DISTURBANCES IN FINANCIAL MARKETS tend to produce short-run instability in macroeconomic variables that are important for the performance of industrial economies. Regardless of whether the disturbances originate in domestic or international markets, the affected variables include notably money stocks and exchange rates. The question that this paper addresses is whether the monetary authorities can reduce both the instability of monetary growth and the instability of exchange rates through the choice of an appropriate short-run strategy, or whether they must choose one of the two objectives.
Except under highly restrictive assumptions, complete stability of monetary growth or of exchange rates would not be an optimal—or even achievable—policy goal. Furthermore, unless the disturbances are exceptionally severe, even the reduction of financial instability is not likely to be a primary goal. The long-run objective of monetary policy is to allow the economy to maintain its potential growth without contributing unduly to inflation. It is nonetheless important that policy actions be implemented in a manner that limits the repercussions from financial disturbances on monetary growth and exchange rates, as long as that objective is consistent with longer-run policy aims.
Short-run instability of monetary growth—that is, substantial month-to-month variation in seasonally adjusted growth rates—is undesirable principally because it can weaken the credibility of the longer-run targets. Regardless of whether short-run growth moves well above or below its target path, market participants and even the authorities may lose confidence in the consistency of current policy actions with the announced targets, making the ultimate achievement of the targets more difficult.1 Short-run instability of exchange rates—substantial variation in exchange rates from month to month or over shorter periods—is undesirable principally because it increases the expense of international trade by increasing the risks associated with uncovered contracts and by increasing the cost of obtaining cover in forward exchange markets.
In practice, fluctuations in monetary growth and exchange rates may serve either to temper or to aggravate the effects of financial disturbances on real activity, depending on the source and permanence of the disturbance. In general, therefore, short-term fluctuations in these variables are not likely to be much help as operational guides for monetary policy unless full information about the disturbances is available to the authorities. The analysis in this paper is based on the presumption that policies are implemented approximately according to a three-stage procedure. First, long-run goals are set in terms of a path for the inflation rate or nominal income. Second, a medium-run target is set for monetary growth, based on estimates of the demand for money, given the goal for income or inflation. Alternatively, the medium-run target may be set in terms of a path for the exchange rate, given estimates of relative monetary conditions in other major countries. In either case, as these estimates change over time, the intermediate target will be adjusted accordingly. Third, a short-run strategy is devised for achieving the medium-run target. It is at this level of operational strategy that choices arise as to how best to reduce short-run instabilities.
The choice of operational strategy may be posed more specifically as the choice of an intervention rule for supplying reserves to the banking system. In the absence of financial disturbances, stable monetary growth and stable exchange rates would both be achievable simply by increasing the supply of bank reserves at a steady rate or, equivalently, by stabilizing short-term interest rates at an appropriate level. In the presence of disturbances, however, the choice of an intervention rule has significant implications for the consequent stability of monetary growth and exchange rates. In general, the preferred strategy depends on both the source of the shock and the parameters of the financial system. Neither strategy will always succeed in reducing instability in both money and exchange rates, but there are circumstances where such success is likely. In those circumstances, monetary stability and exchange rate stability may be said to be operationally consistent policy objectives, and a clear choice may be made in favor of one policy strategy. The purpose of this paper is to isolate and describe the circumstances governing operational consistency in this sense.
This three-stage process presupposes that the amount of information available to the authorities is limited in the short run. Policy decisions are made on the basis of estimates of macroeconomic relationships, such as the demand for money, but those estimates are both imperfect and subject to change over time. Should there occur an important shift, say in the demand function for money, the authorities may be able to determine the source of the disturbance, but in general it is unlikely that they will know precisely either the quantitative importance of the shift or its permanence in time to formulate an optimal policy response. Short-run policy strategies in these circumstances are likely to be specified in terms of fairly simple intervention rules.2
It must be emphasized that all the analysis in this paper rests on the assumption that the ability of the authorities to achieve their intermediate and longer-run objectives is not affected by the choice of a short-run operating strategy. In practice, circumstances may arise in which, say, strict adherence to an interest rate strategy would lead to a cumulative policy error. That type of policy mistake is not the province of this paper. Once the authorities have enough time to assess the quantitative importance and the permanence of any disturbances, it is assumed that they can adjust interest rates or reserve growth in order to regain their intermediate targets within a reasonable period. In the face of major disturbances or political constraints, these adjustments might be quite difficult to implement; this difficulty could offset the advantages of a policy strategy in contributing to short-run stability.
Section I presents a theoretical model of the short-run process affecting exchange rates and monetary growth. Section II describes the methodology required for determining the circumstances under which the targets are operationally consistent, and Section III introduces initial estimates of the model’s parameters. Section IV includes the tests of target consistency, while Section V gives a brief recapitulation of the principal conclusions of the paper.
I. The Model
The purpose of this section is to develop a small theoretical model of the short-run processes that determine changes in exchange rates and money stocks. Because the present study focuses on the short run, it is taken for granted that the long-run equilibrium exchange rate is independent of the relationships described here. This independence is not strictly realistic, but it provides a useful basis for reducing the dimensions of the model to workable proportions. This reduction is accomplished here by ignoring most of the feedback from financial variables to the real sectors of the economy. The exchange rate is thus allowed to deviate from purchasing power parity, while expectations are treated as adaptive rather than as fully rational. The economy is not necessarily at full employment, but any effects from monetary policy on the level of economic activity are assumed to occur slowly enough not to affect the qualitative solution of the model. It is also assumed that there exist several financial assets that are not necessarily perfect substitutes.
The demand function for money describes the portion of total financial wealth (W) that asset holders desire to hold in the form of domestic money (M). This portion depends on the yields on money (rm) and on the substitute assets, domestic bonds (rb) and foreign bonds
where Ėe is the expected rate of change in E, the domestic price of foreign currency.4 A general explanation of the determinants of this expectation would presumably include all the variables, or at least the parameters, in the model as arguments. The present model simplifies by assuming the process to be dominated in the short run by inelastic expectations; that is, market participants expect E to move toward its long-run level.5
where Ē is the expected steady-state value of E. Ē is assumed to be an exogenously determined stochastic variable with unknown probability distribution. A positive value for γ1 implies that the short-run adjustment of E to Ē is expected to be regressively adaptive. A well-established result—see, for example, Henderson and Rogoff (1982)—is that the opposite assumption can produce instability in portfolio balance models. All factors affecting Ėe other than the current change in E are reflected in changes in γ1.
