1. Shifts between exchange rate regimes

Four main exchange rate regime switches have occurred over the last century; the adoption of the international gold standard from around 1870; to World War I ^5/; the switch to fluctuating exchange rates from 1929-33 ^6/; the adoption of the Bretton Woods par value system from 1944-1971/72 ^7/; and the switch to the present international monetary system that is characterized by independent or joint floating by the main industrial countries and a wide diversity of exchange rate arrangements among other IMF member countries.

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) argues that many countries still considered the gold standard to be temporarily suspended as late as 1933. The debates throughout the early 1970s and negotiations over the Second Amendment of the Fund Articles of Agreement from 1974 to 1976 also reflect conflicting views about the permanence of floating rates (see De Vries (1986, pp. 113-115).

Within the present international monetary system, there has been a considerable switching both between and within exchange rate arrangements. In Chart 1, shifts in exchange rate arrangements of a constant group of IMF member countries are tracked from 1969 to 1987. ^8/ 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. ^9/ 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.

Chart 1:

Changing Exchange Rate Regimes

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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 except for two countries had returned to and remained on a more flexible regime. ^10/ Within exchange rate arrangements, shifts are even more marked, especially within the fixed rate group as shown in Chart 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 composite basket (from 18 to 30 percent of the group).

Chart 2:

Fixed Exchange Rate Regimes

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2. Variability of real and monetary shocks

An important aspect of the time-varying environment is time variation in the stochastic environment. We have attempted to capture the historical evolution of the stochastic environment over 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 G-5 countries.

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. ^11/ Table 1 summarizes the average variability (as measured by the standard deviation) of the percentage shocks for each G-5 country for three periods; 1960s, 1970s and 1980s. ^12/ In the upper 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 lower panel shows the standard deviations of the two types of shocks (measured in percent).

Table 1.

Standard Deviations of Real and Monetary Shocks Ratio of normalized standard deviation of real to monetary shocks ^1/

^1/Real and monetary residuals divided by their respective standard deviations for the period 1960(1) - 1987(4).

^2/Sample period for France begins 1965(4).

^3/Sample period ends 1987(4) for U.S., Japan, U.K., France; in 1988(1) for Fed. Republic of Germany.

Table 1.

Standard Deviations of Real and Monetary Shocks Ratio of normalized standard deviation of real to monetary shocks ^1/

Period		United States	Japan	Fed. Republic of Germany	United Kingdom	France 2/
Decade average	1960-69	1.73	1.24	1.04	0.97	1.93
Sub-period	1960-64	2.15	1.02	1.19	0.78	—
Decade average	1970-79	1.85	0.84	1.06	1.06	0.69
Sub-period	1970-74	1.82	0.94	1.45	1.24	0.87
Decade average	1980-87 3/	0.61	0.81	0.89	0.92	0.55
Sub-period	1980-84	0.57	0.69	1.05	0.98	0.74
Standard deviations of real shocks
(in percent)
Decade average	1960-69	0.66	1.61	1.52	1.33	2.57
Sub-period	1960-64	0.71	1.58	1.74	1.29	—
Decade average	1970-79	1.03	1.33	1.19	1.81	0.89
Sub-period	1970-74	1.05	1.71	1.38	2.08	0.98
Decade average	1980-87 3/	0.87	0.71	1.11	1.24	0.77
Sub-period	1980-84	1.02	0.62	1.31	1.33	0.89
Whole period	1960-87 3/	0.86	1.30	1.29	1.49	1.33
Standard deviations of monetary shocks
(in percent)
Decade average	1960-69	0.31	1.09	0.84	1.57	1.74
Sub-period	1960-64	0.26	1.30	0.84	1.88	—
Decade average	1970-79	0.44	1.32	0.65	1.94	1.68
Sub-period	1970-74	0.46	1.53	0.55	1.90	1.47
Decade average	1980-87 3/	1.13	0.74	0.73	1.53	1.82
Sub-period	1980-84	1.42	0.76	0.72	1.54	1.57
Whole period	1960-87 3/	0.69	1.09	0.75	1.70	1.74

^1/Real and monetary residuals divided by their respective standard deviations for the period 1960(1) - 1987(4).

^2/Sample period for France begins 1965(4).

^3/Sample period ends 1987(4) for U.S., Japan, U.K., France; in 1988(1) for Fed. Republic of Germany.

View Table

Table 1.

