Chapter

III Velocity of Money and the Practice of Monetary Targeting: Experience, Theory, and the Policy Debate

Author(s):
International Monetary Fund
Published Date:
January 1986
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Over much of the past decade, monetary policies in most of the major industrial countries have been oriented toward controlling the growth rates of monetary aggregates as a medium-term strategy for bringing down inflation. Although inflation rates rose considerably during the late 1970s, substantial declines since 1980 stand as evidence of an increased commitment to price stability. Indeed, by 1985, the average rate of consumer price inflation in the seven major industrial countries had been reduced to one third of the peak rate in 1980, and to half of the average rate for the decade through 1977.

In their attempts to achieve greater price stability, however, central banks have exercised considerable discretion to deviate from or adjust their monetary targets, instead of following the “monetarist prescription” of precommitting themselves and adhering rigidly to money supply rules.1 Most central banks have exercised discretion to adjust, de-emphasize, or abandon their targets in response to financial innovations and deregulation, which have introduced new instruments to serve as money or money substitutes, with significant unanticipated effects on the relationships between the targeted monetary aggregates and variables such as nominal gross national product (GNP). Discretion has also sometimes been exercised during periods in which unanticipated exchange rate developments have created concerns about the external influences on output and inflation.

This paper examines the behavior of velocity and the practice of monetary targeting in seven major industrial countries—Canada, the Federal Republic of Germany, France, Italy, Japan, the United Kingdom, and the United States. Its purpose is to provide a background for reassessing the practice of monetary targeting, in light of both the experiences of the past decade and the theoretical foundations that have been developed for understanding the behavior of velocity and the different channels through which monetary policy may influence output and other real variables. Those experiences and theoretical foundations have led to different views on the appropriate conduct of monetary policy. Without supporting any particular position, this paper concentrates on clarifying the empirical perspectives and theoretical assumptions that lead to the different conclusions.

The empirical data and experiences are examined in the first major part of the paper. A review of statistical evidence, based on quarterly data for 1974–85, provides two types of perspective. The first is given by data on the variability of the velocities of different monetary aggregates within countries, of similar monetary aggregates across countries, and of particular monetary aggregates during different time periods. The second statistical perspective is provided by the correlations across countries between the variability of monetary growth and the variabilities of both real GNP growth and inflation rates over the twelve-year sample period, and also over each of several four-year subperiods.

The focus on statistics alone can be misleading, however, without an understanding of the macroeconomic interrelationships among prices, output, and money. In particular, the statistical focus does not show how much the variability of velocity has been an “exogenous” development that led central banks to exercise their discretion to deviate from announced targets, or how much the exercise of central bank discretion may itself have “caused” velocity to become more variable.

Additional empirical perspective is provided by a review of the macroeconomic conditions that individual central banks have experienced in pursuing their monetary targets over the past decade. While the period since 1980 has witnessed a decline in inflation in each of the seven major industrial countries, this period has also encompassed extensive changes in exchange rates, nominal and real interest rates, output, and unemployment. Thus, some authorities have been inclined to orient their policies more closely to movements in variables other than the inflation rate.

The renewed focus in recent years on short-term movements in exchange rates, interest rates, output, and unemployment raises the issue of the extent to which the monetary authorities can pursue short-term objectives for such variables without jeopardizing the credibility of their long-term commitment to an anti-inflation policy. Currently, two policy questions in particular appear to be extremely relevant for the conduct of monetary policy: (1) to what extent can monetary policy be used to affect real variables in the short run?; and (2) are attempts to achieve short-run objectives for real variables likely to result in higher levels of inflation over the long run?

The second major part of the paper reviews the theoretical models that have been developed to address these issues by presenting alternative “views of the world” and discussing their implications for monetary policy. Since different views are held by different economists and policymakers, it may not be surprising that the debate over the appropriate conduct of monetary policy has not been resolved. But the debate has also been confused by inadequate recognition of the strengths and limitations of alternative analytic frameworks, and by misperceptions of the types of theoretical models and assumptions that support different conclusions. To reduce this confusion, and to raise awareness of the main issues in the debate, the paper provides a streamlined presentation and comparison of the different theoretical approaches.

Three different theoretical approaches have been developed for analyzing the behavior of velocity and addressing the issue of whether central banks should exercise discretion, aim at fixed targets, or follow activist countercyclical rules. One approach has concentrated on simple or extended models of the demand for money. These models are, however, subject to the general criticism that the level of output, the interest rate and, in some cases, the price level are taken as exogenous, even though the influence of the central bank on those variables may be quite important for understanding the variability of velocity and for drawing inferences about the appropriate conduct of monetary policy. A second approach has analyzed velocity within a complete macroeconomic model, but under the assumption that expectations about future price levels or inflation rates are formed adaptively (as weighted averages of the current and past values of those variables).

The third approach, which has played a central role in reformulating the theory of monetary policy in recent years (and which accordingly receives predominant attention in this study), has gained appeal for its assumption that expectations about inflation and other endogenous variables are rational and forward-looking, in the sense that they incorporate relevant information about the structure of the economy and the expected future values of exogenous variables, including the stance of monetary policy. These models do not assume that economic agents have complete information, but do assume that central banks do not have superior information to other economic agents. The analysis of several different types of complete macroeconomic models has shown that conclusions based on the assumption of adaptive expectations can be modified in a situation where market participants are assumed to be “rational.” Specifically, in contrast to conclusions drawn from the adaptive expectations hypothesis, the rational expectations assumption provides a theoretical case both against central bank discretion in general, and against countercyclical monetary policy in economies in which prices adjust rapidly. Thus, the view that is taken of the expectations-formation process is central to the debate about how monetary policy should be conducted.

The third major part of the paper collects together the main arguments in the policy debate, including a discussion of the pros and cons of alternative types of variables that might be adopted as intermediate targets in designing monetary policy rules. One central issue from which the theoretical analysis has abstracted is the extent to which any theoretical or empirically estimated “model” can provide an adequate characterization of market behavior. It has been argued that insofar as economic behavior shifts over time or cannot be precisely estimated empirically, the case against central bank discretion is weaker than the rational expectations models suggest. Indeed, the predominant challenge to the theoretical case for central bank rules has been the argument that the difficulty of anticipating major shifts in economic relationships or disruptions to macroeconomic conditions implies that a rule would be practically impossible, socially undesirable, and politically infeasible to implement in a credible way.

Data and Experience

Variability of Velocity

The velocity of money is defined in terms of three important macroeconomic variables: the price level, the level of real output, and the money supply.2 Velocity may vary whenever the price level or the supply of output are influenced by factors that do not have contemporaneous and offsetting influences on the money supply, or whenever autonomous changes in the money supply are not reflected in contemporaneous and proportionate changes in the nominal value of output. An understanding of the observed variability of velocity requires an understanding of the exogenous sources of changes in prices, output, and money, and of the time it may take for a change in any one of those variables to influence the others through the responses of private economic agents and policy authorities. This study pursues such an understanding by providing reviews of both the macroeconomic conditions that central banks have confronted during the past decade and the different classes of analytic models that have been developed to explain the observed data. Before turning to these reviews several sets of data are examined. An important distinction should be drawn between factors that have systematic and predictable influences on velocity and factors that influence velocity in random or unpredictable ways. Variability of velocity that is predictable does not, in principle, cause any difficulty for a monetary-targeting approach.

Chart 11 shows the velocities of a number of monetary aggregates for the seven major industrial countries. Throughout this paper the definitions of the monetary aggregates are those used by the national authorities in each country.3 The chart shows that each of the seven countries has experienced pronounced shifts in trend or sharp variations around trend for one or more of its velocity measures since the early 1970s.

Chart 11.Major Industrial Countries: Velocities of Monetary Aggregates, 1970–85

(Indices, first quarter 1973 = 100)
(Indices, first quarter 1973 = 100)
(Indices, first quarter 1973 = 100)

Note: For definitions of monetary aggregates, see the note to Table 32.

The variability of a data sample around its trend can be measured by the standard proportionate deviation of the sample observations around a simple trend line.4 A focus on proportionate deviations is required to allow meaningful comparisons of the variability of narrow money velocity (with a relatively high average value) and broad money velocity (with a relatively low average value). Values of this variability index are shown in Table 32 for each of the velocity series. The focus is on the 1974–85 period, and the sample period has been divided into thirds in order to examine whether variability has increased or declined over time.5

Table 32.Major Industrial Countries: Variability Levels for Velocity, 1974–85
1974–851974–771978–811982–85
Canada
M10.0370.0240.0210.019
M1A0.0800.0270.0170.045
M20.0290.0170.0120.015
M30.0720.0150.0200.019
France
M1R0.0180.0180.0120.009
M2R0.0230.0130.0110.008
Germany, Fed. Rep. of
Central bank money0.0140.0110.0100.009
M10.0390.0230.0180.018
M20.0290.0260.0120.010
Italy
M10.0440.0260.0320.016
M20.0520.0290.0310.016
Japan
M10.0210.0150.0300.009
M2 + CDs0.0110.0080.0110.006
United Kingdom
M00.0270.0170.0200.013
M10.0640.0280.0300.017
£M30.0820.0240.0370.012
United States
M10.0400.0070.0100.019
M20.0330.0090.0130.018
M30.0280.0080.0110.012
Note: The variability levels correspond to the standard proportionate deviations of velocity around its trend for the relevant period or subperiod. Specifically, if vt denotes the observed value of velocity in quarter t and v¯t denotes the trend value of velocity, the variability levels correspond to standard deviations of (vtv¯t)/v¯t.Definitions of the monetary aggregates are those used by the national authorities in each country. The narrow M1 aggregates are generally defined as currency plus domestic demand deposits, while the more broadly defined M2 and M3 concepts add to M1 domestic savings deposits and various managed liabilities of banks and other financial institutions. In Canada, M1A includes daily interest-bearing checkable accounts and nonpersonal notice deposits, in addition to the components of M1 (currency and noninterest bearing demand deposits). In France, M1R and M2R refer to the money holdings of residents; an elaboration is provided in the text. In Germany, central bank money comprises currency held by nonbanks and a weighted average of banks’ deposits, with the weights based upon required minimum reserves calculated at constant (January 1974) ratios; currency in circulation has a weight of 100 percent, sight deposits have a weight of 16.6 percent, time deposits 12.4 percent, and savings deposits 8.1 percent; and only time deposits and savings deposits of less than four-year maturity are included in the latter two categories. In Japan, M2 + CDs comprises currency in circulation, demand deposits, time deposits, and certificates of deposits. In the United Kingdom, M0 is the wide monetary base, defined as banks’ holdings of cash, plus banks’ operational balances at the Bank of England, plus notes and coin. Reference is made elsewhere in the paper to PSL2 in the United Kingdom, which comprises sterling M3 (excluding deposits maturing in more than two years), money market instruments (treasury bills, bank bills, and deposits with local authorities and finance houses), certificates of tax deposit, building society shares and deposits, and other similar forms of liquid savings instruments.
Note: The variability levels correspond to the standard proportionate deviations of velocity around its trend for the relevant period or subperiod. Specifically, if vt denotes the observed value of velocity in quarter t and v¯t denotes the trend value of velocity, the variability levels correspond to standard deviations of (vtv¯t)/v¯t.Definitions of the monetary aggregates are those used by the national authorities in each country. The narrow M1 aggregates are generally defined as currency plus domestic demand deposits, while the more broadly defined M2 and M3 concepts add to M1 domestic savings deposits and various managed liabilities of banks and other financial institutions. In Canada, M1A includes daily interest-bearing checkable accounts and nonpersonal notice deposits, in addition to the components of M1 (currency and noninterest bearing demand deposits). In France, M1R and M2R refer to the money holdings of residents; an elaboration is provided in the text. In Germany, central bank money comprises currency held by nonbanks and a weighted average of banks’ deposits, with the weights based upon required minimum reserves calculated at constant (January 1974) ratios; currency in circulation has a weight of 100 percent, sight deposits have a weight of 16.6 percent, time deposits 12.4 percent, and savings deposits 8.1 percent; and only time deposits and savings deposits of less than four-year maturity are included in the latter two categories. In Japan, M2 + CDs comprises currency in circulation, demand deposits, time deposits, and certificates of deposits. In the United Kingdom, M0 is the wide monetary base, defined as banks’ holdings of cash, plus banks’ operational balances at the Bank of England, plus notes and coin. Reference is made elsewhere in the paper to PSL2 in the United Kingdom, which comprises sterling M3 (excluding deposits maturing in more than two years), money market instruments (treasury bills, bank bills, and deposits with local authorities and finance houses), certificates of tax deposit, building society shares and deposits, and other similar forms of liquid savings instruments.

As a general phenomenon, it may be noted that the variability levels for the three subperiods tend to be lower than the corresponding variability levels over the entire sample, consistent with the fact that trends in the velocity series have shifted. Few of the series exhibited significantly higher variability levels during 1982–85 than in earlier subperiods, with the notable exceptions of MIA in Canada and M1 and M2 in the United States. Within the 1982–85 subperiod, the velocities of broad money (M2 and M3) were less variable than the velocities of M1 in all countries except Italy (where M1 and M2 velocities were equally variable); in addition, the velocities of M1 were more variable than the velocities of central bank money in Germany and MO in the United Kingdom. Over the entire 1974–85 period, the velocities of M2 + CDs in Japan and central bank money in Germany exhibited the lowest variability levels, although it is evident from Chart 11 that the series for Japan was more variable over the period extending back to 1970.

In addition to focusing on the variability of velocity from quarter to quarter, it may be interesting to examine whether relative stability in monetary growth over periods of several years or longer has been associated with relatively stable rates of output growth and inflation. Chart 12 shows percentage changes in real GNP, the GNP deflator, and the money supply over the same period for each of the seven countries. (For each country the chart shows the monetary aggregate that either has served longest as a target or appears to have received predominant attention in recent years.) Some associations in the relative degrees of stability of the various series are visually evident from the chart. A summary of the associations can be provided by calculating correlation coefficients between the variability levels of real GNP growth, inflation, and money growth. It should be emphasized, however, that such correlations do not isolate the causes of any associations. Strong positive correlations might indicate that variability in the money supply had a strong influence in generating variability of prices and output, or it might reflect a process by which price or output variability led to money supply variability through the reactions of central banks, as policymakers shifted their policy stance in an attempt (less than fully successful) to stabilize price and output fluctuations. Or, as a third possibility, it might reflect the simultaneous response of those variables to changes in other factors.

Chart 12.Major Industrial Countries: Money, Real GNP, and the GNP Deflator, 1975–85

(Change from the corresponding quarter of the preceding year, in percent)
(Change from the corresponding quarter of the preceding year, in percent)
(Change from the corresponding quarter of the preceding year, in percent)
(Change from the corresponding quarter of the preceding year, in percent)

Table 33 provide summary measures of the variability of output growth, price inflation, and money growth over the 1974–85 period and within each of the four-year subperiods. Table 34 provides some corresponding correlation coefficients, both between the variability of output growth and the variability of money growth and between the variability of price inflation and the variability of money growth. The data in Table 34 indicate that the degrees of variability in both real output growth and inflation were positively correlated with the degree of variability in money growth across the seven countries during the 1974–85 period and during the most recent two subperiods.6 Along the same lines, it may be noted from Table 33 that the four countries in which money growth was least variable during the 1974–85 period (namely, the Federal Republic of Germany, the United States, Japan, and France) include the three countries in which real GNP growth was least variable (Japan, France, and Germany) and the three countries in which inflation was least variable (Germany, France, and the United States).

