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Estimating implied volatility by inverting the Black-Scholes formula is subject to considerable error when option characteristics are observed with plausible errors. Especially for options away from the money, large changes in volatility produce small changes in option prices. Conversely, small errors in option prices and other option characteristics produce large errors in implied volatilities. In the presence of small measurement errors, unobserved truncation of option prices that violate lower bounds for absence of arbitrage can also lead to systematic volatility smiles. The paper proposes feasible GLS estimators that reduce the noise and bias in implied volatility estimates.

1. Introduction Monetary authorities who choose to reduce their country's rate of inflation, that is, to disinflate, are usually faced with subsequent recessions. A pattern of slower growth in the money supply, followed by a lower inflation rate and lower output, can be seen in historical statistics, such as those examined by Friedman and Schwartz (1963). When there was thought to be a permanent Phillips curve trade-off between inflation and unemployment, an important policy question was what combination of inflation and unemployment was most desirable. As economists came to accept the idea of a short-run but not a long-- run trade-off between inflation and unemployment, the stage was set to ask about how much output is lost as a result of a disinflation. Okun (1978), using results from several econometric models, estimated that an extra 1% unemployment rate for one year would reduce inflation between one-sixth and one-half of 1%. To reduce inflation by 1%, these figures suggested that the unemployment rate needed to be higher by 2 to 6% of the labor force. If one uses an "Okun's law" of 2.5% of gross national product (GNP) lost for an unemployment rate higher by 1%, then the output lost to reduce inflation by 1% would be between 5 and 15% of GNP. The term "sacrifice ratio" is now widely understood to mean the ratio of the cumulated percentage loss of output (at an annual rate) to the reduction in the trend rate of inflation.1 For the disinflation in the early 1980s in the United States, Fischer (1986) figures the sacrifice ratio was about five. Other empirical studies, such as those in Ball (1994b) and Jordan (1997), find a range of estimates around an average sacrifice ratio of about two.2 The pattern of slower rates of growth in the money supply being followed by recessions has posed a challenge to theorists to develop plausible models that help us understand this phenomenon. The existence of staggered price setting is one candidate explanation, and Taylor (1979, 1980) deserves credit for introducing formal analyses of how overlapping wage contracts can lead to a persistence in wages and deviations in output from its natural rate during disinflations. Sargent (1983), in discussing conditions for a successful disinflation without much output loss, characterizes the Taylor model as follows: "In this class of models, in terms of unemployment it is costly to end inflation because firms and workers are now locked into long-term wage contracts that were negotiated on the basis of wage and price expectations that prevailed in the past. . . . In addition, the wage contracting mechanism contributes some momentum of its own to the process, so that the resulting sluggishness in inflation cannot be completely eliminated or overcome by appropriate changes in monetary and fiscal policies" (p. 55). Similarly, Vegh (1992), explaining why ending hyperinflations appears to involve less output loss than ending moderate inflations, writes, "The fact that in hyperinflations backward-looking contracts (so prevalent in industrial and chronic-inflation countries) disappears is probably at the heart of the difference in output costs" (p. 656). In a widely used textbook, Romer (1996, p. 273) writes that "the Taylor model exhibits price level inertia: the price level adjusts fully to a monetary shock only after a sustained departure of output from its normal level. As a result, it is often claimed that the Taylor model accounts for inflation inertia." Romer then adds the provocative sentence: "Ball (1994a) demonstrates, however, that this claim is incorrect." The link between the discrete-time model presented by Romer and the contention attributed to Ball is not immediately evident and needs to be clarified. Beginning with an environment of steady growth in money and prices, Ball (1994a) assumes that a new regime suddenly announces a fully credible continuous linear decline in the growth rate of money. …

IN RECENT YEARS, a number of empirical studies have presented evidence that money supply shocks have asymmetric effects; that is, unexpected negative changes in the money supply slow the economy more than unexpected positive changes accelerate the economy. Evidence of asymmetry was documented by Cover (1992) for the postwar U.S. economy, and his finding was confirmed by De Long and Summers (1988), Morgan (1993), Rhee and Rich (1995), and Karras (1996a, b). Stimulated by these empirical works, several attempts have been made to provide microeconomic foundations for the asymmetric effects of money supply shocks.1 Among those theories, this paper examines the one that focuses on asymmetric price adjustment (and let us call it a sticky price theory). Money supply shocks will have asymmetric effects on real output if prices are less flexible downward than upward. This sticky price theory was proposed by Tsiddon (1993), Ball and Mankiw (1994), and Caballero and Engel (1992). By employing a menu-cost model, the above researchers show that positive trend inflation can produce the asymmetric effects of money supply shocks. The logic of their theory is the following: along with price adjustment costs, positive trend infla

My purpose in wnting the paper "Money in a Real Business Cycle Model" was to explore the idea that the monetary transmission mechanism may be explained in an equilibrium model in which preferences, endowments, and technology are, on their own, insufficient to pin down a unique equilibnum. By the "monetary transmission mechanism" I mean the time series properties of money, interest rates, pnces, and output in data from Europe and the United States. According to a common interpretation of these data, a change in the money supply has real effects on output in the short run but it is neutral in the long run. I had also hoped that an explanation of the monetary transmission mechanism that relies on indeterminacy might rest solely on the idea that money is useful as a medium of exchange. I am indebted to Kirill Sossounov for pointing out a sign error in the computations in my 1997 article and for rescuing the message of the paper with minimal alterations to the basic framework. We have several examples of calibrated models of real economies in which the theoretical structure permits the existence of multiple stationary equilibria and I have argued elsewhere (Farmer 1993) that models of this class can be completed by specifying a rule by which agents form beliefs. These models suggest the possibility that "animal spirits" or ''self-fulEllling prophecies" may have an independent role in propagating business cycles and that this possibility is fully consistent with the hypothesis of rational expectations and market clearing. We also have examples of monetary models in which multiple equilibria may play a role in the transmission of monetary shocks.l But to date, none of these models has been calibrated with the same degree of attention to the explanation of data as has become typical in the real business cycle literature. My 1997 paper, with Sossounov's amendments, goes some way toward filling this gap. From an argument onginally advanced by Negishi in 1960, it is known, if one imposes standard assumptions of convexity of preferences and technology, that infinite horizon economies with a finite number of agents typically contain a finite odd number of equilibna. From this fact, it follows that steady-state equilibna are locally determinate and that multiplicities that are exploited in models of self-fulfilling prophecies cannot occur.

It is well known that market power causes firms to underproduce from a social welfare perspective. Widespread existence of monopolistic elements, as documented for example by Hall [14; 15] and Lebow [16], may provide an argument for government policy designed to increase production at the aggregate level. The literature on macro models of monopolistic competition, e.g., Rotemberg [26], Blanchard and Kiyotaki [10], and others finds that changes in the money stock in principle do not affect aggregate production; a further source of market imperfection in the form of a nominal rigidity is necessary to allow changes in the money stock to generate production effects.

