FROM TIME TO TIME, countries undertake a major reorientation of their exchange rate arrangements. Such a restructuring occurred after World War II with the advent of the Bretton Woods par value system; another change took place in the 1970s with the widespread adoption of flexible exchange rate arrangements by the major industrial countries.1 Each time a major change takes place, it is well understood that the change requires an expensive restructuring of institutions that may have to be altered yet again in the future, when the economic environment so necessitates.
The purpose of this paper is to study the economic environment relevant to recent exchange rate regime switches and to develop a simple model that enables an exchange rate regime switch to be viewed as a forecastable and optimal response by policymakers to the evolving state of the world. The examples we will develop involve switches between fixed and flexible regimes and vice-versa, but the methodology is broader. The framework may be used to analyze switches between other types of exchange rate arrangements; for example, the adoption or disbandment of multiple-tier or composite currency (basket) arrangements or between different general policies (such as interest rate versus monetary targets).
Issues related to the choice between fixed and flexible exchange rate regimes have generated a considerable literature over the past three decades. It is important, therefore, to indicate at the outset the manner in which the present analysis differs from previous work related to the choice of an optimal exchange rate regime. In particular, the focus of the recent literature on the optimal exchange rate regime is to derive the optimal degree of exchange market intervention as a function of the underlying parameters of the economy and of the variances of the existing monetary or real disturbances (see, for example, the papers collected in Bhandari (1985)). The principal result that emerges from these studies is that, for a small country, fixed rates are generally superior to flexible rates when monetary disturbances are dominant, whereas flexible rates are preferable when real shocks are dominant.2
The typical study of the choice of exchange rate regime, however, makes two assumptions that represent an unduly restrictive view of economic reality. First, it is usually assumed that the underlying economic structure (such as parameters and relevant variances) is time invariant, so that the optimal intervention stance (or exchange rate regime) is obtained as a once-and-for-all solution to a static optimization problem (see, however, Flood and Hodrick (1986)). Yet one of the prominent regularities in the financial and real sectors of real-world economies is that they undergo periodic turbulence and tranquility with the relative volatility of real and financial shocks, often exhibiting dramatic shifts. As the underlying economic structure changes over time, therefore, the nature of the optimal exchange rate regime can be expected to vary correspondingly, leading to an “evolution” of exchange rate regimes. Historically, countries have tended to switch back and forth between exchange rate regimes, as discussed in Section I below.
Second, the usual study of the choice of exchange rate regime takes for granted that prospective regime partners have agreed on similar inflation targets for their respective countries. In our view the temporary abandonment of low inflation targets seems to play a major role in the choice of exchange rate regimes and the timing of their adoption. To the extent that the inflation propensities of countries are predictable, the choice of exchange rate regime will also have predictable aspects.
The adoption or disbandment of various exchange rate arrangements over time may then be viewed as a predictable and optimal response to the inherently time-varying nature of the underlying state of the world. Previous analyses of exchange rate regimes have, as noted above, remained primarily concerned with computing the optimal degree of intervention for a fixed economic environment and, as such, cannot provide an explanation of predictably evolving exchange rate regimes. In this study we will begin to address concerns about these aspects of the regime choice problem by developing a theoretical framework that we believe is more in line with empirical regularities. In the model, the underlying stochastic structure of the economy evolves predictably over time, although it is subject to unpredictable shifts at any moment in time. The model is then extended to incorporate government expenditure as a policy goal. By allowing for time variation in desired government spending across exchange rate regimes, the inflation propensity of the country in question also develops predictably over time.3 The decision problem we focus on is at the level of the policymaker. It involves the choice by the policymaker of the exchange rate regime for the next period, together with the formulation of a plan concerning the path of the exchange rate regime over the indefinite future.
Although the following text contains a discussion of substantive results, the most interesting implication of the analysis is that, in the model and its extension, a policymaker can switch from one regime to another while planning to switch back at some point in the future. To our knowledge, this possibility has neither been discussed nor analyzed previously in the literature. This implication is suggestive insofar as changes in the exchange rate policy by some countries may be interpreted as a predictable and optimal response to a changing economic environment.
Section I presents a discussion of the historically observed shifts between exchange rate regimes and empirical observations of the time-varying movements of relative monetary and real variances in the major industrial countries over the past three decades. This section also presents empirical evidence relating to the dispersion of inflation rates in the same group of countries over the same period. Section II sets out the basic analytical framework, which involves a time-varying stochastic structure. Policy choices in the context of this model are studied in Section III. In Section IV, the basic model is extended to highlight the links between government expenditure, inflation rates, and the choice of the exchange rate regime. Section V offers conclusions, and two appendices provide details on estimation methods and data sources.
