the economy has competitive and oligopolistic sectors, general price-level stabilization may put the competitive sector under constant deflationary pressure. And of course, the doctrine has gained credence that economic progress may in a number of situations be served better by some degree of inflation than by price-level stability.11

4. As price-level stabilization declined in favor, its place has been taken in some degree by proposals for steady growth in the money supply, at a rate approximating the long-term growth of the country's real output. Current front-runners among such proposals are those of Milton Friedman and E. S. Shaw.12 Friedman and Shaw would have the money supply increase at a fixed annual percentage rate of 3 to 4 per cent; Friedman tends to favor higher rates than Shaw. As Jacob Viner pointed out at Virginia in the role of devil's advocate,18 neither Friedman nor Shaw include any rapid or automatic mechanism for adjusting monetary growth rates to changes in the long-term growth rate of the economy, to institutional changes in "economizing" the money stock, to changes in preference as between money and other assets, or to changes in the forms and "money-ness" of near-moneys.

These proposals are perhaps descended from the "neutral money" thinking of the 1930's, which ran in terms of a constant money supply, with no provision for growth and a slow fall in the money volume per capita. Neutrality advocates, primarily European, had been struck by the association of stable prices with most of the other features of an inflationary boom, culminating in the crash of 1929. According to such writers as Ludwig von Mises and Friedrich Hayek,14 the price level should have fallen in the 1920's in consequence of technical progress; the "stabilization" measures which prevented its falling were in effect inflationary. These writers were also concerned, as a matter of social ethics, with securing to the rentier a share of the gains from improving technology. They were further concerned, as a matter of resource allocation, with preventing any distortion of relative prices which results from monetary expansion when it increases A's purchasing power in advance of B's.

11 For an introduction to this argument, and a few references to the literature, see Bronfenbrenner and Holzman, A Survey of Inflation Theory, 53 Amer. Econ. Rev. 593, 608-12 (1963).

12 The fullest development of Friedman's proposal is his Program for Monetary Stability (1959). For Shaw's plan, developed independently, so his Money Supply and Stable Economic Growth in United States Monetary Policy 49 (1958). The chapter by Richard T. Selden in Monetary Constitution, op. cit. supra note 8, also considers suggestions along similar lines by James W. Angel and Clark Warburton at 326-33.

13 Viner, The Necessary and Desirable Range of Discretion to be Allowed to a Monetary Authority, in Monetary Constitution, op. cit. supra note 8 at 255-57.

14 Among English translations of neutral-money proposals the most influential has been Hayek, Prices and Production (1932).

V

The writer's thinking on monetary rules is influenced by the American boomlets and recessions of 1955 to 1964, when the Friedman-Shaw rules would probably, on balance, have accentuated the inflation which occurred. Starting from the Friedman-Shaw proposals, I have attempted modifications. for adjustments to fluctuations in the growth rates of real output, and in the velocity of circulation of money. This section is devoted to the prima facie case for this modification, called a "lag rule."15 In subsequent sections, I shall consider the serious difficulties in quantifying some of the terms involved, and in applying the scheme in present-day America (as distinguished from Cloud Cuckoo-Land).

If we write Fisher's equation of exchange in a form relating to Income (here, GNP) rather than to Transactions, we have:

We can also break the income term Y into two components N and л, where N is the labor force and л its average productivity.16 When this is done, (dY/Y) becomes [(dN/N) + (dл/л)], and we have:

If price-level changes (dP) are to be eliminated, we can rearrange terms in this equation, and derive a suggested rule for the behavior of (dM/M), the growth rate of the money supply:

In words; the growth rate of the money supply should equal the sum of the growth rates of the labor force and average labor productivity, less the growth rate of the velocity of circulation of money. Explicit allowance must be taken of the fact that changes in (N, π, V) are observed prior to the resulting

15 Preliminary expositions of the same rule have been made in Bronfenbrenner, Statistical Testing of Rival Monetary Rules, op. cit. supra note 2, and Bronfenbrenner, A Sample Survey of C.M.C. Research Papers, 45 Rev. Econ. Stat. 111, 112-14 (part ü) (1963).

16 Strictly speaking, л is the average productivity of the employed portion of the labor force, excluding those Government employees whose contribution to the national income is arbitrarily equated to their compensation.

change in M. When this allowance is made, the last equation takes on a lagged form:

The common sense of this rule is to propose that the money supply grow as rapidly as the economy would grow at full employment, with a correction for the effects of changing tastes and financial innovations on the velocity of the monetary circulation. If, for example, the growth of financial intermediaries makes the measured money stock circulate faster, the rule counter acts this growth by slowing down monetary expansion in the interests of checking inflation. If, on the other hand, the dominant effect of economic growth is an increase of the proportion of wealth and income people wish to hold in monetary form, our rule counteracts this change too, and accelerates monetary growth in the interests of checking deflation. (Insertion of the velocity term should make it possible to avoid a "switching" expedient suggested by Modigliani,17 which would involve different rules at different phases of the business cycle.)

This rule might, in the absence of cost-push and downward price rigidities, meet the demand for guaranteed full employment and rapid growth without inflation. (Its chances would be best if it were introduced in a period of price stability and high employment, so that the base-year money supply Mo would be "right.") The rule would in any case provide the monetary framework for such a target as growth without inflation, by reducing uncertainty as to what money supply could be anticipated. If pressure groups stay within bounds or guide-lines, the target can be reached with little friction. If they do not-particularly, if there were disputes about distributive shares, or reluctance to reduce particular prices as productivity and progress made them "too high"-the result of pressure-group activity plus pricerigidity under this rule will combine to involve both some short-run unemployment and some short-run inflation. But the cnus for this unemployment and inflation could be focused where it belongs, and the monetary authorities relieved from pressure to validate inflationary price and wage movements by assuming inflationary postures on their own account. The stronger the plausibility of the rule, and the quasi-religious support which it generates, the sooner can inflationary "strikes" against it be overcome, and the more effective are the monetary restraints upon pressure-group activities and upon the downward rigidity of published prices and wages.