The shift parameters (αi) in this model are not to be regarded as constants; they are random variables with unknown distribution. They thus incorporate the constant term, any relevant dummy variables, and whatever residual variance, covariance, and serial correlation may be present in the relationship. If the distribution of the αi were known, then the authorities could exploit that knowledge and apply a more sophisticated control strategy than is contemplated here.
Considerations similar to the foregoing lead to the demand function for domestic bonds (B).
There is also a net demand for foreign currency assets (F) with yield
Ignoring valuation effects resulting from changes in interest rates, the relationship between the asset markets is such that
These restrictions, of course, are well established in the literature on asset markets.
The assumed independence of the real sectors of the economy from short-run changes in financial markets implies that the sum of the current account balance and direct investment may be treated as exogenous. If official reserve transactions are also exogenous, then so will be the domestic currency value of net foreign assets, changes in which are simply the mirror image of the sum of these three items. The exchange rate (E) and the net stock of foreign assets (F) are both endogenous, but their product is constrained by the balance of payments.
The money supply function is a linearization of the process by which interest rates affect portfolio decisions of the public and the banking system and thereby alter the ratio of the money stock to the level of bank reserves or the monetary base (R).
For example, a rise in interbank or other short-term interest rates (rt) is expected to reduce the banks’ desired liquidity ratios, inducing a rise in the ratio of money to the base. A rise in the yield on money balances (rm) will raise the cost of funds to banks, reduce their demand for liabilities, and reduce the supply of money. The nature and the quantitative importance of these interest rate effects in the money supply process are likely to differ substantially across countries. Furthermore, the stability of the money supply process is affected not only by the institutional characteristics of an economy but also by the implementation of monetary policies.
The interest rate (ri) that is relevant to the money supply process need not be the same as the rates (rb and rf) that dominate the model’s demand functions. Specifically, interbank lending rates are likely to be an important element of ri, but they are not directly relevant outside the banking system except through arbitrage by the banks. Such arbitrage will be effective most of the time, but a spread between ri and rb could emerge through changes either in the term structure of interest rates or in risk premiums. These changes are assumed here to be exogenous to the model and are captured by variation in the parameter α5.
Monetary policy is assumed to be implemented through open market operations, which simultaneously increase the monetary base and decrease the public’s holdings of securities. Letting α6 denote the total supply of domestic bonds to the public and the central bank (treated here as exogenously determined by fiscal policy actions), the supply of bonds to the public can be written6
This assumption does not restrict the monetary base to be an exogenous variable. The authorities’ decisions on open market operations may be based on a policy of controlling changes in the monetary base, bank reserves, or a short-term interest rate such as ri. In a longer time frame, almost any other variable in the model could equally well be chosen as the exogenous control variable, including the money stock or even the inflation rate, assuming that the authorities are able in the long run to offset other influences on that variable and that such behavior does not conflict with underlying policy goals. In the short run, it is useful to restrict the analysis to those variables that are closely influenced by policy actions. In this context, either R or ri can be controlled through open market operations, but not both.
Other monetary policy instruments are easily incorporated into this framework, but they add little to the analysis. For example, the primary impact from changes in the discount rate or in required reserve ratios is to alter the ratio of the money stock to bank reserves; these instruments therefore can be captured through variations in the parameter α4. Nonpolicy shocks to the money supply process also operate through changes in α4 (or, equivalently, through changes in β7 or (β8). Exogenous shifts in the desired currency/deposit ratio or among categories of bank deposits figure prominently in this category. If R is defined as the monetary base (bank reserves plus the currency component of the money stock), then an ex ante rise in the currency/deposit ratio will reduce bank reserves in relation to the monetary base and consequently will lower the ratio of money to the base. If R is defined to include only bank reserves, then a rise in the currency/deposit ratio will directly increase M/R. In either case, shifts in the currency/deposit ratio will be reflected in changes in α4, but the results should be interpreted with some caution.
The next equation relates foreign interest rates to domestic interest rates and the exchange rate in a way that generalizes the standard approaches. The general relationship may be written
If domestic and foreign assets are perfect substitutes and financial capital is perfectly mobile, then domestic and foreign interest rates will move pari passu except in response to expected changes in exchange rates. One can then set
With this set of assumptions, the asset demand functions can be simplified by combining them with equation (10’), eliminating rf from the model. As another special case, if the country is sufficiently small, rf may be treated as exogenous. Again, rf is eliminated from the model but with quite different implications for the effects of policy actions.8
Leaving aside these special cases, equation (10) may be interpreted as a reaction function for foreign monetary authorities, describing the effects on rf of their policy responses to changes in the home country’s interest rates and in the exchange rate. If foreign countries maintain the level of their domestic interest rates in the face of fluctuations in these variables, then γ2 will be close to zero; if they attempt to maintain interest parity, then γ2 will be close to unity. If the foreign authorities react to the exchange rate independently of the home country’s interest rate in determining the appropriate level of their interest rates, then γ3 will be positive.9
The distinguishing feature of money in macroeconomic models is that its yield is less variable than those on other financial assets.10 Conventionally, most models assume rm to be zero or otherwise constant. As market interest rates are in some countries now being paid on a portion of (broadly defined) money balances, the distinction between money and securities is becoming blurred. It remains true, however, that rm may be regarded as less flexible than other interest rates, since in all countries a portion of the money stock pays either no interest at all or a rate that is institutionally or legally determined in the short run. In the present model, this relative fixity is expressed in the following relationship11
where γ4 is a function of the portion of money balances held in a form on which market interest rates are paid. An alternative procedure would be to include such interest-bearing assets in B rather than in M; the implications of the two procedures would be similar.
The model is closed by equation (12)
which defines financial wealth held by the private sectors of the economy. Wealth is valued in units of the national currency; therefore, net foreign assets (F) are multiplied by the domestic-currency price of foreign currency (E). Since W enters the model only as a denominator for its components, it is immaterial whether one divides all values by the domestic price index.
II. Method of Analysis
The next task is to determine the properties of the financial model under alternative policy regimes when the economy is subjected to a variety of shocks. At first glance, the model may appear to be intractable for this purpose; it is too general to yield clear analytical results and yet is too stylized to permit direct empirical estimation. This section therefore introduces an intermediate approach, in which a plausible range of parameter values is specified and analyzed, and in which the robustness of the conclusions with respect to parameter or asset values is tested.