I. Stylized Facts
This section examines empirical regularities in the choice of exchange rate regime. First, historical shifts in exchange rate regimes are discussed. Next, we attempt to capture two aspects of the changing economic environment underlying these shifts: the relative variability of real and monetary shocks, and the divergence of inflation rates and government expenditures of the main industrial countries.
Shifts Between Exchange Rate Regimes
Four main exchange rate regime switches have occurred during the past century: the adoption of the international gold standard, from around 1870 to World War I;4 the switch to fluctuating exchange rates, from 1929 to 1933 ;5 the adoption of the Bretton Woods par value system from 1944 to 1971/72;6 and the switch to the present international monetary system, which is characterized by independent or joint floating on the part of the major industrial countries and by a wide diversity of exchange rate arrangements on the part of other member countries of the International Monetary Fund.
From an historical perspective, it is clear that no exchange rate regime has proven to be permanent. Some observers also suggest that policymakers did not expect ex ante that these switches among regimes would be long-lasting. For example, Yeager (1986, p. 374) has argued that, as late as 1933, many countries still considered the gold standard to be suspended temporarily. The debates throughout the early 1970s and negotiations over the Second Amendment of the Fund’s Articles of Agreement from 1974 to 1976 also reflected conflicting views about the permanence of floating rates (see de Vries (1986, pp. 113–15)).
Figure 1.Changing Exchange Rate Regimes
Within the present international monetary system, there has been considerable switching both between and within exchange rate arrangements. In Figure 1, shifts in exchange rate arrangements of a constant group of Fund member countries are tracked from 1969 through 1987.7 The most striking feature of the chart is the shift away from fixed exchange rate arrangements to limited and more flexible arrangements during the period.8 At the start of the period, 87 percent of the group are classified as having adopted a fixed exchange rate regime; at the end of the period, this percentage had fallen to 54 percent. This shift was most marked for the industrial country group; for the developing country group, the percentage in the fixed-rate category fell from 84 percent to 53 percent.
Within the period, shifts between and within exchange rate regimes occurred; in particular, reversible changes were most marked for the developing country group. For example, among 15 developing countries that were classified under more flexible arrangements in 1973, about 60 percent had switched to a fixed arrangement from 1974 to 1976; by 1982 all but two of these countries had returned to and remained on a more flexible regime.9 Within exchange rate arrangements, shifts are even more marked, especially within the fixed-rate group (as shown in Figure 2). For example, in 1973 about 55 percent of the group were pegged to the U.S. dollar, but by the end of 1987 this percentage had fallen to 38 percent. The main offset was a shift to a currency basket (from 18 to 30 percent of the group).
Figure 2.Fixed Exchange Rate Regimes
Variability of Real and Monetary Shocks
An important aspect of the changing economic environment is time variation in the stochastic environment. We have attempted to capture the historical evolution of the stochastic environment during the Bretton Woods and post-Bretton Woods eras by examining the time-series behavior of some aspects of the distributions of estimated real and monetary shocks of the Group of Five (G-5) countries (the United States, Japan, the Federal Republic of Germany, the United Kingdom, and France).
Real and monetary shocks for each country were estimated by first estimating a set of aggregate money demand and output supply equations for each country, deriving the residuals associated with the shocks, and then taking the shock to be the innovation in the residual.10Table 1 summarizes the average variability (as measured by the standard deviation) of the percentage shocks for each G-5 country for three periods: the 1960s, 1970s, and 1980s.11 In the top panel of the table, the standard deviations of real and monetary shocks are normalized by dividing the shock for each period by the associated standard deviation of the entire sample period; the ratio of the normalized standard deviation of the real to monetary shock is then derived. The middle and bottom panels show the standard deviations of the two types of shocks (measured in percentages).
The average variability of real shocks for the United States in the 1970s was almost twice that of the 1960s. In the 1980s, the variability of U.S. real shocks had returned to a level close to the average for the entire sample period, 1959:4–1987:4. A similar pattern of a relatively smaller turbulence of real shocks in the 1980s compared with previous decades is apparent for all G-5 countries. In contrast to real shocks, monetary shocks in the United States show the greatest turbulence in the 1980s,12 their average variability being about three times that of the 1960s and 1970s. Other countries show a mixed pattern; for example, in Japan and the United Kingdom, monetary shocks show a relatively greater turbulence in the 1970s.
|Period||Years||United States||Japan||Federal Republic of Germany||United Kingdom||Franceb|
|Ratio of normalized standard deviation of real to monetary shocksa|
|Standard deviations of real shocks|
|Standard deviations of monetary shocks|
Real and monetary residuals divided by their respective standard deviations for the period 1960:1–1987:4.
Sample period for France begins 1965:4.
