, but rather to the exceptional volatility of monetary growth, which increased the degree of perceived uncertainty and thereby increased the demand for money” (399). Thus, the authorities willing, the equilibrium stock of money would in- crease and velocity would decrease, ceteris paribus. For the real income effect his position is not so precisely stated in this particular paper:

The inertia in inflation and the lengthy lag between monetary change and inflation mean, of course, that the short-run influence of money on nominal income will be reflected primarily in movements in real income (400).

But this, too, would lower velocity when monetary variability in- creases. What is involved are increased transactions costs and increased uncertainty that translate into a reallocation of resources

324

Velocity and the Growth of Money

away from the (prevariability) optimum. This is a recurring theme in other papers by Friedman (1956, 1971, esp. 1977, 1984).

Turning to the existing empirical work, we note that Tatom (1983) produces a result for the effect of money growth on real income and Belongia (1985) successfully considers the influence of monetary velocity on real income (it has a negative effect in this period). For monetary variability the only result is that of Hall and Noble (1987), who do indeed find a causal relation between monetary variability and velocity. Hall and Noble employ a causal procedure, as well, but they barely scratch the surface of the empirical possibilities in their tests. What we propose to do here is to conduct Granger-causality tests of the two hypotheses over the monthly U.S. data, following a procedure for generating monthly GNP data developed by Christian0 (1986).2 These tests will involve a search for the relationship over nine measures of the money stock in an attempt to deal with anomalies that arise because of different definitions of money. The measures employed are simple sum aggregates (as in the Federal Reserve Bulletin), Divisia indices (as in Farr and Johnson 1985), and a velocity-weighted index proposed by Spindt (1985). Various tests investigating the robustness of these results are reported as well.

2. The Empirical Results We are, in this first test, interested in the effect of changes

in money growth on velocity. The hypothesis successfully tested by Tatom (1983), but not in a causal framework, is that money growth affects real income. Testing to see if money causes velocity in the Granger sense, we employ the following regression equation:

Av, = OL, + i oiAv,-i + i PjArnfej + U, . i=l j=l

Here v, and m, are logarithms of velocity and a money stock measure, respectively, and u, is a stochastic disturbance.3

*What we do, following Christian0 (1986) in this respect, is to construct a syn- thetic monthly GNP series by multiplying the industrial production index by the price level. Graphs of these variables in Christian0 (or from the authors of the present study) indicate that this calculation does not alter the basic relationships.

3Note that we are following the advice of Nelson and Plosser (1982) and Chris- tiano (1986) in employing the data in first differences of logarithms. Essentially, the


The Granger procedure requires that we first estimate Equa- tion (1) by ordinary least squares to obtain the unrestricted sum of squared residuals, SSR,. Then, by running another regression un- der the restriction that all pis are zero, the restricted sum of squared residuals, SSR,, is obtained. If ut is white noise, then the statistic computed as the ratio of (SSR, - SSR,)/s to SSR,/(n-r-s-l) has an asymptotic F-distribution with the numerator having degrees of freedom of s and the denominator of n-r-s-l. Put in the standard form of the Granger-causality test, the results appear in Table (l), for the monthly U.S. data (1970:ii to 1985:vii).4

Table (1) is divided into two parts, covering the nine measures of the money stock mentioned above and, in the last three rows, a set of monetary “subaggregates” involving the non-Ml components of the broader measures of money. The set-up of the table is as follows. First, the main entries are values of the F-statistic, as described above, comparing the sums of squares between the unrestricted and the restricted regressions. Then, in parentheses, are the p-values (probabilities) associated with these F-statistics; a level of 0.05 to assert causality is established arbitrarily. Reading across the table, the set of four tests indicates, pretty clearly, that four of the nine standard aggregates definitely show a causal influence on velocity growth. These causal results occur with the narrower measures of money and with MQ, a transactions-velocity measure of moneyness developed by Spindt (1985). Since the narrower aggregates are intended to be measures of transactions balances, the evidence here is clearly that the recent behavior of velocity is related to the behavior of transactions rather than, say, to savings balances, even though all measures of velocity show the decline over the period. This basically confirms Tatom’s (1983) re-

(Note can’t. from p. 325) purpose of this transformation is to achieve stationarity. This choice was not arbitrary, in fact, but the result of a series of Dickey-Fuller (1979) tests, which in general verified that in order to ensure stationarity we needed to conduct our ex- periments with (log) first differences. These results are available from the authors.

