The Demand for International Reserves Under Fixed and Floating Exchange Rates

H. Robert Heller; Mohsin S. Khan

doi:10.5089/9781451930443.024.A001

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The Demand for International Reserves Under Fixed and Floating Exchange Rates

Author: H. Robert Heller and Mr. Mohsin S. Khan

Publication Date:: 01 Jan 1978

eISBN:: 9781451930443

ISBN:: 9781451930443

Language:: English

Keywords:: SP; demand equation; demand function; Quandt log-likelihood ratio test; Arima model; world reserves aggregate; Imports; Reserve positions; Exchange rate arrangements; International reserves; Oil exports; Global

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The standard textbook view, echoed recently by Haberler (1977), argues that in a system of floating exchange rates the need for a country to hold international reserves disappears, since payments imbalances will be corrected by movements in its exchange rate. Notwithstanding this view, it is apparent that under the current exchange rate arrangements countries have not only continued to hold international reserves but have also, on occasion, added significantly to them. An indication of how reserves behaved during the period 1971–77 can be seen from examining Chart 1, where the ratios of reserves to imports of various country groupings are displayed. 1 For the world as a whole (both including and excluding the oil exporting countries and the United States), 2 the ratio of reserves to imports rose fairly rapidly in the two years immediately preceding the move to floating, and then declined in the period 1973–74. A slight increase in 1975 was followed by a decline in the following year, and in 1977 there was an upward movement again. While there is no doubt that the ratio in the period subsequent to 1973 was much smaller than that before, it nevertheless appears to have stabilized since then. The same pattern that is described here is also evident in the behavior of the ratio of reserves to imports of industrial countries and in that of industrial countries excluding the United States. As expected, in the latter case the size of the ratio is clearly larger, since it is the United States that has had a pronounced fall in its level of reserves and its relative size dominates the industrial countries.

Abstract

The standard textbook view, echoed recently by Haberler (1977), argues that in a system of floating exchange rates the need for a country to hold international reserves disappears, since payments imbalances will be corrected by movements in its exchange rate. Notwithstanding this view, it is apparent that under the current exchange rate arrangements countries have not only continued to hold international reserves but have also, on occasion, added significantly to them. An indication of how reserves behaved during the period 1971–77 can be seen from examining Chart 1, where the ratios of reserves to imports of various country groupings are displayed. ¹ For the world as a whole (both including and excluding the oil exporting countries and the United States), ² the ratio of reserves to imports rose fairly rapidly in the two years immediately preceding the move to floating, and then declined in the period 1973–74. A slight increase in 1975 was followed by a decline in the following year, and in 1977 there was an upward movement again. While there is no doubt that the ratio in the period subsequent to 1973 was much smaller than that before, it nevertheless appears to have stabilized since then. The same pattern that is described here is also evident in the behavior of the ratio of reserves to imports of industrial countries and in that of industrial countries excluding the United States. As expected, in the latter case the size of the ratio is clearly larger, since it is the United States that has had a pronounced fall in its level of reserves and its relative size dominates the industrial countries.

For developing countries, however, the ratio of reserves to imports has behaved in a somewhat different manner. The ratio fell in 1971 but rose in the following two years (reflecting perhaps the commodity price boom), carrying over into the year of the adoption of flexible rates. Interestingly, 1973 is the particular year in which the ratio for this group reached a peak. ³ There was a slight decline in 1974 and 1975, but a rapid increase occurred in the following two years.

Quite clearly, the phenomenon of a stable, or, for developing countries, a rising reserves-to-imports, ratio following the change in the exchange rate system does not conform to the standard view, and this has led observers to attempt in various ways to rationalize this seeming inconsistency. For example, on the theoretical level, Williamson (1974) has argued that the standard view rests on the key assumption that demand and supply curves for foreign exchange are invariant with respect to the exchange rate system, and this assumption may not be warranted. In addition, destabilizing capital flows may result in an increased use of reserves in the move from a par value system, and if there is a secular rise in these destabilizing flows, the use of reserves may increase over time. ⁴

Several other reasons attempting to explain the absence of a decline in reserve use were contained in the Fund’s Annual Report, 1974. These are, in brief, as follows: (i) that exchange rates are managed in the new system rather than allowed to float freely without intervention; (ii) that there are motives for holding reserves other than to finance payments imbalances, and that these motives, such as the need to use reserves as a basis for foreign borrowing, may not have changed; (iii) that countries that were floating at that time may well have been anxious to return to fixed rates and accordingly maintained an appropriate level of reserves; and (iv) that the present system is one in which the currencies of the majority of countries are pegged to a single currency or a composite of currencies. In such a framework, it is possible that countries that peg to a single floating currency would increase reserve use because of the added variability in payments balances caused by the movement of exchange rates between third currencies and the intervention currency. ⁵ While the Annual Report, 1974 was concerned with the behavior of reserves in the period 1973–74, some of these arguments continue to be relevant. In particular, the last argument can be viewed as applicable to most non-oil developing countries even now.

