Choice of Intermediate Money Target in a Deregulated and an Integrated Economy with Flexible Exchange Rates

Victor E. Argy

doi:10.5089/9781451930610.024.A003

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Choice of Intermediate Money Target in a Deregulated and an Integrated Economy with Flexible Exchange Rates

Author: Mr. Victor E. Argy¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1983

eISBN:: 9781451930610

Language:: English

Keywords:: SP; oil price; exchange rate; money target; money aggregate; income stabilizer; interest rate shock; stabilizing income; Currencies; Exchange rates; Market interest rates

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In recent years most monetary authorities in industrial countries have chosen to announce money targets in advance. The Federal Republic of Germany (in 1974) and the United States (in 1975) had taken the lead in this respect, and they were subsequently followed by other industrial countries.1

Abstract

Numerous considerations explain this trend toward the announcement of money targets. First, there was the increased influence of monetarism, which stressed the importance of the money supply, especially in the determination of inflation. Second, there was a dissatisfaction with the performance of monetary policy. The use of the interest rate as an intermediate target had produced unsatisfactory results. Moreover, the explosion in monetary growth in the early 1970s and the inflation that followed had led to a rethinking about the importance of money. Third, with large and growing public sector deficits in the mid-1970s, money targeting was viewed as a means of constraining the potential for money creation. Fourth, with the breakdown of the Bretton Woods agreements and the freeing of exchange rates, there was now thought to be a greater ability to control monetary expansion, thus providing greater credibility for targeting. Fifth, the announcement of a money growth target was thought to influence expectations and to provide a more predictable and stable financial environment. Sixth, in the fight against inflation a restrictive monetary policy, which is preannounced and credible, may influence expectations about future inflation, rapidly reduce wage demands, and in this way moderate the potential unemployment costs of the policy.

The particular money aggregate chosen for targeting by individual countries has been varied (Table 1).² In some countries (Australia, France, Japan, the United Kingdom) broad aggregates have been selected; in others (Canada, Switzerland, the United States) narrow aggregates have been selected. In still others (the Federal Republic of Germany, perhaps also Switzerland) something approaching base money is targeted.

Table 1.

Nine Industrial Countries: Intermediate Money Aggregate Targets

^¹Currency in circulation plus minimum reserves (at base-year reserve ratios) on the banks’ domestic liabilities. It is closely associated with M₃.

^²Based on ceiling for total domestic credit expansion in 1981.

^³Notes, coins in circulation, and all sterling deposits (including certificates of deposit—CDs) held by U.K. residents in both the public and private sectors. It differs from M₃ in excluding foreign currency deposits by U.K. residents.

^⁴More importance attaches to M1b.

Table 1.

Nine Industrial Countries: Intermediate Money Aggregate Targets

Country	Intermediate Target
Australia	M₃
Canada	M₁
France	M₂
Germany, Fed. Rep. of	Central bank money ¹
Italy	M₂²
Japan	M₂ + CD₁
Switzerland	M₁
United Kingdom	Sterling M₃³
United States	M_1b, M₂⁴

^¹Currency in circulation plus minimum reserves (at base-year reserve ratios) on the banks’ domestic liabilities. It is closely associated with M₃.

^²Based on ceiling for total domestic credit expansion in 1981.

^⁴More importance attaches to M1b.

Table 1.

Nine Industrial Countries: Intermediate Money Aggregate Targets

Country	Intermediate Target
Australia	M₃
Canada	M₁
France	M₂
Germany, Fed. Rep. of	Central bank money ¹
Italy	M₂²
Japan	M₂ + CD₁
Switzerland	M₁
United Kingdom	Sterling M₃³
United States	M_1b, M₂⁴

^¹Currency in circulation plus minimum reserves (at base-year reserve ratios) on the banks’ domestic liabilities. It is closely associated with M₃.

^²Based on ceiling for total domestic credit expansion in 1981.

^⁴More importance attaches to M1b.

There is now a large empirical literature concerned with determining the “best” definition of money. Three, not unrelated, approaches are used here. One approach regresses income against the different definitions of money (sometimes adding fiscal and other variables) to see which definition provides the best “explanation” for movements in income. A second approach estimates money demand equations using different definitions of money as dependent variables; the best definition is now the one that gives the most stable money demand equation.³

The third approach focuses on estimating substitution elasticities among different monetary assets.⁴ This information is then used to construct a “money” series comprising not only currency and demand deposits but also other assets that are their closest substitutes. Logically, this approach requires an aggregate concept of money that attaches different weights to its components, depending on the “liquidity” of the individual components. The approach has its origins in the contributions made by the Committee on the Working of the Monetary System (1959) and by Gurley and Shaw (1960). These contributions generated considerable interest during the early 1960s, provoking then a large literature on both sides of the Atlantic.

More recently, it has been argued that if a particular definition of money (arrived at in any of these ways) is targeted by the authorities, and hence its supply restricted, this is bound to provoke financial innovations, leading to the creation of substitutes that, in turn, will render the original money concept obsolete. This situation will then require a new extended concept of money, which, in turn, will also become obsolete.⁵

This paper does not attempt any additional empirical work both because such work is already exhaustive (without, in fact, any conclusions) and also (more important) because there are, in fact, conceptual difficulties with such empirical work as a basis for selecting a monetary aggregate when the objective, say, is to stabilize income.⁶

Instead, the paper looks in some detail at the theoretical issues underlying the choice of an intermediate target in a particular type of economy.⁷ The particular type of economy assumed in the analysis is one that is market oriented in three fundamental ways. First, the economy in question has no exchange controls (or the controls are ineffective), so that it is highly integrated with the rest of the world. Second, exchange rates are determined fully by market forces, without any management by the monetary authorities.⁸ Third, the banking system is assumed to be deregulated, in the sense that banks are free to adjust the interest rate on their time deposits and advances.⁹

The paper compares the performance of four money aggregates: base money (H), narrow money (M₁), a broader money aggregate that includes interest-bearing deposits (M₃), and a still broader money aggregate that now also includes holdings of foreign currency by residents (M_3a).

Consider now the issue of the methodological framework to be used in the selection of a money target.¹⁰

The monetary authorities will have several ultimate objectives in mind in designing their monetary policy over a period of, say, one year. They may attach varying weights to expected balance of payments developments, to inflationary developments, and to levels of employment. To simplify slightly, suppose that the monetary authorities have in mind initially some target rate of growth of gross national product (GNP) so that, in effect, the objective of policy is to minimize the welfare losses from deviations from this target.¹¹

It is convenient, in analyzing this problem, to deal first with perfect foresight (the deterministic case). Suppose that the monetary authorities have a model (implicit or explicit) of the economy. This model will contain exogenous variables that include known past values of certain variables and other variables (e.g., fiscal policies, overseas conditions) that will need to be forecast for the year ahead. At the same time, the model will contain structural coefficients indicating how certain variables (e.g., interest rates, income) affect some other variables in the model (e.g., consumption, investment, the demand for money). If the forecasts of the exogenous variables are made with perfect accuracy and if the structural coefficients are also known with certainty, the monetary authorities would not have a problem choosing the appropriate money target. The ultimate outcome (a given rate of growth of GNP) could be made consistent with any potential money target. In other words, one could solve this model for any one of a number of money targets, each of which could, in principle, be targeted. In this context then, and at this level, the question of choosing a target is a trivial and irrelevant one.