AN ESTABLISHED CHARACTERISTIC of macroeconomic fluctuations is the strong positive correlation between variations in the money stock and variations in production, income, and employment at business cycle frequencies. This finding has motivated an enormous literature that has studied the effects of monetary policy disturbances on the real economy, and in particular the role of money in business cycles. Several classes of monetary business cycle models have been developed that feature different channels through which monetary policy can have real effects. One model that has been used widely is the Keynesian model, in which monetary shocks can have important effects on allocations because there are nominal rigidities in prices and/or wages. The Keynesian assumption of sticky nominal prices is often motivated by reference to studies that have analyzed the frequency of nominal price changes. The broad conclusion that emerges from this literature is that there are a number of goods that have prices that appear to change infrequently. For example, Carlton (1989) has reported slow changes in nominal transactions prices for producers' goods even without long-term relationships between buyers and sellers, and has documented that delivery lags and other product characteristics frequently change before nominal prces change. Similarly, Blinder's survey (1991) of firms shows that prices for many goods change only about once per year. While this evidence

The simple quantity theory of money asserts that, because the velocity of money and fullemployment output are constants, if the money supply doubles, the price level must also double [15]. This view of the quantity theory of money is also supported by the policy ineffectiveness proposition put forward by Lucas [16], Sargent and Wallace [20], and Barro [1]. The policy ineffectiveness proposition asserts that real variables like output and unemployment respond only to unanticipated movements in the money supply, but do not respond to anticipated money supply associated with the systematic feedback rules. One of the premises essential to the validity of this proposition is the perfect flexibility of prices. The corollary of the policy ineffectiveness proposition, as expounded by Gordon [12] in invalidating this propositin, is that because output does not respond to anticipated money supply changes and remains at the natural level, the price level responds contemporaneously and proportionately to the anticipated changes in the money supply. This conclusion is also consistent with Barro's hypothesis that "perceived movements in the money stock ... imply equiproportionate, contemporaneous movements in the price level" [3, 565-66]. This one-to-one relationship between the anticipated money supply and the price level has also been shown theoretically by Barro [1] and Hercowitz [13]. It is this conclusion that needs to be tested by accounting for the speed of adjustments of prices. The purpose of this study is to explore theoretically and empirically the link between money supply and price levels by incorporating a gradual price adjustment mechanism. More specifically, this study examines (a) the one-to-one relationship between the log of current money stock and the log of the price level purported by Barro [3]; (b) effects of unanticipated money growth on the aggregate price, and (c) importance of anticipated money growth in determining the price level, given the current money stock and the current and lagged values of the unanticipated money growth. The key element of the study is the realization that the economy is comprised of markets with differing degrees of price adjustments. Numerous cases of price stickiness can be identified in modern economies as enumerated in survey work by Blinder [4]. Also, for instance, Devadoss and Choi [6] observe that the U. S. agricultural program's price-fixing policies such as price

Recent studies of the role of monetary policy in the interwar period and the Great Depression of 1929-33 typically focus on the money supply or the monetary base.' For several reasons, however, it is instructive to study the separate impact of money's three proximate determinants. In this paper we focus on the interwar period and present empirical evidence on the importance of the three proximate determinants of the money supply in explaining fluctuations in output and prices. We define the interwar period as July 1922-June 1938 for reasons explained in Beard and McMillin [2]. As developed by Friedman and Schwartz [15] and extended by Cagan [10], changes in the M2 stock of money can be attributed arithmetically to changes in three proximate determinantsthe monetary base, the ratio of currency to deposits (the currency ratio) and the ratio of reserves to deposits (the reserve ratio).2 The three proximate determinants are affected by different economic forces or react differently to the same variables. Each is under the immediate control of different economic agents. Changes in any one of the three proximate determinants can have, and have had, important effects on the stock of money. Cagan [10] analyzed in detail the contribution of changes in each of the three proximate determinants to cyclical fluctuations in the rate of change in the money stock over the long period 1877 to 1954. The base and the reserve ratio were each responsible for about one-fourth of these variations; the currency ratio was the most important single contributor, being responsible for roughly one-half of the variations. While the contribution of the currency ratio varied from cycle to cycle, major deviations occurred at times of financial panics when it often played a dominant role. Cagan found that the establishment of the Federal Reserve reduced the relative importance of changes in the reserve ratio and increased the relative importance of changes in the base. While the amplitude of cyclical movements in the reserve ratio fell after 1914 and the ratio itself trended downward, there was a sharp increase in the reserve ratio in the 1930s.

The purpose of this article is to employ several nonnested procedures to empirically test the proposition put forward by Mankiw and Summers that consumption rather than income is the appropriate scale measure in the money demand function. Real income, real disposable income, consumer spending on nondurables, personal consumption expenditures, and total private spending are tested as candidates for the scale variable. Tests are carried out for both M1 and M2 concepts of money. The results based on both M1 and M2 support the Mankiw–Summers position, but the results based on M2 are not as strong as those based on M1. Implications for fiscal and monetary policies are discussed.

New measures of stock return volatility are developed to increase the precision of stock option price estimates. With Bayesian statistical methods, volatility estimates for a given stock are developed using prior information on the cross-sectional patterns in return volatil? ities for groups of stocks sorted on size, financial leverage, and trading volume. Call option values computed with the Bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility, standard historical volatility, or even the actual ex post volatility that occurred during each option's life. Although the Bayesian methods produce biased call price estimators, they do reduce the systematic tendency of standard pricing approaches to overprice (underprice) options on high (low) volatility stocks. Little bias improvement is observed with respect to the time to maturity and moneyness of the call options.

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American-style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross-correlations between the changes in call and put implied volatility. AN IMPORTANT AREA OF current research is the estimation and behavior of market volatility implied by option pricing models. For example, Stein (1989) concludes that the S&P 100 index option market is inefficient because longer term options overreact to changes in the implied volatility of short maturity options. Day and Lewis (1988) document an increase in volatility around the quarterly expiration cycle. Schwert (1990) draws conclusions about the behavior of volatility around the stock market crash of 1987 by using implied volatility. All of these studies use a simplified option pricing framework to estimate implied market volatility. Previous research generally assumes that the S&P 100 index option is European-style. This option is actually American-style. It is also common to assume that the dividend yield is constant. The dividends are not constant and exhibit distinct seasonal patterns. Harvey and Whaley (1991b) show that large pricing errors can be induced in the option prices if the American feature and the discrete dividends are ignored. Option pricing errors translate into errors in the implied volatility estimates. This paper uses S&P 100 index call and put transactions and an American-style option pricing model with the exact discrete dividend series to calculate a time-series of implied volatilities. This valuation method

This paper shows that, with the imposition of asymmetric information, monetary shocks can have real effects in a model with optimal employment contracts. Firms are assumed to experience supply shocks that are their own private information. When a bad shock occurs, contractual employment is inefficiently low. Contracts depend upon the probability of a bad state occurring. If the aggregate price level is correlated with the firm's private information, contracts will depend upon prices. It is shown that an unanticipated increase in the money supply increases prices and employment. The authors explore the macroeconomic implications of the model. Copyright 1990 by Ohio State University Press.