17 Modigliani, op. cit. supra note 2, at 237-239, 242. An earlier "switching rule" on a fiscal-policy base of built-in flexibility, was suggested by G. L. Bach, Monetary-Fiscal Policy Reconsidered, 57 J. Pol. Econ. 383 (1949), reprinted in Readings in Fiscal Policy 262 (1955).

VI

On the other hand, the difficulties of applying this lag rule, as a concrete control device, limit advocacy to suggesting some of the background research requisite for near-future application. Proponents of simpler and less flexible rules-Friedman and Shaw, for example may doubt that the probable improvements over the simpler rules are worth their cost, but let us see.

1. Difficulties begin, moving from left to right in the lag formula, with the definition of money M, from which the V term follows as the quotient (Y/M). The conventional definition of money supply includes only circulating currency and "adjusted" demand deposits of commercial banks. (The adjustments exclude interbank deposits from M.) Friedman and others have suggested a broader variant, which seems to behave better in terms of the regularity and stability of its relationship to other economic variables, and which is published continuously for a longer period in the United States. This broader concept of M includes savings deposits in commercial banks. One might consider further extensions to include savings deposits in other banks, plus savings and loan "shares" as well; 18 non-commercial banks and savings and loan companies, however, are not (in America) under the supervision of the general monetary authorities.

2. The appropriate lag period between time (t-1) and time (t) is also problematic. If too long, like the one-year lag of my February 1961 study, a perverse hysteresis effect may be introduced. For example, contractionary medicine (a reduced growth rate of M) may be prescribed for an inflation after it has given way to a recession, or vice versa. In the Keynesian metaphor of the Treatise on Money, too long a lag may cause the money doctors to prescribe castor oil for diarrhea and bismuth for constipation.

A lag period which is too short has problems of its own. Delayed reactions to last year's doses of monetary bismuth may be drastic enough to require larger doses of monetary castor oil this year. The castor oil takes no effect until next year, when it leads to larger doses of bismuth than those which disequilibrated the system last year, "and so proceed, ad infinitum." We should now be prescribing the right medicine for the current ailment, but in successively larger doses which might eventually kill the patient. This too is a form of hysteresis, giving rise to destabilization by explosive oscillations.

To mitigate the destabilizing effects of errors in estimating lags, some modification or limitation of the lag may be desirable or even necessary, if the true lag period cannot be ascertained accurately or varies erratically.19

18 Modigliani makes these extensions for the purpose of testing the Friedman rule, op. cit supra note 2, at 223-227.

19 The range of variation seems to be between 6 and 9 months, both by Friedman's estimates in The Lag in the Effect of Monetary Policy, 69 J. Pol. Econ. 447 (1961), and those of his critics, including Ando et. al., Lags in Fiscal and Monetary Policy, in Stabiliza

The best modifications I can currently suggest are 1) making the lag period as short as possible, and 2) setting upper and lower bounds to the annual monetary growth rate, perhaps an upper bound of 8 per cent and a lower bound of 1 per cent, regardless of the formula's occasional vagaries. A 1 per cent lower limit would be too high in case serious destruction or loss of life reduced the labor force or its productivity in any drastic manner. A change in the geographical circulation area of the dollar might make either limit obsolete. (Further constraints might be imposed, in addition, were we simultaneously to restrain short-term interest-rate fluctuations within acceptable bounds.) These problems illustrate the difficulty of framing any economic rule to cover all contingencies without suspension or supplementary legislation. (See Section IX, below.)

3. There is an ancillary problem of seasonal adjustments if a rule is applied to monthly or quarterly movements of M, or if interpolations must be made in annual data for N, π, and V. There is appeal in a heretical suggestion by Friedman, that in the undeveloped state of the black art of time series analysis, a "least-worst" solution may be to take the figures as they come, without attempting seasonal adjustments at all.20 Before subscribing to this attractive. heresy, however, we need more information, both on the magnitudes of the seasonal interest-rate fluctuations which might result from basing monetary policy on the movements of unadjusted data and on the economic consequences which might be expected from such fluctuations, once they can be hedged against to some degree.

4. Passing from M and t to N, the labor force, possible perversity may result from the apparent tendency of the measured labor force to decline in periods of mild recession, and expand in periods of full prosperity. This tendency can lead, other things equal, to cyclical fluctuations of the monetary growth rate during minor cycles, when counter-cyclical fluctuations are desired. The cause for the perverse fluctuations of the measured labor force is the tendency of potential workers to withdraw from the labor force, or to postpone entering it, unless desirable jobs are available or there is acute pressure to "work or starve." If the measured labor force varies perversely, a possible solution for the monetary authorities might be to use for N and dN the resultant of a series of proportions applied to the population by age, sex, and possibly racial groups. (Each proportion should represent the "normal" labor force participation rate for a particular segment of the population; proportions could be revised at regular intervals to adjust for changes in participation habits.) This solution makes no claims to absolute accuracy, and lags behind participation-rate changes. It does, however, avoid systemation Policies 3 (1963). Compare also Friedman, Note on Lag in Effect of Monetary Policy, 54 Amer. Econ. Rev. 759 (1964).

20 Friedman, Program for Monetary Stability 92 (1959).