The following example illustrates the required methodology for solving the model. Suppose that a shock occurs in the form of a decrease in the demand for money (and consequently an increase in the demand for domestic bonds) resulting from financial innovation or regulatory reform. Even though the authorities may be able to identify the source and direction of the shock, a significant period may elapse before they are able to quantify its effects well enough to offset them. During this interval, the authorities are presumed to follow a fixed intervention rule—the prevention of fluctuations in either a short-term interest rate or the growth rate of some measure of the monetary base.
The assumed decrease in the demand for money will normally reduce the growth of the stock of money regardless of the choice of instrument. If the authorities stabilize the monetary base, the stock of money will fall by less than the demand for money; interest rates will fall to cushion the shock. Policy will be unintentionally expansionary, and the exchange rate will depreciate. If, on the other hand, the authorities stabilize interest rates (undertaking contractionary actions to counter the initial downward pressure on rates), then the stock of money may decrease by more than the initial decrease in demand. Policy will be unintentionally contractionary, and the exchange rate will appreciate.
The critical question at hand is whether the variability of the exchange rate is likely to be greater or smaller under interest rate control than under monetary base control. If it is greater, then the authorities face an unambiguous preference in favor of base control, since, in this example, that strategy also reduces the volatility of the money stock. Otherwise, the preferred choice for the intervention rule depends on the relative importance of monetary and exchange rate stability in the authorities’ objective function. If the authorities choose to stabilize the base, they will have to accept greater volatility of the exchange rate; if they choose to stabilize interest rates, they will have to accept greater instability of the money stock. The two targets will be operationally inconsistent.
In terms of the model developed in Section I, determination of whether the targets are consistent requires computation of the following statistic:
where Z = M or E, and α represents whichever shift parameter is assumed to be varying. For example, a shift in demand between money and domestic bonds is represented as α = α1 – α2; in the discussion that follows, this shift is denoted as α1,2. The numerator of λ is the multiplier effect of α on M or E given that the authorities allow no change in the base; the denominator is the multiplier for given ri. A negative value for λ(M, α) implies that monetary stability is improved under base control, and conversely. Operational consistency requires that λ(M, α) and λ(E, α) not have opposite signs.
As is illustrated by the preceding example, whether the two targets are operationally consistent depends on both the nature of the shock and the structure of the economy. An obvious property of the model is that while base control tends to produce relatively greater monetary stability following a shock to the demand for money [λ(M, α1,2) <0], the opposite is true following a shock to the supply of money [λ(M, α4)>0]. Most of the λ(Z, α), however, are less obvious than these, and even the simplest of them escape analytical solution. Continuing the example, λ(M, α1,2) can be calculated and reduced to the following expression:12
It may be established that, for example, large values of β7 could generate positive values of γ(M, α1,2). The economic logic of this result is simply that an economy with a highly interest-elastic (although completely stable) money supply function might be better controlled through interest rates than through the monetary base. It is thus necessary to quantify the λ’s.
Direct econometric estimation of the model is impossible for two reasons. First, there is no reason to expect the parameters to possess stable statistical properties over time. The expectations coefficient (γ1), the reaction of foreign interest rates (γ2, γ3), the degree of fixity of the return on money (γ4), the structure of domestic interest rates (α5, α8), and the supply of domestic bonds (α6) are most certainly endogenous to the system, and many of the other parameters will be subject to occasional shifts. Nothing has been assumed here about the error structure of the model, and there is no presumption that the residuals are normally or independently distributed. Second, measurement of some of the key variables is, at best, difficult; reliable time series on B, and especially F, are not available in enough detail to permit separation of valuation effects from actual transactions, while measurement of the yield on money—which includes implicit returns that are likely to vary over time—is still in an embryonic state. Furthermore, what is required for the present problem is not a knowledge of quantitative values of the solution but an indication of the likely signs of the λ’s. These signs depend on the relationships among the parameters but may prove invariant within a broad range of assumed values. The proposed approach is therefore to describe an initial set of assumptions about the parameters and then to test the response of the model to variations in them.
III. Parameter Values
Evaluation of the model requires estimates of the relative sizes of the asset stocks (M, B, and F) and interest rates as well as estimates of the parameter vectors β and γ. The tests presented here employ data from two countries with large and complex financial markets and for which complete data on stocks are readily available—the United States and the United Kingdom. It will be seen that, while the results do depend to some extent on the relative magnitudes of financial stocks, most of the conclusions are robust in the face of substantial variation in these values. The general conclusions thus should apply to a broad range of industrial countries with well-developed financial markets and internationally mobile capital.
Measurement of M, B, and F is inherently arbitrary, inasmuch as money may be defined narrowly or broadly, several types of securities might vie for inclusion in B, and the line between real and financial foreign assets and liabilities is ambiguous. In addition, the theoretical construct F—the net stock of assets valued in foreign currencies and subject to exchange risk—is impossible to measure from available data. The following choices thus should be regarded as a starting point, from which variants can be introduced as desired. First, M is the most broadly defined domestic-currency money stock (M3 in the United States, and sterling M3 in the United Kingdom). Second, B includes all interest-bearing obligations of the central government held by the private non-financial domestic sectors. This limitation on ownership is the same as that used in the definition of M. The exclusion of state and local government securities and of those issued by government agencies (in the United States) or by government enterprises (in the United Kingdom) has the effect of treating those securities as equivalent to private bonds that are not net wealth to the private sector; obviously, the line cannot be sharply drawn.
Third, F is defined as the stock of foreign-issue financial assets held by the private nonfinancial domestic sectors, net of the liabilities of these sectors to the rest of the world. For the United States, F is measured as total credit-market instruments issued by the foreign sector, plus bank deposits held abroad, plus net trade debt of the foreign sector, minus corporate securities and U.S. bank deposits held by the foreign sector. This construct is equivalent to the net position of the United States vis-à-vis the foreign sector, minus the net foreign position of the central government, minus the net stock of direct and miscellaneous investments. For the United Kingdom, F equals the sum of the net external portfolio balance and the net banking balance. Data for all these stocks, and the monetary base in each country, are shown in Table 1 for the end of 1980.
|United States||United Kingdom|
|Variable||(In billions of dollars)||(As per cent of wealth)||(In millions of pounds)||(As per cent of wealth)|
The two countries differ substantially in the composition of private financial wealth (W), with money balances accounting for a much larger portion of the total in the United States. Ordinary savings deposits in the United States at the end of 1980 were as large a sum as the total private domestic holdings of government securities, and aggregate money balances were more than four times as large. In the United Kingdom, M and B were more nearly the same size. The contrast is amplified by the fact that a much smaller portion of money balances pays a market-determined interest rate in the United States (about 20 per cent) than in the United Kingdom (about 60 per cent). Thus, if money were redefined to exclude assets paying market interest, M would still account for more than 60 per cent of U.S. financial wealth but only 20 per cent in the United Kingdom.