Sample period ends 1987:4 for the United States, Japan, the United Kingdom, and France; in 1988:1 for the Federal Republic of Germany.
Real and monetary residuals divided by their respective standard deviations for the period 1960:1–1987:4.
Sample period for France begins 1965:4.
Sample period ends 1987:4 for the United States, Japan, the United Kingdom, and France; in 1988:1 for the Federal Republic of Germany.
Our interest is both in the overall levels of the variances of real and monetary shocks and in whether one type of shock tends to dominate the other during or before periods of regime switching as discussed above. The ratio of the normalized standard deviation of real to monetary shocks reflects the net outcome of two effects: the variability of each shock in a particular period relative to the trend for the entire period, and the variability of real relative to monetary shocks. A ratio equal to unity in a particular period signifies that both real and monetary shocks were close to their average level for the whole sample period. A distinct pattern emerges for the 1980s; in all countries the ratio falls below unity and also lies below that of earlier periods. Thus, it may be concluded that the 1980s are a period of relative quiescence compared with the two previous decades, especially for the United States.13 For three countries (the United States, the Federal Republic of Germany, and the United Kingdom), the late 1960s and early 1970s show relatively greater turbulence, whereas for the remaining two countries the average variability of the ratio of real to monetary shocks is greatest in the 1960s.14
Because the United States was the reserve-center country during the Bretton Woods period, the United States may be seen as an exporter of monetary stability or turbulence during the period. By exporting large monetary disturbances to smaller countries through its balance of payments deficit, the behavior of variability in the United States influenced the incentive to switch monetary regimes in other countries. Indeed, the time-varying pattern of real and monetary shocks for the United States and other G-5 countries will prove to be consistent with our analysis of the observed shift toward more flexible exchange rate arrangements during the late 1960s and 1970s.
Figure 3.Standard Deviation of Inflation Rates in the Group of Five Countries
Divergence of Inflation Rates
Central to the second model is the idea that extraordinary events such as wars may necessitate a sharp increase in government spending that in turn generates inflationary pressures incompatible with the continued maintenance of fixed exchange rates. The divergence of inflation rates of the G-5 countries, as measured by their dispersion around the period cross-section mean inflation rate, is given in Figure 3 for the period 1960:1–1988:1. From about mid-1971 to the third quarter of 1975, there was a sharp rise in the divergence of inflation rates. Since that period, the standard deviation of inflation rates has fallen from about 4.8 percent a year to about 0.8 percent a year, roughly equal to the variability at the start of the 1960s. The dispersion of ratios of government consumption to gross national product (GNP) around their mean value rose to about 5.4 percent in this period, before falling back by the end of 1986 to roughly the level attained in the early 1960s.
In summary, certain tendencies in the pattern of real and monetary shocks facing the major industrial countries during the past three decades can be identified. The late 1960s and early 1970s tended to be periods of relatively greater turbulence (as measured by the variability of the ratio of real to monetary shocks) compared with the early 1960s and 1980s. Further, the same group of countries experienced a sharp divergence in inflation rates and government spending in the early 1970s. Both “stylized facts” are consistent with the theoretical analysis of exchange rate regime evolution that follows.
II. The Model
This section describes the analytical framework that will be used in subsequent analysis. We have used a minimal structure involving only three equations (a statement of money market equilibrium, a Lucas-style output supply function, and the purchasing-power-parity relationship), but it is of course possible to incorporate additional structural detail in the model. Most of these details (such as price “stickiness” or the inclusion of an opportunity cost in money demand), however, turn out to leave our substantive results unaffected.
The framework of analysis involves a small country, described by
where mt is the logarithm of the money supply, pt is the logarithm of the price level, yt is the logarithm of output, wt is a white noise velocity shock, and ut is a white noise productivity shock. The shocks wt and ut are uncorrelated, but their distributions may have time-varying elements (to be specified below). We assume purchasing power parity; that is, pt =
The process determining the supply of domestic money depends on the exchange rate regime. If the country adopts flexible exchange rates, mt is exogenously determined and is assumed to be set equal to zero. Under fixed rates, however, mt becomes endogenous and is determined as
Time-Varying Stochastic Structure and Fixed Costs
The model incorporates two disturbances, wt and ut. It is assumed that the velocity shock, wt, has a fixed variance, V(w). In the first model, the variance of u, V(u), is expected to change over time according to
which implies that
In this notation, Vt-1(ut+i) is the variance of ut+i conditional on time t information. More precisely, Vt-1(ut+i) = Et-1[(ut+i)2], where Et-1 is the mathematical expectation operator conditional on time t — 1 information. Equation (3) is an ARCH (autoregressive conditional heteroscedastic) specification of the real disturbance term, and equation (4) is the difference equation derived from the ARCH specification.16
The solution of equation (4) may be written as
where dt-1 = (ut-1)2—z.