Standard Deviations of Real and Monetary Shocks Ratio of normalized standard deviation of real to monetary shocks ^1/

Period		United States	Japan	Fed. Republic of Germany	United Kingdom	France 2/
Decade average	1960-69	1.73	1.24	1.04	0.97	1.93
Sub-period	1960-64	2.15	1.02	1.19	0.78	—
Decade average	1970-79	1.85	0.84	1.06	1.06	0.69
Sub-period	1970-74	1.82	0.94	1.45	1.24	0.87
Decade average	1980-87 3/	0.61	0.81	0.89	0.92	0.55
Sub-period	1980-84	0.57	0.69	1.05	0.98	0.74
Standard deviations of real shocks
(in percent)
Decade average	1960-69	0.66	1.61	1.52	1.33	2.57
Sub-period	1960-64	0.71	1.58	1.74	1.29	—
Decade average	1970-79	1.03	1.33	1.19	1.81	0.89
Sub-period	1970-74	1.05	1.71	1.38	2.08	0.98
Decade average	1980-87 3/	0.87	0.71	1.11	1.24	0.77
Sub-period	1980-84	1.02	0.62	1.31	1.33	0.89
Whole period	1960-87 3/	0.86	1.30	1.29	1.49	1.33
Standard deviations of monetary shocks
(in percent)
Decade average	1960-69	0.31	1.09	0.84	1.57	1.74
Sub-period	1960-64	0.26	1.30	0.84	1.88	—
Decade average	1970-79	0.44	1.32	0.65	1.94	1.68
Sub-period	1970-74	0.46	1.53	0.55	1.90	1.47
Decade average	1980-87 3/	1.13	0.74	0.73	1.53	1.82
Sub-period	1980-84	1.42	0.76	0.72	1.54	1.57
Whole period	1960-87 3/	0.69	1.09	0.75	1.70	1.74

^1/Real and monetary residuals divided by their respective standard deviations for the period 1960(1) - 1987(4).

^2/Sample period for France begins 1965(4).

^3/Sample period ends 1987(4) for U.S., Japan, U.K., France; in 1988(1) for Fed. Republic of Germany.

Interpreting the standard deviations, we see for example that the average variability of real shocks for the United States in the 1970s was almost twice that of the 1960s. In the 1980s, U.S. real shock variability 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 to 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; ^13/ 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.

Our interest is in both the overall levels of the variances of real and monetary shocks and whether one type of shock tends to dominate the other during or prior to periods of exchange rate 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 is a period of relative quiescence compared to two previous decades, especially for the United States. ^14/ 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 while for the remaining two countries, the average variability of the ratio of real to monetary shocks is greatest in the 1960s. ^15/

Because the United States was the reserve center country during the Bretton Woods period, the United States may be seen as an exporter of 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 with the observed shift toward more flexible exchange rate arrangements during the late 1960s and 1970s.

3. 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 G-5 countries as measured by their dispersion around the period cross-section mean inflation rate is given in Chart 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 per year to about 0.8 percent per year, roughly equal to the variability at the start of the 1960s. The dispersion of government consumption to GNP ratios 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.

Chart 3

G5 Countries: Standard Deviation of Inflation Rates First Quarter 1960 to First Quarter 1988

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In summary, we have identified certain tendencies in the pattern of real and monetary shocks over the past three decades facing the main industrial countries. 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) as 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 our theoretical analysis of exchange rate regime evolution that follows.

1. The basic framework

This section describes the analytical framework to be used for our subsequent analysis. We have elected to utilize a very minimal structure involving only three equations, i.e., a statement of money market equilibrium, a Lucas-style output supply function and the purchasing power parity relationship. It is possible of course, to incorporate additional structural detail in the model; however, most of these details (such as for example, price “stickiness” or the inclusion of an opportunity cost in money demand) turn out to leave our substantive results unaffected.

The framework of analysis involves a small country, described by:

and

where m_t is the logarithm of the money supply, p_t is the logarithm of the price level, y_t is the logarithm of output, w_t is a white noise velocity shock and u_t is a white noise productivity shock. The shocks w_t and u_t are uncorrelated but their distributions may have time-varying elements to be specified below. We assume purchasing power parity, i.e., ${\mathrm{p}}_{\mathrm{t}}\mathrm{=}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{+}{\mathrm{s}}_{\mathrm{t}}$, where ${\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}$ is the logarithm of the foreign price level and s_t is the logarithm of the exchange rate, quoted as the domestic-currency price of foreign exchange. In what follows we assume ${\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}$ is constant and set ${\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}=0$. It is also assumed that β, the slope of the domestic-goods supply function is a policy-invariant constant. ^16/

The process determining the supply of domestic money depends on the exchange rate regime. If the country adopts flexible exchange rates, m_t is exogenously determined and is assumed to be set equal to zero. Under fixed rates however, m_t becomes endogenous and is determined as ${\mathrm{m}}_{\mathrm{t}}\mathrm{=}{\mathrm{y}}_{\mathrm{t}}\mathrm{+}{\mathrm{w}}_{\mathrm{t}}\mathrm{-}\overline{\mathrm{s}}$, where $\overline{\mathrm{s}}=0$ is the logarithm of the fixed exchange rate.