While the evidence is clear that reserves continue to be held and used even with the adoption of floating rates, there is the question whether there has been any fundamental change in the basic economic behavior of countries with respect to reserve holdings. This relates to the stability of the relationship between reserves and other economic variables. Apart from general interest in whether the move from a par value system caused a significant change in behavior, the question is relevant for making any judgment about the future need for reserves. As recognized by Crockett (1978, p. 8), for predicting the level of reserves, “The key empirical question is how stable the global demand for reserves is.” Clearly, it is important to determine both if there was a shift in the relationship and if this was a once-and-for-all shift or whether the adoption of floating rates resulted in an erratic (and thus of limited use as a predictive device) demand function for international reserves.

Statistical tests of stability have concentrated primarily on testing whether there was a change in reserves behavior in March 1973. One set of tests, undertaken initially by Williamson (1974), considered various measures of reserve use in the periods before and after that date. While Williamson (1974) found no strong evidence of any difference between reserve use in the two periods, later tests based on his methodology did indicate that adoption of floating led to some reduction in the use of reserves. ⁶ These tests, however, have the problem that by dealing only with the behavior of reserves, they implicitly invoke the ceteris paribus assumption that factors affecting reserves are constant. Clearly, variables such as the level of imports and the variability of payments balances have not remained constant in the two periods. A different, more general test of the stability of the demand for international reserves has been conducted recently by Frenkel (1978) where a demand function is explicitly specified and estimated for the periods up to the adoption of floating and subsequently. Statistical tests were then performed to determine if the functions were different in the relative weights assigned to the various explanatory variables. These tests allowed Frenkel (1978, p. 111) to conclude that while there was some evidence of structural change in 1972, the estimates for the managed float period indicated that “… the patterns of country holdings and usages of reserves resemble to some extent the behavior prescribed for a regime of pegged exchange rates.”

The purpose of this paper is to examine the question of the stability of the reserve demand function for various country groupings. The analysis focuses on the question of whether there was a shift in 1973, and if so, in which direction? Furthermore, could the function after 1973 be regarded as stable or unstable? In general, the approach used here has much in common with the strategy adopted by Frenkel (1978), although there are significant differences. First, the issue was examined for a number of country groups rather than looking only at the categories of developed and developing countries. Second, and perhaps more important, the tests were based on time-series rather than cross-section data. This allowed us to model and test for the possibility of disequilibrium behavior of reserves and thus to overcome the assumption usually made in cross-section studies that countries are always on their equilibrium demand functions. ⁷ Third, several independent tests were used, rather than relying on only one statistical test of stability. This was done because departures from constancy of parameters of the function may show up in different ways, and the various tests may not be equally powerful against the particular kind of departure encountered.

In summary, our approach was to estimate reserve demand equations for the following six aggregates: the world; the world, excluding oil exporting countries; the world, excluding oil exporting countries and the United States; industrial countries; industrial countries, excluding the United States; and the less developed areas. The countries included in these various categories are based on standard classifications used by the International Monetary Fund. The estimates were obtained from quarterly data over the period 1964–76. These estimated functions were then examined for parameter stability using tests that could detect significant shifts in parameters and also could indicate the time when this occurs. This latter capability allows one to ascertain if the movement to floating rates caused a shift in the first or second quarters of 1973, or if there was a lagged response. We also examined empirically, through a forecasting exercise, in which direction floating changed the demand for reserves.

Section I describes the theoretical form of the demand function for reserves that was used and also its empirical counterpart, and briefly discusses the testing procedure. Section II contains both the estimation results and the results of the tests of parameter stability. Section III summarizes these results and their implications. Appendix I describes the models relevant to the forecasting tests, and Appendix II gives the sources and definitions of the data.