III. Policy Choices
This section discusses the nature of policy choices made by a social planner in the context of the model described above.
The Social Criterion
It is assumed that the social planner makes policy choices with the objective of
where Ut+i = yt+i —γ(yt+i)2; Ct+i≥0 is the fixed cost of switching the exchange rate regime during period t + i; λ= 1/(1 +r) is the social discount rate, and r is the social interest rate; and X = FIX, FLEX is the policymaker’s choice variable. The policymaker chooses, at t – 1, the regime to be in place at t and forms a plan for the regimes that will be implemented in periods after period t. The plan, however, need not bind the policymaker. Deviations from the planned sequence of exchange rate regimes can always occur as new information becomes available. The presence of the fixed cost of making any regime switch during period t+i, Ct+i = C≥0 (C = 0 otherwise), can result in postponement of the decision to switch exchange rate regimes.17
Four important properties of the chosen policy problem are (1) the intertemporal separability of the planner’s utility function; (2) the quadratic form of the period utility function; (3) the timing of information relevant to the loss; and (4) the timing of the effects of the policymaker’s actions. Intertemporal separability is defended only on grounds of analytical tractability. The quadratic utility function is defended on the same grounds, although it is acknowledged that this is an economically substantive assumption. The quadratic utility function causes the criterion function to be linear in conditional variance so that the policymaker is risk neutral with respect to variance risk. Literally, the policymaker makes decisions based only on perceptions of the variance of u and is not concerned with the time-varying nature of that variance. The timing of the acquisition of information is also important. In this model, the variance of the u-shock at time t cannot “surprise” agents at time t. Instead, the variance surprise for t occurs during the previous period. At time t of course, the agents will probably be “surprised” about the actual outcome of the real shock. They will not, however, attribute any of this surprise to misperceptions about variance in that period. They will simply update their perceptions of next period’s variance in response to the shock.
For reasons of tractability, it is assumed that the policymaker’s current decision about the exchange rate regime is not implemented until next period.18
Selection of the Appropriate Regime
The state variable for this problem is the existing exchange rate regime. The existing regime enters the policymaker’s decision problem because the fixed cost C is incurred if the exchange rate regime is changed. The time-series model for the variance of u is such that this variance is expected to approach its steady state monotonically.
It will be convenient in what follows to note that
where Vt-1 is defined as the variance operator conditional on period t-1 information. Furthermore, because foreign price is constant, it follows that, under fixed exchange rates,
where Vt-1(yt+i, FIX) is the time t — 1 expectation of the variance of y at time t + i, given that the FIX regime will be operating at t + i, and Vt-1(yt+i, FLEX) is the time t – 1 expectation of the variance of y at time t+i, given that the FLEX regime will be operating at t+i. The expected steady states of Vt-i(yt+i, FIX) and Vt-1(yt+i, FLEX) are
When one of the exchange rate regimes is allowed to have a steady-state advantage, the analysis begins to distinguish itself from the previous literature. Most models of the choice between fixed and flexible exchange rates find that flexible rates have an advantage when real shocks (such as u in the above model) are dominant, and that fixed rates have an advantage when monetary shocks (such as w) are dominant. If the stochastic steady states of the two regimes are assumed to be equivalent, the analysis here conforms with the results emerging from the previous literature. Because allowing steady-state asymmetries presents the possibility of considering a sizable taxonomy of cases, we will limit the taxonomy by studying only the case that we consider most interesting: dt-1>>0, with a steady-state advantage to the fixed-rate regime. We will, therefore, study a case in which there has been a large positive deviation of the variance of u from its steady-state value and in which there is a natural steady-state advantage to a fixed-rate regime.
Figure 4 shows the paths of Vt-1(yt+i, FLEX) and Vt-1(yt+i, FIX). Note that, by assumption, Vt-1(yt+i FLEX) starts lower than does Vt-1(yt+i, FIX), but that Vt-1(yt+i, FLEX) approaches a higher steady state than does Vt-1(yt+i, FLEX). It follows that the paths of Vt-1(yt+i FLEX) and Vt-1(yt+i FIX) must cross at some date in the future. Our assumed time-series process for the variance of u ensures that they cross exactly once. Because time is counted in integers in the model, there is no reason that there should be a date T when Vt-1(yt+T, FLEX) = Vt-1(yt+T, FIX). Nonetheless, we will assume for the purposes of the analysis that there is indeed such an integer-valued date.
If the economy had adopted a fixed exchange rate regime from t until t+T, there would certainly be no reason at t + T to switch to the flexible rate regime. From t + T onward, the period loss is greater with FLEX than with FIX, so that the policymaker would not wish to incur a fixed cost by switching to FLEX. If, however, the economy had been operating under FLEX before t + T, the situation is more interesting. First, note that there is no incentive to switch from FLEX to FIX before t+T, since such a switch would both increase the period loss and incur the fixed cost.