In reality, of course, there are bound to be potential errors (uncertainties in the model). (The model, in other words, becomes “stochastic” rather than “deterministic”) The uncertainties can take two forms: those attaching to the structural coefficients of the model or those attaching to the forecasts of the “exogenous” variables in the model. The latter has been extensively treated and allowed for in the literature; the first type of error, however, is less well treated and raises even more difficult issues. In the analysis here, to make the treatment manageable, assume certainty of coefficients but allow for errors and uncertainties only in the exogenous variables. Now, taking account of potential “forecast” errors, it is no longer true that the monetary authorities will be indifferent to the choice of target. It is the fact of uncertainty that gives meaning to the choice of a money target.

Several sources of errors in projections (unanticipated disturbances) are recognized. These, it is assumed, originate at two levels. First, there are disturbances in financial (asset) markets. Second, there are disturbances in expenditures. It is also assumed that these individual disturbances are uncorrelated with one another.

Allowance is made for six asset market disturbances: four originate within the domestic economy; two represent shifts across international frontiers. Domestic disturbances include (1) a shift out of currency into demand deposits, (2) an increase in the demand for free reserves on the part of the banking system, (3) a shift out of demand deposits into time deposits, and (4) a shift out of time deposits into domestic bonds. International disturbances include (1) a shift out of demand deposits denominated in the domestic currency into demand deposits denominated in a foreign currency (the currency substitution case—highlighted in McKinnon (1982)) and (2) a change in the foreign interest rate.

Using a macromodel, let us evaluate each money aggregate for each disturbance in terms of the objective of minimizing fluctuations in income. At the same time, we review the implications for exchange rate volatility of selecting a particular money aggregate. Also, we examine the implications of “deregulation” for interest rate, exchange rate, and income volatility and for the choice of a money aggregate.

Attention is also paid to the question of what happens, for each disturbance, to the behavior of the money aggregates other than the one that is targeted. Assume that the monetary authorities, in fact, target a broad money aggregate (M₃) that excludes holdings of foreign currency by residents. Also, assume that the target is achieved. Then see to what degree the other money aggregates need to deviate from their originally “projected” levels. The objective of this exercise is to indicate how, in the face of different disturbances, different money aggregates can move in different directions.

The principal conclusion here is that a narrow money aggregate, such as M₁ actually performs relatively well. It is demonstrated that, for realistic assumptions about the sources of disturbances, M₁ will tend to outperform the other money aggregates by the criterion of minimizing the fluctuations around a target growth of GNP.

I. Description of the Model Used

This section will attempt to describe verbally the kind of model used. Technical details and solutions are given in the Appendix.

Residents are assumed to hold six financial assets: currency, demand deposits, time deposits (on which interest is paid), domestic bonds, foreign currency deposits, and foreign bonds. The sum of these six assets makes up private financial wealth. The sum of currency and demand deposits comprises M₁. The addition of time deposits gives M₃. The further addition of foreign currency deposits gives the broadest money aggregate, M_3a.

There are four rates of return on assets: the interest rate on foreign bonds, the expected depreciation of the foreign currency, the interest rate on domestic bonds, and the interest rate on time deposits. In a deregulated system, the interest rate on time deposits is assumed to respond, at least partially, to changes in the domestic interest rate.

In principle, the demand for each financial asset will be a function of own and other rates of return and income, subject to the wealth constraint.¹² However, to be realistic and to simplify a little, it has been assumed that some of these coefficients are zero. For example, currency is not allowed to respond to any rate of return, demand deposits do not respond to the foreign interest rate, and foreign currency deposits respond only to income and the expected devaluation.

Although in the formal model the demand for each financial asset must be determined by overall financial wealth, over the period here, changes in financial wealth are not allowed to affect the demand for any asset. Changes in financial wealth come from two sources: changes in stocks from the current account or from budget deficits, and changes in valuation from exchange rate adjustment.¹³ The former, clearly, has more relevance in a longerterm context; the omission of the latter can be justified on the ground that residents are more concerned with the “expected value” of their wealth and, in the context of a short-run model dealing with short-run reversible disturbances, this expected value may not adjust significantly to current changes in exchange rates.

Since it is assumed that the economy is highly integrated, expected returns on domestic and foreign bonds are assumed to be equalized. This equality is represented by the interest rate parity equation. Risk aversion is disregarded, and the forward rate is assumed to be equal to the expected spot rate. Moreover, since this is a short-run model concerned with the effects of unanticipated random shocks, the expected spot rate is assumed to be stationary. This assumption is not implausible and indeed would be consistent with rationally formed expectations.

There is also a banking sector in the model. The banking system holds only two assets: reserve assets and domestic bonds. There is a mandatory reserve requirement on total deposits and a free reserve component that is influenced by total deposits and, as well (negatively), by the domestic interest rate. Using this representation of the banking system, one can generate a money supply equation in which the supply of money is determined by base money (the sum of bank reserves and holdings of currency by residents), income, and the interest rate. Other things being equal, a rise (fall) in income increases (decreases) demand for currency by residents, depletes (increases) reserves of the banks, and forces a contraction (expansion) in the money supply. Again, ceteris paribus, a rise (fall) in the domestic interest rate reduces (increases) the demand for free reserves and so increases (decreases) the supply of money. Finally, other things being equal, an increase in base money will increase the supply of money through a familiar multiplier process.

The model also incorporates a simple goods market. Aggregate demand is determined by the domestic interest rate and the exchange rate (which is assumed to have a normal nonperverse effect). Given the short-term nature of the analysis, prices are taken as unresponsive to changes in aggregate demand.

Shocks are easily incorporated in the model. A shift out of currency into demand deposits is represented by a negative disturbance term in the demand for currency and the same positive disturbance term in the demand for demand deposits. Shifts out of demand into time deposits or out of time deposits into bonds, or out of domestic into foreign deposits, are represented in similar ways. Since the foreign interest rate appears explicitly in the demand for time deposits, a change in this interest rate has a direct effect on the demand for M₃ and M_3a. Finally, an exogenous change in free reserves is represented by a disturbance term in the banks’ demand for free reserves. It then appears as a disturbance term in the money supply equation. (See the Appendix.)

The concern here is with the relative effects on income, for each disturbance and for each money aggregate taken as a target. To illustrate, suppose that M₃ were the target. Then sum the three asset demands to get a composite demand for M₃. The interest rate on time deposits is then solved by allowing it to respond to the domestic interest rate. If M₃ is the target, it can be assumed to be fixed. This equation, then, combined with the interest rate parity equation and the goods market equation, as well, allows one to solve for income (the principal concern), the domestic interest rate, and the exchange rate. One can proceed along similar lines for M₁ and M_3a, combining each of these in turn with interest parity and the goods market equation to get the solutions.

When base money is the target, the money supply is allowed to respond through the money supply equation. This equation, combined with the corresponding money demand equation, allows one to solve for base money in terms of income, the interest rate, the exchange rate, and disturbance terms. This equation is then used to obtain solutions for income, the interest rate, and the exchange rate.