Table 33.Major Industrial Countries: Variability of Growth Rates of Money, Real GNP, and the GNP Deflator, 1974–85
1974–851974–771978–811982–85
Canada
M10.0470.0430.0350.045
Real GNP0.0290.0220.0130.043
GNP deflator0.0360.0310.0210.033
France
M2R0.0300.0240.0130.016
Real GNP0.0180.0210.0190.008
GNP deflator0.0220.0200.0130.029
Germany, Fed. Rep. of
Central bank money0.0200.0140.0220.014
Real GNP0.0230.0300.0200.019
GNP deflator0.0160.0180.0060.012
Italy
M20.0460.0250.0510.026
Real GNP0.0350.0480.0310.018
GNP deflator0.0390.0360.0290.037
Japan
M2 + CDs0.0240.0170.0170.009
Real GNP0.0090.0060.0060.009
GNP deflator0.0550.0650.0120.007
United Kingdom
£M30.0350.0070.0160.024
Real GNP0.0240.0230.0290.012
GNP deflator0.0680.0630.0420.013
United States
M20.0230.0320.0080.019
Real GNP0.0310.0330.0240.038
GNP deflator0.0230.0170.0100.013
Note: The variability levels represent standard deviations of rates of growth over four quarters. Specifically, if xt, corresponds to the level of the money supply, real GNP, or the GNP deflator in quarter t, the variability level for the growth rate of x is computed as the standard deviation of (xtxt – 4)/xt–4 over the sample or subsample period.
Note: The variability levels represent standard deviations of rates of growth over four quarters. Specifically, if xt, corresponds to the level of the money supply, real GNP, or the GNP deflator in quarter t, the variability level for the growth rate of x is computed as the standard deviation of (xtxt – 4)/xt–4 over the sample or subsample period.
Table 34.Major Industrial Countries: Correlations Between the Variability Levels for the Growth Rates of Money, Real GNP, and the GNP Deflator, 1974–85
1974–851974–771978–811982–85
Between money and real GNP0.5080.1710.2450.687
Between money and the GNP deflator0.311–0.4890.3430.659

Central Bank Experience with Monetary Targeting

A different perspective on the behavior of velocity is provided by the macroeconomic conditions and policy difficulties that central banks have confronted during the periods in which they have used monetary targets. These periods date back to 1975 for the United States, the Federal Republic of Germany, and Canada (although Canada abandoned the practice in 1982), to 1976 for the United Kingdom, and to 1977 for France. Italy and Japan have not adopted monetary targets, although in Italy economic policy has been based on plans that include projections for a range of monetary and credit aggregates, and since 1978 Japan has announced in the first month of each quarter a projection for the year-on-year growth of broad money measured from the same quarter of the previous year.

Table 35 sets out the target growth ranges that central banks have announced, along with the actual outcomes for the targeted aggregates. The United States and, at times, the United Kingdom, have had targets for more than one aggregate simultaneously. However, both countries have changed the relative priorities attached to the different targets. In particular, the United States has announced twice in recent years (during the second half of 1982 and the fourth quarter of 1985) that its M1 target would be de-emphasized, whereas the United Kingdom maintained targets for M1 and PSL2 for only two years, and chose to de-emphasize its sterling M3 target during the course of 1985.

Table 35.Major Industrial Countries: Targets and Outcomes for Monetary Growth Rates, 1975–85
19751976197719781979198019811982198319841985
Canada1
M1target10.0–15.08.0–12.07.0–11.06.0–10.05.0–9.04.0–8.04.0–8.0
outcome10.98.39.28.06.23.93.5
France2
M2, M2Rtarget12.512.011.011.010.012.5–13.59.05.5–6.54.0–6.0
outcome13.912.214.49.811.411.510.27.66.9
Germany, Fed. Rep. of3
CBMtarget8.08.08.08.06.0–9.05.0–8.04.0–7.04.0–7.04.0–7.04.0–6.03.0–5.0
outcome9.99.39.011.46.44.83.56.17.04.64.5
United Kingdom4
M3, £M3target9.0–13.09.0–13.08.0–12.08.0–12.07.0–11.06.0–10.08.0–12.07.0–11.06.0–10.05.0–9.0
outcome7.315.411.410.319.412.811.29.511.916.5
M1target8.0–12.07.0–11.0
outcome12.314.0
PSL2target8.0–12.07.0–11.0
outcome11.512.6
M0target4.0–8.03.0–7.0
outcome5.73.3
United States5
M1target5.0–7.54.5–7.54.5–6.54.0–6.53.0–6.04.0–6.53.5–6.02.5–5.54.0–8.04.0–8.04.0–7.0
outcome5.35.87.97.25.57.32.38.510.05.211.9
M2target8.5–10.57.5–10.57.0–10.06.5–9.05.0–8.06.0–9.06.0–9.06.0–9.07.0–10.06.0–9.06.0–9.0
outcome9.710.99.88.78.39.69.59.28.37.78.6
M3target10.0–12.09.0–12.08.5–11.57.5–10.06.0–9.06.5–9.56.5–9.56.5–9.56.5–9.56.0–9.06.0–9.5
outcome12.312.711.79.58.110.211.410.19.710.57.4
Note: Annualized growth rates with outcomes corresponding to the target periods, except where indicated in the following footnotes. Definitions of the monetary aggregates are those used by the national authorities in each country; see the note to Table 32. Aggregates with identical labels are comparable but not identical across countries, and in some cases countries have modified the coverage of their monetary aggregates over time. In such cases, the numbers in the table correspond to the definitions existing during each indicated period.

For Canada, the targets indicated for the years 1976–80 are the annualized target growth rates announced for the periods beginning, respectively, in the second quarter of 1975, February–April 1976, June 1977, June 1978, and the second quarter of 1979. The targets indicated for the years 1981 and 1982 correspond to the objective announced for the period beginning in August–October 1980 which continued to apply until the practice of monetary targeting was discontinued in November 1982. Outcomes correspond to annualized actual rates of growth between the beginning of successive target periods, except for 1981, which is an annualized rate from August–October 1980 through December 1981, and for 1982, which is from December 1981 through December 1982. The somewhat arbitrary assignment of target periods and outcomes to calendar years has been adopted from the Bank for International Settlements, 53rd Annual Report, June 1983, p. 71.

For France, the target periods are from December to December for the years through 1982, and from November–January averages to November–January averages for subsequent years. The target was specified for M2 from 1976 through 1983 and for M2R in 1984 and 1985; see the text for further discussion of the monetary definitions for France.

For Germany, the 1975 target is for the rate of growth from December 1974 through December 1975; the targets during 1976–78 are for rates of growth on an annual average basis; and beginning in 1979 the targets are for rates of growth between the fourth quarter of the previous year and the fourth quarter of the target year.

For the United Kingdom, the targets are for periods beginning in April for each year from 1976 through 1978, in June 1979, and in February for subsequent years. For 1980 through 1984, the outcomes are annualized rates for 14-month periods from February of the target year through April of the following year. For 1985, the outcomes are for the 12 months through April 1986. A target for M3 was set only in 1976; thereafter the indicated targets and outcomes are for sterling M3.

For the United States, target growth ranges correspond to annual percentage changes from the fourth quarter of the previous year through the fourth quarter of the target year, except in 1975, for which the target period was from March 1975 through March 1976, and for the M2 target in 1983, which was from the February–March average through the fourth quarter. The targets also correspond to objectives set around the beginning of the target year, rather than any tentative objectives indicated earlier or any revisions of the objectives during the target year. In February 1980, the U.S. monetary aggregates were redefined, and for 1980 and 1981 the M1 targets in the table are those for M1–B and shift-adjusted M1–B, respectively; M1–B was relabeled M1 in January 1982. Outcomes correspond to actual rates as reported at the ends of the policy periods.

Note: Annualized growth rates with outcomes corresponding to the target periods, except where indicated in the following footnotes. Definitions of the monetary aggregates are those used by the national authorities in each country; see the note to Table 32. Aggregates with identical labels are comparable but not identical across countries, and in some cases countries have modified the coverage of their monetary aggregates over time. In such cases, the numbers in the table correspond to the definitions existing during each indicated period.

For Canada, the targets indicated for the years 1976–80 are the annualized target growth rates announced for the periods beginning, respectively, in the second quarter of 1975, February–April 1976, June 1977, June 1978, and the second quarter of 1979. The targets indicated for the years 1981 and 1982 correspond to the objective announced for the period beginning in August–October 1980 which continued to apply until the practice of monetary targeting was discontinued in November 1982. Outcomes correspond to annualized actual rates of growth between the beginning of successive target periods, except for 1981, which is an annualized rate from August–October 1980 through December 1981, and for 1982, which is from December 1981 through December 1982. The somewhat arbitrary assignment of target periods and outcomes to calendar years has been adopted from the Bank for International Settlements, 53rd Annual Report, June 1983, p. 71.

For France, the target periods are from December to December for the years through 1982, and from November–January averages to November–January averages for subsequent years. The target was specified for M2 from 1976 through 1983 and for M2R in 1984 and 1985; see the text for further discussion of the monetary definitions for France.

For Germany, the 1975 target is for the rate of growth from December 1974 through December 1975; the targets during 1976–78 are for rates of growth on an annual average basis; and beginning in 1979 the targets are for rates of growth between the fourth quarter of the previous year and the fourth quarter of the target year.

For the United Kingdom, the targets are for periods beginning in April for each year from 1976 through 1978, in June 1979, and in February for subsequent years. For 1980 through 1984, the outcomes are annualized rates for 14-month periods from February of the target year through April of the following year. For 1985, the outcomes are for the 12 months through April 1986. A target for M3 was set only in 1976; thereafter the indicated targets and outcomes are for sterling M3.

For the United States, target growth ranges correspond to annual percentage changes from the fourth quarter of the previous year through the fourth quarter of the target year, except in 1975, for which the target period was from March 1975 through March 1976, and for the M2 target in 1983, which was from the February–March average through the fourth quarter. The targets also correspond to objectives set around the beginning of the target year, rather than any tentative objectives indicated earlier or any revisions of the objectives during the target year. In February 1980, the U.S. monetary aggregates were redefined, and for 1980 and 1981 the M1 targets in the table are those for M1–B and shift-adjusted M1–B, respectively; M1–B was relabeled M1 in January 1982. Outcomes correspond to actual rates as reported at the ends of the policy periods.

As Table 35 indicates, monetary targets have been specified sometimes as points and sometimes as ranges of up to 5 percentage points. Because countries have aimed at different targets for different aggregates and under different macroeconomic conditions, it may not be very meaningful to compare their rates of success with hitting the targets they have announced. Nevertheless, it may be noted that Canada missed its announced target range in just one of the first six years, and then only very marginally, before it abandoned monetary targeting in the seventh year.7 France held its monetary growth to within 1½ percentage points of its (point) target, or of the center of its relatively narrow target range, in six out of nine years. Germany exceeded its target by nearly 3½ percentage points in 1978, but hit or fell below its target in each subsequent year. And the United Kingdom and the United States each hit their target ranges about half of the time.

Although central banks cannot control their monetary aggregates precisely, an outcome of deviating from the center of a target range by as much as 1 or 2 percentage points over a period as long as a year can probably be considered as largely a matter of central bank discretion. A review of the individual experiences of central banks in different countries reveals a variety of reasons that they have chosen in some cases to aim either high or low in their target ranges, and in some cases to miss or modify the targets that they had previously announced.

In the Federal Republic of Germany, the Bundesbank has on several occasions been concerned with relieving the impact of exchange rate developments on domestic inflation and real activity. The role of exchange market pressures in affecting the behavior of velocity and creating a dilemma for the Bundesbank is illustrated by experiences in 1977–78 and 1980–81. In the first period, the predominant pressures came from the exchange rate of the deutsche mark against the U.S. dollar. The mark appreciated about 20 percent against the dollar from the middle of 1976 through the middle of 1978, and roughly 10 percent more during the second half of 1978. Partly in association with such exchange market developments, real activity growth slowed and inflation rates declined in Germany.8 The Bundesbank held the growth of central bank money fairly close to its target in 1977 and the first half of 1978, but permitted a sharply increased pace of money growth after the middle of the latter year in response to external pressures. In its December 1978 Report, the Bundesbank explained its policy as follows:9

In recent months the Bundesbank’s policy has mainly been guided by the need to take account of the extremely unstable situation in the exchange markets …. on several occasions, under the prevailing domestic and external conditions it was extremely difficult for the Bundesbank to curb monetary growth. A switch to a more restrictive monetary policy seemed inappropriate as long as the economic upswing had not taken more definite shape.

The opposite experience occurred several years later. From the end of 1979 through February 1981, the mark depreciated more than 20 percent against the dollar, close to 25 percent against the pound, and more than 30 percent against the yen. Consistent with these depreciations, the domestic inflation rate began to rise in Germany and the Bundesbank chose to aim for central bank money growth around the lower limits of its target ranges in both 1980 and 1981. In its March 1981 Report, the Bundesbank explained its policy as follows:10

The final objective of … [monetary policy] is to maintain price stability. The formulation of the monetary growth target and the measures taken to achieve this target are an “intermediate” objective. It is important in this connection to pay attention to the balance of payments and the exchange rate of the Deutsche Mark as well because, in the prevailing circumstances, it is not possible to defend the value of money in the domestic economy while disregarding the special influences that may proceed from the external value of the currency. If, as hitherto, inflationary tendencies can largely be kept out of Germany, the principal condition for sound long-term economic growth and for a high level of employment will be safeguarded.

The experience in Canada illustrates the difficulties of relying on a monetary targeting strategy during a period of financial innovations. Until late 1982, the Bank of Canada operated with a target for its M1 aggregate, and through 1980 it consistently announced and hit a sequence of progressively lower target ranges. Shortly after the period of monetary targeting began, however, the authorities were apparently confronted with a shift in the demand for money related to innovations in cash management accounts for businesses. This development made it difficult to judge the degree of monetary restraint implied by the target settings, and these difficulties were compounded by inflationary pressure arising from the sharp increases in oil prices. In retrospect, the degree of monetary restraint was insufficient to keep the cost-price spiral from accelerating. During 1977 and 1978, the Canadian dollar depreciated against the U.S. dollar, even with U.S. inflation on the rise, and in 1979 Canadian inflation began to escalate (see Chart 12).

Starting in late 1980, Canadian monetary policy was tightened considerably. However, continuing financial innovations, which were induced to some extent by the high levels of inflation and interest rates in Canada, generated further instability in the relationship between M1, nominal income, and interest rates. The shift of funds out of accounts included in M1 (currency and non-interest-bearing demand deposits) resulted, after mid-1981, in a relatively sharp divergence between the growth rates of M1 and M1A (which includes interest-bearing checkable deposits and nonpersonal notice deposits). M1 velocity increased, M1A velocity declined, and the Bank of Canada was led to conclude that since neither “the process of financial innovation” nor “the response of bank customers” could be reliably predicted, “appropriate ranges for the future growth of M1 cannot be chosen with any confidence.”11 For the same reasons, it was felt that M1A would also be an unreliable guide. Moreover, while the broader aggregates, such as M2, seemed to be less affected by financial innovations, in the view of the Bank of Canada the problems of controllability and interpretation were sufficiently great to make those aggregates unsuitable as well as intermediate targets for conducting monetary policy.

The Canadian experience through 1982 indicates that the consistent achievement and progressive lowering of monetary targets provides no guarantee that inflation rates will decline. Since the end of 1982, Canada has followed a different approach to monetary policy, based on a variety of economic and financial indicators, including in particular the exchange rate between the Canadian and U.S. dollars. In following such an eclectic approach, the Bank of Canada has described its “ultimate guiding objective” as “the achievement of long-term price stability,” has stressed that it has not set an exchange rate target because it is not possible to know in advance what a sensible target path would be, but has emphasized that “the appropriate approach of monetary policy to the exchange rate is to resist sharp exchange rate declines that threaten to undermine our progress on inflation.”12

In France, monetary policy objectives have been stated in the form of simple target numbers or relatively narrow target ranges for the growth of M2 (from 1977 through 1983) or M2R (in 1984 and 1985). The shift from M2 to M2R narrowed the definition of the targeted aggregate to one that included only the M2 holdings of resident nonfinancial agents; the French definition of M2R therefore corresponded more closely to the definitions of M2 that were used in most other major industrial countries.