The current operating procedure of the Federal Reserve, as described by Richard Davis and interpreted by me, entails picking long-term growth rates (meaning six months and longer) for monetary aggregates, while simultaneously specifying short-run conditions for the federal funds rates and monetary aggregates which are felt to be consistent with long-term goals. But, he also states, because of “shorter term developments,” that the specified shorter term growth rates for monetary aggregates might not be equivalent to the desired long-term growth rate. This operating procedure disturbs me for two reasons. First, there is evidence demonstrating that different growth rates in the money stock which last as long as six months result in different levels of economic activity; thus six months should be the maximum control period not the minimum. Secondly, I don't see what meaning a long-term growth path for monetary aggregates can have if the Federal Reserve lets “shorter term” development define the short-term growth paths for money in a way which is inconsistent with the longer term goals.

RESERVE REQUIREMENTS HAVE BECOME a common institutional feature of our monetary systems. They are widely held to be indispensable for zfficient control of the financial sector of the economy. Yet, relatively little analysis has been directed at the question of what constitutes an optimal level and structure of reserve requirements. In the traditional literature, the major exceptions concetn some discussions of the extreme values of 100 percent or zero requirements, especially the former (see, e.g., [1, 5, 6, 7, 10]). For a zero required reserve proposal, see [3]. In recent years, some newer studies dealing with these issues have appeared (see, e.g., [8, 9, 11, 12, 15]). In all of these studies, the focus is almost exclusively on money stock control. Generally speaking, their results support the 100 percent reserves idea, though such a scheme is usually seen as infeasible for political or institutional reasons, leading to recommendations to set requirements as high as possible against deposits included in the money stock, subject to whatever constraints of this nature are perceived. The underlying idea, of course, is that this minimizes the influence of private sector disturbances on the money stock by lowering the money multiplier (and making it equal to one in the extreme case of a 100 percent requirement). Reserve requirements are comparable to a tax on a particular economic activity, namely, the production of deposit accounts. As such, they have efficiency effects similar to those of a tax on other types of activities. Although this has always been

AN important development in the methodology of policy evaluation research in macroeconomics is the growing emphasis on the effects of policy systems-operating either by institutional arrangement or formal policy rules-rather than on the effects of one-time changes in the policy instruments. For instance, many studies on monetary policy in recent years have focused on the effect of a system in which the money supply systematically responds to the state of economic activity; previously the focus was on the effect of a change in the money supply at a particular date. Recent examples of policy proposals resulting from such research include rules for the Federal Reserve to increase interest rates by a certain amount whenever the consumer price index rises above a fixed target or, alternatively, rules to hold the growth rate of money constant except for temporary countercyclical deviations keyed to the unemployment rate or to the growth rate of nominal GNP. i As these examples

This paper presents a formal general-equilibrium model of a monetary economy in which agents' decision rules are derived from the underlying preferences, technology, endowments, and information. Firms face kinked demand curves for the reason given by J. Stiglitz (1979)-customers know the price at their current firm but not at other firms. The results are compatible with extreme Keynesian macroeconomic predictions, as presented by G. Woglom (1982). There is no automatic tendency to full employment, and a change in the money supply may cause a permanent change in real output with no change in prices.

THE QUESTION OF CREDIT RATIONING has been the subject of a number of theoretical discussions during the past twenty-five years. Credit rationing arguments occupied an important place in the so-called availability doctrine. The availability doctrine became prominent during the early fifties as a theory explaining how monetary policy could have eSects on spending and the real sector of the economy even in the presence of "Keynesian" difficulties then widely believed in, such as insufficiently interest-elastic investment demand. The doctrine, whose most articulate exponent was Roosa [38],1 emphasized that reductions in the money supply would have significant restrictive eSects on spending, even if they result in only a small interest rate increase, or if spending is not, or only insufficiently, curtailed by such an increase. This was simply because banks would be forced to reduce the amount of credit they could extend to their customers, even if customers did not lower their demand. That is, spending was viewed as being constrained by the availability of credit, which was allocated by banks to their customers, to some extent, through nonprice means, i.e., through some kind of rationing scheme. Thus, the doctrine suggested an alternative transmission channel for monetary policy that was, to an important extent, based on a credit rationing argument.

In recent years the importance of the role of the money stock has been increasingly emphasized in analysis and in FED policy making. During the 1970's the FED has established money stocK targets and has sought to make the money supply conform to those targets. In addition to concerns as to whether the targets of the FED are appropriate or not, professional and public concern has been expressed about the relative successfulness of the FED in achieving short-run and long-run targets. It has been suggested that money market reactions to the success or lack of success of the FED in achieving its targets influence interest rates. The FED has often warned that short-term variations in the money stock and failures to achieve the monthly tolerance ranges for the money stock may have no significance and that speculation based on such data is inappropriate. Nevertheless, the notion that movements in interest rates may reflect expectations about the future course of money stock and the perceived targets of the FED appears to have achieved some acceptance and is worth empirical investigation [17]. If expectations about the course of the money supply and surprises due to the actual unfolding path of the money supply produce changes in interest rate expectations that alter current interest rates, there may result changes in real economic variables [15]. This paper will specify and test the hypothesis that revisions in interest rates forecasts are systematically related to the market's forecast of monetary growth and subsequent unanticipated growth of the money stock. Section I posits a simple model of the structure of interest rates through which changes in interest rate expectations can be modeled.

This paper argues that an aggregate preferred habitat for investors exists on (or about) the last day of the calendar month, due to standardizations in the nation's payments system resulting in a concentrated flow of funds on this date. Thus, equilibrium yield discounts are predicted for securities maturing on such dates. Empirical tests on monthly and daily Treasury bill data support the principal hypothesis, as well as several ancillary hy? potheses. The results have implications for Treasury debt management, for the short-term cash and debt management practices of businesses and banks, and for the empirical esti? mation of daily, weekly, or monthly return premiums on risky securities.

Monetary Growth and Price Stability: France, I650-I700 European monetary historians usually explain long-run price behavior by the version of the Quantity Theory of Money developed by Irving Fisher: MV = PT. Rising or decling prices are related to increases or decreases in the supply of money. Some historians also tie monetary and price movements to real economic growth. In both approaches it is assumed that velocity (v) is constant.l Modern quantity theory has improved on the constant velocity assumption, and suggests a number of economic factors that can produce trend as well as cyclical movements in v. In this article the existing evidence on the money stock, prices, and levels of income in France from I650 to I700 are considered within an income version of the equation of exchange (MV' = Py). The evidence about these variables suggests that increases in the money stock relative to output do not explain price level movements.