II. The Results

The results of the analysis using the model described in Section I are summarized in Table 2. The findings are now explained in some detail.

Table 2.

Relative Performance of Money Aggregates

^¹From best to worst:

e₁ = Shift out of currency into demand deposits.
e₅ = Increase in banks’ demand for free reserves.
e₂ = Shift out of demand into time deposits.
e₄ = Shift out of time deposits into “bonds.”
e₃ = Shift out of domestic demand deposits into foreign currency deposits.
rf = A change in the foreign interest rate.
u₁ = An expenditure shift.

^²Probable outcome. See discussion in the text.

Table 2.

Relative Performance of Money Aggregates

Disturbances	Performance of Money Aggregates¹	Behavior of H, M₁, M_3a When M₃ Targeted (Deviation from projection)
money supply	M₁ = M₃ = M_3a>H	M₁, M_3a no deviation H will fall below projection
e₅	M₁= M₃=M_3a>H	M₁, M3a no deviation H will be above projection
money demand
e₂	M₃ = M_3a = H > M₁	H, M_3a no deviation M₁ will be below projection
e₄	M₁,>H>M₃>M3a	M₁ and H above projection M3a below projection
e₃	M_3a>H>M₃M_3a > M₁M₁ ambiguous vis-á-vis H and M₃	M₁ ambiguous; H above projection M_3a above projection
rf	M₁ and H difficult to compare
realexpenditure
u₁	M₁>M₃>²M_3a	H and M₁ above projection²
	H > M₃ >²M_3a	H and M₁ above projection²M_3a below projection
	M₁ and H difficult to compare

^¹From best to worst:

e₁ = Shift out of currency into demand deposits.
e₅ = Increase in banks’ demand for free reserves.
e₂ = Shift out of demand into time deposits.
e₄ = Shift out of time deposits into “bonds.”
e₃ = Shift out of domestic demand deposits into foreign currency deposits.
rf = A change in the foreign interest rate.
u₁ = An expenditure shift.

^²Probable outcome. See discussion in the text.

Table 2.

Relative Performance of Money Aggregates

Disturbances	Performance of Money Aggregates¹	Behavior of H, M₁, M_3a When M₃ Targeted (Deviation from projection)
money supply	M₁ = M₃ = M_3a>H	M₁, M_3a no deviation H will fall below projection
e₅	M₁= M₃=M_3a>H	M₁, M3a no deviation H will be above projection
money demand
e₂	M₃ = M_3a = H > M₁	H, M_3a no deviation M₁ will be below projection
e₄	M₁,>H>M₃>M3a	M₁ and H above projection M3a below projection
e₃	M_3a>H>M₃M_3a > M₁M₁ ambiguous vis-á-vis H and M₃	M₁ ambiguous; H above projection M_3a above projection
rf	M₁ and H difficult to compare
realexpenditure
u₁	M₁>M₃>²M_3a	H and M₁ above projection²
	H > M₃ >²M_3a	H and M₁ above projection²M_3a below projection
	M₁ and H difficult to compare

^¹From best to worst:

e₁ = Shift out of currency into demand deposits.
e₅ = Increase in banks’ demand for free reserves.
e₂ = Shift out of demand into time deposits.
e₄ = Shift out of time deposits into “bonds.”
e₃ = Shift out of domestic demand deposits into foreign currency deposits.
rf = A change in the foreign interest rate.
u₁ = An expenditure shift.

^²Probable outcome. See discussion in the text.

Consider first the shift out of currency into demand deposits (e₁). If high-powered money were targeted, the banks would be left with excess reserves, and this would lead to a multiple expansion of deposits. The interest rate and the exchange rate would both fall, while income would rise.

Suppose that one of the other money aggregates were targeted. Now the moment that excess reserves start exerting upward pressure on the money supply, the monetary authorities would take corrective action (e.g., sell bonds to the banks) to remove these reserves. In the end, the exchange rate, the interest rate, and income would all remain unchanged.

If M₃ were actually targeted, M₁ and M_3a would also conform to the implicit projections for these aggregates. H, however, would deviate from its projection. As shown earlier, the removal of excess reserves to restore M₃ means that base money will now be allowed to fall below the projection (Table 2, last column).

Consider now the case in which there is an exogenous increase in the demand for free reserves (e₅). If base money were the target, this would be allowed to follow its course. There would be downward pressure on the money supply, upward pressure on the interest rate and the exchange rate, and income would fall. If, however, the other money aggregates were targeted, the incipient downward pressure on the money supply would be offset by the injection of base money. The monetary authorities would end up accommodating the increased needs of the banking system, again leaving interest rates, exchange rates, and income all unchanged.

As in the previous example, if M₃ were actually the target, M₁ and M_3a would be in line with projections, while base money would be above its projected level.

For “money supply” shocks, then, base money is a poor performer, while the three other money aggregates are equally good performers—in each case completely sheltering exchange rates, interest rates, and income from such shocks. Again, in the face of such shocks, if M₃ were in fact targeted, only base money would record deviations from its projections.

Now consider a variety of “money demand” shocks. Suppose first that there were an exogenous shift out of demand into time deposits (e₂). Now M₁ would fall but M₃ and M_3a would remain unchanged. If M₃ or M_3a were the money target, no corrective action would be taken, and interest rates, exchange rates, and income would all remain unaffected. Also, if base money were targeted, it, too, would be unchanged by the shift, so that no corrective action would need to be taken, again ensuring that the economy is completely sheltered from the disturbance.

The situation, however, would be different if M₁ were the money target. With M₁ down, the monetary authorities would need to take corrective action to restore the original target, and base money would be injected into the economy. This action would lead to a fall in interest rates and the exchange rate and, as well, to a rise in income.

If M₃ were in fact the target of policy, M_3a and H would stay on their projected levels, but M₁ would be allowed to fall by the amount of the switch (Table 2, last column).

A shift out of time deposits into bonds (e₄) is more complicated. Suppose, to begin with, that M₁ were the target. The shift would initially put downward pressure on the interest rate and the exchange rate. In turn, this would exert upward pressure on income. With interest rates also falling on time deposits (by assumption, some adjustment is allowed in line with market rates) and income rising, there would be some observed increase in M₁. At this point, the monetary authorities would take some action to reduce the growth of M₁. In doing this, they would restore the original exchange rate, interest rate, and nominal income. In other words, as long as income is above the original level and the interest rate is below the original level, the observed M₁ will be above its target level, so that action to restore the target will serve to completely stabilize the economy.

The economy would not, however, be stabilized if any of the other money aggregates were targeted in the face of this particular shock. Compare high-powered money with M₃. If M₃ were the target, the above-mentioned effects on interest rates, exchange rates, and income would be allowed to follow their course. If H were the target, the outcome would be different. With income rising, there would be an increased demand for currency, so that with the same targeted level of H, the money supply would be forced down. At the same time, with interest rates falling, the banks would wish to hold more excess reserves in relation to their deposits; this would also force the money supply down. The fall in the money supply would serve to partially stabilize the level of income. For these reasons, then, H would be a better stabilizer than M₃.

M₃, however, will be a better stabilizer than M_3a. The reason is that as income increases there is, by assumption, a fall in demand for foreign currency deposits. If M_3a were the target, the monetary authorities would try to offset the fall in foreign deposits by increasing domestic money (M₃), which would be destabilizing.