In both countries, the net stock of foreign assets is a small positive number. Simple portfolio balance models in which the exchange rate is determined entirely by valuation effects are unstable in the region of F = 0, and E is indeterminate at that point. The addition of expectations effects, as in the present model, implies that F can be negative without generating perverse results, as long as the expectations effects dominate the perverse valuation effects. The problem does not arise for the data in Table 1, but F is small enough that data for other years could easily become negative. Tests of the range of permissible values for F are presented in Section IV.
Table 1 also gives values for the monetary base (R) in each country. These values are similar in relation to total wealth, but the ratios of the money stock to the base are quite different (12.3 in the United States, 6.7 in the United Kingdom). More important, the stability of the money-to-base relationship appears to be much greater in the short run for the United States than for the United Kingdom. The coefficient of variation for monthly changes in the U.K. ratio over the period 1980/81 was 2.3, while for the United States it was only 1.1. This difference alone does not imply that the one is less controllable than the other, but it does suggest that the parameter α4 is probably subject to greater variation in the United Kingdom than in the United States, and that β7 and β8 may be larger.
Estimation of the parameters of the model has an inherently arbitrary component, whether accomplished through regression analysis or not, because of the interplay among model specification, estimation technique, and statistical results. The one function in the model that has been studied extensively is the money demand function; available estimates of the steady-state elasticity of demand for broadly defined money with respect to yields on domestic securities range from near zero to about –0.6 in the United States and from near zero to well over –1 in the United Kingdom.13 Since this model is short run in nature, an estimate toward the lower end of the range would appear to be appropriate. It is initially assumed that the short-run elasticity [denoted η(Md, rb)] is –0.02 in the United States and –0.1 in the United Kingdom,14 but a range of values is also considered.
The interest elasticity of the demand for money provides a basis for determining the overall scale of the parameter vector β. The individual parameters then depend on the hierarchy of asset sub-stitutability. Recall that the various financial assets are not perfect substitutes; if they were, then a portfolio balance model would serve no purpose; M, B, and F could be collapsed into a single asset, and all interest rates would always be equal. A slightly weaker assumption would be that all assets are equally but finitely substitutable, implying that portfolio allocation would be unaffected by an equiproportionate change in all interest rates. That assumption, however, is not supported by available evidence; studies of the demand for money, for example, typically find relatively little effect from foreign interest rates. The effect of the own yield on money is more difficult to measure, but again the evidence suggests that the effect is not sufficient to leave money demand unchanged in the face of a general rise in interest rates. The implication of these findings is that asset demands are asymmetric, the degree of substitutability depending on the characteristics of the assets involved.
In light of these considerations, and in the spirit of seeking plausible initial estimates around which tests can be made, the following assumptions have been made to generate the coefficient vector β.
(a) The elasticity of the demand for money to its own yield is equal in absolute value to the elasticity to yields on domestic securities.
(b) The elasticity of the demand for money to yields on domestic securities is twice the elasticity to yields on foreign securities.
(c) The elasticity of demand for foreign securities to yields on domestic securities is twice the elasticity to yields on domestic money.
(d) In the demand for domestic bonds, domestic money and foreign securities are equal substitutes.
(e) The partial-vector elasticity of demand for foreign securities is the same as the partial-vector elasticity of demand for domestic securities.
where r represents the vector of interest rates (rb, rm, rf).15
(f) The total elasticity of money supply to yields on domestic securities is a multiple of the absolute value of the demand elasticity; this multiple (K3) is given a value of 2 for the United States and 4 for the United Kingdom.16
(g) The elasticity of money supply to its own yield is equal to the absolute value of the elasticity to interbank rates.
The asymmetries in assumptions (b) and (c) imply that domestic securities are a closer substitute for domestic money than are foreign securities and—as a corollary—that domestic securities are a closer substitute for foreign securities than is domestic money. Alternative approaches, including the imposition of symmetry (k2 = 1), are to be examined as well. The foregoing assumptions, combined with end-1980 data for assets and interest rates, produce the β values shown in Table 2.17 A number of the assumptions are highly arbitrary, so that a finding as to the robustness of the model’s properties is essential.
|Coefficient||United States||United Kingdom|
The γ vector contains four elements: the exchange rate expectations coefficient (γ1), the parameters of the foreign authorities’ reaction function (γ2 and γ3), and the response of the yield on money to yields on securities (γ4). A reasonable (although arbitrary) value for γ1 may be derived by making the following assumption.
(h) The partial elasticities of r*f to rf and E are the same in absolute value.
Next, the reaction function may be estimated from available studies. The values for γ2 and γ3 shown in Table 2 are derived from the reaction functions for ten industrial countries in Black (1983). Not surprisingly, these estimates indicate that U.S. interest rates and U.S. dollar exchange rates have a major impact on the policy reactions of other countries; reactions to the corresponding U.K. data are much smaller.
(i) The elasticity of rm to rb is set equal to the portion of money balances on which market interest rates are paid (K4).
ε(rm, rb) = k4
The parameter γ4 then depends also on the level of rm, which is determined not only by the direct payment of interest on deposits but also by the indirect returns from deposit services, such as bookkeeping and check clearing. These indirect returns are assumed to be on the same order of magnitude as the fixed interest payments on savings deposits in the United States—an assumption that is consistent with the findings of most studies of implicit deposit returns.18
The responses of the model to monetary and fiscal policy actions are summarized in Table 3. The purpose of these simulations is not to attempt to measure the policy responses that would in fact occur in the United States or the United Kingdom, but rather to determine whether the assumed parameter values are internally consistent in the sense of generating sensible solutions. The first simulation is for an increase of 1 per cent in the monetary base (R), which produces the normal responses of a rise in M, a fall in interest rates, and a depreciation of the exchange rate (an increase in E). The two versions of the model differ somewhat in their responses, with the U.K. parameters producing relatively smaller changes in the money stock (because of the greater supply-side interest elasticity) and larger changes in the exchange rate (because of the larger role for F and the smaller reactions in foreign interest rates) than in the U.S. version.
|Effect in Per Cent or Percentage Points|
|Monetary base increased by 1 per cent||Interest rates (ri) increased by 1 point||Supply of bonds (α6) increased by 1 per cent|
The middle columns in Table 3 illustrate the effects of monetary policy when the control variable is the short-term interest rate rather than bank reserves. These responses are, of course, in strict proportion to the corresponding entries in the first simulation, because both policies are implemented through open market operations in domestic securities. But whereas a change of 1 per cent in the monetary base has a relatively small impact on the money stock with the U.K. parameters, a change of 1 point in interest rates has a relatively large impact for exactly the same reason, viz., that the supply of money is assumed to be relatively more elastic with respect to interest rates. The impact on the exchange rate is again magnified in the United Kingdom because of the relatively small offset through adjustments in foreign interest rates.