On 6 October 1979 the FOMC announced a shift from federal funds rate (FFR) to nonborrowed reserves (NBR) targeting. The sequence of events preceding this major policy change are well-known and require only a brief recounting here. Prior to the 1979 announcement, the FOMC implemented monetary policy by confining the FFR to a narrow band about 50 to 100 basis points in width. Any tendency for the rate to move outside this range was countered by providing more or fewer NBR to the banking system. The underlying assumption upon which this strategy was based was that money demand was stable. The Fed could then control the money stock by altering interest rates, thereby moving the public along a fixed money demand function. During the mid-1970s, however, various events in the money market (e.g., income and supply shocks, financial innovation, and portfolio readjustments) lessened the stability of money demand and brought the twin objectives of monetary control and financial market stability into frequent conflict. The record shows that these conflicts were usually resolved in favor of interest rate stability rather than monetary control. The consequence of FFR targeting was inflation; attempts to maintain a stable FFR at the operating level in the face of money demand shifts forced the central bank to exceed its money growth targets for periods long enough to increase nominal aggregate demand in the economy. With the adoption of the NBR strategy, the Fed attempted to achieve better control over inflation by short-circuiting the endogenous influences of spending on the growth of the money stock. In contrast to the pre-1979 policy, spending shocks would now be reflected in FFR movements which would, to some extent, generate pressures to return money growth to its desired path. Subsequent to the announced policy shift there was much doubt about whether the Federal Reserve was successfully executing a NBR plan. The gist of this skepticism centers on the belief that the new procedures were technically flawed. Specifically, that reserves targeting, when combined with lagged reserve accounting and borrowings projection errors, resulted in short-run accommodation, increased interest rate and money growth volatility

STRICT MONETARIST THEORY, IN AN EXTREME FORM, holds that excessive money growth, or the expectation of future money growth, shows up immediately in the rapid inflation of goods prices. However, it is widely argued that for most goods prices are in fact sticky in the short run and reflect money growth only in the long run. If one seeks a sensitive market measure of the perceived looseIless or tightness of monetary policy, one must. look elsewhere than at the general price level. Interest rates, being determined in quickly adjusting financial markets, are free to respond immediately to expectations regarding monetary policy. In 1981 and 1982, every Friday at 4:10 P.M. Eastern Standard Time the Federal Reserve Board would announce the money stock for the week ending nine days previously. If the announced money stock was different from what the market had been expecting, interest rates generally jumped in the same direction. Clearly they were responding to revisions of the expected future path of the money stock. But nominal interest rates are an ambiguous indicator of expectations. On the one hand, an announced increase in the money stock may be received by the market as indicating a higher

In an interesting paper published in this Journal, Douglas Needham (1973) has commented on and extended my analysis (Blomqvist, 1970) of the assignment problem under fixed exchange rates. In the original treatment of this problem by Mundell (1962), monetary policy was identified with changes in the rate of interest. The main purpose of my paper was to investigate whether the principle he derived, i.e., that fiscal policy should be assigned to the employment objective and monetary policy to the external-balance objective, would remain valid when monetary policy is instead identified with changes in the money supply, as is done in the usual Hicksian IS-LM analysis. Assuming the same type of policy-making behavior as that implied by Mundell, i.e., that one disequilibrium at a time is eliminated, I found that there were cases, associated with a low interest elasticity of the demand for money and a high interest-responsiveness of external capital flows, in which the Mundell assignment would lead to cyclical behavior in employment and interest rates, and even to progressive divergence from equilibrium. For the latter case, I showed that the reverse assignment, i.e., using fiscal policy to correct external imbalance and monetary policy to correct internal disequilibrium, would generate stable behavior. As Needham observes, the assumption that policy-makers behave in such a way as to eliminate one disequilibrium at a time, is unrealistic; actual policymaking is considerably more complex and may involve simultaneous adjustments of monetary and fiscal policy, time lags in recognizing disequilibria, different speeds of adjustment of policy tools, etc. It is therefore of interest

This paper discusses some misinterpretations that can arise when cyclical data are incorrectly assumed to be generated by movements between equilibria. One example is the cyclical behaviour of the real wage, an issue discussed by Grossman (1973) and others. In Section II a small dynamic model is examined which can give a procyclical pattern of the real wage even though it has a negative equilibrium relation between employment and the real wage. This suggests that predicting the cyclical pattern of the real wage from the equilibrium relations of a model can give incorrect results. The theoretical model is used to reinterpret the empirical evidence on the cyclical pattern of the real wage (Bodkin, 1969). Another area of possible dynamic mis-specification is the Phillips Curve literature. Two important studies, Cagan (1968) and Desai (1975), which use unconventional estimation techniques, are examined using a dynamic model. The conclusion is that the methods of these two studies do not guarantee against a confusion of equilibrium and cyclical relations. The discussions of the Phillips Curve and the movement of the real wage provide potential applications of the econometric tests for mis-specification developed by Hendry (1974). Section I presents some properties of a cyclical dynamic system which simplify the economic analysis of Section II. These results can also be applied to other discussions of cyclical data and dynamic mis-specification. For example, the analysis by Tobin (1970) of the cyclical relation between changes in the money supply and nominal income, and that by Grossman (1974) of cyclical rotations about the Phillips Curve, can be simplified using Section I.

IN RECENT YEARS considerable effort has been directed towards establishing the nature of the relationship between "money" and "nearmonies" but with mixed success. The approaches vary from multi-interest-rate single equation studies to the careful simultaneous equations studies summarized (and amended) by Feige and Pearce (1977) and extended recently by Donovan (1978), Offenbacher (1979), and Barnett (1980). The empirical results also vary, with numerous studies favoring only one interest rate (see the surveys in Fisher 1978, 1983), some claiming that a variety of entities are close substitutes for money (e.g., Chetty 1969), and others showing that weak substitution or even complementarity may be the result of the measurement of elasticities of substitution between money and a number of other assets (e.g., Feige and Pearce 1977, Offenbacher 1979, and Barnett 1980). The debate seems to have overshadowed a second and equally intriguing issue which centers on the establishment of an acceptable definition of money. The basic idea of this study is to take an approach that takes account of the different degrees of "moneyness" possessed by the various monetary assets. This paper produces quantitative estimates of the degree of substitutability of other monetary assets for money in the context of a flexible functional form model (with a

Ever Since the publication of the "St. Louis Equation" by Anderson and Jordan and its later appearance as a conerstone of the St. Lois Model, the equation has been the subject of great debate. The equation showed that quarterly changes in the money stock exerted a much greater influence on nominal GNP than did quaterly changes in high employement federal spending.