If M₃ were in fact the target, M₁ and H would end up being above projection, while M_3a would be below projection. M₃ would be above the projected level because, as indicated above, the rise in income and the fall in interest rates would raise M₁. H would be above the projected level because, again as shown earlier, if it were the target, M₃ would be forced down below its target; so, to restore target M₃, H must be allowed to rise. Finally, M_3a would fall because foreign currency holdings would be reduced.

Consider now a currency substitution (e₃) Compare first M₃ and H. The considerations here are similar to the switch out of time deposits into bonds. There is a fall in the demand for M₃, domestic interest rates and the exchange rate fall, and income rises. H is the better stabilizer for reasons discussed in the previous case: with H targeted, M₃ will fall because of pressure on both currency and free reserves. M_3a, however, will now be a perfect stabilizer. By keeping an eye on M_3a, the monetary authorities will reduce the supply of M₃ to offset the increased holdings of foreign currency. The economy will thus be completely stabilized.

M₁ is now an ambiguous performer. The initial switch is out of M₁ so that there is, effectively, an exogenous fall in the demand for M₁. If M₁ is targeted, this will lead to some fall in interest rates and the exchange rate and to some rise in income. Compare now M₁ and M₃. The test here is what happens to M₁ if M₃ were targeted. If M₁ rises (falls), M₁ would be the better (inferior) stabilizer. What in fact happens to M₁ is ambiguous. There is an initial fall in the demand for M₁ but M₁ will also increase both from the fall in interest rates and the rise in income.

Now consider a disturbance in the foreign interest rate (rf). This case is more complicated than the others. Compare, to begin with, m₃ and H. If M₃ is the target, there will be an excess supply of M₃, interest rates and the exchange rate will fall, and income will rise. The higher foreign interest rate will also exert further pressure on exchange rates (through the interest rate parity equation) and in turn on income and domestic interest rates. In the end, the domestic interest rate will rise but by less than the foreign interest rate, while the exchange rate will fall, opening up a forward premium on the domestic currency to offset the interest rate differential. At the same time, income will rise.

If base money were the target, M₃ could rise or fall, depending on the relative effects of income and interest rates. The first influence reduces the money supply by increasing the demand for currency and depleting bank reserves; the second increases the money supply by reducing the demand for free reserves. It is likely that the first effect will be the dominant one; in this case, H is the preferred target.

For reasons already discussed, M₃ is preferred to M_3a. Compare now M₁ and M₃. The rise in interest rates will tend to reduce M₁ but the rise in income will increase M₁. If the latter is dominant, as seems likely, M₁ will be the better stabilizer.

Finally, consider the important case of a real expenditure disturbance (u₁). As with a disturbance in the foreign interest rate, none of the money aggregates would serve as perfect stabilizers. Compare first H and M₃. In both cases, the increase in expenditure would put upward pressure on the currency and the interest rate, but income would rise. If, with H as the target, M₃ fell (rose), H would be preferred (inferior) to M₃. Whether M₃ will in fact rise or fall if H were targeted depends on the relative influence of rising income (which, as we have seen, increases the demand for currency and puts downward pressure on bank reserves) and the rise in interest rates (which reduces the demand for free reserves). It has been argued that it is likely that the first effect would be the dominant one; in this case, H would be the preferred target.

Compare now M₁ and M₃. The rise in income will tend to raise the level of M₁; the rise in interest rates, however, will reduce M₁ because there will now be an incentive to shift into time deposits. If M₁ rises (falls), on balance, M₁ will be a better (worse) stabilizer because now corrective measures will require that less (more) base money be injected into the economy. As has been argued previously, it seems reasonable to suppose that Mi will rise in the face of an expenditure shock, so that M₁ is likely to be the better performer, but this conclusion becomes weaker, the greater the adjustment of the time deposit rate to market interest rates.

For reasons already discussed, M₃ too will be a better stabilizer than M_3a. As income rises, falling foreign currency holdings will, if M_3a were the target, force the authorities to actually increase M₃.

M₁ and H are, however, more difficult to compare. The issue may be put as follows: If H were the target, what would happen to Mi? If Mi fell (rose), H would be the better (inferior) target. Suppose that the currency-drain effect offsets the free-reserves effect; there would be downward pressure on M₃ but not necessarily on Mi: Mi might nevertheless rise because of the income/interest rate effects noted earlier. On balance, then, it is difficult to judge the relative performance of M₁ and H.

If M₃ were the target, what would happen to the other money aggregates? H would probably be above projection (because, as noted, with H targeted, M₃ would probably fall); M₁ would probably also be above projection (assuming that income is the dominant influence on M₁), while, finally, M_3a would be below projection.

III. Differential Reserve Requirements and Performance of the Money Aggregates

In some economies (e.g., the United States and the Federal Republic of Germany), there are different reserve requirements on demand and time deposits. This possibility has been disregarded in the formal model. Now one must ask, briefly, how the results here might be different if reserve requirements were higher on demand than on time deposits.

To begin, the results for M₁ M₃, and M_3a are basically unaffected by different reserve requirements. If these money aggregates were targeted and, by assumption, controlled, the results would all remain the same. It is different, however, with base money. Now different reserve requirements, for given base money, do affect the money supply process and, hence, outcomes.

Everything turns on what happens to the composition of deposits between demand and time deposits. If the weight of demand deposits increases, the higher reserve requirements will force a contraction in the money supply. The weight of demand deposits will increase (decrease) when income rises (falls) and interest rates fall (increase). When income and interest rates move in the same direction, the outcome for demand deposits is strictly ambiguous. It has, however, been suggested that the income effect might be the dominant one. Bearing in mind these comments, now consider briefly each disturbance in turn.

For a shift out of currency into demand deposits, the weight of demand deposits will increase, and this will be stabilizing. For an increase in the demand for free reserves, the weight of demand deposits will fall, and this again will be stabilizing because it will slow down the contraction in the money supply.

For a shift from demand deposits into time deposits, there will be some expansion in the money supply, which is destabilizing. For a shift from time deposits into bonds, the weight of demand deposits will increase, and this should be stabilizing. For a currency substitution, the outcome is ambiguous. For a change in the foreign interest rate, the outcome is also strictly ambiguous; if, however, one assumes that the income effect is dominant, the effects on the money supply will be stabilizing. Finally, for an expenditure disturbance, again the outcome is strictly ambiguous because income and interest rates both rise. If, however, again the income effect is dominant, the outcome will also be stabilizing.

To conclude, then, there is only one unambiguous case in which the performance of high-powered money actually worsens when there are differential reserve requirements. In all other cases, the outcome is either ambiguous or favors high-powered money. On balance, it would seem that the performance of high-powered money as an intermediate target is probably enhanced by the existence of differential reserve requirements.

IV. Some Conclusions About Performance of the Money Aggregates

The following would seem to be the principal conclusions of the analysis:

(1) Except for currency substitution, the broadest money aggregate—which includes foreign currency holdings—turns out to be inferior to M₃. There is, it appears, little to be said for such a broad money aggregate.