Although the French authorities announced simple target numbers for monetary growth during the 1977—81 period, in each of those years except 1979, the growth of the M2 aggregate was held within 1.5 percentage points of its target and would thus have fallen within the types of ranges announced by most other countries. As in Canada, however, that achievement did not prevent inflation rates from rising. One factor contributing to the rise in inflation was the substantial increase in oil prices.

Since the middle of 1982, French inflation rates have declined considerably. French M2R growth has also declined (Chart 12), although it has remained above its target levels and might have been higher still during recent years in the absence of financial innovations. In particular, deposit balances have been withdrawn in quite significant amounts in recent years to purchase new types of liquid short-term mutual and investment funds, which banks have been offering to the public since late 1981, but which are not included in the M2R concept that was targeted during 1984–85. These funds have been invested predominantly in variable rate bonds or bonds nearing maturity, and apparently a perception that the capital risks of such assets are limited has made them attractive substitutes for other forms of liquid savings. Partly as a consequence of the implications of these developments for the interpretation of the aggregates, the Bank of France announced in November 1985 that it would redraw its monetary definitions to shift from a classification based on institutional criteria to a new system based on the nature and the substitutability of the financial assets involved. Subsequently, the authorities have adopted a redefined concept of M3 as the target aggregate for 1986. (The redefined M3 consists of currency plus the deposits of resident nonfinancial agents at financial institutions (including term deposits, certificates of deposit, and foreign-currency deposits) plus repurchase agreements and short-term bonds (bons).)

As in other countries, the experience with monetary targeting in the United Kingdom illustrates the difficulties of setting policy during a period of extensive financial liberalization when different monetary aggregates are expanding at different rates. The U.K. authorities first announced a monetary target for the M3 aggregate in 1976; in 1977 they shifted to specifying a target for sterling M3. Under the Conservative Government that came to power in 1979, monetary targeting has been a centerpiece of the medium-term financial strategy. The strategy has involved the announcement of target ranges for sterling M3 for several years ahead, with a stated goal of progressively slowing its rate of expansion. The removal around mid-1980 of the supplementary special deposits scheme (the “corset”), which had restricted the deposit-taking activities of banks, contributed to a substantial overshooting of the sterling M3 target for 1980, and from mid-1980 onward the velocity of sterling M3 had a downward trend, in contrast to a strong previous uptrend. The budget presented in the spring of 1982 emphasized the difficulties of relying too heavily on sterling M3 as an indicator of monetary policy. Accordingly, in 1982 and 1983 the target for sterling M3 was supplemented with targets for M1 and PSL2. (PSL2 includes deposits at building societies, which are excluded from sterling M3; see the note to Table 32.) The practice of targeting M1 and PSL2, however, was abandoned after two years, in association with financial innovations that had altered the previous relationships of those aggregates with national income. At the same time, the authorities in 1984 adopted a target for M0, the wide monetary base.

Notwithstanding the fact that the targets were overrun for sterling M3 in 1980, 1981, and 1984 (as well as for M1 in 1982 and 1983 and PSL2 in 1983), the progressive lowering of monetary growth over the 1980–84 period contributed to a substantial decline in British inflation (Chart 12). During 1985, the authorities were confronted with conflicting signals from sterling M3, which had been expanding more rapidly than the upper bound of its target growth range, and M0, which was close to the lower bound of its target range. The authorities continued to regard the aim of monetary policy as that of ensuring sustained and steady downward pressure on inflation. Moreover, the Chancellor of the Exchequer, in his October speech at the Mansion House, emphasized that:

… it remains operationally necessary to conduct monetary policy through the use of intermediate targets—taking account of relevant information such as the behavior of the exchange rate—rather than by attempting to target money GDP directly.

At the same time, the British authorities stated their assessment that the recent behavior of sterling M3 had been affected by structural changes and was not inconsistent with declining inflation, given that narrower measures of money had been growing relatively slowly, that the exchange rate was relatively firm, that real interest rates remained high, and that forecasts for business activity did not suggest inflationary pressures. For those reasons, they decided to de-emphasize the sterling M3 target at that time. Subsequently, in announcing monetary objectives for the period from February 1986 through April 1987, the authorities set a target range of 2–6 percent annualized growth for M0, compared with the 3–7 percent range they had set for M0 during the previous period, while raising the target range to 11–15 percent for sterling M3.

In the United States, monetary policy has pursued target growth rates for multiple monetary aggregates since 1975. However, a major shift in monetary strategy was announced in October 1979, and another shift occurred around October 1982.

The performance of the monetary aggregates and inflation during the period prior to October 1979 contributed, in the opinion of some close observers, to an erosion of the credibility of U.S. monetary policy.13 Although M1 growth was held within its target ranges during 1975 and 1976, the Federal Reserve allowed M1 to overrun its targets in 1977 and 1978, and to land in the upper part of its range in 1979. In addition, during each of the latter three years the outcomes for M2 and M3 were either above or in the upper thirds of their target ranges. Moreover, through the beginning of 1979, new one-year targets were adopted every quarter, with a regular practice of rebasing to the outcome for the most recent period, which typically overshot the level specified by the previous target.14

In October 1979, as part of a broad anti-inflation program, the Federal Reserve decided to shift its operating techniques to a procedure that placed greater emphasis on controlling reserves directly through the specification of a “target” path for nonborrowed reserves, thus abandoning its previous procedure of maintaining the interest rate on federal funds within a relatively narrow range.15 In doing so, an “important objective” of the U.S. authorities was “to help convince the public that the Federal Reserve would in practice achieve its monetary targets … and thereby increase the credibility of monetary policy and facilitate the transition to a noninflationary environment.”16 Without question, in the ensuing years U.S. monetary policy regained its credibility by playing a major role in reducing U.S. inflation substantially, yet during each year of the 1980–82 period, the growth rates of M2 and M3 exceeded the upper bands of the initial targets for those years. M1 growth also exceeded its initial targets in 1980 and 1982. Just as the Canadian experience during the late 1970s indicated that adherence to monetary targets could not guarantee lower inflation, the U.S. experience during the early 1980s indicated that monetary policy could contribute to an improved inflation performance even if targets for the monetary aggregates were not achieved.17

The period since October 1979 has been described as one in which the U.S. monetary authorities were:18

… confronted by shifts both in the demand for goods and services, given interest rates, and in the demand for money, given interest rates and income. Downward shifts in the demand for goods and services seemed evident from the psychological impact associated with initiation of the credit control program in early 1980 and during the recession of 1982 when inflationary expectations began to wane; upward shifts appeared as the credit control program was lifted and more recently in the wake of the turn to a quite expansionary fiscal policy. …Meanwhile,…there were widespread institutional and regulatory changes introducing new instruments to serve as money or money substitutes … that also led to shifts in the demand for money relative to historical experience.

Those shifts led to extremely wide fluctuations in interest rates under the operating procedures that had been adopted in October 1979. Partly for that reason, in October 1982 the Federal Reserve again decided to change its operating procedures, this time toward a more judgmental approach based on targeting on borrowed reserves. Since that time, U.S. monetary policy has been exercised with considerable discretion, but “as a continuing struggle to attain and maintain credibility in the face of continuing shocks and disturbances in money, credit, and goods markets.”19

It is noteworthy that the Federal Reserve has been criticized strongly over the past decade both for deviating from and for adhering to its targets. Just as associations have been drawn between the acceleration of inflation and the growth of monetary aggregates above their target ranges prior to October 1979, associations have also been drawn between the depth of the U.S. recession in 1982 and the Federal Reserve’s adherence to its targets during the first half of that year. By the end of 1981, U.S. wage and price inflation had been brought down considerably (Chart 12), and most econometric forecasts predicted moderate activity growth during 1982. Such strength failed to materialize during the first two quarters of the year, however, and the velocities of the U.S. monetary aggregates continued to drop sharply. Critics have argued that the Federal Reserve should have responded sooner than it did to counter the decline in velocity with an increase in monetary growth, particularly with short-term real interest rates in the range of 10 percent per annum. But a substantial reduction in taxes was scheduled to become effective at mid-year, and it was difficult to predict what impact the fiscal stimulus would have on economic activity. By contrast, in the second half of 1982, the Federal Reserve changed its policy stance, allowing U.S. interest rates to decline sharply by permitting M2 and M3 to grow rapidly and to exceed the upper limits of their target ranges for the year as a whole.20 The recession continued through the fourth quarter, however, and the recovery did not gain strength until the second quarter of 1983.

During 1985, the Federal Reserve faced the choice of how to react to M1 growth considerably in excess of its target range. Although the economy was not in a recession, as it had been in the first half of 1982, signs of economic activity growth and inflationary pressures did not appear to be strong, and velocity levels had dropped significantly. Accordingly, in July the Federal Reserve rebased its M1 target at a higher level and also widened the target range. By the fourth quarter, M1 velocity had dropped even more, and the members of the Federal Reserve policy committee agreed at their November meeting that:21

… the behavior of M1 needed to be judged in the context of the performance of the economy and the fact that the broader aggregates were growing at rates within their ranges. Under prevailing circumstances, and unless the dollar declined sharply further, the strength of M1 thus far did not appear to suggest strong inflationary consequences.

Accordingly, it was decided that growth of M1 above its revised target range would be acceptable for the second half of the year.

Lessons from Experience

There is disagreement over the policy lessons that should be drawn from the observed behavior of velocity and the central bank experience with monetary targeting over the past decade. There are advocates of three different schools of thought. Advocates of passive rules have not been dissuaded by the past decade of experience, but argue that discretion is inherently inflationary and destabilizing, and contend that the difficult choices that central banks have confronted can partly be attributed to the fact that they did not adhere sufficiently closely to the targets they announced. Advocates of activist rules suggest that some of the difficulties confronted by central banks could be alleviated by shifting from the types of fixed monetary targets that have been announced over the past decade to rules that provide an explicit prescription for countercyclical behavior. Advocates of discretion argue that no mechanical rule can respond adequately to all contingencies that may arise.

The sources of these disagreements, and the strengths and weaknesses of the three schools of thought, may be illuminated by a review of the different types of models that have been developed for analyzing the behavior of velocity and for drawing inferences about the appropriate conduct of monetary policy.

Velocity and Monetary Targeting: Theoretical Foundations

As has already been emphasized, a focus on statistics and experience alone cannot isolate the extent to which the variability of velocity has been an “exogenous” development that has led central banks to exercise discretion, or the extent to which the exercise of such discretion may itself have “caused” velocity to become more variable. Because velocity reflects the joint behavior of the price level, the level of real output, and the money stock, the interpretation of the statistics and the central bank experiences requires a focus on the sources of short-term fluctuations in prices, output, and money and the transmission mechanisms through which “exogenous” changes in the money stock can influence prices and output.

This part of the paper provides a streamlined presentation and comparison of the different types of models that have been used to analyze the interrelationships between prices, output, and money and the behavior of velocity. Its purpose is to shed light on important conceptual issues in the debate over the appropriate conduct of monetary policy, which to a considerable extent has been confused by an inadequate recognition of the strengths and limitations of alternative analytic frameworks, and by misperceptions of the types of theoretical models and assumptions that support different conclusions.

Three different approaches have been developed for analyzing the behavior of velocity and for addressing questions about the appropriate conduct of monetary policy. The first approach has concentrated narrowly on the demand for money; however, the lack of a complete framework of analysis (recognizing the endogenous nature of the arguments in the money demand function) limits the usefulness of such models for economies in which income, prices, and money interact simultaneously. A second approach, consisting of the so-called “disequilibrium” models, employs a complete macroeconomic framework and generally bases its analysis on the assumption that expectations about future price levels or inflation rates are formed adaptively (as weighted averages of the current and past values of those variables). The third approach, which has gained increasing attention in recent years, also employs a complete macroeconomic framework, but under the assumption that expectations about inflation rates and other endogenous variables are rational and take account of relevant information about the structure of the macroeconomic system and expectations about the future values of exogenous variables, including the setting of monetary policy. These three approaches are each reviewed separately below.

Demand for Money Framework

In much of the literature, the behavior of velocity has been analyzed in terms of the “demand for money.” A centerpiece of these analyses is the classic specification of the long-run money demand function, in which the demand for real money balances depends (positively) on the level of real income and (negatively) on a measure of the interest rate foregone by holding money.22 Specifically:

where m* = the logarithm of the real demand for money; md = the logarithm of the nominal demand for money; p = the logarithm of the domestic price level; y = the logarithm of real income and output; i = the nominal interest rate; and the parameters βi are positive. The subscript t denotes time. The logarithm of velocity (vt) is simply obtained by subtracting the logarithm of income from both sides of equation (1). Thus:

As a special case of this general formulation, if the income elasticity of the demand for money (β1) happened to equal one, movements in velocity would depend only on movements in the nominal rate of interest. Moreover, velocity would be constant over time if, in addition, the demand for money was insensitive to the interest rate (if β2 = 0). These features are in accordance with one extreme case of the simple Keynes-Hicks IS-LM model, in which prices are assumed to be fixed in the short run and the interest rate provides the transmission mechanism through which the money supply affects the level of output. The extreme case is that in which the demand for money is insensitive to the interest rate (so the LM curve is vertical) but saving and investment are not, and in which the demand for money has a unitary income elasticity. In that case, an increase in the money supply would require income to change proportionately in order to restore equilibrium in both the goods and money markets.23 In such circumstances, velocity would not be affected by the change in the money supply.

While equation (1) has been widely adopted as a description of the long-run demand for money, much of the empirical literature has hypothesized that adjustment costs can result in short-run deviations of actual from desired real money balances. Typically, adjustment costs have been represented simply by adding a lagged dependent variable to equation (1). Thus, a representative short-run money demand function is:24

where a0 = ηβ0; a1 = ηβ1; a2 = ηβ2; and η is a coefficient of adjustment that describes the speed at which an excess demand for or supply of money is eliminated.

Throughout the past decade of monetary targeting, central banks relied heavily on relationships like equation (2) in analyzing the behavior of their monetary aggregates. One difficulty is that the function has kept “shifting” over time; that is, the estimated parameters from fitting equation (2) over a given sample of data have generally led to poor predictions of the behavior of the demand for money, and hence velocity, when extrapolated into the post-sample period. This puzzle has been well documented for the United States, although it is by no means unique to that country.25 An enormous literature has thus emerged, seeking to produce a more stable money demand function by suggesting alternative variables as arguments in the function or by experimenting with alternative estimation techniques and lag structures.

One line of argument for modifying equation (2)—reflecting the central bank experience reviewed in the previous part of the paper—is the “financial innovations” approach. Some economists have argued that the modification of simple velocity functions to recognize institutional developments can improve the explanation of both long-run and short-run movements in velocity.26 The basis for this view is that the introduction of attractive new financial instruments that are close substitutes for the components of a given monetary aggregate will decrease the demand for the aggregate at given levels of income and interest rates and, hence, will increase its velocity. (The velocities of monetary aggregates that include the new financial instruments will similarly decrease.) As has already been discussed, several of the major industrial countries have experienced significant shifts in velocity associated with financial innovations; indeed, such shifts contributed importantly to the Canadian decision to abandon the practice of monetary targeting in 1982, and to the U.S. decisions to shift-adjust their aggregates and de-emphasize M1 in the early 1980s. Note, however, that while sustained changes in the level or trend of velocity might, at least partially, be explained by financial innovations, it is difficult to attribute reversible fluctuations in velocity to financial innovations, since there generally is no reason for the demand for the monetary aggregate ever to shift back to its preinnovation level.27

A second argument for modifying equation (2) is the fact that the nominal money supply for the economy as a whole is controlled by the monetary authorities. Thus, if the public wishes to adjust its real money balances, given the amount of money supplied by the authorities, such adjustment must take place through variations in the price level.28 More specifically, this approach hypothesizes that the current price level will increase relative to the previous period’s price level whenever the level of actual holdings of nominal money balances is greater than the nominal-equivalent level of desired holdings of real money balances evaluated at the price level inherited from the previous period.29 Under that description of the price-adjustment process, the short-run demand for money function is then modified to take the following form:

The only difference between equations (2) and (3) is that the lagged dependent variable of equation (2) has been replaced in equation (3) by a current money supply aggregate deflated by the price level for the previous period, reflecting the hypothesis that the public slowly adjusts its holdings of real money balances through variations in the price level. A fundamental implication of this difference is that the aggregate demand for money equation “is really a model of price adjustment to nominal money supply changes.”30 It should be emphasized, however, that equation (3) is a reduced form model that combines a demand for money function and a price adjustment hypothesis. Moreover, it is possible to obtain the same type of reduced form equation from a large number of models that use equation (1) as one of their structural components. Thus, unstable estimates of equation (3) would not necessarily imply that the demand for money was misspecified, but might reflect instability in other sectors of the economy.