A large institutional literature has been concerned with restructuring the banking system in such a way as to decrease uncontrolled variation in the money supply. Some advocate this restructuring as a means of getting increased control over an "intermediate" target variable; apparently they reason that tighter control of an intermediate target variable will ultimately lead to better control of "final" target variables such as inflation or unemployment. More recently, control theorists have acknowledged the fact that monetary authorities do not exert direct control over the money supply or interest rates, and a number of control engineering studies have been concerned with the optimal control of various intermediate financial variables. Common to all of this literature (and perhaps current FOMC policy making as well) would appear to be the basic premise that the optimal control problem can be divided into two separate control problems that are solved sequentially: First, in the "final" control problem, one pretends that the intermediate variables are set directly and finds the intermediate variable path (called the intermediate target path) that will make the final variables track their target path as well as possible. Then, in the "intermediate" control problem, one finds the path for the actual instruments of monetary policy that will make the intermediate variables track the intermediate target path as well as possible. The purpose of this note is to show that this basic premise is not generally valid, that the second step in the procedure constitutes an improper specification of the intermediate control problem, and that the intermediate control problem, properly specified, is fundamentally different from the standard control problem. Two examples will illustrate situations in which the two-step procedure described above leads to an incorrect solution, and the difference between standard and properly specified intermediate control problems will be characterized. Both examples will be constructed within a very simple setting: The relationships between the true instruments of monetary policy and the intermediate variable, which is taken to be the money supply M, will be viewed as a black box generating the random variable M. The monetary authority will be assumed to be able to control both the mean and the variance of the random variable emanating from the black box by judicious setting of its true instruments. That is, letting M = M + m, where m is a random variable with zero mean and variance 2, the monetary

* We would like to thank Esmond Adams, Helen Farr, Edward Fry, Charles Lieberman, Richard Marcis, Thomas Mayer, William Poole, Richard Puckett, V. Kerry Smith, Helmut Wendel and an anonymous referee for helpful comments on earlier drafts of this paper, and Lauren Dillard and John DuBois for invaluable research assistance. The views expressed in this paper do not necessarily reflect those of anyone in the Federal Reserve System. 1 While monetary researchers have frequently alluded to several of the points raised in this paper, until recently only Kaminow [16] and Poole and Lieberman [26] have actually examined any of the issues surrounding the quality of the money stock data. In early 1974, however, the Board of Governors of the Federal Reserve System announced the formation of a special committee of prominent academic experts to review the statistics on the monetary aggregates. The report of this committee was published in the spring of 1976 [27] and their discussion of the issues where applicable to this paper is presented below. identify and adjust for seasonal variation obscures important issues underlying cyclical and seasonal movements in time series. In addition, the results of frequency domain and time domain tests are presented which support the view that present adjustment techniques produce a distorted seasonally adjusted series. It is suggested that correcting such distortions will require a structural model of seasonality similar to those commonly used to investigate cyclical relationships among series. While the focus of this paper is on the money stock series, many of the issues discussed, distortions identified, and solutions offered, have general applicability. A major implication of our findings is that the confluence of seasonal and cyclical forces operating on short-run movements (month-to-month, and quarter-to-quarter) in key published series, such as the seasonally adjusted money stock, may often generate misleading signals for those trying to evaluate the thrust of policy and the pace of economic activity.

One effect of a postal strike is an increase in the money supply. A plausible explanation for this phenomenon is that a postal strike tends to delay customers' payments to firms. Although their revenues are delayed, firms have financial obligations such as payrolls which cannot be postponed. Consequently, they find themselves temporarily liquidity-constrained and they borrow from the banking system. The Bank of Canada's policy has been to accommodate this additional and temporary demand for liquidity. Agents who have bills to pay mentally debit their accounts and therefore think of themselves as holding their desired cash balances. However, their actual cash balances are, in fact, higher than desired balances. This phenomenon causes standard demand for money equations to underestimate substantially money demand at the time of a strike. Furthermore, because of their dynamic aspect (i.e., the presence of a lagged dependent variable), these specifications overestimate demand the following period. For example, a model identical to the one presented below but excluding any strike variable was estimated by S. Poloz (1980). His equation underestimated and then overestimated real money demand by 3.21 per cent and 6.05 per cent and by 5.84 per cent and 1.71 per cent for the 1974ii and 1975iv postal strikes respectively. In a recent paper, Clinton and Lynch (1979) proposed the use of two dummy variables to capture the effect of the 1974ii and 1975iv postal strikes. Although the coefficients of the dummy variables have the right sign and are

Increasing reliance on the monetary aggregates as indicators of economic activity in conducting monetary policy led the Federal Reserve to change its operating procedure in October 1979. In an attempt to gain greater control over the monetary aggregates, the Fed switched from using the federal funds rate as its operating instrument to operating by means of nonborrowed reserves. Subsequent increased volatility in interest rates coupled with sharp fluctuations in money growth and economic activity led the Fed to modify its procedure once more in the autumn of 1982, switching its operating target from nonborrowed to borrowed reserves. This paper examines empirically the money supply process from 1970 to 1986. We find that the process itself was not invariant to the Fed's changes in operating procedure.' Thus, the effect of these changes did not lead to more or less control of money by the Fed under the same money supply process. Rather, the changes in the Fed's procedure led to changes in the money supply process which, in the case of the first change in procedure at least, largely thwarted the aims of the Fed regarding money control. We show that the switch to a reserves operating procedure, which has since been modified but not completely abandoned, has failed to overcome the short-run endogeneity or demand-determination of money which the Fed had experienced prior to October 1979 because the banking system has changed its behavior with respect to the link between reserves and money supply under the newer procedure.

IN A SERIES OF PAPERS, BARRO ( 1977, 1978), BARRO and Rush (1980), Vittorio and Tanner (1983), Bellante, Morrell, and Zardkoohi (1982), and others have tested the rational expectations hypothesis that only unexpected changes in the money supply affect real variables. Mishkin (1982), Merrick (1983), Sheehey (1984), Small (1979), and others have criticized this work for various reasons. None of the cnticisms, however, has addressed the question of possible endogeneity of the money supply (M1) used. Moreover, most of this literature uses only data from after World War II. This paper builds on the previous literature in several directions. First, it differs from most other work by following Blejar and Fernandez (1980) and Rush (1985) in using the base money supply as the monetary aggregate. This controls for the possible endogeneity of the M1 money supply typically used by other researchers. Moreover, it allows the sample period to be extended through 1983 without worrying how the recently changing definitions of M1 affect any results. Next, a longer sample period, roughly from 1920 to 1983, is used. This time span is interesting for a couple of reasons. It allows an assessment of the role played by

A recent paper by Frankel and Hardouvelis (1985) examined the impact of money supply announcement surprises on the commodity markets. The purpose of this comment is to correct some errors we discovered in the regression results reported in their paper. We received a copy of Frankel and Hardouvelis' data set from the Journal of Money, Credit, and Banking. While examining this data we discovered that approximately one-half of the commodity price data had erroneously been collected a day earlier than intended. Therefore we decided to reestimate their regression equations with commodity data collected from the Dow Jones News Retrieval Service. In each equation the dependent variable is the difference between the closing price of the next maturing contract one hour before the weekly money announcement and the opening price of the same contract the following morning. The independent variable is the difference between the announced change in the money supply (M 1) and the change forecasted (based on a survey by Money Market Services). As with Frankel and Hardouvelis, the equations were estimated for both the 1978-79 (pretargeting), and 1980-82 periods. The results are qualitatively similar to those reported by Frankel and Hardouvelis, although there are substantial differences for individual commodities such as sugar, cocoa, silver, and gold. Perhaps the most significant difference is that during the money targeting period (1980-82), the nine-commodity average is now significant at the .001 significance level (as compared to a .05 significance level found by Frankel and Hardouvelis). The new estimates provide even stronger evidence in favor of the "policy anticipations hypothesis" which views the market response during 1980-82 as an anticipation of future policy actions by the Fed. Neither the "inflationary anticipations hypothesis" nor the "real activity signaling hypothesis" would seem consistent with such a large qualitative change in market responses between 1978-79 and 1980-82.