At t+T – 1, the switch becomes more tempting. According to the assumption that Vt-1(yt+T, FLEX) = Vt-1(yt+T, FIX), the switch would certainly not be made at t+T — 1 to be effective in t + T. No net gain during period t + T in terms of the period loss function would be realized by making the switch, and the fixed cost, C, would have to be incurred in t+T — 1. Consequently, the decision in t+T—1 is straightforward—the policymaker will not switch regimes. According to our assumptions, the policymaker expects that during period t+T+1, Vt-i(yt+T+1, FLEX)>Vt-1(yt+T+1, FIX). Therefore, there would be a net gain in terms of the period loss function from switching at t + T. But the policymaker must weigh the present value of this gain against the gain from waiting until next period to incur the fixed switching cost. This gain is rC (where r is the social interest rate as defined above). By delaying switching until the next decision point, the economy must forgo γρ[Vt-1(yt+T+1, FLEX) - Vt-1(yt+T+1, FLEX)], but it obtains a gain of rC by deferring the fixed switching cost that must be incurred.
Figure 4.Expected Time Paths of Real Output Variance for Fixed and Flexible Regimes
The policymaker will make the switch at T +k — 1, where k is the smallest integer such that
In the present example, k is the smallest integer such that
where δ > 1 is the ratio
Now consider the plans and actions of the policymaker at time t — 1. There are two possibilities to consider: first, at t — 1 the economy is operating FLEX; and, second, at t — 1 the economy is operating FIX. Consider these possibilities in order. If the economy is operating FLEX during t — 1, then the realization of the state in t — 1, with a high value of dt-1, would not indicate a move to FIX. Indeed, we have just established that if an economy is operating on FLEX With state dt-1 then the planned switch date is t +T +k, which must be greater than t.
Now suppose that the economy is on FIX during period t — 1 and experiences a relatively large value of dt-1, as would happen if a period of substantial real turbulence were encountered. The policymaker must decide at t — 1 whether to switch from FIX to FLEX effective at t, knowing that if the switch is made, the policymaker will switch back effective at t +T +k. The alternative to switching is obviously not to switch. In the model, the gain from delaying a switch for one period is always rC. The gain from switching from FIX to FLEX is at its greatest in period t and thereafter declines toward zero in period t +T. Therefore, if the policymaker plans to switch from FIX to FLEX, it is optimal to make the switch immediately—that is, in period t. The policymaker’s decision, therefore, is between planning to follow FIX indefinitely and switching now to FLEX, while planning to follow FLEX from t until t +T +k — 1 with a subsequent switch again at t +T +k. The latter path involves two switches. It is optimal to make the switch at t effective for t + 1 if and only if is satisfied. It is possible to evaluate this expression further in terms of its underlying determinants, but this is left to the interested reader.
This section has discussed regime selection in the context of a framework that incorporates stochastic evolution of the underlying variances in the economy as well as a cost associated with regime switches. An important result obtained in this section relates to the possible reswitching to the prior regime. This property will be seen to survive the modification in the extension of the model.
IV. Model Extension: Inflation, Government Expenditure, and Regime Choice
In the analysis so far we have implicitly assumed that domestic inflation is equal, on average, to rest-of-the-world inflation regardless of the exchange rate regime. Yet an important consideration in choosing exchange rate regimes is the respective inflation propensities of prospective exchange rate regime partners. In particular, we know of no case in which a high-inflation industrial country has managed to maintain a fixed exchange rate in relation to a low-inflation industrial country.19
This section extends the previous model to highlight the links between government expenditure policy, inflation rates, and the choice of the exchange rate regime. This is done by incorporating government expenditure as a policy goal and allowing for time variation in desired government spending across exchange rate regimes. The model is incomplete because it ignores the role of government revenue and hence the role of differing propensities to generate government revenue across exchange rate regimes. Extraordinary events such as wars may necessitate sharply increased government expenditures, which in turn generate inflationary pressures incompatible with the continued maintenance of fixed exchange rates. Thus, during major economic disturbances such as wars, governments attach high priority to attaining specific expenditure targets (in order to finance the war effort) and may be willing to accept the resulting inflation (and consequent abandonment of fixed rates) temporarily. To focus on the novel elements introduced by these modifications, we abstract at present from the time-varying element of underlying variances and also from the fixed cost of changing regimes.20
The first modification involves an extension of the policymaker’s loss function to include the government’s expenditure goal. The modified period loss function is
where ut is as defined above; gt is the logarithm of government spending, ĝt is the logarithm of desired government spending; and ψ is the priority attached by the policymaker to achieving the desired spending level. With the fixed cost of regime switching set at zero, the policy problem now becomes one of period-by-period optimization. It is assumed that the exchange rate regime for period t is set in period t — 1 to minimize Et-1 Wt.