2. Time varying stochastic structure and fixed costs

The model incorporates two disturbances, w_t and u_t. We assume that the velocity shock w_t, has a time-invariant variance, V(w). In our first model, the variance of u, V(u), is expected to vary through time according to:

which implies:

In our notation, V_t-1(u_t+i) is the variance of u_t+i conditional on time t information. More precisely, V_t-1 (u_t+i) = E_t-1 [(u_t+i)²], where E_t-1 is the mathematical expectation operator conditional on time t-1 information. Equation (3) is an ARCH specification of the real disturbance term and equation (4) is the difference equation derived from the ARCH specification. ^17/

The solution of (4) may be written as:

where d_t-1 = (u_t-1)² - z.

1. The social criterion

It is assumed that policy choices are made by a social planner whose objective is to:

where U_t+i = y_t+i - γ(y_t+i)², C_t+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 concerning 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 cost C_t+i = C ≥ 0 if any regime switch is made during period t+i and zero otherwise. It will be seen below that the presence of this fixed cost can result in postponement of the decision to switch exchange rate regimes. ^18/

Four important properties of our 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 its decisions based only upon perceptions of the variance of u and is not concerned with variability (however defined) 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 we assume that the policymaker’s current decision about the exchange rate regime is not implemented until next period. ^19/

2. 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. Our 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:

V_t-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:

Under a flexible exchange rate regime, equations (1) and (2) can be used to yield,

where V_t-1(y_t+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 V_t-1(y_t+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.

When we allow one or the other of the exchange rate regimes to have a steady state advantage, our 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, like u in the above model, are dominant and fixed rates have an advantage when monetary shocks, like w, are dominant. If the stochastic steady states of the two regimes are assumed to be equivalent, our analysis is in conformity with the results emerging from the previous literature. Since allowing steady state asymmetries presents the possibility for considering a sizable taxonomy of cases, we will limit the taxonomy by studying only the case which we consider most interesting, which is d_t-1 ≫ 0 with a steady state advantage to the fixed rate regime. We will therefore, study a case where there has been a large positive deviation of the variance of u from its steady state value and where there is a natural steady state advantage to a fixed rate regime.

Figure 1 shows the paths of V_t-1(y_t+i, FLEX) and V_t-1(y_t+i, FIX) which we will examine. Note that by assumption V_t-1(y_t+i, FLEX) starts lower than does V_t-1(y_t+i, FIX), but that V_t(y_t+i, FLEX) approaches a higher steady state than does V_t(y_t+i, FLEX). It follows that the paths of V_t-1(y_t+1, FLEX) and V_t-1(y_t+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. Since time is counted in integers in our model, there is no reason there should be a date T when V_t-1(y_t+T, FLEX)=V_t-1(y_t+T, FIX). Nonetheless, we will assume for the purposes of our analysis that there is indeed such an integer valued date.

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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 onwards 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 FLEX before t+T, however, 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 our assumption that V_t-1(y_t+T,^FLEX) = V_t-1(y_t+T, FIX) the switch would certainly not be made at t+T-1 to be effective in t+T, because there is no net gain during period t+T in terms of the period loss function 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, i.e. the policymaker will not switch regimes. According to our assumptions, the policymaker expects that during period t+T+1, V_t-1(y_t+T+1, FLEX) > V_t-1(y_t+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 forego γρ[v_t-1(y_t+T+1, FLEX) - V_t-1(y_t+T+1, FLEX)] but it obtains a gain of rC by deferring the fixed switching cost which must be incurred.

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 V_t-1(SS, FLEX)/V_t-1(SS, FIX). Clearly, if C = 0, k = 1. It is possible that no positive integer k fulfills condition (10). This would be true, for example, if C were very large so that it would never be worthwhile to switch regimes. In what follows, however, we assume that there exists an integer k≥1 which fulfills (10).

Now consider the plans and actions of the policymaker at time t-1. There are two possibilities to consider: (1) at t-1 the economy is operating FLEX; and (2) 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 d_t-1 would not indicate a move to FIX. Indeed, we have just established that if an economy is operating on FLEX with state d_t-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 d_t-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 it makes the switch, it plans to switch back effective at t+T+k. The alternative to switching is obviously not to switch. In our 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, i.e., in period t. The policymaker’s decision is therefore, between planning to follow FIX indefinitely or 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 which 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 re-switching to the prior regime. This property will be seen to survive the modification in the extension of the model.