I. Specification of the Model

theoretical formulation

Following the literature on the subject, the demand for international reserves (R^D) can be related to three variables: (a) the ratio of imports to domestic income (I/Y); (b) the level of imports (I); and (c) a measure of variability of the balance of payments (σ²): ⁸

\begin{matrix} R^{D} = g (I / Y, I, σ^{2}) & (1) \end{matrix}

In this formulation the dependent variable is generally defined as gross reserves, or unconditional liquidity—that is, the reserves that a country actually holds without any allowance for foreign liabilities. This concept of reserves includes the monetary authorities’ holdings of gold and convertible foreign exchange (gross), reserve position in the Fund, and holdings of special drawing rights (SDRs). ⁹

While other measures, such as “net reserves” (that is, reserve holdings adjusted for foreign liabilities), may well be more relevant in assessing the “true” liquidity position of a country, the gross reserves concept is the better one from the point of view of a study such as this one. This is so because we want to explain the level of reserves that a country “demands.” If it borrows in order to add to its stock, then that is taken to imply that the accumulation is a reflection of increased demand.

The relationship between the demand for reserves and the first of the three explanatory variables—the ratio of imports to domestic income—is ambiguous in nature. If this ratio is taken to represent the “openness” of the economy, as has been argued by Cooper (1968) and Iyoha (1976), then obviously the relationship would be a positive one. On the other hand, if the ratio is a proxy for the marginal propensity to import, and therefore its inverse is an indication of the amount of domestic adjustment required to produce a particular level of reserves, then the relationship would be negative. ¹⁰ Recently also Frenkel (1978, Appendix I) has shown that, in a model that emphasizes the role of relative prices, the price level, and the demand for money, the effect of the average propensity to import (I/Y) on reserve demand cannot be unambiguously determined, but that under a fairly reasonable set of assumptions the effect would be positive.

The effect of the scale variable is more obvious—an increase in imports will result in an increased demand for reserves. The interesting issue in this particular relationship is whether reserves increase proportionally to imports, or whether there are any economies of scale. The use of the ratio of reserves to imports as an indicator of reserve adequacy, discussed earlier, implies the former, while studies by Olivera (1969; 1971), and, more recently, Officer (1976) argue that the elasticity of reserves with respect to imports should be significantly less than unity. This is a testable hypothesis, and the answer is important in trying to determine what the future growth of reserves should be.

The last variable in the function—namely, the variability of the balance of payments—is entered to reflect the theoretical concepts of risk and uncertainty. Greater variability in the balance of payments, by creating greater uncertainty, is expected to increase the demand for reserves. ¹¹

One further variable that has on occasion been introduced into a function such as equation (1) is the opportunity cost of holding resources in the form of reserves. Because there has been in Williamson’s (1973) words, a “uniform lack of success” with using various proxies for this variable, we followed Frenkel (1978) and Clark (1970) in excluding it from consideration. ¹²

In summary then, we expect that the partial derivatives of equation (1) would have the following pattern of signs:

\frac{{\partial R}^{D}}{\partial (I / Y)} ≷ 0; \frac{{\partial R}^{D}}{\partial I} > 0; \frac{{\partial R}^{D}}{{\partial σ}^{2}} > 0

empirical specification

Estimating equation

The estimating equation for reserves is specified in log-linear terms as:

\begin{matrix} \log R_{t} = a_{0} + a_{1} \log {(I / Y)}_{t} + a_{2} \log I_{t} + a_{3} \log σ_{t}^{2} + u_{t} & (\begin{matrix} 2 \end{matrix}) \end{matrix}

where u_t is an error term, and the other variables are defined as before. The specification in logarithms allows reserves to react proportionally to a rise or fall in the explanatory variables, and also, because of the assumption of constant elasticities, it avoids the problem of a secular fall in the elasticities as reserves rise over time. We have also assumed that R^D = R, and that this implies instantaneous adjustment of reserves to changes in demand. Lagged adjustment (as shown later), however, was allowed for by operating on the error structure, u_t.

The only variable that needs further explanation is the measure employed for the variable reflecting the payments imbalances, σ². In the literature, several methods to calculate this variable have been proposed. For example, Kenen and Yudin (1965) and Clark (1970) define it as the variance or standard deviation of the residuals obtained from estimating a first-order autoregressive process for the level or change of reserves. Heller (1966) calculates it as the mean absolute first-difference of the trend-adjusted past values of reserves, while Frenkel (1974; 1978) uses the standard deviation of these values. Defining σ² as the variability of export receipts has been proposed by Kelly (1970) and Iyoha (1976). In this study, we define σ² as the variability of reserves and employ a two-step procedure to calculate it. In the first stage, we utilize the time-series methodology of Box and Jenkins (1970) and estimate autoregressive integrated moving average (ARIMA) models for reserves of the six country groupings. More specifically, after transforming the level of reserves R_t into a stationary series $R_{t}^{*}$ ,¹³ we fit the ARIMA model described as:

\begin{matrix} φ (L) R_{t}^{*} = θ (L) v_{t} & (\begin{matrix} 3 \end{matrix}) \end{matrix}

where φ (L) and θ (L) are polynomial functions of the lag operator, L, and v_t are serially uncorrelated, white noise errors. In the Box-Jenkins framework, φ (L) corresponds to an autoregressive (AR) process and θ (L) to a moving average (MA) process.