The third simulation in the table is for an increase in the supply of domestic bonds such as would result from an expansion in the public sector deficit. Holding constant the monetary base, an increase of 1 per cent in the supply of domestic bonds drives up interest rates and hence induces a small increase in the money stock along with an appreciation of the exchange rate. The relative responses under the two assumed sets of parameters are similar to those found in the first two simulations.
IV. Target Consistency Tests
The question that this model is designed to answer is whether a simple policy rule can be designed so that by stabilizing one target variable the authorities can stabilize the other as well. The answer to this question depends on the signs of the λ vector, which are indicated in Table 4 for the basic set of assumed parameters. In the table, a negative value for λ indicates that the target variable is relatively more stable when the authorities control the monetary base, while a positive λ indicates that stability is improved when the authorities control the path of interest rates. A value of zero implies that the choice of intervention rule does not affect the degree of instability in the target variable. It is readily apparent that for a number of shocks, the signs differ between λ(M, α) and λ(E, α), suggesting that the two targets are operationally inconsistent. It also turns out, however, that for other shocks the two are consistent, so that a judgment on the issue requires further knowledge of which shocks are quantitatively important in the particular circumstances of the moment and place.
|United States||United Kingdom|
|λ(M, α)||λ(E, α)||λ(M, α)||λ(E, α)|
|Shifts in asset demand|
|α1, 2 (Md, Bd)||–||–||–||+|
|α1,9 (Md, Fd)||–||+||–||+|
|α2, 9 (Bd, Fd)||—||—||—||—|
|Shifts in asset supply|
Positive signs indicate a preference for an interest rate rule; negative signs, for a monetary base rule; and zero, for either one.
Positive signs indicate a preference for an interest rate rule; negative signs, for a monetary base rule; and zero, for either one.
The signs on the λ(M, α) are mostly negative except for α4, confirming the standard result: if a well-defined relationship exists between the monetary base and the stock of money, then the authorities can control monetary growth better through the base than through interest rates, regardless of the source of the shock. If, however, the supply relationship is itself subject to change, then interest rate control is preferred. If stability of monetary growth were the sole target for monetary policy, the choice of instrument would depend only on one’s judgment of the relative importance of changes in α4.
Introducing desired exchange rate stability complicates the analysis substantially. Suppose, for example, that an exogenous shift occurs in the public’s preferences, away from holding domestic money in favor of holding foreign assets (α1,9 decreases). If the authorities hold the growth of the monetary base constant, this shift will cause a direct decrease in foreign interest rates, a smaller indirect decrease in domestic interest rates, a depreciation of the exchange rate, and a decrease in the growth rate of the money stock (induced by the decrease in interest rates). If, instead, the authorities act to stabilize domestic interest rates—selling domestic securities to prevent ri from falling—then the decrease in monetary growth will unambiguously be larger than before. Whether the exchange rate depreciates more or less than before is an empirical question. The larger decrease in the money stock mitigates the depreciation, but this effect could be more than offset if the shift in interest rate differentials is larger than before. For both sets of initial parameters in this model, the movement in the exchange rate is reduced under interest rate control [λ(E, α1,9)> 0], implying that for this type of disturbance, the two targets are operationally inconsistent.
This example illustrates a point that is essential for understanding the complexity of the relationship between interest rates and exchange rates. In response to this shift in asset demands, the interest rate differential shifts in favor of the home country. At the same time, also as an endogenous response to the shift in asset demands, the exchange rate depreciates. It is not possible to define a straightforward causal relationship between interest rate differentials and exchange rates, because both are responses to functional shifts. For the same reason, it is not possible to conclude that stability of interest rate differentials will necessarily contribute to stability of exchange rates. In some circumstances, it is necessary for the authorities to allow the interest rate differential to adjust to reflect the shift in asset demands.
Suppose next that the initial shift in preferences is from B to F (a decrease in α2,9) rather than from M to F. Foreign interest rates again decrease, but now domestic interest rates rise if the authorities are stabilizing the monetary base. The rise in domestic rates induces an increase in monetary growth; again, the exchange rate depreciates. If the authorities purchase securities to prevent the increase in interest rates, they will aggravate the increase in monetary growth and thus are likely to aggravate the exchange rate depreciation as well. This second case therefore is likely to imply target consistency, as it does under both sets of parameters in Table 4. The difference in these two cases is that a change in α1,9 affects primarily the demand for money; M and E respond in opposite directions, and any monetary policy designed to stabilize one will aggravate the other. When α2,9 changes, the primary effect on M is through the money supply function; M and E respond in the same direction, and the two may be stabilized consistently. More generally, the normal implication of most disturbances that affect the supply of money more than the demand for money will be that the targets will be consistent. An increase in ri relative to rb (an increase in α5), for example, has effects similar to those of a decrease in α2,9. Shifts in the money supply relationship itself (α4) also produce conditions under which the two targets are consistent.
A possible exception to the supply-side consistency rule arises in response to a shift in the yield on money balances. Suppose, for example, that a change in regulation or in competitive conditions forces the banking industry to pay (implicitly or explicitly) higher returns on deposit accounts, indicated as an increase in α8. The rise in rm reduces the profitability of providing deposits, so that the supply of money is reduced while the demand is increased. By assumption, the supply of money is more interest-elastic than the demand; the stock of money therefore will decrease. Interest rates rise, and the exchange rate appreciates. If the authorities now act to offset the rise in interest rates, the net impact on the stock of money is likely to become positive. Depending on how much monetary expansion is required to prevent domestic interest rates from rising, the exchange rate may appreciate by a smaller amount than initially, or it may depreciate. Normally, then, the two targets are likely to be inconsistent, since interest rate control leads to a smaller change in the exchange rate. However, if the exchange rate were to depreciate under interest rate control by more than the appreciation under base control, while the money stock increased by a relatively small amount, then the two targets would be consistent with base control preferred for both. That configuration would appear to require a narrowly restricted and highly unlikely set of parameter values. On the other hand, if under interest rate control the money supply increased only moderately while the exchange rate appreciated by less than under base control, then an interest rate strategy would be preferred consistently.