(2) In general, M₁ appears to be a better performer than M₃. Only when there is an exogenous switch out of demand deposits into time deposits is M₃ unambiguously the better performer. For money supply shocks, the two perform equally well. For expenditure shocks, as well as for two money demand shocks, M₁ appears to be the better performer.

The principal reason why M₁ performs well is that M_x is predominantly income determined. If the objective is to stabilize income, M₁ will rise and fall as income rises and falls. By targeting M₁ and correcting for these fluctuations in M₁, the authorities will help to stabilize income.

The more that demand deposits are used almost exclusively for transactions purposes, the less sensitive will demand deposits be to interest rate shifts, and the less will tend to be the exposure to exogenous shifts from demand deposits to time deposits. This increases the relative advantage of M₁ as a money target.¹⁴

(3) A good theoretical case could be made for announcing targets in several money aggregates and, as well, using target bands for each aggregate (as, for example, in the United States). One could then exploit information that becomes available about disturbances in the course of a year to decide what deviation will be allowed from the mean target for each money aggregate. To provide a concrete illustration, suppose that a target band were announced for M₁ and M₃. If all projections were realized, the authorities would aim at the mean target growth in the two money aggregates. Suppose, however, that in the course of the year it were known that there was an exogenous movement out of demand into time deposits. In this case, M₁ would be allowed to fall below its mean target while M₃ would be observed. Now, suppose that income is growing too rapidly and that this is reflected in an unexpected growth of M₁ above the mean target. Then, in this case, the monetary authorities would be trying to maintain the mean M₁ target but would allow M₃ to fall below the mean target.

In practice, this fine tuning might be difficult to achieve. Nevertheless, there is still a case to be made for multitargeting with bands, in that it allows the authorities some discretion when reliable information is available.

(4) H is a particularly poor performer for money supply shocks. Its performance vis-à-vis M₁ is ambiguous for several disturbances. Given these uncertainties, it would seem reasonable to conclude that M₁ is “safer” than H as an intermediate target.

V. Exchange Rate Effects

It is of some interest to examine the implications for exchange rates of selecting different money aggregates as intermediate targets.

It is easily shown that, except for an expenditure shock, the larger the income effect, the larger will be the exchange rate adjustment. Hence, for all monetary shocks (supply or demand), the monetary aggregate that best stabilizes income will also be the one that best stabilizes exchange rates.

For expenditure shocks, however, the opposite holds. To illustrate this point, compare M₃ and H. If M₃ were the target, an expenditure shock would create an excess demand for money (the domestic interest rate would rise and the currency would appreciate, thus opening up an expected depreciation that would offset the higher domestic interest rate). The higher interest rate as well as the appreciation serves to dampen the rise in income. Suppose now that H were the target and suppose, as has been contended, that in these circumstances M₃ would be likely to fall. This would serve to raise interest rates and to strengthen the currency further and thus would be stabilizing. So, the money aggregate that is the more stabilizing would also be associated with a larger exchange rate adjustment. There is then a trade-off. Stabilizing income would, in this case, destabilize exchange rates.

VI. Implications of Deregulation for Volatility of Interest Rates, Income, and Exchange Rates and for Choice of Intermediate Target

Table 3 sets out in some detail the implications of deregulation for the volatility of market interest rates, income, and exchange rates.

Table 3.

Effects of Deregulation on Volatility ofY, E, andrdfor Each Money Aggregate¹

^¹↑ = Increases volatility, ↓ = Decreases volatility. 0 = No effect on volatility.

The results for H, M₃, and M_3a are quite similar and they can be readily summarized. For all monetary shocks, other than those arising from changes in foreign interest rates, deregulation at once tends to destabilize income, interest rates, and exchange rates. The reason is straightforward enough. Interest rate effects will tend to be magnified by deregulation because time deposit rates will adjust, at least partially, to market rates. Suppose that market rates were falling; time deposit rates would adjust downward; this further reduces the demand for broad money, lowering market interest rates further and thus accentuating income and exchange rate effects.

For real shocks or shocks that are due to changes in foreign interest rates, the conclusions, for the same money aggregates, are different. Consider a real shock. Market interest rates rise; with deregulation, time deposit rates will also adjust upward, increasing the demand for money, which, in turn, pushes market interest rates up further. This attenuates the increase in income but accentuates the upward movement in the currency. Thus, for real effects, deregulation stabilizes income but destabilizes interest rates and exchange rates. For a rise in the foreign interest rate, deregulation forces the interest rate up further, which again stabilizes income but now also stabilizes the currency (which is falling).

To conclude then, if H, M₃, or M_3a were the money targets, deregulation would always destabilize market interest rates, but what happens to income and exchange rates depends on the kind of shock to the system. Income will be stabilized for real and foreign interest rate shocks. The exchange rate, however, will be destabilized except for the foreign interest rate shock. Thus, deregulation is almost certain to destabilize both interest rates and exchange rates but may stabilize or destabilize income.

The results for M₁ are different again. For monetary shocks other than those that are due to changes in foreign interest rates (more particularly, e₂ and e₃), deregulation stabilizes interest rates, income, and exchange rates. Consider, by way of illustration, a shift out of demand into time deposits. With regulation, there would be monetary expansion, and market interest rates would fall. If interest rates were deregulated, the interest rate on time deposits would adjust downward; this change would increase the demand for M₁. The monetary authorities would try to reverse this by reducing bank reserves; this would force market interest rates up and slow down the increase in income and the fall in the currency.

For a real shock, interest rates will rise, followed—without regulation—by a rise in time deposit rates. This, in turn, reduces the demand for M₁ which now forces the monetary authorities to be more expansionary. This attenuates the rise in market interest rates and the currency but accentuates the rise in income.

For a foreign interest rate shock, again the interest rate will be higher. Without regulation, there will be a sympathetic upward movement in time deposit rates; this reduces the demand for M₁, which again forces the monetary authorities to be more expansionary. Thus, while the effect on the interest rate is dampened, the effects on income and the currency are accentuated.

For M₁, then, deregulation actually serves to stabilize interest rates; it also almost certainly stabilizes exchange rates. What it does to income, however, depends on the source of the shock.

Is it possible, in the light of these results, to say anything about the implications of deregulation for the choice of intermediate target? If M₁ were chosen in preference to H, M₃, or M_3a, interest rates and exchange rates would be stabilized. The relative advantage of M₁ as an income stabilizer may, however, be weakened if the dominant shocks are real and/or come from changes in foreign interest rates.