Nevertheless, this approach correctly identifies the endogeneity of the price level and thereby makes a valuable contribution to understanding the behavior of velocity. Indeed, equation (3) implies that velocity depends (negatively) on the contemporaneous level of the money supply; an increase in the money stock in one period does not lead immediately (but only after a lag) to equiproportionate increases in the levels of prices and nominal GNP:

This dependency of velocity on the contemporaneous money stock distinguishes equation (4) from the description of velocity corresponding to equation (2). In equation (4), the money supply is an exogenous variable; so too are the levels of output and the interest rate.

A third reason for modifying equation (2) is to relate the behavior of money demand to exchange rate expectations. It can be argued that, in deciding on their holdings of money denominated in a given currency, individuals take into account not only expected rates of return on domestic-currency-denominated substitutes for domestic money, but also expected rates of return on assets denominated in foreign currencies. The expected rate of change in the exchange rate is then introduced into the model in the form of a relationship between domestic and foreign interest rates. The implied association between the level of money demand and the expected level of the exchange rate is consistent with the fact that central bankers in a number of countries have faced the choice of keeping their monetary aggregates near the centers of their target ranges and accepting undesirable consequences for exchange rates, or of damping undesirable exchange market pressures but moving toward or beyond the bounds of their monetary target ranges; recall the discussion of Germany’s experience.

The development of this line of argument in the literature, however, has not been entirely satisfactory, as is shown in Appendix VIII. This Appendix extends the analysis to show that an increase in the expected rate of depreciation of the domestic currency will raise velocity by making it attractive to hold less domestic currency at given levels of domestic income and interest rates. In particular, the expression for velocity is:

where the parameters b1, b2, b3, and b4 are all greater than zero; DMt and FMt respectively represent the world supplies of domestic and foreign currencies at time t, and et+1e is an expected future level of the exchange rate (in units of domestic currency per unit of foreign currency). As in equation (4), velocity depends negatively on the contemporaneous supply of the domestic currency. But, again, the behavior of velocity is described by a reduced form of a system of equations rather than by a structural money demand function alone. While equation (4) is based on the assumption that the price level is endogenous, equation (5) is derived from a model that takes the behavior of the contemporaneous exchange rate as endogenous.31 However, as in equation (4), the level of income and the interest rate are taken as exogenous, as is the expected future level of the exchange rate. Hence, the short-run interaction between money, income, and the interest rate is not completely explained, even though the nature of that interaction may be quite important for understanding the behavior of velocity.

It is beyond the scope of this study to cover the many other types of “extended” money demand models that have been developed in the literature. In general, however, the foregoing criticisms of the technique of analyzing the behavior of velocity with models that focus narrowly on extended money demand functions rather than on complete macroeconomic models raises an important caveat about their relevance for policy analysis. It is often argued, following Poole (1970), that central banks should adopt a monetary aggregate rather than an interest rate as an intermediate target only if the financial sector of the economy is subject to less variability than the real sector of the economy. Accordingly, empirical evidence that “the demand for money function keeps shifting” would seem to provide support for an interest rate target. The caveat, however, is that the argument is not based on a complete macroeconomic model. When a more extended model is employed, and when expectations are assumed to be rational, it can be shown that, in contrast to Poole’s conclusion, setting an interest rate target can be counterproductive.

Complete Macroeconomic Models with Adaptive Expectations

The need to explain velocity in the context of a more “complete” macroeconomic framework gives rise to the issue of model selection. This section considers a set of models that has become known as the “disequilibrium” framework.32 The focus here is restricted to the most popular class of disequilibrium models, which share two common assumptions: (1) that the process of price adjustment is slow, so that a “disequilibrium” in the money market can affect the level of output in the short run; and (2) that expectations about prices or inflation are formed in an adaptive way, based on current and past values of those variables.33 (The next section will analyze the behavior of velocity in models in which expectations about prices or inflation are rational and forward-looking, taking account of relevant information about the relationships between macroeconomic variables and the expected future courses of policy variables.)

The disequilibrium models under consideration here incorporate a long-run money demand function of the kind described in equation (1). In addition, the models specify an equation describing the aggregate demand for output (in general the supply of output is assumed to adjust instantaneously to satisfy aggregate demand, regardless of the price level), a type of “Phillips curve” equation that determines the short-run behavior of inflation, and an equation that describes the formation of price expectations according to an adaptive errorlearning hypothesis.34Appendix II provides an example of such a model.

This framework explains the interrelations between money, output, and prices (and hence the behavior of velocity) in the following way. After an exogenous change in the money supply, individuals find themselves holding a different level of real money balances than they desire; thus, they revise their expenditure plans and, in doing so, induce a deviation in output from its full employment level. This deviation, however, is temporary; prices will react, although sluggishly, and will in turn influence expectations, generating a dynamic pattern of price and output adjustment that continues until prices have moved to the same extent as money and the disequilibrium in the money and output markets has vanished.

The disequilibrium model that is presented in Appendix II leads to the following reduced form equation for velocity:35

In this equation, the zi are positive coefficients; y* is the “long-run” full employment level of output; Δmt is the contemporaneous rate of growth of the money supply; and Δpt-1 is the previous period’s rate of inflation. Notice that equation (6) describes the behavior of velocity completely in terms of exogenous variables (the money supply and the long-run level of output) or predetermined variables (the past values of the price level). Notice also that equation (6), like equations (4) and (5), shows that a contemporaneous change in the money supply has a negative effect on velocity. Hence, all these equations imply that the variability of velocity is not independent of the behavior of the monetary authorities.

One important feature of this disequilibrium model is that changes in the money supply, even when they are entirely expected, can influence real variables such as the level of output. As will be emphasized in the following section, this type of “effectiveness” of monetary policy has an important policy implication; in particular, it implies that a countercyclical monetary policy rule can be used to dampen the business cycle, even when the rule is known to the public.36

Complete Macroeconomic Models with Rational Expectations

In recent years, economic theory has moved increasingly away from analysis based on the assumption of adaptive expectations toward analysis based on the assumption that expectations are formed rationally, in the sense that agents take account of whatever relevant information is available about the structure of the economy and the values of exogenous or predetermined variables.37 Although the notion that expectations are completely rational is extreme, the hypothesis of rationality is attractive relative to other assumptions about expectations, and the policy implications of the rational expectations assumption have received considerable attention.

Several different types of complete macroeconomic models have been used to address questions about the appropriate conduct of monetary policy under the assumption that expectations are formed rationally. It is now appreciated that the answers to these questions depend critically on the effectiveness of monetary policy, within the different types of models, at generating changes in the short run in the relative prices and other variables that influence the supply decisions of firms and factors of production, which in turn combine to influence the aggregate level of output for the economy as a whole. To illustrate these points, this section first presents a “classical” model in which monetary policy actions can affect the supply of output in the short run only if they surprise the public. The classical model is then used to discuss both the case for a money supply target and the choice of instruments for controlling the money supply. After that, the analysis turns for purposes of comparison to an alternative model in which multi-period labor contracts, or other institutional rigidities, make anticipated monetary policy “effective” in influencing microeconomic supply decisions.

It should be emphasized at the outset that the theoretical conclusions about alternative types of central bank rules, and especially the theoretical case against central bank discretion, have been challenged by arguments that the analytic models oversimplify the stability and predictability of macroeconomic relationships. These arguments will be reviewed later. It should also be emphasized, however, that the models discussed in this paper do not assume that economic agents have complete information about the structure of the economy, but only that private economic agents have as much information as central banks. (In this regard, it should be noted that the results derived from these models are based on the assumption that agents have incomplete information on the current values of economic variables, in particular the general price level.) The section ends with a focus on the implications of incomplete information for the distinction between activist rules and discretion.

A “Classical” Model with Rapid Price Adjustment

In addition to assuming (1) that economic agents are optimizing units that use whatever relevant information is available when forming their expectations about future variables, the classical models hypothesize (2) that the supply of output depends positively on the gap between the current price level and prior expectations of the current price level, and (3) that prices adjust rapidly to allow for continuous clearing in all markets.38Appendix III presents a typical example of such a model. The second assumption, which has been labeled the Lucas aggregate supply relation, is based on the theory that optimizing firms will increase production as the observed prices of their own output rise relative to their expectations about the general price level, on which information becomes available with a lag.39 Under that assumption, only an unexpected increase in the general price level can lead to an increase in the supply of output for the economy as a whole, because only an unexpected rise in the price level may be interpreted by firms (mistakenly) as an increase in the relative prices of the goods they are supplying. The lack of full current information prevents firms from distinguishing between relative and absolute movements of the price level. This is the source of the inverse correlation between inflation and unemployment, as depicted by the Phillips curve, in the classical model. An alternative model, discussed later, relies on a certain type of stickiness in the price-adjustment process, rather than on a current misperception of relative price changes, for influencing the supply decisions of microeconomic agents.

In models based on rational expectations, a forecast for one particular variable takes into account whatever relevant information is available about other variables that are known to affect the behavior of the forecast variable. In a model in which prices adjust rapidly to clear all markets continuously, rational individuals know that changes in the money supply will quickly affect the general price level. Thus, their expectations about the price level depend on their expectations about the money supply. Accordingly, an unexpected increase in the money supply will lead to an unexpected increase in the general price level, which will result in an increase in output. On the other hand, if changes in the money supply are fully anticipated, they will not give rise to any “price surprises” and, hence, will not affect the level of output.

The important implications for monetary policy in this kind of model are derived from the fact that only the unexpected component of the money stock affects the supply of output, and even then only for the short time that it takes firms and other economic agents to perceive that their expectations were incorrect. By contrast, both the expected and the unexpected components of the money supply affect the price level. This is a “typical” result of combining the Lucas aggregate supply relation with the assumption of rational expectations and is “robust” under different specifications of the other equations in the model. Note also that even if the rate of growth of the money supply is anticipated and, therefore, does not affect output, it will nevertheless affect the nominal interest rate through its impact on inflation. This relation follows from the Fisher condition, whereby the nominal rate of interest is equal to the real rate plus the expected rate of inflation.

The example of a classical model that is presented in Appendix III follows the literature in focusing on the case of a closed economy. In the example, the derived solution for velocity takes the following form:

Here, mte is the period t level of the money supply that is expected at the end of the previous period, such that mtmte equals the unexpected component of the money supply; ht is the anticipated rate of growth of the money supply; εt, nt, and ut represent the effects of random disturbances on the demand for money, the demand for output, and the supply of output, respectively; and the ci coefficients are functions of all the structural parameters in the model, reflecting the macroeconomic interrelations across all economic sectors.

The random disturbances in equation (7) reflect the important fact that the world is “stochastic” and, thus, that there are always some influences on economic decisions that cannot be totally captured in a particular model. Unless the contrary is stated, the analysis will assume that the disturbance terms are independent of their previous values.

Equation (7) reflects the fact that an unexpected change in the money stock affects the behavior of velocity through its effects on both the nominal interest rate and the level of output. However, although an unexpected increase in the money supply always increases the level of output, its effect on the nominal rate of interest may be positive or negative, and thus its overall effect on velocity is ambiguous.40 By contrast, an expected increase in the money supply does not affect the level of output, but raises the inflation rate and the nominal interest rate, and hence has an unambiguous positive effect on velocity. The model also implies that unexpected changes in money cause velocity and the nominal interest rate to increase or decrease together, but lead to an ambiguous correlation between changes in output and changes in velocity (see Appendix III).

The implications of this classical model differ in several important ways from the implications of the demand for money and disequilibrium approaches. In general, the ambiguous correlation between changes in output and changes in velocity within the classical macroeconomic framework emphasizes again that inferences drawn from the money demand approach may be misleading. In addition, equation (7) differs very significantly from the solutions for velocity presented in equations (4), (5), and (6) in that a distinction is made between the expected and unexpected components of the money supply. This distinction will give rise to important differences in the conclusions that are drawn about the appropriate role of monetary policy as a tool for stabilizing output and employment.

The Case for a Passive Monetary Target

Models with rapid price adjustment and rational expectations provide theoretical support for a money stock target. The support is based on two propositions: first, that the exercise of discretion by central banks can surprise the public temporarily and can thereby have short-lived effects on output, but can do no more to output than create variability around its expected time path; and second, that once discretion has been ruled out, a money stock target appears superior to a nominal interest rate target. (By contrast, in both the disequilibrium models and the demand for money framework, the choice between a money stock or an interest rate target depends on the relative variability of real and monetary disturbances and on the estimated values of the coefficients in the model.) These propositions are demonstrated below. The analysis does not address the question of whether a money stock target is superior to a target for some other nominal magnitude, such as nominal GNP; that issue is discussed in the next major part of the paper.

Two distinctions should be kept clear throughout the analysis: that between discretion and rules; and that between active and passive rules. As defined earlier, discretion should be understood to refer to monetary policy that does not follow a prespecified and preannounced rule. However, the fact that central bankers choose to follow a rule does not imply that they must try to achieve a fixed target for the monetary aggregate (a passive rule).41 An alternative is for the monetary authorities to follow an activist rule under which the authorities’ target for the controlled variable reacts countercyclically to the current and past values of relevant economic variables, such as prices and output, or serves as an automatic stabilizer in reacting to various types of disturbances to macroeconomic conditions. (Activist rules will be considered later.)

The analysis of macroeconomic models under the rational expectations assumption leads to a number of strong conclusions, labeled theoretical to indicate that they have been challenged (for reasons that will be elaborated later). In addition to presenting the theoretical case based on these models against central bank discretion and to suggesting that a monetary target is preferable to an interest rate target, it will now be demonstrated that the assumptions of rapid price adjustment and rational expectations together provide a theoretical case in favor of passive rules and against active countercyclical rules. It will then be shown that this case is not necessarily undermined when prices adjust slowly, but that if prices in some markets are sticky for long enough to allow anticipated monetary policy to influence relative prices in the short run, rational expectations models provide a case for an activist countercyclical monetary rule.

An underlying premise of the theoretical case against central bank discretion is the inference that unexpected fluctuations in money growth around its expected path lead to unexpected fluctuations in prices and output. In the classical rational expectations model, monetary policy cannot improve welfare by changing the expected path of output over time, since as soon as the behavior of the money stock becomes anticipated it no longer affects output.42 Thus, discretion can only create unexpected variability, and to the extent that unexpected fluctuations in prices and output are undesirable in the short run, central bank discretion will tend to reduce welfare by leading directly to unexpected fluctuations in those variables. (Unexpected changes in the money stock will “cloud the picture” for economic agents, who will then be confused between changes in the relative and absolute levels of prices and will, therefore, make suboptimal decisions about their levels of production.) By contrast, and to anticipate the discussion of a different model, to the extent that monetary policy is capable of affecting output in the short-run through channels other than surprise, the rational expectations hypothesis provides a case for monetary policy to react in a systematic way to dampen the impacts of any disturbances to the economy, but it also provides a case for avoiding any discretion or additional surprise in its own response to disturbances. This line of argument leads to the conclusion that central banks should minimize the unpredictable elements of their behavior and constitutes the theoretical case in favor of a central bank rule.