The residuals, ${\hat{v}}_{t}$ , are obtained after estimating this equation (3), and their squared values, ${\hat{v}}_{t}^{2}$ , are interpreted as a measure of the variability of reserves. ¹⁴

Since it is fairly obvious that past values of ${\hat{v}}_{t}^{2}$ rather than only the current values also can be expected to have an effect on the current level of reserves, in our second stage we estimate equation (2) with a polynomial lag function imposed on ${\hat{v}}_{t}^{2}$ :

\begin{matrix} \log R_{t} = a_{0} + a_{1} \log {(I / Y)}_{t} + a_{2} \log I_{t} + a_{3} Σ_{i = 0}^{k} α_{i} \log {\hat{v}}_{t - i}^{2} + u_{t} & (4) \end{matrix}

The α_i, are the weights attached to the current and lagged values of ${\hat{v}}_{t}^{2}$ , and k represents the number of lagged periods to be considered. In the estimation, it is assumed that a second-degree polynomial with a constraint of zero at the 12th lag is adequate for our purposes. A weighted average of the ${\hat{v}}_{t}^{2}$ s is calculated using the weights obtained from this estimation, starting at the period when the weight becomes significantly different from zero at the 5 per cent level and stopping at the last significant weight, in other words:

\begin{matrix} σ_{t}^{2} = Σ_{i = 0}^{12} {\hat{α}}_{t} {\hat{v}}_{t - i}^{2}, \frac{{\hat{α}}_{i}}{{\hat{σ}}_{α i}} > t^{*} & (5) \end{matrix}

where t^* is the chosen t-value at some significance level.

The possibility of lagged adjustment of reserves is taken into account by assuming that the errors in the equation, that is, the u_t, follow an autoregressive process of the form:

\begin{matrix} {\begin{matrix} u \end{matrix}}_{t} = ρ u_{t - 1} + ϵ_{t} & (6) \end{matrix}

where ρ is the coefficient of autocorrelation, |ρ| < 1, and ϵ_t is a series of random errors. The solution of equations (2) and (6) yields the reduced form equation:

\begin{matrix} \log R_{t} = (1 - ρ L) a_{0} + (1 - ρ L) a_{1} \log (I / Y) + (1 - ρ L) a_{2} \log I_{t} \\ + (1 - ρ L) a_{3} \log σ_{t}^{2} + ρ \log R_{t - 1} + ϵ_{t} & (7) \end{matrix}

which is identical to one that is obtained if any one of the three explanatory variables is characterized as an “expected” rather than actual value, and expectations are determined through an “adaptive-expectations,” or “error-learning,” mechanism. The final equation (7) thus can be viewed as incorporating dynamic or disequilibrium behavior into the determination of reserves.

Stability tests

Two of the tests of parameter stability performed on equation (7) utilize the methodology of “recursive regressions” proposed by Brown, Durbin, and Evans (1975). These tests have the advantage over others that they do not require any a priori knowledge of when the change, if any, occurs in the regression relationship. Even though part of our analysis is designed to ascertain whether the move to a new exchange rate system caused a shift in the demand function, so that we are aware of the possible breakpoint in the data, it is nevertheless conceivable that there was a delayed response to the move to floating. In such a case, these tests are more appropriate than ones that prejudge the issue, choose the time in advance, and test the stability hypothesis, conditional on this assumption. Two tests are used, since one (“cusums”) is better able to detect gradual or systematic changes, while the other (“cusumssquared”) is preferable when the changes are more random in nature.