The monetary approach to exchange rate determination attributes the observed volatility of floating rates to revisions of expectations about current and future disturbances that affect the supply and demand conditions in the money market see, for example, Frenkel and Mussa (1980). A number of recent studies have proposed and implemented variance bounds tests of monetary exchange rate models along the lines of bond-price and stock-price volatility tests pioneered by LeRoy and Porter (1981), Shiller (1979, 1981), and Singleton (1980). Huang (1981) presents evidence apparently demonstrating that some exchange rates are more volatile than a simple monetary model based on the assumptions of purchasing power parity and uncovered interest parity can rationalize. Meese and Singleton (1983) derive (but do not test) the variance bounds implied by a number of monetary models. Vander Kraats and Booth (1983) (henceforth referred to as V&B) implement volatility tests for three monetary models. They conclude that only a variant of the sticky-price model developed by Dornbusch (1976) can potentially explain (under certain rather implausible assumptions about parameter values) the observed volatility of the exchange rates included in their sample. In the literature, this evidence of excess volatility of floating rates is considered damaging to the monetary approach and/or to the rational expectations hypothesis. For example, in his recent survey of the literature, Richard Levich remarks that, on the basis of Huang's results, it "follows that either the market is inefficient . . . or that the rational expectations monetary model is incorrect, or both" (Levich 1985, p. 994). The primary purpose of the present paper is to point out that the excess volatility evidence presented by Huang and by AI&B arises from a calculation error. Namely, the value they assign to the interest semielasticity of money demand may be appropriate for a study using annual time series but is inappropriate for their monthly data. Once this error is corrected, their exchange rate series no longer violate the variance bounds they test.

A plethora of recent literature has dealt with the monetary approach to the balance of payments and/or exchange rate determination, all of which is based upon the notion that a country's external balance is primarily the result of adjustments in the money stock. Ultimately, the models which have been presented reduce to relationships of internal and external supply and demand for money. That is, one country's domestic monetary conditions relative to that of the world (or some "key" country) is the determining factor for reserve flows and/or exchange rate movements. Several studies have offered empirical evidence as to the validity of the general monetary approach theory.' Almost all models, when estimated, depend upon direct comparison of relative growth rates of domestic money demand/supply between two countries, or between one country and the rest of the world. Direct empirical comparisons of two countries through the goods market equilibrium assumption have been made by W. Michael Cox and D. Sykes Wilford [5] and D. Sykes Wilford and Walton T. Wilford [20] for the fixed exchange rate period. John F. 0. Bilson [3], Jacob Frenkel and Kenneth Clements [6], Robert J. Hodrick [II], Thomas Humphrey and Thomas Lawler [12], and Bluford H. Putnam and John Woodbury [18] have tested the model under flexible rates; while Lance Girton and Don Roper [8] analyzed a combination of the two periods. In all these works, the domestic rate of real growth relative to that of the rest of the world appears as a determinant of relative money demand. In this paper we discuss the possible bias introduced in the reduced form equation coefficients by this specification of the income differential elasticity and offer an alternative specification to account for this bias. Empirical evidence is provided which supports our specifications and the monetary approach in general, accounting for the bias generally strengthens the statistical results.

A MUCH-DEBATED ISSUE over recent years has been the relationship between money and stock prices. Among the better-known papers that have appeared are [6, 10, 11, 12, 23, 25]. Useful critical summaries of much of this work have been provided in [22, 23]. Frequently, the concern is with the closely connected relationship between inflation and stock prices (see, especially, [22]). Central to the issue of the effect of money on stock prices is, of course, the effect of money on corporate earnings. The pattern of effect on expected corporate earnings, in conjunction with the investor's required rate of return on stocks, will determine the effect on stock prices. (On the relationship of actual and expected earnings, see [20].) Because the principal concem of most researchers has been with stock prices, the primary link between money and earnings has not been directly studied. It is the purpose of this paper to fill this gap and present evidence on the relationship between changes in the money supply and pretax corporate earnings.

This paper tests the ability of the American option pricing model proposed by Parkinson [18] or Mason [14] to explain the pricing of the foreign currency options traded on the Philadelphia Stock Exchange from February 28, 1983 to March 26, 1985. We find that the model underprices out-of-the-money options relative to at-the-money and in-the-money options. This relative underpricing is driven by an underpricing of out-of-the-money call options of short maturity. In addition, the degree of relative mispricing for most categories of options is shown to be a decreasing function of the time to maturity of the options. Longer maturity options appear to trade at similar levels of implied volatility whether they are in, at, or out of the money. Most of these biases appear consistent with the fact that the underlying spot currency rate follows a mixed jump diffusion process as described in [17].

The question of whether large banks should be allowed to fail brings us face to face with a conflict between two social goals. On the one hand, the goal of optimal resource allocation suggests that even very large banks, like other firms, should be allowed to fail. On the other hand, the stabilization goal suggests that, given the present institutional structure, failures of large banks should be prevented lest they lead to runs on other banks and to a significant reduction in the money stock. The solution suggested here for this conflict is small changes in the institutional structure.

The relationship between the weekly money supply announcement and interest rates has attracted the attention of a large number of economists. Recent research by Cornell [2; 3], Engel and Frankel [5], Gavin and Karamouzis [6], Grossman [7], Hardouvelis [9], Naylor [10], Nichols, Small, and Webster [11], Roley [12], Roley and Walsh [13], Urich [14], and Urich and Wachtel [15] indicates a positive correlation between unanticipated changes in the announced money supply and interest rates. The consensus on the relationship between unanticipated changes in money supply announcements and interest rates, however, disappears in the explanation of the phenomenon. Two competing explanations and thus, two hypotheses are offered. The main difference between the two hypotheses lies in the interpretation of future money growth conditioned on the information provided by the money supply announcement. According to the first hypothesis, also known as the "expected liquidity hypothesis," market participants believe that the Federal Reserve will promptly offset any deviations in the money supply from its target level. This implies that an unanticipated increase in the money supply revealed by the announcement will be followed by a monetary tightening and, hence, an increase in real short-term interest rates. According to the second hypothesis; also known as the "inflation premium hypothesis," market participants interpret the change in the money supply revealed by the announcement as a permanent deviation from the money supply target. This implies that an unanticipated increase in the money supply will not be offset and hence, will raise the inflation premium. Therefore, according to the first hypothesis, an increase in nominal interest rates caused by an unanticipated increase in the announced money supply is due to a rise in real interest rates. According to the second hypothesis, it is due to an increase in the inflationary premium. In order to distinguish between the two hypotheses, evidence has been presented from the foreign exchange and long term bond markets. After analyzing the correlation between unanticipated money growth and the change in the level of spot exchange rates before and after the announcements, Cornell [2; 3], Engel and Frankel [4], Hakkio and Pearce [8], and Hardouvelis [9] find support for the "expected liquidity hypothesis." Based on the correla