One of the issues that has received attention in the literature is whether a money supply rule is preferable to a nominal interest rate rule. It is now widely recognized that a nominal interest rate target may have the undesirable feature of leading to an indeterminate price level in the long run.43 To see how this indeterminacy may result, consider a slight variation of the long-run demand for money function presented in equation (1):44

where y* is long-run output, and εt a random variable.

Now, assume a passive interest rate rule, such that the authorities always allow the money supply to adjust to the level consistent with some fixed nominal interest rate target, i.45 In that case, any increase in the price level will be followed by a proportional increase in the nominal supply of money in order to maintain the nominal interest rate at its target level; consequently, there are an infinite number of combinations of the price level and the money supply that are consistent with any target level of the interest rate. Thus, monetary policy does not provide a nominal anchor to hold down the price level. This indeterminacy result can be viewed as a price instability problem.46

The instability problem does not arise when the authorities choose a money stock target. In fact, assuming that central banks decide on a passive target for the rate of growth of the money supply, the solution for velocity will be given by equation (7) without the term (mtmte), which equals zero since the unanticipated component of the money supply vanishes. Then, fluctuations in the levels of prices, output, and velocity will depend only on the random disturbances that are not under the control of the authorities. By setting a passive money supply rule, central banks cannot totally eliminate output and employment fluctuations, but they can minimize them.47

Whether a passive money supply rule is preferable to an activist rule for adjusting the money supply in reaction to disturbances to the economy is a separate issue. The answer depends not only on whether expectations are formed rationally, but also on whether institutional constraints prevent or delay some prices from responding to anticipated changes in the money supply. For rational expectations models with rapid price adjustment, an activist rule cannot stabilize output following disturbances to the economy, and accordingly is no better than a passive rule, since a rational public would take the rule into account in forming its expectations and adjusting rapidly to the disturbances.48 Moreover, as stated above, since the money stock affects the level of prices, the simplest anticipated monetary rule aimed at controlling the inflation rate would appear to be the least costly and the most efficient: a passive rule is an optimal rule in the context of rapid price adjustment. Consideration is given later to a model in which a different price adjustment process provides a theoretical case for an active rule.

The Choice of Instruments for Controlling the Money Supply

The theoretical case for adopting a money supply rule leaves an important policy issue outstanding: which policy instrument should the monetary authority use in attempting to adhere to a money supply rule when it can only control the money supply indirectly? This issue was widely discussed in the United States, for example, during the years before and after the shift in the operating procedures of the Federal Reserve in October 1979. Although that discussion focused in part on political considerations, the issue can be addressed in economic terms by comparing two alternative techniques of monetary control. The first technique attempts to achieve a money stock target by manipulating interest rates; the second operating technique is to control some monetary base. (Although the theoretical analysis assumes that the economy is closed, there is a presumption that the qualitative nature of the conclusions would extend to an open economy to the extent that countries can pursue independent monetary policies in an environment of flexible exchange rates.)

The analysis depends on a description of the relationship between the money supply, the monetary base, and the level of interest rates. A simple but appealing form of that relationship is:49

where bt is the monetary base, γ is the “reaction” coefficient of the money supply to changes in the interest rate, and ωt is a random disturbance to the banking system.

Notice that the money supply is no longer exogenous; it is now a policy variable with a target level that the monetary authorities try to achieve by controlling one of their two instruments, but without control over the random disturbance ωt.

The implications for the levels of prices and output that can be derived from these alternative instruments are presented in Appendix V. In each case, velocity depends on the expected level of output (y*) and a combination of the different random disturbance terms (nt, ut, εt and ωt). Under an interest rate regime:

while under a monetary base regime:

where the di and the fi are functions of the parameters in the system.

How do equations (9) and (10) compare? Notice that the random disturbance to the financial sector, ωt, is present in the latter but not the former. That does not necessarily imply, however, that the choice of a monetary base instrument is inferior to the choice of an interest rate instrument for controlling the money supply. It can be shown, for instance (see Appendix V), that a random shock to the demand for money, εt, affects velocity proportionally under the interest rate regime, but less than proportionally under a monetary base regime; that feature would favor choosing the latter instrument if the disturbances in the money market were believed to have a larger variance than other disturbances in the system. In general, therefore, such considerations suggest that the appropriate instrument is an empirical choice that depends on both the values of the structural parameters in the economy and the relative variances of the random disturbances affecting the system.

A Case for an Activist Monetary Rule

Two basic conclusions have been derived from the analysis of the classical model with rapid price adjustment and rational expectations. First, if the authorities aim to stabilize output, prices, and hence, velocity, the best policy is a monetary rule that eliminates any unanticipated behavior by the monetary authorities. Second, if a money supply rule is chosen but the money supply is not a variable under the direct control of the authorities, the best control instrument depends on the structural parameters of the economy and the relative variances of the different types of disturbances. It should be emphasized, as well, that if the authorities adopt and gain credibility in their adherence to a money supply rule, the absence of unanticipated behavior by the monetary authorities by itself adds a stabilizing element to the economy, thereby easing the authorities’ task of estimating the true structural parameters in the system.

It is now appropriate to consider how changes in the structural model can modify the theoretical conclusions by providing a channel for anticipated changes in the money supply to affect the level of output. Contrary to previous conjectures,50 it is now recognized that the “policy ineffectiveness” proposition does not simply derive from the assumption that prices adjust rapidly; anticipated monetary policy may be “ineffective” in influencing output even when prices adjust slowly. The general nature of price adjustment, however, does have an important bearing on the effectiveness of monetary policy. In particular, if producers engage in contracts (to purchase labor or to supply output) that set prices over a fixed multi-period horizon, a countercyclical monetary policy response to the unanticipated disturbances can affect the profit-maximizing supply of output.

Consider first an economy similar to the classical model presented earlier, but with the modification that prices adjust toward their equilibrium levels in a process that can be described as a case of slow partial price adjustment:

where the partial adjustment coefficient λ is positive but less than one (λ = 1 means prices adjust fully) and p¯t is the market clearing value of the price level. (Since p¯t corresponds to the market-clearing value of the price level, its solution will be identical to the one discussed in the rapid price adjustment model and derived in Appendix III.) It is sometimes contended that such partial adjustment processes for the aggregate price level reflect the costs that microeconomic agents would incur if they changed their prices continuously or too frequently.

What are the implications for monetary policy in this context?51 Consider the expectations held at time t – 1 about the outcomes for variables at time t. Since agents are rational, any expected change in the money supply will be expected to affect the equilibrium price level (p¯t). Consistently, according to equation (11), the public will correctly expect the observed price level to increase by a fraction λ of the change in p¯t. Prices will not adjust completely to their new long-run equilibrium level, but the amount that prices do adjust will not surprise the public. Accordingly, to the extent that only unexpected changes in the general price level can lead firms to adjust their output (recall the discussion of the microeconomic foundations for the Lucas aggregate supply relation), any expected change in the money supply will not affect the behavior of output. Thus, neither active nor passive monetary rules will be able to dampen fluctuations in output, and for purposes of controlling the price level, passive rules will be preferable on grounds of simplicity and efficiency.

From equation (11), it is clear that the only difference between the solutions for the price level under rapid adjustment (p¯t) and slow adjustment (pt) is that the latter is a fraction λ of the former plus a fraction (1 – λ) of the previous period’s price level. Appendix VI obtains the solutions for the level of output, the price level, and velocity. The level of output is independent of the expected change in the money supply but does depend on the value of the partial adjustment coefficient λ, given the past history of the economy. In addition, the nominal interest rate is affected by the expected change in the money supply because the level of prices does not immediately adjust by the full proportionate amount of the change in the money supply, and because the level of output does not adjust at all; thus, the interest rate must adjust in the short run to maintain equality between money demand and the money supply. Moreover, just as the interest rate is affected by expected changes in the money stock, so is the level of velocity, even though the level of output is not. The implied solution for velocity depends on the speed of adjustment λ and is identical to equation (7) in the limiting case in which prices adjust fully every period (that is, for λ = 1).

The economic intuition for the results just derived is based fundamentally on the microeconomic foundations for the aggregate supply function. These foundations reflect the assumption that the profit-maximizing levels of output for microeconomic producers depend on relative prices, such that firms will not adjust their levels of output in response to a change in the general price level unless they believe that relative prices have changed. In the model just examined, firms observe their own price level before they obtain complete information about the current general price level, and will only believe that relative prices have changed if they make errors in predicting the general price level. Accordingly, the assumption of slow price adjustment is not sufficient for an active countercyclical monetary policy rule to affect output, since under such a rule both the actual and the expected levels of prices will adjust “slowly” but equally, without generating expectational errors. Thus, a case for activism must be based on an alternative framework for generating perceptions of relative price changes. One alternative framework emphasizes the existence of institutional constraints that prevent prices in some markets from adjusting to unexpected disturbances with the same speed as the money supply would adjust under a countercyclical rule. Under such institutional constraints, some prices will remain inflexible even though expectations of the general price level are allowed to adjust.

To develop these arguments more formally, consider a case of long-term contracting in which stickiness in price behavior is introduced by assuming that firms and workers enter into labor market contracts that last for two or more periods. In particular, suppose that while firms are free to adjust the price of their own output, the contracts in the labor market specify nominal wages over a multi-period horizon.52 To simplify the analysis, also assume that under the contracts the real wage rate is expected to remain constant in the sense that the contracts specify the nominal wage rate as follows:

In equation (12), t - iWt, is the nominal wage to be paid in period t as specified in contracts drawn up at (t - i), and tipte is the period t - i expectation of the price level that will prevail in period t.

In every period, firms are constrained by those labor contracts signed in the past. As profit-maximizing units, firms will increase their output if they perceive that the actual price level in their market is greater than their prior expectations, since according to equation (12), this will imply that actual prices have increased relative to the wage rate set by the contract, and hence that the profit rate has increased. The important consequence of these contracting arrangements is that with many firms, existing contracts will overlap in time, and, in the aggregate, output supply decisions will be based not only on a single period’s errors in price expectations, but rather on multi-period expectational errors about the current price level.53

The case for an active monetary rule in this context is straightforward: between the time a contract is drawn and the last year of operation of that contract, there is scope for the monetary authority to react to new information about recent economic disturbances. Since the contracts have fixed the nominal wage, current monetary policy that affects the price level will affect the real wage and hence will influence output supply decisions.54

In this context, an anticipated active monetary rule can be used as an effective tool to minimize fluctuations in the level of output. Appendix VII shows the price and output solutions implied by the simplifying case in which two-year nominal wage contracts prevail. The corresponding velocity equation is:

where the ki are functions of the structural parameters in the model. As equation (13) shows, both the expected and unexpected components of the money stock affect velocity as a result of the effects that the money stock has on both the output level and the interest rate.

Incomplete Information and the Distinction Between Activist Rules and Discretion

The theoretical conclusions that have been discussed in this part of the paper are based on models and assumptions which oversimplify issues that many central bankers and economists consider to be quite relevant. Accordingly, the debate over the appropriate conduct of monetary policy in practice has not been resolved.

Before turning to a more complete overview of the policy debate in the next part of the paper, it may be useful to focus somewhat further on the distinction between activist rules and discretion, and to re-emphasize that the theoretical case for an activist rule does not presume that central banks or other economic agents have complete information about either the behavioral relationships in the economy or the current values of economic variables. As applied by the models discussed in this paper, the rational expectations hypothesis simply assumes that private economic agents have as much information (or ready access to information) as the central bank, and that they use whatever relevant information is available in forming their expectations.

If the existence of contracts or other institutional rigidities provides scope for monetary policy to have short-run effects on output through channels other than surprise, there may well be a case for using an activist monetary policy to counter the impacts of disturbances or shocks to the economy, depending on the objectives of the central bank. For example, a variety of monetary policy actions were discussed as possible responses to the unexpected oil-price increases of the 1970s, ranging from tightening policy to resist increases in the general price level to easing policy to resist declines in output and employment.55 Whatever objectives the monetary authorities have a mandate to pursue, however, they will want to react to a surprise in oil prices in a manner that attempts to stabilize prices and output around whichever feasible time path is most preferred. In theory, an activist rule that is consistent with the central bank’s objectives and known to the public can serve as an automatic stabilizer following surprising disruptions to the economy, whereas a discretionary response is inferior to an “optimal” activist rule to the extent that it adds another element of surprise that increases the variability of output relative to the most desirable path that an activist rule would be capable of achieving.

Although the distinction between discretion and a rule can be defined clearly in theory as simply a matter of whether behavior follows a prespecified and preannounced formula, some have argued that the distinction becomes clouded in practice when attempts are made to specify a rule for reacting to the different types of disturbances that central banks may seek to infer from a large but incomplete set of information. In theory, incomplete or inexact information about the structural forms of economic relationships, or about the values of structural parameters and the measured data on economic variables, does not preclude the design of an optimal activist rule: any optimal quantitative method for interpreting whatever information is available will imply an optimal specification for a monetary rule. In reality, however, few central bankers or economists use strictly quantitative methods for interpreting information: most empirical economic model builders and forecasters (both inside and outside central banks) regularly superimpose judgment or discretion in selecting, modifying, and generating forecasts from their models.

That perspective provides one of the main arguments that has been put forth in support of central bank discretion, as will be discussed in the next part of the paper. It should be recognized, however, to be an argument about the difficulties of designing an “ideal” activist rule in the context of incomplete and inexact information, which by no means precludes the selection of a simplified activist rule that may be less than ideal.

Policy Debate Over Monetary Targeting

The previous part of the paper has reviewed the theoretical foundations for analyzing the behavior of velocity and has clarified the types of assumptions that support different “theoretical” conclusions about the appropriate conduct of monetary policy. The assumption that expectations are formed rationally provides a theoretical case against central bank discretion (even when prices adjust slowly). In addition, the assumption that monetary policy can induce short-run changes in output through channels other than “surprise”—as a result, perhaps, of the existence of fixed nominal wage contracts or other institutional rigidities—provides a theoretical case for central banks to follow activist countercyclical rules rather than pursuing the fixed or passive types of targets that they have announced over the past decade.

A qualification to the theoretical conclusions is that the difficulties of interpreting information about economic behavior may in fact limit the options for activist rules to a set of simplified formulas. That qualification leaves open all of the possible preference orderings between passive rules, simplified activist rules, and discretion. A simplified activist rule may be preferred if there is scope for anticipated monetary policy to stabilize output and a desire to avoid the variability that can be associated with discretion. On the other hand, with the same scope for stabilizing output, discretion may be preferred if it is felt that the simplifications of an activist rule leave scope for important gains from overriding the rule. Or as a third possibility, a passive rule may be preferred if it is felt either that monetary policy can have only a weak stabilizing influence on output or that the potential stabilizing influence is outweighed by the potential destabilizing influences of discretion or an oversimplified activist rule.56

With that central perspective on why the policy debate remains unresolved, it is relevant to provide a somewhat more extensive discussion of the issues that have been raised.57

Alternative Target Variables

The debate over the appropriate conduct of monetary policy has included a focus on the pros and cons of targeting alternatives to a money supply measure, including a nominal or real interest rate, an exchange rate, a price level or inflation rate, and the level of nominal GNP or some other aggregate from the national income and product accounts. Discussions of the advantages and disadvantages of the proposed target variables have focused on at least five issues: (1) the effectiveness of the proposed target variables in providing an anchor for the price level and other nominal variables; (2) the relative magnitudes of important structural parameters and the types of unexpected shocks that may disturb macroeconomic conditions; (3) the issue of stretching out the economic adjustments to unexpected disturbances; (4) the timeliness and quality of data and the imprecision of central bank control over the proposed target variables; and (5) certain political considerations.58 Discussions have also focused on the advantages and disadvantages of alternative monetary aggregates as target variables. In practice, the choice of which monetary aggregates to target has taken into consideration the relative predictability of the velocities of the different aggregates, as well as their controllability and the timeliness with which data become available.