Desired government spending is exogenous to the economy and follows
where xt is a white noise, constant variance shock that is uncorrelated with other shocks in the model.21
The next step is to link actual government expenditure with the choice of the exchange rate regime. In the present model, the only method of government finance is money creation. The rate of money creation, however, is sensitive to the choice of the exchange rate regime. For example, under fixed exchange rates, domestic inflation and money creation are restrained by “the discipline of world inflation.” Because money creation is the only source of revenue in the model, it follows that actual government expenditure is endogenously constrained under fixed exchange rates. Specifically, the government budget constraint is
where Dt is the level of the domestic credit portion of the money supply, Pt is the price level, and G, is the level of real government spending. The domestic money supply is Mt = Rt+Dt, which may be log-linearized as mt=(1 — θ)rt +θdt, where rt is the logarithm of the beginning-of-period stock of foreign exchange reserves held by the central bank, and 8 is the share of domestic credit in the monetary base.
Because the rest of the model is log-linear, it is necessary to also log-linearize equation (14) as
where dt is the logarithm of Dt, θ is the share of domestic credit in the monetary base, c is a linearization constant, and η is the ratio of government spending to real balances, which in this model is, on average, equal to the ratio of government spending to output.
Under fixed exchange rates the permissible rate of money creation is set equal to the domestic inflation rate, which in turn must equal the foreign inflation rate.22 Thus, it follows that
where π* is the foreign inflation rate (treated as a constant).
The next step is to compute Et-1 Wt(FIX), which is the expected value of the loss if fixed rates are adopted. Combining equation (18) with the fact that yt = ut under fixed rates (see equation (2) above) and using the period loss function, one obtains
where Ω=(1+χ)=V(u) + χ[V(w) +V(x)]; V(x) is the constant variance of the government-spending shock, x; V(u) is the constant variance of the real shock, u; and V(w) is the (now) constant variance of the money demand shock, w. It may be noted at this point that equation (19) is time dependent and will vary through time because of the stochastic evolution of desired government spending.
Next consider a regime of flexible exchange rates. On the one hand, the usual analysis of fixed versus flexible exchange rates requires that, when flexible rates are adopted, the systematic part of the rate of money growth be determined before the realization of the state of the system. On the other hand, the analysis often requires that, under fixed rates, the money supply respond to the current state because the state influences the demand for money. There is therefore an asymmetry in the typical treatment of monetary policy under the two regimes.23 In this section we deviate from typical practice, in that under flexible rates we set the rate of domestic money creation at exactly the level required to finance the desired level of domestic government spending. In our view this is a more symmetric treatment of the two regimes than is typical in the literature because in both regimes monetary policy is primarily directed toward a goal other than output stabilization.
The first setting for domestic credit growth was dt — dt-1 = θ-1 π, which we referred to as fixed exchange rates. The alternative setting for domestic credit growth ensures that
Under flexible rates, domestic inflation and money creation are no longer constrained by the world inflation rate, so that government expenditure is exogenous.24 Using equation (15) along with equation (1) to calculate the price-surprise term (Et-1pt– pt) and then substituting this into the output supply function, equation (2), yields the expected value of the loss function:
where K =[1 + β(1 + η)]-1. Note that because gt = ĝt under FLEX and the fixed cost is set equal to zero, the expression reported in equation (21) is equivalent to the expected value of the loss function—that is, Et-1, Wt(FLEX). Note also that, unlike the expression for FIX (equation (19)), equation (21) contains no time-varying elements because desired and actual expenditures are equal.
The following additional observations relating to equations (14) and (21) may also be made. First, flexible rates still have an advantage in coping with supply shocks. This point follows from equations (19) and (21) because the coefficient of V(u) in equation (21), K2, is less than unity whereas the coefficient of V(u) in equation (19) is (l + χ)>l . Results of comparing the loss functions are ambiguous with respect to how the two regimes cope with monetary and “fiscal” shocks, V(w) and V(x), respectively.25
The above comparisons, however, are static and are not the principal novel result of this section. The most interesting aspect of the comparison of equations (19) and (21) is that equation (19) contains a time-varying element, whereas equation (21) is purely static. Specifically, the time-varying element in equation (19) is
which responds through time to variations in desired government spending. Disturbances to desired government spending—the fiscal, or x-shocks—will affect this time-varying element through equation (18). Furthermore, high values of x-shocks may lead to formulation of a plan involving the current abandonment of fixed exchange rates until the shocks have run their course, coupled with a current plan to reimplement fixed rates in the future. For example, this scenario would apply to a country that was operating on fixed rates where the fixed-rate regime had a steady-state advantage in terms of the loss function but that received a large shock to desired government spending (due, perhaps, to a major event such as war).