The opposite circumstance—in which the initial disturbance is to the demand for money—is more complex; the targets may or may not be consistent. Consider a shift in fiscal policy, represented in the model as a shock to α6. An expansionary fiscal policy increases the demand for money, which in turn produces an increase in interest rates, a small induced rise in the stock of money, and an appreciation in the exchange rate. If the monetary authorities accommodate this expansion by offsetting the increase in interest rates, the rise in M will be larger, and the exchange rate may depreciate. The depreciation in E could be larger or smaller than the appreciation under reserve control. The assumptions underlying Table 4 imply that the depreciation resulting from accommodation is small in the United Kingdom [λ(E, α6) > 0] and large in the United States [λ(E, α6) < 0]. Hence, only with the U.S. parameters are the two targets operationally consistent. Quite similar results follow from an initial shift in demand from B to M(α1,2).
Finally, one may analyze the effects of shocks to the supply of F (α3) or to the anticipated return on foreign assets (α7). An increase in the supply of F leads directly to an appreciation in the domestic currency, along with an increase in
Whether stability of exchange rates and monetary growth are consistent targets under conditions of shifting supplies of foreign assets depends entirely on the sign of the endogenous response of domestic interest rates. Clearly, monetary growth will be more stable in these circumstances if the authorities control the monetary base than if they control interest rates. If interest rates rise while the base is fixed (the U.S. example), then the alternative policy regime will require expansionary operations that will amplify the initial increase in M but reduce the appreciation in the exchange rate; the two targets will be operationally inconsistent. But if interest rates decrease initially (the U.K. example), then a policy of stabilizing interest rates will require contractionary action that will amplify both the decrease in M and the appreciation in E. In this case, the two targets will be consistent.
Similarly, an increase in α7 initially increases both rf and
The nine disturbances listed in Table 4 may now be grouped according to their implications for target consistency. First, there is a set of shocks for which stability of M and of E are operationally consistent objectives under normal conditions, regardless of the specific parameter values. These include shifts in the demand for domestic securities relative to that for foreign assets (α2,9) and shifts in the structure of domestic market interest rates (α5), both of which require a strategy of base control; and shifts in the money supply function (α4), for which a strategy of interest rate control is preferred. In addition, shifts in foreign interest rates (α7) have no domestic effects—unless they are large enough to affect the real sectors directly—and therefore do not create a policy dilemma. Second, there is one disturbance for which monetary stability almost unambiguously requires base control while exchange rate stability requires interest rate control: shifts in demand between money and foreign assets (α1,9). Finally, there is a group of disturbances for which consistency is an empirical question to a much greater degree than in the first two groups; this set includes shocks to the supply of F (α3), fiscal policy (α6), shifts in demand between money and domestic bonds (α1,2), and shifts in the yield on money relative to market interest rates (α8).
The sensitivity of these conclusions to changes in the assumptions in the model is explored in the next two tables; Table 5 indicates the implications of a number of special cases, and Table 6 examines the effects of allowing selected parameters to vary across a wide range of values. Both tables show only the ;’s for which one or more experiments reverse the signs on at least one λ. Throughout this exercise—except in two extreme circumstances noted in Table 6—target inconsistency holds for α1,9 while consistency holds for α2,9 and for α4 and α5.
|United States||United Kingdom|
|Assumptions||α1, 2||α3||α6||α8||α1, 2||α3||α6||α8|
|(1) Initial parameters||–||+||–||+||+||–||+||+|
|(2) rf exogenous (γ2 = γ3 = 0)||+||+||+||+||+||—||+||+|
|(3) Ms exogenous (β7 = β8 = 0)||+||+||—||+||+||—||+||+|
|(4) Md and Fd independent (K2 = 0)||—||+||—||+||+||+||—||+|
|(5) Symmetrical substitutions (K2 = 1)||+||+||—||—*||+||—||+||— *|
|(6) M defined narrowly (γ4 = 0)||—||+||—||+||—||—||—||+|
A negative sign here indicates that M and E are consistent, and conversely. In general, a minus sign (–) implies that λ(E, α) and λ (M, α) are both negative; a plus sign (+) implies that λ(M, α) <0 and λ(E, α) > 0. An asterisk (*) indicates that both are positive.
A negative sign here indicates that M and E are consistent, and conversely. In general, a minus sign (–) implies that λ(E, α) and λ (M, α) are both negative; a plus sign (+) implies that λ(M, α) <0 and λ(E, α) > 0. An asterisk (*) indicates that both are positive.
|Target inconsistency range for|
|α1, 2||1.323||1.5||0.683||1.0||0||0.63||–||0||0.375||– 0.062||0.018|
|α5||–||–||–||–||–||– 0.062||– 0.041|
|Target inconsistency range for|
|α1, 2||+||+||0||11.83||0.273||1.0||0||0.243||– 0.290||0.139|
Where values are not given, “ – ” and “ + ” indicate consistency or inconsistency, respectively, throughout the allowed range.
Where values are not given, “ – ” and “ + ” indicate consistency or inconsistency, respectively, throughout the allowed range.
Row 1 of Table 5 recalls the basic result from Table 4, with all the parameters at their initially assumed values. For the remaining rows, one or more parameters have been set to an extreme value, reducing the dimensions of the model accordingly. The first experiment (row 2) takes foreign interest rates to be fixed, effectively eliminating the foreign reaction function. This assumption forces larger adjustments in exchange rates, especially when the authorities are controlling the monetary base and allowing domestic interest rates to fluctuate. It thus becomes somewhat more likely that inconsistent (+) situations will arise in which monetary stability requires base control while exchange rate stability requires interest rate control. Similar conclusions follow if the money supply is independent of interest rates (row 3). Now the advantages of base control for monetary stability are enhanced, while interest rates and hence exchange rates become more volatile than before under base control.
One of the principal differences in the two sets of parameters is that the effects from direct substitution between money and foreign assets are relatively greater in the United Kingdom than in the United States. Consequently, the restoration of equilibrium requires relatively smaller shifts in the differential between domestic and foreign interest rates. The removal of direct substitution between r*f and the demand for money (row 4) brings the properties of the U.K. solution more nearly into conformity with those under the U.S. column. In the opposite case (row 5), in which asset substitutions are assumed to be fully symmetrical, the U.S. results approach those for the United Kingdom in that the targets become inconsistent in the face of shocks through demand shifts between M and B. Moreover, for row 5, interest rate control is consistently preferred in both countries in the face of shifts in the yield on money balances.