The selection of either a monetary aggregate, a price level, or the level of nominal GNP as a target would place a direct anchor on that particular nominal variable and would presumably place an indirect anchor on all other nominal variables in the economy. By contrast, as discussed earlier, the selection of an interest rate as a target might be ineffective for stabilizing prices and other nominal variables.59

The issue of targets or target zones for exchange rates has received considerable attention in recent years. France, the Federal Republic of Germany, Italy, and other members of the European Monetary System have pursued exchange rate objectives over much of the past decade, and to varying extents other countries have also adjusted monetary conditions to stabilize their exchange rates. It has been contended, however, that one major difficulty with an exchange rate target is the instability of the empirical relationships between the exchange rate and other economic variables, including both the variables that central banks directly control and ultimate target variables such as the levels of prices and output.

The issue of whether anticipated changes in the money supply are effective in stabilizing output is one of the central considerations in the choice of a target variable (as well as in the choice between an active or passive rule). If anticipated changes in monetary policy variables have no short-run effects on output, for example, the adoption of a nominal GNP target would not be desirable; monetary policy actions could only stimulate nominal GNP by fueling inflation.

Under the assumption that anticipated monetary policy can indeed have short-run effects on output, the choice between targeting the price level, the money supply or the level of nominal GNP depends to some extent on the relative magnitudes of different types of disturbances and certain structural parameters. Consider, for example, the shocks or disturbances to the prices of oil and other commodities that have disrupted macroeconomic conditions since the early 1970s. With a price level target, the pressures that are exerted by such shocks on the general level of prices must be offset by adjusting monetary policy instruments, which essentially transfers the pressures to (or increases the pressures on) output and employment variables; in that regard, the recessions of the mid-1970s and early 1980s might have been significantly deeper if policy instruments had been adjusted to offset entirely the impacts of the oil-price shocks on the general price levels of the industrial countries.60 By contrast, with a nominal GNP target, the authorities have some flexibility to absorb shocks by allowing both prices and output to adjust in a manner that constrains only the nominal value of output. In this case the closer to zero is the price elasticity of aggregate demand, the stronger is the policy response that is required to offset a supply-related price shock. And if the price elasticity is one, monetary policy may be irrelevant for responding to supply shocks to the extent that such shocks do not affect the level of nominal GNP.

Among the contributions to the debate, Hall (1984) has proposed a flexible price standard that would allow central banks to accept some fluctuations in the price level in order to stabilize employment and output in the short run, but would place limits on the extent to which the price level could deviate from a long-run target. Hall’s proposal goes beyond the discussion of alternative target variables and raises the issue of specifying a central bank rule in a manner that allows a stretching out of the economic adjustments to unexpected disturbances. This type of proposal can also be viewed as a combination of rule and discretion and will be discussed further in the next section.

The debate about the relative merits of money supply and nominal GNP targets has focused on the relative timeliness and quality of data and the relative imprecision of central bank control over the two types of variables. It has been argued that money supply data are available on a more timely basis and are subject to less substantial revisions than data on nominal GNP; such arguments are more forceful for narrow monetary aggregates than for broad aggregates. In addition, it has been contended that central banks have very imprecise control over nominal GNP but do have the ability to control the monetary aggregates fairly closely on average over periods of several quarters. (The earlier discussion and Appendix V indicate the different types of disturbances that can affect the central bank’s control over the money supply, even when it is a targeted variable.)

Political considerations have also been raised in addressing the pros and cons of alternative targets. To the extent that the money supply may be a variable to which the public is less directly sensitive than interest rates, exchange rates, unemployment, or prices, a money supply target might also subject the central bank to less intense political pressures than other possible targets. Regardless of whether that feature might be desirable, however, the issue raised by political considerations would not be relevant if the objective was to specify a rule that entirely eliminated the discretion of the central bank.

Rules Versus Discretion

The debate over rules versus discretion has involved a number of arguments. The theoretical arguments in support of rules, as provided by the different types of rational expectations models, have already been reviewed. A related set of arguments has focused on the “time inconsistency” of policy rules previously selected as optimal, which is a problem that arises to the extent that in each time period the opportunity to exercise discretion provides central banks with an incentive to abandon a previously selected policy course. The policy course selected as optimal in the past is thus “time inconsistent,” since at a subsequent time the authorities perceive that they can do better through changing course to exploit the opportunity to “surprise” other economic agents.61 If the “surprise” is an increase in the money supply intended to reduce unemployment in the short run, rational economic agents will recognize this incentive, and their reactions will raise the expected and actual rate of inflation that is associated with the equilibrium level of unemployment in the long run. One proposed solution for obtaining superior outcomes for inflation and unemployment over the long run is thus to remove the central bank’s discretion to make period-by-period attempts to “surprise” the public.

Turning to arguments that have been presented in support of central bank discretion, it has been contended that:62

… policy rules are a myth of economic theorists’ simplified models. It is in practice impossible … to prescribe in advance for all contingencies … [and] not credible that responsible officials will not react to the circumstances of the day as they and their constituents perceive them.

Thus, it is alleged to be impossible in practice to prescribe a rule that will not sooner or later become outmoded or regretted in the light of events that were not anticipated when formulating the rule (events such as major changes in oil prices or exchange rates, financial or technological innovations, and major crop failures or other output shortfalls). Implicitly, moreover, the argument that it would be infeasible politically to abide by a rule that failed to prescribe in advance for the circumstances of the day is an argument that society would sooner or later incur welfare losses if it locked itself into a mechanical rule. Consistent with this view, attention has been drawn to the recent evolution of monetary policy in the United States:63

In October 1979 and February 1980 our Federal Reserve announced two monetarist decisions. The first concerned its operating procedures. … The other concerned its targets for intermediate monetary aggregates: the Fed intended to lower their growth rates steadily … until they would no longer accommodate inflation. This intention was stated unconditionally; it was to be carried out regardless of the state of the real economy.

In August–October 1982 the same Fed, under the same chairman, abandoned the second of these two decisions…. Over the … recovery that followed the Fed’s policy reversal, I think it is safe to say, its operations have been oriented to macroeconomic performance, with the aggregates in a subordinate role….

We all know the reasons and the rationales for the 1982 decisions. Because of a big negative velocity shock in 1982, adherence to the monetary targets was producing a lot less nominal GNP than expected or intended. The consequences for the real economics of the United States and the rest of the world were scary. So were the prospects of financial disasters, overseas and at home. That financial and institutional innovation and deregulation were altering in uncertain ways and degrees the meanings—read velocities—of the monetary aggregates was both a valid consideration and a useful rationale.

A different but related argument that has been presented against mechanical rules—particularly rules in which a monetary aggregate is specified as a target variable—is the suggestion that over time, changes in institutions or economic behavior can defeat the purpose of a rule even if the central bank succeeds in hitting its quantitative target. Thus, the adoption of a particular monetary aggregate as a target variable might induce changes that destabilized the velocity of that aggregate, since:64

… statistical relationships derived from the past depended on the particular kind of policy aim pursued by the authorities over the period considered…. In other words, although velocity has been fairly stable in the past this would be no guarantee of its stability in the future if the authorities chose to alter the rules of the game.

Moreover, the extent to which the adoption of a rule actually induces the changes in institutions or economic behavior is not a central consideration in the argument. An environment of regulations, taxes, and rewards to technological change provides numerous incentives for institutions and economic behavior to change in ways that are effective for circumventing the regulations and taxes, or for reaping the rewards of technological change. Thus, regardless of whether or not central banks act with discretion or follow rules, it is possible that financial innovations will emerge over time to introduce attractive substitutes for the components of any monetary aggregate that they might choose to monitor or target.

While it seems undeniable that the theoretical case against central bank discretion is weakened by recognizing the oversimplifications and abstractions of the analytical models, it is equally noteworthy that the opponents of mechanical central bank rules have increasingly recognized the importance of the credibility and reputation of the monetary authorities, which are generally earned through predictable behavior. It is also notable that in addition to the arguments for rules versus discretion, some support has emerged for intermediate positions. Axilrod (1985b, p. 600) has argued that rules have the virtue of holding central banks “reasonably responsible and accountable … [but should] be implemented rather flexibly, and may even be changed (with public announcement) for clear and sufficient cause.” Hall (1984) has proposed a scheme (mentioned in the previous section) whereby central banks would be committed to an “elastic price standard” which specified a fixed price-level target that they must continuously aim to hit in the long run, but which also left it for central banks to exercise discretion in choosing how rapidly to guide the economy toward that target in the short run. In Hall’s judgment:65

… jumps in oil prices and in other determinants of the overall price level … are critical for the design of monetary strategy. More than anything else, the strategy must be formulated to deal intelligently with the burst of inflation and higher unemployment set off by each shock….

It is neither practical nor desirable to dictate to the Fed exactly how it should proceed. … As financial markets evolve and the Fed learns how best to operate to achieve the target, procedures will change and performance will improve.

Thus, Hall would specifically fix a price target at some level and permit the actual price level to deviate from its target by a percentage no greater than a specified “elasticity” parameter times the percentage departure of the unemployment rate from an estimate of its equilibrium or natural rate. Beyond that, the central bank would be free to exercise its discretion and would be judged only by performance.

Rogoff (1985) has contributed a different approach toward middle ground in terms of a formal model that analyzes the optimal degree of commitment to a central bank rule. Rogoff argues that society can design its institutions to counteract the inflationary bias that has been associated with central bank discretion by the rational expectations models and the time inconsistency problem. In particular, societies can appoint and give discretion to central bankers who will pursue lower inflation rates (and accept higher unemployment rates) than might appear to be socially optimal in the short run in order to counteract any bias toward inflation over the long run.

Summary and Concluding Observations

In adopting strategies for monetary policy over the past decade, the authorities have confronted a number of basic questions. These include: (1) is it desirable to adjust monetary targets in light of financial innovations and changes in the regulatory environment; (2) how far should concern about exchange rate variability temper the pursuit of monetary objectives; and (3) does the restoration of “reasonable” price stability increase the scope for central bank discretion?

To a large extent, such questions can only be answered by adopting a particular position in the general debate over the appropriate roles of rules and discretion in the conduct of monetary policy. Accordingly, while this paper has to some extent reviewed the specific issues that central banks have confronted, its larger purpose has been to balance the lessons from empirical experience and theoretical analysis in providing a perspective for the main issues in the general policy debate.

In reviewing the statistical evidence, the paper focused first on the behavior of velocity since the mid-1970s in each of the seven major industrial countries. No attempt was made to unravel the causes of the observed variability of velocity. Comparisons were presented of the variability of the velocities of different monetary aggregates within countries, of similar monetary aggregates across countries, and of particular monetary aggregates during different time periods. These comparisons suggested: (1) that in recent years the velocities of M1 aggregates have been more variable than both the velocities of the broader aggregates in all countries and the velocities of the wide monetary base and central bank money concepts that have been targeted in the United Kingdom and the Federal Republic of Germany, respectively; (2) that Japan and the Federal Republic of Germany experienced the lowest variability of velocity over the 1974–85 period; and (3) that variability levels in most cases were no greater during 1982–85 than during previous four-year periods.

A second set of statistical material shifted focus from the variability of quarterly data on velocity to the correlations between the variability levels of rates of inflation, rates of real GNP growth, and rates of money supply growth over the entire 1974–85 period and several four-year sub-periods. Correlation coefficients for the cross-section of seven industrial countries indicate that relatively low variability of monetary growth has been associated with relatively low variability of real output growth and relatively low variability of inflation.

Statistics alone, however, cannot provide an adequate perspective on the observed variability of velocity; without a firm understanding of the interrelationships between prices, output, and money, and the transmission mechanisms through which an exogenous change in any one of those three variables may influence the other two, statistics alone can be misleading. In particular, the statistics do not isolate either the extent to which the variability of velocity has “caused” central banks to exercise their discretion to deviate from their announced monetary targets, or the extent to which the exercise of central bank discretion has “caused” velocity to be variable.

An additional empirical perspective was provided by reviewing the macroeconomic conditions that central banks have experienced in pursuing their monetary targets over the past decade. These conditions have presented central banks with observed or prospective shifts in velocity which, in turn, have been associated with a variety of developments, including unanticipated exchange market pressures, unanticipated global “shocks” to the price of oil, the unpredicted effects of financial innovations on the demands for different types of money or money substitutes, and other factors leading to unexpected shifts in the strength of domestic economic activity or inflationary pressures.

Although an appreciation of the difficulties that central banks have faced provides an understanding for why central banks have chosen to exercise discretion, a review of the experience cannot provide unambiguous inferences about the appropriate conduct of monetary policy without an analysis of the origins of the difficulties that central banks have experienced and the extent to which the behavior of the central banks themselves may have contributed to the macroeconomic conditions they confronted. Just as the focus on purely statistical material cannot separate the channels of causation between the variability of velocity and the exercise of central bank discretion, the review of experience does not separate the channels of influence between the macroeconomic conditions that central banks have confronted and the discretion they have exercised.

A major part of the paper has been devoted to addressing the issue of causation with the aim of providing an organized and streamlined presentation and comparison of the different types of models and assumptions that have been employed to analyze the behavior of velocity and to debate the appropriate conduct of monetary policy. To a considerable extent, the debate has been confused by an inadequate recognition of the strengths and limitations of alternative analytical frameworks, and by misperceptions of the types of theoretical models and assumptions that support different conclusions. One popular class of models has concentrated attention on the demand for money, with some attempts to make allowances for financial innovations, exchange rate expectations, and the process of price adjustment. Such a narrow focus, however, is subject to the general criticism that the level of output, the interest rate, and in some cases, the price level are taken as exogenous, even though the influence of central bank behavior or those variables may be quite important for understanding the behavior of velocity and for drawing inferences about the appropriate conduct of monetary policy. Several other classes of models have been developed for analyzing the behavior of velocity within a “complete” macroeconomic framework, including a class of so-called “disequilibrium” models, which has analyzed velocity under the assumption that expectations about prices or inflation rates are formed adaptively (based only on current and past values of those variables).

In recent years, however, the analysis of velocity and its implications for monetary policy has shifted not only away from models of money demand toward complete macroeconomic models, but also away from the assumption of adaptive expectations toward the assumption that expectations are formed rationally—in the sense that agents take account of whatever relevant information is available about the relationships between economic variables, the current and past values of economic variables, and the expected future values of exogenous variables, including the expected course of monetary policy. These models recognize that economic agents have incomplete information about the economy, but assume that private agents have as much information (or access to information) as central banks. Although the notion that expectations are completely rational is extreme, and there remains considerable reluctance to accept the implications of any theoretical model without appropriate qualifications, the assumption of rationality in determining expectations is attractive, and the policy implications of the rational expectations assumption have received considerable attention. It should be emphasized, as well, that many different types of complete macroeconomic models can be analyzed under the rational expectations assumption. In distinguishing among the different models, some important differences in theoretical conclusions are associated with different types of assumptions about the existence and nature of labor contracts or other institutional factors that introduce rigidities into nominal wages or prices. It is the existence of such rigidities that provides a mechanism for anticipated monetary policy to affect the relative prices (or other variables) that influence the supply decisions of firms and factors of production, and thereby to affect the aggregate output of the economy.

One of the inferences that has been drawn from the analysis of complete macroeconomic models (including models in which the price adjustment process occurs slowly) is that if expectations are indeed formed rationally, unanticipated behavior by the monetary authorities creates variability in output and prices but has no stabilizing effects that could not also be achieved if the monetary authorities allowed their behavior to be completely anticipated by precommitting themselves to follow a monetary rule; thus, to the extent that output and price variability is undesirable, other things equal, the assumption that expectations are rational provides a theoretical case against central bank discretion. Whether or not the monetary rule should be a fixed target or a formula for activist responses to counter disturbances to the economy depends on whether changes in monetary policy variables can affect output through channels other than surprise.