Relatively little effort has been devoted so far to lay the microeconomic foundations of the behavior of commercial banks. The omission is unjustifsed in view of the role of commercial banks in the money creation process. The present enquiry constitutes an attempt to further the understanding of the behavior of commercial banks with respect to their demand for reserves. The assumptions of the model to be developed below differ from those of other stochastic models of bank behavior (see [4, 7, 10, 11, 12] ) in that the bank is supposed to interfere with the fluctuations in the amount of its reserves whenever the latter deviates from limits set by the bank, but not as long as the amount of reserves remains within those limits. The appropriateness of this strategy when earning assets cannot be acquired and sold costlessly has been recognized by Baltensperger [2] and Frost [6], yet they failed to analyze the bank's behavior irl a dynamic framework, as does the present model.1 Furthermore, most previous models came in one way or another to the conclusion that, if the penalty the bank has to pay in the case of reserve deficits is smaller than the rate of interest earned on loans, no reserves will be held by the bank. This prediction has never been borne out by the observed behavior of commercial banks. The model developed here does not postulate any specific relationship between the

This paper analyzes the consequences of wage rigidity in a model with rational expectations. To accomplish this, a distinction is made between equilibrium wage changes and actual wage changes. The model used implies that the short-run Phillips curve is not vertical, although the long-run Phillips curve is vertical. A study is also made of the development of inflation and unemployment when the rate of growth in the money supply is constant. The paper concludes with an analysis of a problem of optimizing the development of inflation and unemployment.

There have been two distinct arguments in favor of government intervention in the money industry. Both arguments involve an inherent instability of competition in the production of money other than a pure commodity money. The first and possibly the most pervasive failure of competition in the production of an non-full-bodied money is the alleged fact that the competitive producers of a homogeneous money will drive the value of that money to zero [2, 6-7; 9, 128-129]. The second argument asserts that even if a competitively produced money supply is not inherently explosive, such a system will not yield a unique price level. Thus, with a competitive money industry the economy will be in a meta-stable equilibrium so far as the aggregate price level is concerned.1 Benjamin Klein in an important 1974 paper, argues that individual firm identification and competition are not inconsistent [4]. Indeed, since product quality must be homogeneous in competition, producer identification is a necessary but not sufficient condition for a competitive money industry.2 In effect, consumers will require information concerning the quality of money before such money can circulate. It is just these demand restrictions which will result in the production of a competitively supplied money whose value does not tend to zero.

PpT HE subject assigned for this session covers too broad an area to be given even a fairly cursory treatment in a single paper. Accordingly, we have chosen to concentrate on the part of it that relates to monetary factors in economic fluctuations. We shall still further narrow the scope of the paper by interpreting "monetary factors" to mean the role of the stock of money and of changes in the stock thereby casting the "credit" market as one of the supporting players rather than a star performer and by interpreting "economic fluctuations" to mean business cycles, or even more exactly, the reference cycles studied and chronicled by the National Bureau. The topic so interpreted has been rather out of fashion for the past few decades. Before the Great Depression, it was widely accepted that the business cycle was a monetary phenomenon, "a dance of the dollar," as Irving Fisher graphically described it in the title of a famous article.' Different versions of monetary theories of the business cycle abounded, though some of these were really "credit" theories misnamed, since they gave little role to changes in the money stock except as an incident in the alteration of credit conditions; and there was nothing like agreement on the details of any one theory. Yet it is probably true that most economists gave the money stock and changes in it an important, if not a central, role in whatever particular theory of the cycle they were inclined to accept. That emphasis was greatly strengthened by the course of economic events in the twenties. The high degree of economic stability then achieved was widely regarded as a consequence of the effectiveness of the monetary policies followed by the only recently created Federal Reserve System and hence as evidence that monetary factors were indeed a central factor in the cycle. The Great Depression radically changed economic attitudes. The failure of the Federal Reserve System to stem the depression was widely interpreted-wrongly as we have elsewhere argued 2 and elaborate below to mean that monetary factors were not critical, that "real" factors were the key to economic fluctuations. Investment which had always had a prominent place in business cycle theories received new emphasis as a result of the Keynesian revolution, so much so that Paul Samuelson, in the best selling textbook in the country, could assert confidently, "All modern economists are agreed that the important factor in causing income and employment to fluctuate is investment." 3 Investment was the motive force, its effects spread through time and amplified by the "multiplier," and itself partly or largely a result of the "accelerator." Money, if it entered at all, played a purely passive role. Recently, a revival of interest in money has been sparked less by concern with business cycles than with concern about inflation. Easy money policies were accompanied by inflation; and inflation was nowhere stemmed without a more or less deliberate limitation of growth of the money stock. But once interest was aroused, it naturally extended to the cycle as well as to inflation. In the United States, indeed, there has been something of a repetition of the I920's. A high degree of economic stability has been accompanied by a large measure of talk about an active monetary policy, and the monetary authorities have often been given credit for playing an important role in promoting stability. As the experience of the twenties suggests, this fair-weather source of support for the importance of money is a weak reed. Examining the present state of our understanding about the role of money in the business cycle, we shall first present some facts that seem reasonably well established about the cyclical behavior of money and related

Since the introduction of the distinction between inside and outside money it has been generally conceded that the classical argument concerning the real balance effect holds only for outside money (see [2], pp. 73-74 and [5], pp. 297-98). Thus, in a system of only inside money the real balance effect cannot return the economy to full-employment from an unemployment situation (see [3], pp. 342-43). Even in a system containing both inside and outside money, part of the classical argument breaks down in that money is no longer neutral. That is, unless both inside and outside money change proportionately, changes in the money supply will not result in equiproportionate changes in the price level and no change in the rate of interest (see [2], pp. 83-86, [5], pp. 297-98, and [3], pp. 34042). Thus, the insideoutside money distinction appears, as Harry Johnson indicated, to have left traditional monetary theory in the predicament of being "dependent on adventitious, institutional or historical details" (see [3], p. 342). However, I shall show below that the present distinction between inside and outside money depends for its validity on either (1) an assumption of asymmetric behavior on the part of the members of the community or (2) the complete exclusion of some members of the community from the decision-making process. In effect, the argument presented is related to an argument presented by Boris Pesek and myself in 1967 and by Harry Johnson in 1969 (see [7], ch. 8 and [3]). However, the discussion here is restricted to the real-balance