For row 6 of Table 5, money is defined more narrowly, excluding all assets on which market rates of interest are paid. This change has the effect of reallocating wealth from money to domestic securities and of making the yield on money smaller and exogenous. These modifications magnify the response of market interest rates to the monetary base, increasing somewhat the likelihood that a policy of stabilizing the base will help to stabilize the exchange rate as well as monetary growth. For two cases shown in Table 5 (shocks to α1, 2 and α6 with the U.K. parameters), target inconsistency disappears under these assumptions.
Table 6 presents a more general description of the effects of changes in several assumptions underlying the solution of the model. In general, the solution depends on ki, i = 1,…, 4; γii = 1, 2, 3; η(Md, rb); and the relative sizes of the asset stocks.20 The sign vector λ, however, is independent of some of these assumptions. Most important, λ is completely unaffected by changes in η(Md, rb) or in γ1 or γ3, as long as η(Md, rb) is negative and γ1 + γ3 is positive. Table 6 indicates the effects on λ as each of the remaining parameters varies over its full potential range, holding all other parameters constant at their initial values. Note, however, that, in general, the entire β vector is affected by a change in any of the assumed parameters. In addition, the table includes a test of the effects of changing F while holding B constant.
The allowed ranges of parameters are determined partly by prior assumption and partly by ruling out perverse results. For k1, the minimum value (1.0) implies that the demand for money responds to its own yield with the same absolute elasticity as to domestic security yields; the maximum value (1 + k2) implies that the elasticity to the own yield is equal to the sum of the cross elasticities. Larger values of k1 would imply that an equiproportionate increase in all interest rates would increase the demand for money. The range of k2 is restricted only to rule out the possibility that foreign interest rates affect the demand for money by more than domestic interest rates. The ratio of the absolute interest elasticities for money supply to money demand (k3) is allowed to take on any value, as long as it does not become large enough to eliminate the positive effect of an increase in the base on the stock of money. The parameter k4 is allowed to range from 0 (rm fixed) to 1 (rm fully reflecting changes in rb), provided that the βi do not become negative as k4 approaches unity.21 The maximum value for γ2 (∂rf/∂rb) is the value above which an expansionary monetary policy would lead to currency appreciation; similarly, the range for F is restricted to rule out perverse effects on E from monetary policies or negative values for the βi. Recall that negative values of F are acceptable, as long as they are dominated by expectations effects working through γ1 and γ3.
The large number of sign changes in Table 6 reveals the extent of sensitivity of λ to several of the quantitative assumptions. The central conclusion to be drawn is that it is difficult to derive general implications about target consistency in the face of most of the shocks listed in the table. There are, however, some notable exceptions. First, as noted earlier, the targets are unambiguously consistent for shocks to α2,9or α7 and unambiguously inconsistent for shocks to α1, 9. Second, for both countries, the targets are consistent under shocks to α4 or α5 unless F is negative and near the limit of its nonperverse range. Third, with the U.S. data, the targets are invariably inconsistent under shocks to the supply of F (α3). Fourth, the targets are inconsistent in the United Kingdom in the face of shifts between domestic money and domestic bonds (α1, 2) unless one or more of the parameters differ radically from their assumed values (i.e., at least doubled or halved). In the other listed cases, relatively minor shifts in at least one assumption can reverse the consistency conclusion.
This paper has examined the extent to which monetary authorities can choose an operational strategy that will improve the stability of both monetary growth and exchange rates. The clearest examples of situations where the two can be stabilized through the appropriate choice of intervention rule arise whenever the supply of money is less stable than the demand for money. If the ratio of the money stock to the monetary base is unstable, then a strategy of allowing the base to fluctuate in order to prevent fluctuations in interest rates will serve to moderate the consequent movements in both money and exchange rates. A more subtle example arises when there is a shift between the demand for domestic securities and the demand for foreign securities. With no shift in the demand for money, the primary impact on monetary growth is through the interest elasticity of the supply of money. In this case, a strategy of providing steady growth in the monetary base will allow interest rates to adjust freely to reflect the desired portfolio shift. It will thus help to stabilize the exchange rate as well as monetary growth. Similarly, a strategy that focuses on the monetary base is preferred when there is a disturbance affecting the structure of domestic interest rates.
The authorities may also be able to find a consistent strategy when the demand for money shifts, but the scope for doing so is much more limited. If the demand for money accelerates, then a strategy of controlling the monetary base is most likely to help to stabilize monetary growth; that strategy, however, will in effect be restrictive and will tend to generate an appreciation in the exchange rate. Alternatively, an intervention rule that attempts to stabilize interest rates will lead to greater monetary growth and could cause a depreciation in the exchange rate. It has been shown here that the appropriate strategy for stabilizing the exchange rate depends on the nature of the shift in the demand for money, the parameters of the model, and the relative importance of money, domestic securities, and net foreign assets in the public’s portfolios. In general, when the demand for money is unstable, or when other shocks such as changes in fiscal policy alter the demand for money, exchange rate stability can be attained only if the authorities permit monetary growth to fluctuate in response to the shocks.
Recall that the value of the total elasticity of the demand for money to rb is assumed to be given. Allowing for interest arbitrage, this elasticity may be written as
By a similar process, the assumptions (a-i) in Section III can be converted from elasticities into coefficient equations as follows:
These ten equations, plus the additive constraints ((5’)-(5”‘)), generate the eleven βi, plus γ1 and γ4, for given values of
The two parameters in the reaction function (γ2, γ3) are derived from Black (1983). Black estimates a number of reaction functions for the central banks of ten industrial countries. The equations from which γ2 and γ3 are derived regress the discount rate in each country on two internal variables—inflation and unemployment—and four external variables—the ratio of reserves to imports, the ratio of exports to imports, the foreign interest rate (measured as the yield on three-month Eurodollar deposits), and the real exchange rate (measured by relative normalized unit-labor costs adjusted for changes in the nominal effective exchange rate). The coefficients on these last two variables provide the basis for estimating γ2 and γ3, respectively. This procedure implies (rather arbitrarily) that these coefficients apply to domestic interest rates generally, and not just to the discount rate.
For the United States, γ2 is equal to the weighted average of the coefficients on Eurodollar rates, the weights being taken from the multilateral exchange rate model (MERM). (See Artus and McGuirk, 1981.) For the United Kingdom, it has been assumed that each country’s reaction to a change in Eurosterling interest rates would equal its response to Eurodollar rates times the ratio of that country’s U.K. weight to its U.S. weight in the MERM. The U.S. Federal Reserve System, however, is assumed not to respond at all to changes in external variables.