This paper has constructed and analyzed two separate examples that are capable of explaining two types of exchange rate regime switches made by policymakers. The first type is a response to an unexpected event such as upheaval in the relation of real to monetary variances or a sudden large change in desired government spending. The second type is the possible expected return to the prior regime. The first example uses a time-varying variance structure to generate optimal regime collapse and regeneration. In the second example, shocks to desired government spending, such as wars, are used to produce the same type of behavior. Brief study of the empirical regularities surrounding exchange rate regime shifts since World War II indicates that our theory is in broad conformity with the data and that elements from both of the examples appear to be present in the actual decisions involving major shifts in exchange rate regimes.
Estimation of Real and Monetary Shocks
Estimation of real and monetary shocks requires estimation of the behavioral functions associated with the shocks. Although in the text stripped-down versions of standard aggregate supply and money demand behavior functions were assumed for purposes of exposition, we used somewhat more elaborate specifications in the empirical work. In this Appendix we will explain, first, our estimation of monetary shocks and the normalized-shock monetary variance and, then, our estimation of the real shocks and the normalized-shock real variance.
Estimation of Monetary Shocks and the Monetary Variance
For the United States, monetary shocks are defined as
where w1 is innovation in the money demand shock and w2 is innovation in the money supply shock.
For all other countries, only money demand shocks were estimated, and we defined wt = w1t.
For all countries, a common money demand specification was used (with correction for first-order autocorrelation; all variables are in logarithms):26
where vt = ρvt-1 + wlt. The money supply equation for the United States was specified as
where μt=mt—mt-1. It was found that v2t did not exhibit first-order serial correlation, so we took v2t to equal w2t. Coefficients and residuals in equation (23) were estimated using a two-stage technique (with it-1 and mt-1 as instruments for it, and yt-i, and (m - p)t-1 as the instrument for yt). Coefficients and residuals in equation (24) were estimated by ordinary least squares.
With respect to monetary shocks, the United States was treated differently from the other G-5 countries because the United States was the reserve-center country in the Bretton Woods system during much of the sample period. The variance of money supply residuals is quite small relative to the variance of money demand residuals, so that the results reported in Table 1 of the text will, we think, be robust to a variety of money supply treatments.
The normalized monetary standard deviation is the standard deviation of the monetary shock for period t divided by the standard deviation of monetary shocks for the entire sample period.
Estimation of Real Shocks
For all countries the output function was specified as shown below and estimated by a two-step procedure:
where xt = (1 —L)yt.
First, unexpected price, pt– Et-1 pt, was modeled as the residual in a price autoregression:
Ordinary least squares was applied to equation (25) with the constraint imposed. We included lags of yt until there was no evidence of first-order serial correlation as judged by the Durbin-Watson statistic.
The normalized real standard deviation for period t was derived as the standard deviation of real shocks in period t divided by the standard deviation of real shocks over the entire sample period, J.
Data Sources and Estimation
All data originated from the Fund’s International Financial Statistics (IFS) data base as of September 1988. Money is from IFS lines 34 and 35 (money plus quasi-money); interest rates from line 60c for the United States and United Kingdom, and from line 60b for the remaining countries (short-term rates). Prices are the consumer price index, line 64. Gross national product is at fixed prices and comes from line 99a.r for the United States, Japan, and the Federal Republic of Germany, from line 99b.p for the United Kingdom, and from line 99b.r for France. Government consumption is from line 91. Logarithms were taken for all variables except interest rates and government consumption. For estimation purposes, data were deseasonalized and filtered.
To accommodate breaks in the data owing to different coverage and redefinitions, dummy variables were constructed and used in the regressions. In all cases these dummies assumed a value of zero before the break point and of unity after the break point. A full description of the dummies and estimation results are available from the authors on request.
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Driskill, R., andS.A.McCafferty, “Exchange Market Intervention under Rational Expectations with Imperfect Capital Substitutability,”in Exchange Rate Management under Uncertainty,ed. byJ.S.Bhandari (Cambridge, Massachusetts: MIT Press, 1985).
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Mr. Flood is a Senior Economist in the Research Department. He obtained his Ph.D. from the University of Rochester.
Mr. Bhandari, an economist in the European Department, obtained his Ph.D. in economics at Southern Methodist University. He also holds a J.D. degree from Duquesne University.
Ms. Home is a Senior Economist in the Fiscal Affairs Department and obtained her Ph.D. in economics from the Graduate Institute of International Studies, University of Geneva.