Since these particular tests indicate only the approximate region when the structural change occurs, we pinpoint the timing of the break more precisely by the use of the Quandt log-likelihood ratio rest. This test, designed by Quandt (1960), unfortunately cannot be used rigorously on its own because the distribution of the test statistic is not known. However, in tandem with the tests of Brown, Durbin, and Evans (1975), much useful information can be derived. ¹⁵

A further test that we conduct is much more impressionistic than the others, since no formal statistical analysis is performed. In this test, we estimate the reserves equation through 1972 and then utilize it to predict the level of reserves for the period 1973–76. These predictions are compared with both the actual values of reserves in the subperiod and forecasts obtained from the ARIMA model fitted up to the end of 1972. The first comparison, that is, between the forecasts of the demand equation and the actual stock of reserves, is a rough test of the predictive qualities of the model, while the second should indicate whether forecasting is improved by the introduction of explanatory variables. ¹⁶ Finally, a comparison between the ARIMA forecasts and the actual values should indicate whether the change in the exchange rate system has resulted in an increase or a decrease in the level of reserves relative to the level indicated from their past pattern of behavior.

II. Results

ARIMA model estimates

Appropriate ARIMA models are identified and fitted to the data on international reserves for the six country groupings over the period beginning in the second quarter of 1960 through the fourth quarter of 1976, and the results are shown in Table 1.

Table 1.

ARIMA Model Estimates for Reserves, Second Quarter 1960—Fourth Quarter 1976 ¹

^¹t-values in parentheses below coefficients. SSR = sum of squared residuals; DF = degrees of freedom.

Relatively simple models—namely, first-order autoregressive and first-order moving average—are found to be adequate for five of the country groups. ¹⁷ Interestingly, there does not appear to be any particular seasonal pattern present in the series in question. For reserves of countries included in the less developed areas, the relevant model turns out to be an autoregressive process with first-order, fourth-order, and fifth-order terms. Some seasonality is therefore indicated, which apparently is subsumed when the reserves of industrial countries are added with them to form the world reserves aggregates. All six models pass the test of yielding errors that are free from serial correlation. ¹⁸

The residuals from these estimated models are extracted, and after being squared, ¹⁹ are introduced into the reserves equation with the imposition that their lagged values lie along a second-degree polynomial function. Using the strategy of starting at the first significant weight, we form the weighted moving averages of the squared residuals to calculate the variability of the balance of payments measure. The particular lags involved in this calculation are shown in Table 2.

Table 2.

Formulation of Weighted Averages for Variability Measure

Table 2.

Formulation of Weighted Averages for Variability Measure

Country Grouping	σ²
World	$Σ_{i = 6}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
World (excluding oil exporting countries)	$Σ_{i = 6}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
World (excluding oil exporting countries and the United States)	$Σ_{i = 6}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
Industrial countries	$Σ_{i = 7}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
Industrial countries (excluding the United States)	$Σ_{i = 7}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
Less developed areas	$Σ_{i = 1}^{5} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$

Table 2.

Formulation of Weighted Averages for Variability Measure

Country Grouping	σ²
World	$Σ_{i = 6}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
World (excluding oil exporting countries)	$Σ_{i = 6}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
World (excluding oil exporting countries and the United States)	$Σ_{i = 6}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
Industrial countries	$Σ_{i = 7}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
Industrial countries (excluding the United States)	$Σ_{i = 7}^{12} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$
Less developed areas	$Σ_{i = 1}^{5} {\hat{α}}_{i} {\hat{v}}_{t - i}^{2}$

behavioral model estimates

The results obtained from estimating the reserve demand equation (7) with the definitions of σ² shown in Table 2, are reported in Table 3. For the three world groupings, as well as for the less developed areas, we employ a second-order autoregressive process in the errors, that is,

\begin{matrix} u_{t} = ρ_{1} u_{t - 1} + ρ_{2} u_{t - 2} + ϵ_{t} & (8) \end{matrix}

while for the categories of industrial countries (both including and excluding the United States) a first-order process is utilized. In Table 3 are given the values of the elasticities with their respective t-values, the estimated coefficients of autocorrelation (also with their t-values), the standard errors of the estimated equations (SEE), the adjusted coefficients of determination $({\bar{R}}^{2})$ , and the Durbin-Watson test statistics (D-W).

Table 3.

Demand Forreserves, First Quarter 1964-Fourth Quarter 1976 ¹

^¹t-values in parentheses below coefficients.

Table 3.