As for exchange rate effects, Black’s coefficients indicate the effect on each country’s domestic interest rates of a change in its real effective exchange rate. These coefficients, times the effect of a change in the value of the U.S. dollar or the pound sterling on each other country’s effective exchange rate (i.e., the U.S. weight or the U.K. weight in the country’s MERM index), weighted in the same way as for γ2, give the required values of γ3. Note that the model used in this paper assumes that relative costs are fixed in the short run, so that changes in real and nominal exchange rates are equal.
ArtusJacques R. and Anne KennyMcGuirk “A Revised Version of the Multilateral Exchange Rate Model” Staff Papers Vol. 28 (June1981) pp. 275–309.
BlackStanley W. “The Use of Monetary Policy for Internal and External Balance in Ten Industrial Countries” in Exchange Rates and International Macroeconomicsed. by JacobFrenkelNational Bureau of Economic Research (University of Chicago Press1983).
BoughtonJames M. “Recent Instability of the Demand for Money: An International Perspective” Southern Economic Journal Vol. 47 (January1981) pp. 579–97.
CoghlanRichard T. “A Transactions Demand for Money” Bank of England Quarterly Bulletin Vol. 18 (March1978) pp. 48–60.
FrenkelJacob A. and CarlosA. Rodriguez “Exchange Rate Dynamics and the Overshooting Hypothesis” Staff Papers Vol. 29 (March1982) pp. 1–30.
HendersonDale W. “The Role of Intervention Policy in Open Economy Financial Policy: A Macroeconomic Perspective” in Political Economy of Domestic and International Monetary Relationsed. by RaymondE. Lombra and WillardE. Witte (Iowa State University Press1982).
HendersonDale W. and KennethRogoff “Negative Net Foreign Asset Positions and Stability in a World Portfolio Balance Model” Journal of International Economics Vol. 13 (August1982) pp. 85–104.
LaidlerDavid E.W.The Demand for Money: Theories and Evidence (New YorkSecond Edition1977).
MeltzerAllan H. and others “Is the Federal Reserve’s Monetary Control Policy Misdirected? Resolved: That the Federal Reserve’s Current Operating Procedures for Controlling Money Should Be Replaced” (debate) Journal of Money Credit and Banking Vol. 14 (February1982) pp. 119–47.
PooleWilliam “Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model” Quarterly Journal of Economics Vol. 84 (May1970) pp. 197–216.
RadeckiLawrence “Short-Run Monetary Control: An Analysis of Some Possible Dangers” Federal Reserve Bank of New York Quarterly Review Vol. 7 (Spring1982) pp. 1–10.
ScaddingJohn L. “An Annual Money Demand and Supply Model for the U.S.: 1924-1940/1949-1966” Journal of Monetary Economics Vol. 3 (January1977) pp. 41–58.
StartzRichard “Implicit Interest on Demand Deposits” Journal of Monetary Economics Vol. 5 (October1979) pp. 515–34.
TobinJames “A General Equilibrium Approach to Monetary Theory” Journal of Money Credit and Banking Vol. 1 (February1969) pp. 15–29.
Mr. Boughton, Senior Economist in the External Adjustment Division of the Research Department, is currently on leave of absence from Indiana University, where he is Professor of Economics. He holds advanced degrees from the University of Michigan and Duke University and has published two books on monetary economics, as well as a number of articles in economic journals.
The author is indebted to Michael Dooley and Willard Witte, in addition to Fund colleagues, for their clarifying suggestions.
This argument is made, for example, by Meltzer in Meltzer and others (1982), pp. 138–39. The counterargument, that excessive attention by the central bank to short-run control may destabilize economic activity, has been made by Ra-decki (1982).
The problem of determining optimal policies when the authorities do have sufficient information about the distribution of disturbances to the economy has been the subject of extensive study, following the seminal paper by Poole (1970). For a recent example of an application to an open economy, see Henderson (1982).
In a more general model of the demand for money, inflationary expectations would also enter the equation as a component of the relative return on real assets. They are omitted from the demand functions of the present model on the grounds that inflationary expectations are unlikely to respond systematically to short-run financial shocks or to generate systematic shifts between financial assets at given interest rates.
In this paper, shift parameters are denoted by αi, structural coefficients by βi, and expectational and reaction coefficients by γi. All the βi, and γi are hypothesized to be nonnegative.
This expectations function is similar to that of Frenkel and Rodriguez (1982), where it is shown that under rational expectations, γ1 (θ in their notation) may be derived as a function of the model’s parameters.
B includes only government bonds, since private domestic bonds are not net wealth to domestic asset holders. Neither the decision to exclude private bonds nor the decision to include government bonds is without controversy, but the issues are primarily relevant to long-run analysis. See, for example, Tobin and Buiter (1978). Foreign bonds held by the domestic public—net of domestic bonds (government and private) held abroad—are included in F rather than in B.
For example, under perfect mobility of capital the exchange rate might over-shoot or move perversely in response to monetary control; see Frenkel and Rodriguez (1982).
A negative value for γ3 would imply a destabilizing policy.
See Tobin (1969). This point does not deny that the economically relevant distinction of money is its negotiability, but in a macromodel the quality of negotiability does not enter directly and is captured only in interest rate fixity.
The restriction γ4 < 1 ensures that a given change in market interest rates results in a smaller change in rm, and α8> 0 ensures that the elasticity of rm to rb is less than unity.
To simplify the notation, E and W have been normalized on unity; M, B, and F thus are measured as portions of W.
These estimates are from Boughton (1981). Since the present model includes a broader range of interest rates, these estimates are applied to the total elasticities to rb, not the partials. In the notation of this paper, η indicates a total elasticity, and ε indicates a partial elasticity.
For example, ε(Fd, r) ≡ Σjε(Fd, rj).
The figure for the United States is based on Scadding (1977). The higher value for the United Kingdom is assigned on the basis of the relative variation in the money-to-base ratio described earlier.
The derivation of the vectors β and γ is explained further in the Appendix.
See, for example, Startz (1979).
Specifically, with R fixed, it may be shown that
The parameter λ4 is determined primarily by k4 and hence does not play an independent role.
With the U.S. parameters, k4>0.782 generates negative values for β7 and β8; the permitted range has been truncated accordingly.
Recall that the initial values of E, Ē, and W are set equal to unity. Interest rates are expressed as ratios (e.g., 10 per cent = 0.1).