APPENDIX

Technical Representation of Model and Solutions

Notation

Key definitions

Household demand for financial assets

\begin{matrix} C = {- b}_{1} r d - b_{2} r t - b_{3} r f - b_{4} (\frac{E e - E}{E}) + b_{s} Y + b_{6} W - e_{1} & (1) \end{matrix}

\begin{matrix} D C = & - b_{7} r d - b_{8} r t - b_{9} r f - b_{10} (\frac{E e - E}{E}) \\ + b_{11} Y + b_{12} W + e_{1} - e_{2} - e_{3} (2) \end{matrix}

\begin{matrix} D T = & - b_{13} r d - b_{14} r t - b_{15} r f - b_{16} (\frac{E e - E}{E}) \\ - b_{17} Y + b_{18} W + e_{2} - e_{4} (3) \end{matrix}

D B = b_{19} r d - b_{20} r t - b_{21} r f - b_{22} (\frac{E e - E}{E}) - b_{23} Y + b_{24} W + e_{4} (4)

\begin{matrix} E · {D C}_{F} = & - b_{25} r d - b_{26} r t - b_{27} r f - b_{28} (\frac{E e - E}{E}) \\ - b_{29} Y + b_{30} W + e_{3} (5) \end{matrix}

\begin{matrix} E · {D B}_{F} = & - b_{31} r d - b_{32} r t - b_{33} r f - b_{34} (\frac{E e - E}{E}) \\ - b_{35} Y + b_{36} W (6) \end{matrix}

Given the wealth constraint, the following would hold:

b₆ + b₁₂ + b₁₈ + b₂₄ + b₃₀ + b₃₆ =₁
b₁₉ = b₁ + b₇ + b₁₃ + b₂₅ + b₃₁
b₁₄ = b₂ + b₇ + b₂₀ + b₂₆ + b₃₂
b₃₃ = b₃ + b₉ + b₁₅ + b₂₁ + b₂₇
b₂₈ + b₃₄ = b₄ + b₁₀ + b₁₆ + b₂₂
b₅ + b₁₁ = b₁₇ + b₂₃ + b₂₉ + b₃₅
e₁ represents the switch from currency to demand deposits
e₂ represents the switch from demand deposits to time deposits
e₃ represents currency substitution
e₄ is the shift from time deposits to domestic bonds

As explained in the text, the model used here is considerably simplified. Wealth is dropped out of the equations, and several coefficients are constrained to be zero. The asset demands used are as follows:

\begin{matrix} C = α_{1} Y - e_{1} & (7) \end{matrix}

\begin{matrix} D C = {- α}_{2} r d - α_{3} r t + α_{4} Y + e_{1} - e_{2} - e_{3} & (8) \end{matrix}

\begin{matrix} D T = {- α}_{20} r d + α_{5} r t - α_{6} (r f + \frac{E e - e}{E}) - α_{7} Y + e_{2} - e_{4} & (9) \end{matrix}

\begin{matrix} E · {D C}_{F} = α_{18} Y + α_{9} (\frac{E e - E}{E}) + e_{3} & (10) \end{matrix}

The constraints imposed on the original model are as follows:

b₁ = b₂ = b₃ = b₄ = b₈ = b₉ = b₁₀ = b₂₅ = b₂₆ = b₂₇ = 0

Also,

b₁₅ = b₁₆

Banking system and money supply equation

\begin{matrix} R R = d_{1} (D C + D T) & (11) \end{matrix}

\begin{matrix} F R = d_{2} (D C + D T) - d_{3} r d + e_{5} & (12) \end{matrix}

These equations represent required reserves and free reserves, respectively. These equations together with the definition of base money and M₃ allow one to derive a money supply equation for M₃, as follows:

\begin{matrix} M_{3} = \frac{1}{m} H - \frac{α_{1} (1 - m)}{m} Y + (\frac{1 - m}{m}) e_{1} + \frac{3}{m} r d - \frac{1}{m} e_{5} & (13) \end{matrix}

where

m = d_{1} + d_{2}

The economics underlying this money supply equation is explained in the text.

Deregulation and banking system

The letter ρ represents the proportion of total deposits held as cash on which interest (rk) may or may not be earned. Suppose that a proportion (α₃₀) of the bank lending is longer term on which the interest rate is fixed, so that (1 – α₃₀) represents the proportion of the loan portfolio on which the new interest rate may be earned. If total bank assets are given, how will interest rates on time deposits (rt) adjust to a change in the market interest rate?

The increased earnings on loans and cash resulting from the increase in the market interest rate will be

\begin{matrix} (1 - α_{30}) (1 - p) (D C + D T) Δ r d + p (D C + D T) Δ r k & (14) \end{matrix}

In a competitive banking system, to offset these increased earnings requires

\begin{matrix} {D T}_{Δ} r t = (1 - α_{30}) (1 - p) (D C + D T) Δ r d + p (D C + D T) Δ r k & (15) \end{matrix}

Suppose that

\begin{matrix} Δ r k = α_{50} Δ r d where α_{50} < 1 & (16) \end{matrix}

Then, one has

\begin{matrix} Δ r t = [(1 - α_{30}) (1 - p) + p α_{50}] \frac{D C + D T}{D T} Δ r d & (17) \end{matrix}

With α₃₀, p, and α₅₀ all less than 1, the bracketed expression must be less than 1. The expression will approach 1 as $α_{30} \to 0 and α_{50} \to 1. With \frac{D C + D T}{D T} > 1,$ the coefficient of adjustment could be greater than 1.

\begin{matrix} Δ r t = α_{9} Δ r d where α_{9} = [(1 - α_{30}) (1 - p) + p α_{50}] (\frac{D C + D T}{D T}) & (18) \end{matrix}

Interest rate parity

\begin{matrix} r d = r f + \frac{F + E}{E} & (19) \end{matrix}

\begin{matrix} F = E_{e} & (20) \end{matrix}

Returning to the original set of demands for financial assets, the assumption of perfect integration implies that b₁₉ = b₃₁ = b₂₁ = b₃₃ = b₂₂ = b₃₄ = ∞. The two equations for bonds (equations (4) and (6)) in effect drop out of the system and are not needed.

Money demand and base-money equations

\begin{matrix} M_{1} = (α_{1} + α_{4}) Y - (α_{2} + α_{3} α_{9}) r d - e_{2} - e_{3} & (21) \end{matrix}

Aggregating equations (7) and (8) and substituting equation (18):

\begin{matrix} M_{3} = & (α_{1} + α_{4} - α_{7}) Y - (α_{2} + α_{3} α_{9} + α_{20} - α_{5} α_{9}) r d \\ - α_{6} (r f = \frac{E e - E}{E}) - e_{3} - e_{4} (22) \end{matrix}

Aggregating equations (7)–(9) and substituting equation (18):

\begin{matrix} M_{3 A} = & (α_{1} + α_{4} - α_{7} - α_{8}) Y - (α_{2} + α_{3} α_{9} + α_{20} - α_{5} α_{9}) r d - α_{6} r f \\ - (α_{6} - α_{9}) \frac{E e - E}{E} - e_{4} (23) \end{matrix}

Aggregating equations (7)–(10) and substituting equation (18):

\begin{matrix} H = & [α_{1} (1 - m) + m (α_{1} + α_{4} + α_{7})] Y - (1 - m) e_{1} - m (e_{3} + e_{4}) + e_{5} \\ - m α_{6} (r f + \frac{E e - E}{E}) - [d_{3} + m (α_{2} + α_{3} α_{9} + α_{20} - α_{5} α_{9})] r d (24) \end{matrix}

Combining equations (13) and (22).

To simplify a little, assume that α₆ = α₉, so that the expression for the expected percentage change in the exchange rate drops out of the equation altogether. This amounts to saying that if there is a change in exchange rate expectations, there is an equivalent switch out of time deposits into foreign demand deposits.

Goods market

\begin{matrix} Y = - α_{10} r d + α_{11} E + u_{1} & (25) \end{matrix}

Aggregate demand is determined by the interest rate, the exchange rate, and a disturbance term (u₁).