Demand Forreserves, First Quarter 1964-Fourth Quarter 1976 ¹

Country Grouping	$\log R_{t} = a_{0} + a_{1} \log {(I / Y)}_{t} + a_{2} \log I_{t} + a_{3} \log σ_{t}^{2}$
Country Grouping	a₀	a₁	a₂	a₃	ρ₁	ρ₁	SEE	${\bar{R}}^{2}$	D-W
World	0.192 (0.27)	–0.713 (7.06)	0.854 (8.64)	0.999 (4.12)	1.399 (10.80)	–0.473 (3.60)	0.026	0.719	2.04
World (excluding oil exporting countries)	1.151 (1.76)	–0.608 (6.79)	0.691 (8.17)	1.064 (4.80)	1.442 (11.71)	–0.555 (4.47)	0.026	0.774	2.27
World (excluding oil exporting countries and the United States)	2.211 (4.15)	–0.498 (7.05)	0.600 (8.50)	1.052 (6.28)	1.522 (13.38)	–0.643 (5.74)	0.029	0.823	2.30
Industrial countries	–0.620 (0.60)	–0.770 (4.12)	0.852 (5.98)	0.789 (2.14)	0.916 (18.92)	—	0.037	0.495	1.72
Industrial countries (excluding the United States)	0.428 (0.51)	–0.635 (3.67)	0.757 (5.74)	0.686 (2.35)	0.918 (15.92)	—	0.047	0.428	1.53
Less developed areas	0.522 (1.24)	–0.290 (4.88)	0.687 (6.32)	0.395 (0.84)	1.300 (9.18)	–0.360 (2.60)	0.040	0.451	1.84

^¹t-values in parentheses below coefficients.

Table 3.

Demand Forreserves, First Quarter 1964-Fourth Quarter 1976 ¹

Country Grouping	$\log R_{t} = a_{0} + a_{1} \log {(I / Y)}_{t} + a_{2} \log I_{t} + a_{3} \log σ_{t}^{2}$
Country Grouping	a₀	a₁	a₂	a₃	ρ₁	ρ₁	SEE	${\bar{R}}^{2}$	D-W
World	0.192 (0.27)	–0.713 (7.06)	0.854 (8.64)	0.999 (4.12)	1.399 (10.80)	–0.473 (3.60)	0.026	0.719	2.04
World (excluding oil exporting countries)	1.151 (1.76)	–0.608 (6.79)	0.691 (8.17)	1.064 (4.80)	1.442 (11.71)	–0.555 (4.47)	0.026	0.774	2.27
World (excluding oil exporting countries and the United States)	2.211 (4.15)	–0.498 (7.05)	0.600 (8.50)	1.052 (6.28)	1.522 (13.38)	–0.643 (5.74)	0.029	0.823	2.30
Industrial countries	–0.620 (0.60)	–0.770 (4.12)	0.852 (5.98)	0.789 (2.14)	0.916 (18.92)	—	0.037	0.495	1.72
Industrial countries (excluding the United States)	0.428 (0.51)	–0.635 (3.67)	0.757 (5.74)	0.686 (2.35)	0.918 (15.92)	—	0.047	0.428	1.53
Less developed areas	0.522 (1.24)	–0.290 (4.88)	0.687 (6.32)	0.395 (0.84)	1.300 (9.18)	–0.360 (2.60)	0.040	0.451	1.84

^¹t-values in parentheses below coefficients.

Considering the results in order, we observe that in the world reserves equation all the estimated elasticities are significantly different from zero at the 5 per cent level. The ratio of imports to income appears to exert a negative effect, implying a more “Keynesian” role for this variable. ²⁰ The elasticity of reserves with respect to imports is close to unity, indicating, therefore, that world reserves apparently grow in proportion to trade with not much evidence of economies of scale. This result tends to support the judgment of Polak (1970) that this particular elasticity would lie in the region of 0.8–1.0, and also does not reject the hypothesis made by Olivera (1971) that the elasticity should be between 0.5 and 1.0. The variability of payments elasticity is almost equal to unity—an increase in variability, say, from 5 per cent to 10 per cent would appear to result in an increase in the demand for reserves of 5 per cent.

For reasons that are fairly obvious, the inclusion of oil exporters in the analysis may distort the results. Therefore, an equation was estimated that excluded their data from the time series employed. In this estimate, the elasticity of the ratio of imports to income is somewhat lower in size, ²¹ but it continues to be negative and to be significant at the 5 per cent level. The elasticity with respect to imports indicates some economies of scale in the holdings of reserves, while the variability elasticity continues to be close to unity. The exclusion of oil exporters from the relationship does yield a slightly better fit (as measured by the ${\bar{R}}^{2}$ ); however, generally speaking, leaving them in does not appear to have a major distorting effect on the basic relationship.

The fact that the United States can be viewed as a major supplier of international reserves over much of the period makes it desirable to estimate the model excluding both oil exporting countries and the United States. In this equation, both the elasticities with respect to the import/income ratio in absolute terms and the level of imports are lower, although both are significantly different from zero. The effect of the variability measure on reserve demand continues to be approximately one to one. The fit of the equation is better when the data for the United States are excluded, but the improvement, as when oil exporters were excluded, is only very slight.