4The data on Sum Ml, , and Sum L are the official definitions of money found in the Fe&r& Reserve Bulletin; they are simple sum aggregates. The Divisia Ml, , and Divisia L numbers refer to the Monetary Services Indices that appear in Farr and Johnson (1985); these are Fisher Ideal Indices of monetary quantities and are close to the indices implied by aggregation theory (see Barnett 1980). MQ is Spindt’s (1985) Monetary Quantities index and is a velocity-weighted index. While it is based on the notion that “money is what money does,” it does not have a clear-cut interpretation in aggregation theory (see Barnett 1987).

326


TABLE 1. Tests of Granger-Causality From Money Growth to Velocity Growth

Effect

Sum Ml Veloc

Sum M2 Veloc

Sum M3 Veloc

Sum L Veloc

Divisia Ml V.

Divisia M2 V

Divisia M3 V

Divisia L V

MQ Velocity

Sum M2 (net of Ml)

Sum M3 (net of Ml)

Sum L (net of Ml)

Cause 8 Lags 6 Lags 4 Lags Ft’E Lags

Sum Ml 4.343” 6.111* 8.820* [l, 61 6.467* (O.ooo) (0.ooo) (0.ooo) wm

Sum M2 4.233* 5.717* 8.636* [2, 21 15.006* (O.ooo) (0.ooo) (0.ooo) (O.@m

Sum M3 0.807 0.880 1.020 [l, 11 2.459 (0.597) (0.510) (0.398) (0.118)

Sum L 1.182 1.374 1.457 [l, 11 5.272* (0.313) (0.227) (0.217) (0.020)

Div. Ml 2.565* 3.220* 3.861* [l, l] 8.183* (0.011) (0.005) (0.004) (0.004)

Div. M2 1.402 1.749 2.723* [l, 21 2.445 (0.199) (0.112) (0.031) (0.089)

Div. M3 0.852 1.066 1.576 [l, 01 (a) (0.558) (0.385) (0.182)

Div. L 0.700 0.821 1.223 [l, 01 (a) (0.691) (0.555) (0.302)

MQ 2.602* 3.430* 4.629* [l, 31 4.695* (0.010) (0.003) (0.001) (0.003)

Sum M2 3.421* 4.589* 6.872* 12, 21 13.517* (net of Ml) (0.001) (0.002) (0.000) ww

Sum M3 1.016 0.717 0.530 [l, 131 2.471* (net of Ml) (0.426) (0.636) (0.713) (0.~)

Sum L 1.211 0.949 1.275 [l, 131 1.992* (net of Ml) (0.275) (0.461) (0.281) (0.032)

NOTES: The sample period was 1970% to 1985:iii. The numbers in parentheses are p-values. No lag, indicated by (a), was chosen for the causal variable in these cases.

*Significance of 0.05 or better.

suit, although not exactly in the way he found it, being the result here of an investigation with a causal set-up.5

The last column in Table (1) presents statistics from a second run of the Granger-causal model on the same data. This retesting involves selecting the length of the lags, r and s, as described in

Equation (1). In the literature r and s are frequently chosen to have the same value (lag length) for both independent variables (fre-

‘We re-ran the tests omitting 1979:x through 1982:uiii in order to see whether the “growth hypothesis” was dependent on that period alone. The reason one might suspect this is on account of the rapid changes in the growth rate of money over that period. The growth hypothesis continued to hold without these data, with the Sum-Me, Divisia-M2, and Me-net-of-Ml all showing up over the remaining data.

327


quently 4, 6, or 8). We actually did this, in columns (1) through (3) in the table, but because this approach is essentially arbitrary and since it has been shown that Granger-causality tests are sen- sitive to the lag structure specified (Hsiao 1979a, 1979b), we took an alternative approach in order to appraise the sensitivity of our results to the lag specification. This approach involves using Akaike’s (1970) Final Prediction Error (FPE) criterion in order to select (from the data) the optimal lags for each of the independent variables. The FPE is calculated as the product of (n+r+s+l)/(n-r-s-1) and SSR/n, where n is the number of observations and SSR is the sum of squared residuals. This procedure balances the fit of the equation with the degrees of freedom, and is judged by an F-test. The results, with the lags chosen appearing in square brackets, are given in the last column of Table (1); they show, first, that the optimal lag structures are generally quite short and, second, that only with the Sum Ml is the lag on the causal variable as long as six months. The Divisia Ml, in particular, has only a one-month lag on the independent variable. Even so, with the exception of Sum L velocity, the results obtained with the arbitrary lags are still upheld, at least with respect to the influence of money growth on monetary velocity growth. We note, finally, in the last three rows of the table, that (by the FPE procedure), netting out Ml from M2, M3, and L does not change these results, in general. That is, the money- growth Granger-causal effect on velocity does appear to occur with both the narrow and broad components of the money stock measures.