The Radcliffe Report2 has touched off a lively debate on the theoretical conceptions underlying monetary policy, and in particular on the significance of the operations of non-bank financial intermediaries. Comment on this, as on other aspects of the Report, has been copious, but fragmentary. The object of this article is to bring together, from several sources, some of the more controversial opinions that have been expressed on this problem; and to attempt a critical assessment. Over-simplifying for clarity's sake, we may take as our startingpoint the basic Radcliffe theory and an opposing view which I shall label " traditionalist ". Thus we have the traditionalist approach emphasizing, so to speak, the medium of exchange function of money, a function in which money (defined as coin, notes and bank deposits) has virtually no effective substitute. It is therefore reasonable to expect, so the argument runs, that control of the stock of money will have significant influences on the flow of expenditure. These influences may work through the direct route, because, say, a reduction in the money supply makes people feel illiquid, so that to restore liquidity they are induced to restrict spending. Or they may work through the indirect route, because a reduction in money supply and the liquidity of the public causes an unwillingness to part with money evidencing itself in rising interest rates; the demand for credit then tends to contract and loan-financed expenditure to fall. Against this there is the Radcliffe approach, which from one standpoint may be regarded as emphasizing the store of value function of money, a function in which money has a number of close substitutes capable of neutralizing any potential effect of a reduction in the money supply on spending. The argument is that a relatively small rise in the rate of return on such substitutes will induce some holders of money balances to transfer part of their balances to intermediaries, who will re-lend them for the finance of various classes of expenditure.3 This summary of the opposing viewpoints is brief to the point of caricature, but it highlights the aspects most relevant to the subsequent

Messrs. Bell and Berman's paper2 contain an interesting exposition of statistical data which show how the realized demand for domestic bank finance was connected to the realized supply-bank liabilities-over the 1954-64 period. The authors apply an accounting methodology set out by R. Triffin in 19463 to perform what is now known as a monetary analysis. These exercises depict how inter-sector demands and supplies of funds may be linked together with the changes in the domestic money supply. In addition, they re-open the old controversy as to the explanatory content (in a causal sense) which such expositions have or should have4; and perhaps they have helped to settle it. Their attempt to inject causality into this framework fails, and it blurs some of the descriptive value of their contribution. The examination of this attempt, to which this Note is addressed, should make this point clear: the job of the compilers of statistics is ". . . to present the data in as much detail as feasible, and with logical classification (from a definitional, not causal point of view)".5 Otherwise their compilation may be misleading, and there is evidence that Bell and Berman's work is misleading. They seem to have inspired this comment in a financial weekly: "In these circumstances, no one quite knows what determines the credit base, or how to influence it."6 This is an opinion which must win sympathy if one accepts the Bell and Berman findings that sales of government securities to the banks increase the money supply, and that the operation of the Exchange Equalisation account actually makes the domestic money supply more rather than less sensitive to surpluses and deficits on the balance-of-Dayments account (DD. 152 and 155).

THIS study is concerned with the optimal, or warranted, growth of the monetary system. It constructs a rudimentary model of financial developrlent and deduces optimal trends in the money supply from a demand equation for money balances that is sensitive to both real and financial phenomena of growth. This model, we suggest, is relevant in both retrospect and prospect to the American economy. Against the trends that emerge from the model we array data on this country's financial and monetary experience since i8oo. The fit may be good enough to justify further experimentation with the demand equation for money as one basis for defining secular standards of monetary policy and for revising the structure and interrelationships of our financial institutions, monetary and nonmonetary alike.

1. There has recently been a revival of interest in the behaviour of the money supply both in the United States and in the United Kingdom.2 Most of the discussion, especially in the United States, has been concerned with the variables influencing the demand for money and the stability of various prescribed functions. When the discussion has focused on the factors affecting the money supply, the analysis usually has been limited to the influence of particular variables such as the supply of Treasury bills on bank deposits. This article is different in approach and sets out a statistical framework for analysing the impact of government borrowing operations, the balance of payments position and the banking sector's lending operations to the private sector3 on the money supply over a period of eleven years.

W E shall not know for many months if AVIV~the introduction of direct controls over wages and prices in late 1971 was followed by a significant slowdown in the trend of price and wage increases. Even if inflation will moderate somewhat, as is likely, economists will still be debating for years whether this can be attributed to the controls or whether it is simply the delayed result of considerable slack in the economy. But whatever the outcome of this future academic debate, some form of direct control is likely to be with us for some time. The establishment of direct controls on August 15, 1971 was popular among the public at large and subsequent opinion polls indicate that this program, despite its uncertain performance to date, has not become a political liability. The controls are only likely to be abandoned if they seriously hurt some important pressure group without visible offsetting benefits elsewhere, but this has not happened so far. Although some discontent among West Coast longshoremen gave most of the labor representatives on the Pay Board a pretext for walking out, most union members, and even the departed leaders themselves, are apparently quite willing to live with continued controls. The Price Commission has so far managed to avoid widespread criticism, except on the issue of food prices over which the Commission has only limited jurisdiction. Aside from public reaction, another reason for thinking that controls will not disappear soon is that inflationary pressures are likely to become more intense as the economy comes closer to capacity operation. If there is a case for controls when unemployment is around 6 per cent, it will be even stronger if unemployment drops to a more sustainable level. Unlike the control programs imposed in wartime, the present program has no natural termination point. The view that the present controls will be effective mainly by bringing about a reversal in inflationary psychology is not likely to be substantiated unless inflation can be curtailed much more drastically than official pronouncements suggest. A reduction in the inflation rate from 4 per cent to 3 per cent, while welcome, will scarcely allay widespread apprehension about large budget deficits and rapid monetary expansion. In fact, the belief that sheer psychology, as opposed to expectations based on experience, plays an important role in the inflationary process does not appear to be supported by any evidence. Unless real output can be made to grow at a much higher rate than has so far been achieved, the rapid growth in the money supply combined with the usual lags virtually guarantees the preservation of inflationary pressures well into 1973, if not longer.1 A recent Brookings study (Schultze et al. 1972, especially chapter 13) suggests that the Federal budget will not be a restraining influence either. If this prognosis for controls is correct, the question is what they will actually achieve. Even if attained, the modest reduction in the inflation rate officially set as a goal provides only weak justification for this drastic departure from our generally successful economic traditions. There is some indication that the Pay Board and Price Commission will serve less as a means of curtailing inflation than as watchdogs over big business and big labor. The three-tier classification of business firms by the Price Commission is one indication in this direction, and it has been further reinforced by the recent exemption of most small enterprices from price and wage controls. The Pay Board and the Construction Industry Stabilization Committee already spend most, if not all, of their time on organized labor. There is indeed a case for better supervision of the labor unions. In the last few years we