At least two other major realignments can also be discerned: the adoption of the gold standard from approximately 1870 until World War I and the switch to floating rates during 1929–33. These realignments, along with the two mentioned above, were major in the sense of involving a substantial number of countries. There are, of course, numerous cases of single countries experimenting with alternative exchange rate arrangements in isolation.
These results have been shown by various authors to be robust in a wide variety of alternative model specifications, involving, for example, staggered wage setting (Bhandari (1982)), complex intervention rules (Turnovsky (1985)), and finite or perfect asset substitutability (Driskill and McCafferty (1985)). Note, however, that this proposition may not survive incorporation of differentiated or heterogeneous information sets (Bhandari (1985)).
An international gold standard exists when most major countries maintain convertibility between gold and their national monetary units at fixed ratios. Before the gold standard, a form of loose “bimetalism” existed (see Yeager (1976, pp. 295–97)).
During the period 1929–33, 35 countries abandoned the gold standard.
The breakdown of the Bretton Woods system can be dated from 1971, when its two main features—par values and U.S. dollar convertibility—were no longer operative (see de Vries (1986, chaps. 2 and 3)).
The classification of exchange rate regime is based on the Fund’s exchange rate arrangements classification (see International Monetary Fund (1987)). Important changes in this classification system occurred over the sample period, especially in 1973 and 1982. In particular, a new category, “exchange rate not maintained within relatively narrow margins,” was introduced in 1973; in 1982, this category was replaced by two new classes: “limited flexibility” and “more flexible” arrangements.
The original Articles of Agreement of the International Monetary Fund reflected the requirement of an agreed par value. Under temporary and specified circumstances, however, the Fund supported deviations from exchange rate arrangements, including fluctuating rates (for example, Canada during September 1950-May 1962; see de Vries (1986, pp. 49–56)). The classification of countries in the nonfixed category in the pre-1973 period is based on the criterion that either the country did not maintain a par value or adopted a freely fluctuating unitary effective rate.
Adjustable indicators were classified under a fixed-rate category before 1982. This change in classification affects four countries within the group.
A detailed description of the methodology used to estimate these shocks is given in Appendix I. For the United States, both money demand and money supply equations were estimated. Our emphasis is on the time-series behavior of the relative shocks—in contrast to Obstfeld (1985), who used cross-sectional data to show the relative dominance of real shocks in the early post-Bretton Woods period.
The sample period ends in 1987:4 for all countries except the Federal Republic of Germany, for which it ends in 1988:1.
When the 1980s are broken into the subperiod 1980–84, the standard deviation of monetary shocks rises to 1.42, reflecting the well-documented instability in U.S. money demand.
Interpreted in the above sense, a period such as the 1980s may be described as relatively tranquil, yet may still be characterized by large shocks in absolute terms.
The sharp rise in the variability of the ratio of real to monetary shocks in France in the 1960s reflects primarily a large real shock in 1968. For the United States, this statement is true for the decade average notwithstanding a large jump in the ratio of real to monetary shocks in the early 1960s.
In Flood and Marion (1982) p is treated as policy-varying, whereas in Flood and Hodrick (1986) p is time-varying and moves in accord with agents’ perceptions of an endogenously time-dependent stochastic structure.
Even if C = 0, the model predicts regime switches. C > 0 allows the possibility that switches will be delayed. We also assume symmetry in costs for the two regimes. It is possible that costs may differ from one regime to another or at different times for an individual country with respect to one regime. In the absence of any compelling rationale, however, it seems reasonable to retain the assumption of symmetry.
It is possible, of course, to allow for the immediate implementation of a current decision relating to the exchange rate regime. This leads, however, to algebraic complications without affecting any of the principal conclusions of the analysis.
The examples of a high-inflation country fixing its exchange rate to a low-inflation country seem to involve foreign exchange rationing on the part of at least one of the countries.
This does not make the subsequent analysis static. As will be seen below, time dependency in the present model is introduced through the government expenditure process.
A stabilization role for g could be built around a covariation of xt with wt or u t. However, we assume away such covariation.
Other settings for the rate of domestic money creation are possible. An attractive alternative would have θ(dt – dt-1) = π* +ut – ut-1 +wt – wt-1, which would accommodate shifts in domestic money demand. The policy setting here was chosen for simplicity.
This asymmetry occurs because a flexible rate is not a policy in the same sense as a fixed rate. Flexible rates simply set out what monetary policy is not and do not constitute a policy of fixing the exchange rate. See, however, Aizenman and Frenkel (1985).
This, of course, is the point of a flexible exchange rate policy: to “free up” government spending as a tool for, say, war management.
For example, a switch to fixed rates would require small coefficients on the ambiguous effects.
Linear homogeneity was imposed on the money demand function by setting a1= 1