The analysis of complete macroeconomic models has also demonstrated that the pursuit of an intermediate target for a nominal interest rate can be counterproductive or ineffective for stabilizing the price level in the long run; in that sense, an interest rate target appears to be inferior to a money supply target. Given that a central bank may choose to target a monetary aggregate that it cannot control directly, however, the question of whether to adopt an interest rate as a control instrument in aiming at the money supply target arises as a separate issue from the question of whether to adopt an interest rate as a target per se. Reliance on an interest rate as an operating instrument or control variable is not necessarily inferior to monetary base control: the optimal choice depends on both the structural parameters of the economy and the relative variances of the different types of unexpected disturbances to the economy.

Needless to say, many central bankers and economists consider that conclusions based on theoretical models and assumptions, including in particular the theoretical case against central bank discretion, tend to oversimplify a number of relevant issues; accordingly, the debate over the appropriate conduct of monetary policy has not been resolved. The last part of the paper has collected together the main arguments in both the debate over rules versus discretion and the related debate over alternative variables that might be chosen as targets in prescribing central bank rules. Discussions of alternative target variables have focused on at least five issues: (1) the effectiveness of the proposed target variables in providing an anchor for the price level and other nominal variables; (2) the relative magnitudes of different types of unexpected disturbances to the economy and of certain important structural parameters; (3) the associated issue of stretching out the economic adjustments to unexpected disturbances; (4) the timeliness and quality of data and the imprecision of central bank control over the proposed target variables; and (5) certain political considerations.

In the general debate over rules versus discretion, the theoretical case for central bank rules that has been provided by the rational expectations assumption has been supplemented with a related set of arguments about “time inconsistency.” From the opposite point of view, the predominant objection to rules is the contention that it is impossible in practice to anticipate all the macroeconomic disruptions to which it would be socially desirable for the central bank to react, and accordingly, that rigid adherence to any mechanical rule would be socially undesirable and politically infeasible. A second and somewhat related argument against rules is the possibility that once a variable is chosen as a target, new institutions or adjustments in economic behavior may develop over time to defeat the underlying objectives for having a target, even if the target is achieved in a strictly quantitative sense.

Part of the debate over rules versus discretion has supported intermediate positions. One of these intermediate positions is that rules or guidelines have the virtue of holding central banks reasonably responsible and accountable, but should be changed or implemented flexibly when sufficient causes arise. A second intermediate position is the proposal that central banks be committed to a target for the average value of the price level or some other objective over the long run, but with scope to exercise discretion in cushioning the impacts of disturbances to output and employment in the short run. A third and somewhat similar intermediate position is to shift the focus of analysis explicitly toward the issues of the appropriate degree of commitment to a central bank rule and the types of institutional arrangements that might induce or constrain central banks to exercise an appropriate amount of discretion.

Nevertheless, while the past decade has provided central banks with a wide range of experience and has focused considerable attention on the theoretical foundations for analyzing the appropriate conduct of monetary policy, it has provided no strong consensus on how the practice of central banking can actually be improved. Disagreements remain on almost all of the issues that arise in designing a strategy for monetary policy, and those disagreements in turn reflect basic differences in the “views of the world” that are held by the advocates of discretion, the proponents of fixed or passive targets, and the supporters of activist countercyclical rules. From one point of view, activist countercyclical rules have an advantage over the types of passive targets that central banks have announced over the past decade to the extent that monetary policy is capable of operating, through channels other than surprise, to counter the effects on output of various types of disturbances to the economy. From a second point of view, discretion has an advantage over activist rules to the extent that it is impossible in practice to devise a mechanical rule that prescribes adequately in advance for all contingencies. Yet, from a third point of view, passive rules have an advantage over discretion to the extent that the exercise of discretion can be destabilizing and inflationary over the long run.

These three different points of view summarize the central issues in the debate. The issue raised by the first point of view is the extent to which monetary policy can have systematic effects in the short run, through channels other than surprise, on the relative prices or other variables that influence the supply decisions of firms and factors of production at the microeconomic level, and thus on the scales of output and unemployment at the macroeconomic level. The issue raised by the second point of view is the extent to which activist rules that are sufficiently simple to put into practice would fail to provide appropriate responses to different types of economic disturbances. And the issues raised by the third point of view are the extent to which expectations are forward looking, and the implications of forward-looking expectations for the degree to which discretionary policies can be destabilizing and inflationary over the long run.

Appendix I Short-Run Demand for Money Under the “Price-Adjustment” View

This view suggests that the long-run demand for money equation of the main text:

should be complemented with an adjustment equation such as:

The hypothesis embodied in equation (I.2) states that the percentage change in the price level is proportional to the difference between the exogenous nominal money supply (mt) and the nominal money equivalent of the public’s desired level of real money balances evaluated at the price level of the previous period (mt*+pt1).

In combination, equations (I.1) and (I.2) yield the following short-run demand for money function:

which is identical to equation (3) in the main text. Notice that equation (I.3) can also be solved for the price level as follows:

where L is a one period lag operator. Thus, equation (I.3) can be considered to be a model of price adjustment to nominal money supply changes.

Appendix II Simple Disequilibrium Model

Consider a simple version of a disequilibrium model which follows Laidler (1985):

where the new variables still undefined in the paper are:

Δpt=the rate of inflation
Δpt1e=the expected rate of inflation during period t – 1

Equation (II.1) is a long-run interest-rate-inelastic demand for money function where the long-run or “natural” rate of output is assumed to represent the relevant income term. Equation (II.2), the output determination equation, embodies a key argument of disequilibrium models: deviations of money supply from the long-run money demand level are assumed to cause short-run deviations of output from its full employment level. Equation (II.3) is a “Phillips curve” equation which postulates that the observed level of inflation depends both on deviations of output from its full employment level and on the expected level of inflation. Equation (II.4) describes the formation of price expectations in an adaptive way.

The model has three observable endogenous variables: the level of output, the price level and the desired level of money balances.66 The solution for the price level takes the following form:

where z1, z2, z3 are positive “reduced form” coefficients. From equation (II.5) it is straightforward to derive an implied reduced-form equation for velocity which is identical to equation (6) in the main text.

Appendix III Price, Output, and Velocity Behavior in an Equilibrium Rational-Expectations Model

Consider the following model, which is similar to a framework used by Sargent and Wallace (1975):

In these equations the new variables are:

rt=the real rate of interest;
ytd=the log of the demand for real output;
t1pte=the period t price level that is expected at the end of period t – 1;

where E is the expectations operator, and ut, nt, and εt are uncorrected white noise disturbances.

Equation (III.1) is the Lucas (1973) “surprise” aggregate supply function, as motivated in the main text. Equation (III.2) postulates that the aggregate demand for current-period output depends inversely on the real rate of interest, consistent with intertemporal optimizing behavior of microeconomic units. Fiscal variables are not included in the aggregate demand function since it would require assumptions about the way in which debt-financed fiscal deficits influence private behavior.67 Equation (III.3) is a stochastic version of equation (1) in the main text. Equation (III.4) is Fisher’s interest rate parity condition; equations (III.5) and (III.6) are market-clearing conditions; and equation (III.7) is the rational expectations hypothesis in the sense of Muth (1961), in which Ωt denotes the available information set during period t.

The model can be viewed to provide a rational expectations solution for the behavior of velocity, although the particular specification of this model requires some ad hoc assumptions. (Specifically, the ad hoc assumptions include restrictions concerning the technology of transactions or the utility function that must be imposed to generate a demand for money function that depends on the level of income. In addition, if capital markets are assumed to be perfect, the real interest rate should be an argument in the supply of output function.) Substituting equation (III.4) into equation (III.3), the model solves for the equilibrium levels of prices, output and the real interest rate as functions of the money supply (which is assumed to be exogenous in this model) and the random disturbances. The stochastic process that describes the behavior of the money supply is assumed to take the simple form:

where h is a fixed trend rate of growth and xt is a random disturbance that is normally distributed with mean 0, variance σx2, and an independent distribution from the other stochastic variables in the model.

The model is solved under the assumption that the information set upon which agents base their expectations is formed by all the past values of the relevant variables at every point in time. Thus, at the end of period t-1, the expected level of the money supply in period t will be t1mte=mt1+h, since agents will know the value taken by the variable m up to period t–1, and will update their expectations by the observed constant rate of monetary growth. Correspondingly, xt represents the unexpected component of the money stock.

The method of “undetermined coefficients is used to solve this model.68 The solutions for the price level, the level of output and the nominal interest rate are:

where:

θ0 = a0/a1

θ1 = –1/a2

θ2 = 1

θ3 = (a1 + a2)/a1

θ4 = (a1 + a2)/(δ + a1 + a2)

θ5 = a3/(δ + a1 + a2)

θ6 = a4/(δ + a1 + a2)

θ7 = –1/(δ + a1 + a2)

A solution for the behavior of velocity is obtained by combining the solutions (III.9) and (III.10) with equations (III.3), (III.5) and (III.8).

where

a0 = (β2α0 – α1β0)/(β2 + β1α1)

a1 = α1/(β2 + β1α1)

a2 = α1β2/(β2 + β1α1)

a3 = –α1/(β2 + β1α1)

a4 = β2/(β2 + β1α1)

Thus, when xt is replaced by mtmte, equation (III.12) is identical to equation (7) in the main text, where the ci are functions of the structural coefficients: the αj, βj, and δ.

Appendix IV Price Level Indeterminacy Under an Interest Rate Rule

The Long-Run Case. Consider the model formed by equations (III.1) to (III.7) in Appendix III. In the long run when expectations are realized and the expected values of the random disturbances equal zero, equation (III.1) implies:

Now assume a fixed interest rate rule where the interest rate is set at the constant level i. Substituting equation (IV.1) into the long-run version of equation (III.2) and solving for the price level we obtain:

Equation (IV.2) is a nonconvergent difference equation and hence the solution for the price level is indeterminant. The long-run indeterminacy of the price level extends to the long-run nominal money supply, moreover, which adjusts passively to money demand according to:

The Short-Run Case. Assuming it = i, solve the model in Appendix III for the price level as a function of the exogenous variables (y*, ut, nt), the policy target (i) and the expectational variables (t1pte,tpt+1e):

Taking expectations on both sides of (IV.4) conditional on the period t – 1 information set, we obtain:

Equation (IV.5) is a nonconvergent difference equation. Thus, the expected price level, and hence the actual price level (because expectations are rational) are indeterminant. Notice that this result would not hold under the assumption of adaptive expectations since in that case, price level expectations would be tied down to the behavior of prices in the past. Thus, the prior evolution of prices would provide an anchor for the current price level.

Appendix V Price and Output Fluctuations Under Alternative Techniques of Monetary Control

The analysis in this section follows the methodology presented in Parkin (1978) and is based on an equilibrium-rational expectations framework. Specifically, the model in Appendix III will now be solved under the new assumption that the monetary stock is not an exogenous variable under the direct control of central bankers; instead the monetary authorities have to manipulate either the interest rate or the unborrowed monetary base in order to attempt to achieve a particular money supply target. The assumed relationship between the money supply, the unborrowed base and the interest rate has been presented in the main text as equation (8) and will be repeated here for convenience:

where bt is the unborrowed monetary base and ωt is a normally distributed random disturbance to the banking system that is assumed to have an expected value of zero and to be uncorrelated with the other disturbances in the model.

Throughout the analysis it will be assumed that the public and the authorities share the same information set, that the authorities announce and try to achieve a target level m¯ for the money supply, and that the public believe that the authorities will behave as announced. Given m¯, the authorities (and the public) are assumed to use equations (III.1) through (III.7) and (V.1) to forecast the expected levels of output and prices, conditional on settings for the chosen policy instrument, it or bt.69 Thus:

Note that this system of equations contains none of the random disturbance terms, since the expected values of those disturbances are zero. If the chosen instrument is the interest rate, then equation (V.5) provides a forecast of the expected level of the unborrowed base, conditional on the deterministic value of it:

Alternatively, if the chosen instrument is the unborrowed base, equation (V.5) provides a conditional forecast for the expected interest rate:

and the “expected” interest rate should also replace it in equations (V.3) and (V.4).

The solution to the system (V.2)–(V.4), with (V.5′) or (V.5″) as appropriate, determines the level of the chosen instrument that is expected to be consistent with achieving m¯. The choice of which instrument to control, however, depends not on the expected outcomes for money, output and prices, which are the same under either instrument, but rather on comparisons of how widely the actual outcomes may vary around their expected values under the alternative control instruments, given the variances of the random disturbance terms. These comparisons rely on the solutions for the actual levels of output, prices and the money supply when the deterministic value of the control instrument is substituted into the system of equations (III.1) through (III.7) and (V.1). (Note that the actual level of the money supply does not have to be equal to its target or expected level, since only the instrument is set deterministically.) Those solutions will now be considered.

For the case of interest-rate control, the solution to system (V.2)–(V.5) implies that the value of the interest rate should be set as:

Substituting equation (V.6) into equations (III.1)–(III.7) and (V.1) the solutions for the actual levels of the endogenous variables (using the method of undetermined coefficients again) are then:

Notice that when the money supply is a target and the interest rate is an instrument, the price level is not indeterminate. By contrast, the indeterminacy of the price level under an interest rate target (as demonstrated in Appendix IV) would arise from the fact that the nominal money supply was not tied down through its target level.

The velocity solution implicit from equations (V.7)–(V.9) is:

which is equivalent to equation (9) in the main text. Note that money supply terms do not appear in equation (V.11), in contrast with the velocity equation when the money supply was not controlled (equation (III.12)). In equation (V.11) the behavior of velocity is determined by all the random disturbances in the system, excluding the disturbance affecting the banking sector. The absence of ωt is due precisely to the choice of the instrument: setting the interest rate in a deterministic way isolates the real sector from disturbances in the banking system.

Next consider the case of unborrowed monetary base control. The solution to the system (V.2) through (V.5) implies that the value of the unborrowed base should be set as:

Substituting equation (V.12) into equations (III.1)–(III.7) and equation (V.1), the solutions for the actual levels of output, prices, the interest rate and the money supply can be obtained. In particular, the solution for the level of output is:

where: d = γ1 + δ) + α1β2 + δβ2 + δα1β1

The expression for velocity is:

where j is a composite of the parameters in the system. Equation (V.14) is equivalent to equation (10) in the main text.

Appendix VI Price, Output, and Velocity Behavior in a Model with Slow Price Adjustment and Rational Expectations

Consider the model presented in Appendix III and replace the goods market equilibrium condition (equation III.6) by the assumption of slow price adjustment:

where p¯t corresponds to the level to which prices would rise if they were fully flexible and, hence, its solution corresponds to equation (III.9). Substituting (III.9) into equation (VI.1), the solution for the actual level of prices is obtained:

Taking expectations of both sides of equation (VI.2) conditional on the relevant information available through the end of period t – 1, we obtain:

Substituting equations (VI.2) and (VI.3) into equation (III.1), the solution for the supply of output (and hence, the level of employment) is obtained:

Equations (VI.2) and (VI.4) can now be substituted into equation (III.3) to obtain the solution for the nominal interest rate:

Finally, the solution for velocity can be obtained by combining equations (VI.2), and (VI.4) with equations (III.3), (III.5), and (III.8):

Appendix VII Effects of Long-Term Contracts in the Labor Market on the Behavior of Output and Velocity

Assume that firms and workers engage in contracts that set the nominal wage rate for two subsequent periods. In addition, assume that these contracts specify the nominal wage rate according to equation (12) in the main text:

where, expressed in logs, t – iwt, is the nominal wage to be paid in period t as specified in contracts drawn up at (t – i) and tipte is the expectation of the price in period t evaluated at the end of period t – i.