Effects of a change in exchange rate expectations

The effects of an exogenous change in exchange rate expectations (Ee) in the model are exactly the same as the effects of a change in the foreign interest rate for M₁, M₃, and H. There is, therefore, no need to treat this as an additional disturbance, insofar as these three alternative money targets are concerned.

However, for the broadest money aggregate (M_3a), there is an important distinction between the two disturbances stemming from the particular assumptions that have been made about asset demands. This is easily seen by looking again at equations (21)–(24). If rd is removed from each of these equations by using equations (19)–(20), it is seen that the coefficients for rf and Ee are the same for M₁ M₃, and H but not for M_3a.

Solutions

As described in the text, the solutions are obtained by deriving a money market equation for each money aggregate to be targeted and then combining it with interest rate parity and the goods market equation. These solutions are shown in Table 4.

Table 4.

Solutions for Income

It is argued in the text that, if M₁ were purely demand determined (i.e., used only for transactions purposes and insensitive to interest rates), M₁ would be very stabilizing vis-à-vis income. This special case would be represented by α₂ = α₃ = 0. Now only shifts from demand deposits to time deposits and currency substitutions produce any real effects. In all other cases, the effect on income is zero.

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Mr. Argy, consultant in the Fund’s European Department when this paper was written, is Professor of Economics at Macquarie University, Sydney, Australia

See, on this, Friedman (1977), McClam (1978), OECD (1979), Bryant (1980), Sumner (1980), Argy (1981), Griffiths and Wood (1981), and Kimelman (1981).

In the past two years, there has been some rethinking about money targets and money aggregates in several industrial countries, notably in Canada, the United Kingdom, and the United States. For a review of these experiences, see Argy (1983 a).

For a multicountry study of the latter, see Boughton (1979); for a recent study of the former, see Lawler (1981).

Chetty (1969), Broaddas (1975), Berkman (1980), Barnett and others (1981), Boughton (1981), and Cockerline and Murray (1981).

Porter and others (1979), Wenninger and Sivesind (1979), Goodfriend and others (1980), Arak (1981), Dotsey and others (1981), Solomon (1981), and Howard and Johnson (1982).

To illustrate this contention, consider first money demand equations. Suppose that the foreign interest rate appears in a broad money aggregate but not in a narrow money aggregate. Suppose, too, that the foreign interest rate is very unstable. Then, although a broad money aggregate in which the foreign interest rate appears as an argument is stable, it nevertheless might be quite unsuitable as a target. Again, M₁ might be more stabilizing for real shocks than a broader money aggregate would be, for reasons discussed in the text; but this would not be reflected in a more stable money demand for M₁. These objections do not, however, apply to the first approach. The difficulties with the first approach are (a) to decide what other variables to include (fiscal, exports, etc.), (b) to decide how to define these other variables, and (c) to interpret the overall findings from the point of view of the optimal money aggregate for targeting.

The results, therefore, are specific to the particular regime assumed.

For a discussion of the experience with such management, see Argy (1982 a).

Assumptions about institutional structure and the selection of the monetary aggregates to be evaluated were made with the United Kingdom particularly in mind, although, of course, the analysis is also highly relevant to other economies with similar institutional structures (e.g., Canada) or to economies proposing to move toward such institutional structures (e.g., Australia—see Committee of Inquiry (1981)). In the United Kingdom, exchange controls were abandoned in 1979 (in any event, there is some question about how effective they had been); also, although there was in 1981/82 some rethinking about exchange rates, since late 1977 those rates have been determined principally by market forces. “Competition and credit control,” which came into force in September 1971, effectively deregulated the banking system. After that, the use of the “corset” on an on/off basis and the imposition of some relatively minor controls over interest rates reintroduced various forms of banking regulation. Since 1980, however, the banking system has again been free of interest rate regulation. (For an analysis of these banking regulations, see Argy (1983 b).) Finally, the United Kingdom initially flirted, briefly, with a very broad money aggregate (M_3a) as the target; after that, it set a target in sterling M₃. There has, however, been a lively debate about different money aggregates as potential targets, with considerable interest shown in a base money or a narrower money aggregate. (See Savage (1980), Artis and Lewis (1981), Buiter and Miller (1981), Bank of England (1982), and “Intermediate Targets” (1982).)

The seminal work here is by Poole (1970). Bryant (1980) has an insightful analysis of methodological issues in target choice in the open economy.

The question of whether the authorities ought to announce a target growth of GNP, bypassing money altogether, is discussed in Argy (1982 b). Briefly, the argument in this paper is that the authorities should announce a nominal income growth target and use the “interest rate” as the means of monitoring income growth. As long as income growth is on target the interest rate will also be held on target. When income is growing faster (slower) than target, the interest rate is allowed to rise (fall) above (below) its target level. This turns out to be stabilizing for both real shocks and demand for money shocks.

The portfolio-balance model is now widely used. Its origins for the closed economy are in Tobin (1969) and it has since been extended to the open economy by, among others, Kouri and Porter (1974); Kouri (1976); and Branson (1980). A recent review of these models is to be found in Murphy and Van Duyne (1980). See also White (1981).

If a country is a net creditor (debtor), a devaluation will increase (decrease) financial wealth.

The new money series constructed by the U.K. authorities conforms almost exactly to the concept identified here. See Bank of England (1982, p. 224), “The objective was to design a new measure which could be expected to be more directly related to transactions in goods and services than sterling M₃, and somehow less sensitive to relative interest rates than M₁.” Thus, if the reasoning in the text is correct, this ought to be the money definition that the authorities should target from now on.

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IMF Staff papers: Volume 30 No. 4

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1983: Issue 004

Publisher:: International Monetary Fund

ISBN:: 9781451930610

ISSN:: 1020-7635

Pages:: 223

DOI:: https://doi.org/10.5089/9781451930610.024

Disturbance	rd	Y	E
e2	$H, \underset{M_{1} ↓}{M_{3}, M_{3 A}} = 0$	$H, \underset{M_{1} ↓}{M_{3}, M_{3 A}} = 0$	$H, \underset{E ↓}{M_{3}, M_{3 A}} = 0$
e₁	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{E ↑}{M_{3}, M_{3 A}} = 0$
e5	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$
e4	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A ↑}}{M_{1} = 0}$	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A ↑}}{M_{1} = 0}$	$\overset{}{H ↑} \overset{M_{1} = 0}{M_{3} ↑} \overset{}{M_{3 A} ↑}$
e3	$\underset{}{H ↑} \underset{M_{1} ↓}{M_{3} ↑} M_{3 A} = 0$	$\underset{}{H ↑} \underset{M_{1} ↓}{M_{3} ↑} M_{3 A} = 0$	$\underset{}{H ↑} \underset{M_{3 A} = 0}{M_{3} ↑} \underset{}{M_{1} ↓}$
rf	$\underset{}{M_{1} ↓} \underset{M_{3 A} ↑}{H ↑} \underset{}{M_{3} ↑}$	$\underset{M_{3} ↓}{H ↓} \underset{M_{3 A} ↓}{M_{1} ↑}$	$\underset{M_{3} ↓}{H ↓} \underset{M_{3 A} ↓}{M_{1} ↑}$
u₁	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A} ↓}{M_{1} ↑}$	$\underset{M_{3} ↓}{H ↓} \underset{M_{3 A} ↓}{M_{1} ↑}$	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A} ↓}{M_{1} ↑}$