The equation for industrial countries yields elasticities that are all significantly different from zero, and, reflecting the dominant position in the world of this group, the estimates are very close to the ones we obtained for the world as a whole. An interesting result in this regression equation is the relatively low value of the variability elasticity. It can be argued that since industrial countries have greater access to world capital markets and swap arrangements, increased variability in their balance of payments has less of an effect on their stock demand for reserves. Unexpected shocks can be met by borrowing from other central banks or from the market. The equation estimated after excluding the United States from the aggregate for the industrial countries does not change the elasticities by very much.

It appears from our results that for less developed countries the effect of the import/income ratio is fairly small, although the elasticity is significantly greater than zero. A far greater internal adjustment would be called for in this group of countries than would be necessary for industrial countries to achieve a given stock of reserves. In contrast to Frenkel’s (1978) conclusion that developed countries may have larger possibilities for economies of scale in reserve management than developing countries, we find that such possibilities exist equally for the latter group. Finally, in view of the relative difficulties that these countries have in being able to accommodate unexpected shocks by borrowing abroad, it is surprising that variability in the balance of payments has a lower weight than it does on the demand for reserves of industrial countries. However, since the size of this elasticity is not independent of the particular value of the variability measure, not too much should be made of this result.

stability tests

We turn now to the various tests of parameter stability. The reasons for using more than one test were pointed out earlier. For purposes of these tests, it is necessary to assume that the estimated coefficients of autocorrelation are constant, so that the relevant variables are transformed by these values. For example, each of the variables in the equation are multiplied by $(1 - {\hat{ρ}}_{1} L - {\hat{ρ}}_{1} L^{2})$ , or for the two industrial country groupings, by $(1 - {\hat{ρ}}_{1} L)$ . ²² The results of the tests of stability utilizing these transformed variables are shown in Table 4.

Table 4.

Stability Tests for Demand for Reserves Equations, Third Quarter 1964-Fourth Quarter 1976

^¹Significant at the 10 per cent level.

Table 4.

Stability Tests for Demand for Reserves Equations, Third Quarter 1964-Fourth Quarter 1976

Test Procedure		World	World (Excluding Oil Exporting Countries)	World (Excluding Oil Exporting Countries and the United States)	Industrial Countries	Industrial Countries (Excluding the United States)	Less Developed Areas
Cusums		0.881 ¹	0.751	0.453	0.896 ¹	0.976 ¹	1.043 ¹
Cusums-squared		0.273 ¹	0.356 ¹	0.269 ¹	0.298	0.306 ¹	0.160
Log-likelihood ratio test
	Minimum value point	Fourth quarter 1973	Fourth quarter 1973	Fourth quarter 1973	Fourth quarter 1973	Fourth quarter 1973	Second quarter 1972

^¹Significant at the 10 per cent level.

Table 4.

Stability Tests for Demand for Reserves Equations, Third Quarter 1964-Fourth Quarter 1976

Test Procedure		World	World (Excluding Oil Exporting Countries)	World (Excluding Oil Exporting Countries and the United States)	Industrial Countries	Industrial Countries (Excluding the United States)	Less Developed Areas
Cusums		0.881 ¹	0.751	0.453	0.896 ¹	0.976 ¹	1.043 ¹
Cusums-squared		0.273 ¹	0.356 ¹	0.269 ¹	0.298	0.306 ¹	0.160
Log-likelihood ratio test
	Minimum value point	Fourth quarter 1973	Fourth quarter 1973	Fourth quarter 1973	Fourth quarter 1973	Fourth quarter 1973	Second quarter 1972

^¹Significant at the 10 per cent level.

Taking the results of the cusums and cusums-squared tests together, we find that the null hypothesis that the estimated parameters are constant over the sample period is rejected at the 10 per cent significance level for all six groups. ²³ By and large, we can conclude with a substantial degree of confidence that the estimated parameters of the relationship cannot be assumed to have remained constant over the entire period running from 1964 to 1976.