Since contracts overlap in time, when period t arrives some firms will be in the first year of their contracts and some others will be in the second year of their contracts. Firms will find it optimal to increase their supply of output every time their actual price level exceeds the fixed-in-advance wage rate since that would imply a lower-than-anticipated real wage. Thus, at the aggregate level, the supply of output will take the following form:

Substituting equation (VII.1) into (VII.2), the output supply function can be expressed in terms of price level “surprises”:

To derive the implications of this kind of aggregate supply function for the levels of prices and output, the model in Appendix III will now be solved under the assumption that equation (VII.2′) replaces equation (III.1). As in Appendix III, the method of undetermined coefficients is used to solve the model. The solutions for the price level, the level of output, and the nominal interest rate are:

where:

Combining the solutions (VII.3) and (VII.4) with equations (III.3), (III.5), and (III.8), the solution for the behavior of velocity is obtained:

Equation (VII.6) is equivalent to equation (13) in the main text where the ki are functions of the θ^j and the expression (mte=mt1+h) has been used.

Appendix VIII Currency Substitution and the Behavior of Velocity

As part of the literature relating currency substitution and velocity behavior, Brittain (1981) provides a model in which currencies are regarded as elements of internationally diversified portfolios. In his view, two direct implications are: (1) movements in domestic velocity may be explained, at least partially, by shifts in the composition of the international money portfolio; and (2) velocities across countries are interrelated. Following this approach the arguments of the demand for domestic money should include a term reflecting the expected opportunity cost of holding various currencies. Thus, the proposed function would expand equation (1) in the main text in the following way:

where itf is a foreign interest rate.

The innovation in equation (VIII.1) is the addition of the uncovered interest rate differential in the arguments of the money demand function. Brittain’s underlying hypothesis is that the higher the foreign interest rate relative to the domestic rate, the higher is the opportunity cost of holding the foreign currency and hence the higher is the demand for the domestic currency. Accordingly, a derived equation for velocity will incorporate the international portfolio variable (itfit) with a negative sign. It should also be obvious that equation (VIII.1) assumes substitution across two currencies, but that nothing prevents the expansion to more monies.

Brittain’s model bears some similarity to the so-called “currency substitution approach to exchange rate determination” developed by Girton and Roper (1976, 1981), Calvo and Rodriguez (1977) and Bilson (1979). However, it can be shown that Brittain’s model, as represented by the single equation (VIII.1), does not correctly deal with the issue of currency substitution. This contention is based on the following arguments.

Brittain’s hypothesis is that domestic residents will hold balances of both domestic and foreign currencies, but his model does not specify the domestic demand function for foreign currency. Such a specification can be added by drawing on the currency substitution literature, which emphasizes that demand functions for the two types of money should be specified symmetrically, except for considerations that influence the ratio of domestic to foreign money holdings. The ratio of the two types of money holdings depends on the differential between the real returns on the two monies which, under the assumption of zero nominal interest payments on money, equals the differential expected rate of inflation. Thus, the demands of domestic residents for the two types of money will depend on the expected inflation differential along with the domestic interest rate and domestic income. In addition, under the assumption of ex ante purchasing power parity, the differential expected rate of inflation will equal the expected rate of change in the exchange rate. Hence, the relevant system of equations consistent with currency substitution would be:

In these equations: et is the exchange rate, defined as the domestic currency price of the foreign money; dmd and fmd refer to the domestic demands for domestic and foreign currencies, respectively; and the superscript “e” refers to expectations.

Conditions (VIII.2) and (VIII.3) have several appealing properties. Notice that the domestic demand for foreign money is expressed in terms of its purchasing power over domestic goods (Bilson (1979)), implying that neither currency is discriminated against when used for transactions purposes. Also the coefficients of the interest rate on the nonmonetary asset and of the level of income are the same in both equations, consistent with the notion that the relative holdings of the two currencies should be independent of changes in those variables. In addition, an increase in the expected rate of appreciation of the foreign currency reduces the demand for domestic money and increases the demand for foreign money. Combining equations (VIII.2) and (VIII.3) we obtain:

where a0 = β0 – γ0; a1 = β3 + β4

What does currency substitution then imply for velocity? It is clear that for given levels of the currency holdings of domestic residents, equation (VIII.4) would be a model of exchange rate determination, where the formation of exchange rate expectations would remain to be specified. However, if the currencies are also demanded in the rest of the world, it is still necessary to specify the “foreign country” demand functions. Assuming that those functions are similar in nature to equations (VIII.2) and (VIII.3), the “integrated” resulting equation for the exchange rate will be of the form:

where DM and FM represent the exogenous world supplies of domestic and foreign currencies, respectively. If the solution for the exchange rate is then substituted back into equation (VIII.2), the income velocity of domestic currency will take the form:

where b1, b2, b3, b4 > 0. Equation (VIII.6) is identical to equation (5) in the main text.

Notice that for given levels of output and the interest rate, velocity will fluctuate with changes in the expected value of the exchange rate and with changes in the difference between the two nominal supplies of monies.70 This result has been derived by using the system of equations implied by the proper interpretation of currency substitution, which improves upon Brittain’s focus on a single money demand equation.

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A rule is a prespecified formula that defines the desired outcome for some selected variable. The exercise of discretion is defined as the alternative to following a rule. A distinction is also drawn between passive and activist rules. An activist rule for the money supply means that the central bank responds to the state of the economy according to a prespecified formula, which might, for example, prescribe a countercyclical path for the money supply. The types of money supply targets that have been announced over the past decade correspond to passive rules, even though in many cases the targets have been specified as ranges.

The measures of velocity that are used in the World Economic Outlook are constructed by dividing the nominal level of GNP by the corresponding monetary aggregate. Some other measures of velocity are based on measures of income other than GNP.

See the note to Table 32.

For a precise definition, see the note to Table 32. It should be recognized that the choice of measuring deviations around a simple trend line is arbitrary. Alternative choices would include moving averages of arbitrary lengths and procedures for modeling the time series properties of velocity.

The exclusion of the period prior to 1974 reflects a recognition that under fixed exchange rates, changes in foreign exchange reserves limit the central bank’s control of the money supply.

It may be noted, however, that with only seven observations it is not possible to place high degrees of confidence in rejecting the hypothesis that the “true” correlations are zero.

As indicated by footnote 1 of Table 35, however, it is somewhat arbitrary to describe the target periods for Canada as seven successive years.

Of course, exchange market developments themselves are not “exogenous,” although in the 1977–78 experience the appreciation of the mark against the dollar may have been “caused” to a considerable extent by economic outcomes and prospects in the United States, which were exogenous to Germany.

Monthly Report of the Deutsche Bundesbank, December 1978, p. 11.

Ibid., March 1981, p. 9.

Bank of Canada, 1982 Annual Report, p. 27.

Bank of Canada, 1984 Annual Report, pp. 7–10.

See Axilrod (1985a) for an expression of this opinion. It has been argued that the depreciation of the dollar during the 1977–79 period supports this view.

The practice of respecifying targets each quarter ended with the specification of targets for the period from fourth-quarter 1978 through fourth-quarter 1979.

A “target” range for the federal funds rate continued to be specified but was made much wider and was no longer regarded as binding.

The reviews of the experiences in France and the United Kingdom have revealed similar disparities between the degrees of success at achieving intermediate targets and ultimate objectives.

Ibid., p. 14. Since October 1979, the Federal Reserve has redefined the monetary aggregates on several occasions, prompted by financial developments that altered the meaning and reduced the significance of the old measures.

A de-emphasis of the M1 target during the second half of 1982 was precipitated by uncertainty over how M1 would be affected when the public reinvested the very large volume ($31 billion) of all savers certificates that matured in October; see Axilrod (1985a), p. 18.

Federal Reserve Bulletin, February 1986, p. 131.

In this part of the paper, no distinctions are drawn between different monetary aggregates, and “the” interest rate is taken to be the relevant opportunity cost of holding money.

The increase in the money supply (which would shift the LM curve) would initially generate an excess supply of money and an excess demand for goods. The interest rate would decline, stimulating investment and output (along the IS curve) until the level of income had increased proportionately to the money supply, restoring equilibrium.

Measurement errors in the arguments of the long-run money demand function may provide another motivation for the lagged term; see Goodfriend (1985).

For the United States, see for example, Enzler, Johnson, and Paulus (1976). The problem has become known as the “Goldfeld puzzle,” after the “failure” of Goldfeld (1976) to obtain a specification capable of explaining both the pre-1974 and post-1974 behavior of M1 demand in the United States. For an analysis of money demand elsewhere, see, for example, Brittain (1981).

See, for example, Bordo and Jonung (1981) and Lieberman (1980). For a review of the issues involved in the financial innovations approach, see Judd and Scadding (1982).

By increasing productivity, a financial innovation may lead to an increase in the amount of real output and income that can be sustained by a given stock of real money balances. Hence, it is possible for an increase in velocity to result from an increase in the level of income rather than a reduction in the amount of money demanded. In other words, the income effect of a financial innovation on the demand for money may be greater than the substitution effect brought about by the innovation. If that is the case, money demand may increase (at a given price level) and still be consistent with a rise in velocity.

This argument was initially made by Walters (1965) and later by Laidler (1982) and Coats (1982). It was recently extended by Carr and Darby (1981). This viewpoint is distinct from Goldfeld’s (1973) suggestion that the public adjusts its real money balances through the passive supply of nominal money by the authorities.

See Appendix I, equation (I.2), which is taken from Hetzel (1984).

The domestic price level is also endogenous in the model underlying equation (5) through the assumption of purchasing power parity.

For examples of disequilibrium models applied to industrialized countries, see Laidler and Bentley (1983) and Knight and Wymer (1978).

Given slow price adjustment, money market disequilibrium is included as a variable explaining the behavior of output, rather like the lagged dependent variable is included in the short-run demand for money to represent adjustment costs (see equation (2)). Note also that some disequilibrium models have moved away from the adaptive expectations assumption to specifications in which expectations about prices take account of other relevant variables in the model. For examples, see Jonson (1976) and Laidler and O’Shea (1980).

In models that incorporate nonmonetary assets, additional equations describing the behavior of the real rate of interest are included, together with the Fisher hypothesis for linking nominal and real interest rates.

The example abstracts from the role of interest rates and, for additional simplicity, defines velocity with respect to the full-employment level of output.

Although the above presentation has not included the interest rate, in most disequilibrium models the choice of whether to specify a countercyclical rule in terms of a monetary aggregate or an interest rate is generally an empirical issue, depending on the estimated coefficients of the model.

Expectations about the price level (or any other variable) that are formed adaptively as a weighted average of the past levels of that variable are rational only if the actual behavior of the price level (or any other variable) follows a random walk; see Muth (1960).

The supply function in the classical model replaces the short-run Phillips curve used as a price equation by the disequilibrium models. Disequilibrium models provide a solution for the price level, but contrast with the classical model by assuming that supply always adjusts to demand independently of the price level. On price adjustment in the classical model, see, for example, Sargent and Wallace (1975).

The intuitive explanation for the ambiguous effect on the nominal interest rate is that an unexpected increase in the money supply will stimulate output and income, which will in turn increase money demand by an amount that may be either more or less than the increase in the money supply, thereby creating either upward or downward pressure on the interest rate; see Appendix III.

Although a fixed target is set at a level that is independent of the state of the economy, random shocks are allowed to influence the outcome for the target variable to the extent that the authorities cannot control it precisely.

The long-run ineffectiveness of discretion is not unique to rational expectations models; the argument holds whenever an “expectations-augmented Phillips curve” is used to explain the relation between output and prices, since such a relation is predicted to vanish in the long run (that is, expectations are always rational in the long run).

Sargent and Wallace (1975) prove that indeterminancy can apply even in the short run. See Appendix IV for a similar mathematical proof based on the model presented in Appendix III.

The only differences between equations (1) and (1″) are that the long-run level of output has been substituted for the current level, and that a random shock εt, has been added to stress the fact that economic variables follow stochastic paths.

There is no need to assume a passive interest rate rule to obtain indeterminate prices. In fact, Sargent and Wallace (1975) assume a sophisticated rule allowing for feedbacks in response to shocks to output and prices and still arrive at the same result.

Instability arises because in the context of flexible prices and predictable monetary behavior, rational agents will expect the real money supply to remain constant as long as the interest rate rule is being followed. Had the authorities chosen to have a mixed target, in which interest-rate fluctuations are resisted in the short run while over time the interest rate is gradually adjusted to offset departures of the money stock from its target path, with a view to adhering to monetary targets in the long run, the solution for the actual levels of prices and the money supply may be either stable or unstable, as a result of two forces acting simultaneously. On the one hand, the money supply target provides an anchor for the price level, but on the other hand the attempt to smooth interest rate fluctuations constrains the behavior of the interest rate, preventing it from attaining the path consistent with price stability. See Lane (1984).

Notice that since the variability of velocity under a passive rule would reflect only the random shocks εt, ut, and nt, the expected level of velocity would be a constant whose value depended on the expected level of output.

One modification of the analysis that might allow an activist monetary rule to affect the level of output in an environment of rapid price adjustment and rational expectations would be to assume that the monetary authority had superior information about the nature of the rule or the complete model underlying the behavior of the economy. However, Barro (1976) has shown that even under such circumstances an activist rule is not superior to a passive rule if the criterion is to minimize fluctuations in output about its long-run value.

This functional form assumes that the ratio of the money stock to the unborrowed base (the “multiplier”) depends on the interest rate. The addition of a constant to the right-hand side of equation (8) would not affect the analysis significantly.

See, for example, Phelps and Taylor (1977).

The case against an active monetary rule based on rational expectations models with sticky prices of the sort developed here was first presented by McCallum (1977).

The case for active monetary policy based on multi-period wage contracts has been developed by Fischer (1977). Taylor (1979) obtained the same result by assuming that multi-period arrangements affect output prices, as well as wages.

Of course, the “previous periods” that are relevant here are those within the life of the contract. For instance, if a firm is engaged in a two-period contract, it will be concerned with the expectations of the current price level formed two years ago when the contract was signed.

Contracts that involve fixed nominal interest rates are also prominent in reality, and in that context it is widely appreciated that monetary policy can have important wealth effects on debtors and creditors, although on balance the sum of such wealth effects will not necessarily affect the aggregate output of the economy in a predictable way.

The possibility that an oversimplified activist rule may generate explosive cycles in economic activity can be demonstrated through simulations of macroeconomic models.

Another consideration that makes it difficult to resolve the debate is the “observational equivalence problem” suggested by Sargent (1976), which is the difficulty of distinguishing empirically between models in which anticipated monetary policy affects output and models in which it does not.

Hester (1981) has argued, however, that different types of instability problems can arise if real interest rates are unconstrained; in particular, high real interest rates can destroy socially valuable financial institutions, industrial enterprises, farms, and households, while negative real interest rates can induce indiscriminate borrowing. In this context, however, it may be noted that negative real interest rates can result from imposing ceilings on nominal interest rates for the purpose of preventing high real interest rates.

By the same token, Fischer (1985) argues that the recessions were in fact deeper than they would have been had central banks not attempted to offset any of the price level effects of the oil shocks.

Tobin (1985), pp. 605–06.

Hall (1984), pp. 145–46.

The solution to the complete model takes the following form:

Xt = A0 + A1Xt - 1 + A2Et + A3Et - 1 + A4 ΔXt - 1 + A5ΔEt

where Xt is a 3x1 vector of observable endogenous variables: yt, pt, mtd; A0 is a 3x1 vector of intercepts; Ai (i = 1,…,5) is a 3x3 matrix of coefficients; Et is a 3x1 vector of exogenous variables; Xt–1 and Et–1 are 3x1 vectors of lagged endogenous and exogenous variables, respectively; and ΔXt – 1, and ΔEt – 1 are 3x1 vectors of first differences.

Whether or not such deficits represent a net increase in private real wealth is a controversial issue (see Barro (1974)) that is not addressed in this paper.

See McCallum (1983) on the topic of undetermined coefficients.

This is equivalent to taking the expected value of the system formed by equations (III.1) through (III.7) and equation (V.1).

Strictly speaking, models of currency substitution will derive implications for the “world” income velocity of a given currency rather than for “national” concepts of velocity.

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