Disturbance	rd	Y	E
e2	$H, \underset{M_{1} ↓}{M_{3}, M_{3 A}} = 0$	$H, \underset{M_{1} ↓}{M_{3}, M_{3 A}} = 0$	$H, \underset{E ↓}{M_{3}, M_{3 A}} = 0$
e₁	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{E ↑}{M_{3}, M_{3 A}} = 0$
e5	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$	$H, \underset{H ↑}{M_{3}, M_{3 A}} = 0$
e4	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A ↑}}{M_{1} = 0}$	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A ↑}}{M_{1} = 0}$	$\overset{}{H ↑} \overset{M_{1} = 0}{M_{3} ↑} \overset{}{M_{3 A} ↑}$
e3	$\underset{}{H ↑} \underset{M_{1} ↓}{M_{3} ↑} M_{3 A} = 0$	$\underset{}{H ↑} \underset{M_{1} ↓}{M_{3} ↑} M_{3 A} = 0$	$\underset{}{H ↑} \underset{M_{3 A} = 0}{M_{3} ↑} \underset{}{M_{1} ↓}$
rf	$\underset{}{M_{1} ↓} \underset{M_{3 A} ↑}{H ↑} \underset{}{M_{3} ↑}$	$\underset{M_{3} ↓}{H ↓} \underset{M_{3 A} ↓}{M_{1} ↑}$	$\underset{M_{3} ↓}{H ↓} \underset{M_{3 A} ↓}{M_{1} ↑}$
u₁	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A} ↓}{M_{1} ↑}$	$\underset{M_{3} ↓}{H ↓} \underset{M_{3 A} ↓}{M_{1} ↑}$	$\underset{M_{3} ↑}{H ↑} \underset{M_{3 A} ↓}{M_{1} ↑}$

C	= Currency held by households
DB	= Bonds denominated in domestic currency, held by households (fixed market value—flexible rates)
DB_F	= Bonds denominated in foreign currency, held by households
DC	= Demand deposits held by households
DC_F	= Demand deposits denominated in foreign currency, held by households in foreign banks
DT	= Time deposits held by households
E	= Exchange rate (units of domestic currency per unit of foreign currency)
Ee	= Expected exchange rate
F	= Forward exchange rate
FR	= Free reserves of domestic banking system
GR	= Gross reserves of domestic banking system
H	= Base money (high-powered money)
M₁	= Narrow money—includes currency and domestic demand deposits held by households
M₃	= M₁plus DT
M_3a	= M₃ plus DC_F
RR	= Mandatory reserve requirements against total deposits of banking system
rd	= Domestic interest rate
rf	= Foreign interest rate
rt	= Interest rate on time deposits
W	= Household financial wealth
Y	= Gross national product

C	= Currency held by households
DB	= Bonds denominated in domestic currency, held by households (fixed market value—flexible rates)
DB_F	= Bonds denominated in foreign currency, held by households
DC	= Demand deposits held by households
DC_F	= Demand deposits denominated in foreign currency, held by households in foreign banks
DT	= Time deposits held by households
E	= Exchange rate (units of domestic currency per unit of foreign currency)
Ee	= Expected exchange rate
F	= Forward exchange rate
FR	= Free reserves of domestic banking system
GR	= Gross reserves of domestic banking system
H	= Base money (high-powered money)
M₁	= Narrow money—includes currency and domestic demand deposits held by households
M₃	= M₁plus DT
M_3a	= M₃ plus DC_F
RR	= Mandatory reserve requirements against total deposits of banking system
rd	= Domestic interest rate
rf	= Foreign interest rate
rt	= Interest rate on time deposits
W	= Household financial wealth
Y	= Gross national product

M₁	= C + DC
M₃	= C + DC + DT
M_3a	= C + DC + DT + DC_F
W	= C + DC + DT + DB+ E · DC_F + E · DB_F
GR	= RR + FR
H	= GR + C

Disturbance	H	M₁	M₃	M_3a
e₁	$\frac{\frac{1 - m}{m} (α_{10} + α_{11})}{D_{1}}$	0	0	0
e₂	0	$\frac{α_{10} - α_{11}}{(α_{1} + α_{4}) (α_{10} + α_{11}) + α_{2} + α_{3} α_{9}}$	0	0
$D_{1} = (α_{1} + α_{4} - α_{7}) (α_{10} + α_{11}) + α_{6} + α_{2} + \underset{α_{5} > α_{3}}{α_{3} α_{9}} - α_{5} α_{9} + α_{20} + \frac{d_{3}}{m} + \frac{α_{1} (1 - m)}{m} (α_{10} + α_{11})$
e₅	$\frac{\frac{1}{m} (α_{10} + α_{11})}{D_{1}}$	0	0	0
e₄	$\frac{α_{10} + α_{11}}{D_{1}}$	0	$\frac{α_{10} + α_{11}}{D_{2}}$	$\frac{α_{10} + α_{11}}{D_{3}}$
e₃	$\frac{α_{10} + α_{11}}{D_{1}}$	$\frac{α_{10} + α_{11}}{(α_{1} + α_{4}) (α_{10} + α_{11}) + α_{2} + α_{3} α_{9}}$	$\frac{α_{10} + α_{11}}{D_{2}}$	0
		$D_{3} = (α_{1} + α_{4} - α_{7} - α_{8}) (α_{10} + α_{11}) + α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20}$
		$D_{2} = (α_{1} + α_{4} - α_{7}) (α_{10} + α_{11}) + α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20}$
rf	$\frac{α_{11} (α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20} + \frac{d_{3}}{m})}{D_{1}}$	$\frac{α_{11} (α_{2} + α_{3} α_{9})}{(α_{1} + α_{4}) (α_{10} + α_{11}) + α_{2} + α_{3} + α_{9}}$	$\frac{α_{11} (α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20})}{D_{2}}$	$\frac{α_{11} (α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20})}{D_{3}}$
u₁	$\frac{(α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20} + \frac{d_{3}}{m})}{D_{1}}$	$\frac{α_{2} + α_{3} α_{9}}{(α_{1} + α_{4}) (α_{10} + α_{11}) + α_{2} + α_{3} α_{9})}$	$\frac{α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20}}{D_{2}}$	$\frac{α_{6} + α_{2} + α_{3} α_{9} - α_{5} α_{9} + α_{20}}{D_{3}}$

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Abstract

I. Description of the Model Used

II. The Results

III. Differential Reserve Requirements and Performance of the Money Aggregates

IV. Some Conclusions About Performance of the Money Aggregates

V. Exchange Rate Effects

VI. Implications of Deregulation for Volatility of Interest Rates, Income, and Exchange Rates and for Choice of Intermediate Target

APPENDIX

Technical Representation of Model and Solutions

Notation

Key definitions

Household demand for financial assets

Banking system and money supply equation

Deregulation and banking system

Interest rate parity

Money demand and base-money equations

Goods market

Effects of a change in exchange rate expectations

Solutions

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