The second variable recently proposed as an influence on velocity is the variability of the money growth rate. The formal model is the same as before, and the results appear in Table (2). Again, results for three arbitrary sets of lags and for the lags judged as optimal by the Akaike (1970) FPE test (in the last column) are pre- sented.

These results indicate a strong confirmation of the monetary variability hypothesis.6 In particular, the standard deviations of the narrower measures of money (whether MQ, simple sum, Divisia, or M2-net-of-Ml) Granger-cause the appropriate measures of ve-

‘Again we omitted the 1979 to 1982 subperiod in a re-test of the FPE results. In this case, as one might suspect, the variability hypothesis actually fails to show causality on the remaining data. The implication, at least by the FPE standard, is that the results for the entire period are largely traceable to the extreme volatility of the money growth rate during the “policy regime” that ruled from 1979 to 1982.

328


TABLE 2. The Znfluence of Money Stock Variability on the Velocity of Money

Effect (Changes in Standard Deviations of the Data)

Cause 8 Lags 6 Lags 4 Lags FPE Lags

Sum Ml Vel

Sum M2 Vel

Sum M3 Vel

Sum L Vel

Div Ml Vel

Div M2 Vel

Div M3 Vel

Div L Vel

MQ Velocity MQ

Sum M2 (net of Ml)

Sum M3 (net of Ml)

Sum L (net of Ml)

Sum M2 (net of Ml)

Sum M3 (net of Ml)

Sum L (net of Ml)

Sum Ml

Sum M2

Sum M3

Sum L

Div Ml

Div M2

Div M3

Div L

2.532* (0.012) 3.691*

ww 0.744

(0.658) 1.014

(0.427) 2.106*

(0.038) 1.287

(0.254) 0.810

(0.594) 1.237

(0.281) 2.420*

(0.017)

3.542* (0.002) 4.295*

(O.cw 0.635

(0.702) 0.851

(0.532) 2.689*

(0.016) 1.428

(0.207) 0.714

(0.638) 1.238

(0.289) 3.302*

(0.004)

5.410* (0.000) 5.811*

ww 1.516

(0.199) 1.840

(0.123) 2.558*

(0.040)* 2.774*

(0.028) 1.569

(0.184) 2.297

(0.061) 5.264*

10.000)

t3, 121

[3, 111

[3, 01

13, 31

t3, 61

[3, 41

t1, 01

[3, 121

[3, 41

4.163* (O.@m 0.592

(0.783) 2.062*

(0.042)

4.870* VW 0.366

(0.899) 1.796

(0.103)

6.204* (0.000) 0.653

(0.625) 2.372

(0.054)

13, 111

t3, 11

[3, 21

3.614* @.0(-w

5.014* (O.@w

(4

2.261 (0.083)

2.873* (0.010) 2.792*

(0.028) (4

2.509* (0.004)

5.263* mow

5.111* (0.000) 0.417

(0.519) 2.586

(0.078)

NOTES: The sample period for this table was 1970:x to 1985:uii. As indicated by (a), there are no significant lags on the causal variables. For other notes see Table (1).

locity. Notice that the FPE lags are much longer in this case than they are in the case of the rate of growth itself. With the exception of the somewhat anomalous result for Divisia L velocity, these results indicate that no matter what method of monetary aggregation is chosen to represent money balances, the monetary growth and variability hypotheses come through clearly, especially at the short end of the monetary spectrum. There are some slight differences across the aggregates, with the Divisia Ml and the MQ indices far- ing slightly better than the others over all tests, but the differences are essentially unremarkable. This is interesting if only because of the tradition in this literature that in practice sharp differences exist among the indices.

329


3. Conclusions This paper has considered several tests of the determinants of

velocity in the United States; these tests have involved monetary growth and its variability. These two variables have been investi- gated in recent studies, even causally to some extent, but the existing tests have stopped well short of a thorough investigation, especially across the various potential monetary aggregates. Because it is important to the correct measurement of velocity to have correct measures of the money stock available, it has been necessary to investigate a total of nine measures of velocity for moneyness measured by simple sum, Divisia, and MQ indices. In any case, the results differ somewhat across these techniques of aggregation, differ considerably when compared by the broadness of the index, and even differ for different time periods (at least with respect to the variability hypothesis). Our approach appears justified on these empirical grounds. In any case, both of the variables proposed here have been shown to Granger-cause velocity growth. This effect is generally on narrower measures of the money stock and suggests a transactions (or possibly precautionary) interpretation of the behavior of velocity. There are some slight differences across the different monetary aggregates of equal breadth, but generally it can be claimed that no matter what the method of aggregation the influence of money growth and its variability show up on velocity in a (Granger-) causal sense.

Received: August 1987 Final version: October 1988

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velocity and the growth of money in the united states, 1970–1985

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