To identify the quarter in which this shift in the estimated equations occurs, we apply the Quandt log-likelihood ratio test. The minimum value of the test statistic indicates when the change happens, and the relevant quarter is identified in Table 4. The first surprising aspect of the results is that for most cases the test indicates that the shift in the relationship occurred in the last quarter of 1973 rather than in the first or second quarters. As the change in the exchange rate system took place in March 1973, it would be expected a priori that this would have affected the demand for reserves in that, or at most the following, quarter. Instead, there was a significant lag of two to three quarters between the announcement and the corresponding adjustment to the new system of exchange rates. ²⁴ The second, and equally surprising, result is that the function explaining reserves of the less developed countries apparently shifted in the second quarter of 1972. This change seems to coincide with the boom in commodity prices and consequent increase in the reserves of primary producing countries, rather than with the move to floating. This is understandable, since less developed countries in general continued to remain pegged to another currency, and thus there was no real change in their own particular exchange rate arrangements.

comparison of forecasts for the managed-floating period

Another empirical exercise provides some further evidence on the stability of the behavioral model, and also indicates the direction of the shift. Insofar as this latter aspect is concerned, on theoretical grounds one might have expected that a floating exchange rate would result in a reduced demand for reserves, so that a downward shift in the function would result. This hypothesis is tested by estimating the demand equation up to the fourth quarter of 1972, and then utilizing it to forecast the level of reserves from the beginning of 1973 through 1976. These forecasted values of reserves are then compared with the actual values of reserves during these 16 quarters, and with the forecasted values obtained from estimating the ARIMA models to the end of 1972 and predicting through 1976. ²⁵ The comparison between the actual values and the ARIMA forecasts can be interpreted as providing an indication as to how reserves have behaved relative to their past behavior pattern.

The two sets of forecasts and the level of reserves for the period 1973–76 are plotted in Charts 2–7. Even a cursory look at these charts shows that during 1973 reserve holdings were higher than the level that would have been indicated on the basis of the past patterns of behavior. It can be argued that this phenomenon is what led Williamson (1974) to conclude that reserve use was higher, rather than lower in the initial period following the adoption of floating exchange rates. For the world as a whole, reserves tended to be generally above the ARIMA forecasts until about the second quarter of 1975, after which they fell below ²⁶ and remained there through the end of 1976. The behavioral model underpredicts reserves up until the same point (the second quarter of 1975), and then starts to overpredict systematically. The behavioral model does, however, do better than the ARIMA model, in terms of having lower forecast errors for the period.

Excluding oil exporters, Chart 3 shows that after the fourth quarter of 1973 world reserves were lower than would have been expected had the same time-series pattern continued. The same conclusion is evident when the United States is excluded, as is shown in Chart 4. In both cases, even though there are fairly large forecast errors, indicating the instability that we observed earlier, the behavioral model tends on average to perform somewhat better than the ARIMA model.

The reserves of industrial countries were also lower than the ARIMA forecasts after the fourth quarter of 1973 (Charts 5 and 6). When the United States is excluded, the path of reserves seems even flatter, implying that reserve levels for these groupings have remained relatively constant. There is, however, some indication that their reserves started to grow again in 1976. ²⁷ As before, the behavioral model apparently does better than the ARIMA model.

Leaving aside the case of the world including oil exporters, we are able to see from Charts 3-6 the direction of the shifts in the demand functions. In each case, the model systematically overpredicts reserve holdings, implying that there has been a downward shift in the function. However, since quarter-to-quarter movements in reserves are being mirrored to some extent by the forecasts of the behavioral model, one can reasonably conclude that the shift in the estimated equation was a once-and-for-all type. Since 1974 the basic relationship appears to have been re-established.

For less developed countries, a different conclusion emerges from an examination of Chart 7. Apart from one short episode from the second quarter of 1975 to the second quarter of 1976, actual reserve holdings were above the levels that were predicted by the ARIMA models. The movement to a floating rate system seems to have caused these countries, perhaps because of greater uncertainty, to hold more reserves. ²⁸ While up to 1975 the behavioral model predicted actual reserves very accurately, ²⁹ since then it has tended to underpredict. It could be argued that since then the function has shifted upward. However, in view of the very few observations where this occurs, it would be premature to draw any firm conclusions.

III. Conclusion

The purpose of this paper was to examine the demand for international reserves during the period when the international monetary system shifted from par value arrangements to greater exchange rate flexibility. We investigated the behavior of countries’ international reserve holdings during the period when the change in the international monetary system occurred. Theory would suggest that the move toward more flexible rates would lower the need, and thus demand, for countries to hold resources in the form of international reserves. We investigated in detail whether the demand function remained stable in the period 1973–76, so as to determine whether countries’ holdings of reserves continued to be determined by the same forces that had governed their behavior in the fixed exchange rate period.

To provide some quantitative evidence on these two issues, we initially specified and estimated reserve demand equations for six country groupings. The estimation, utilizing time-series data, covered the period 1964 to 1976. A combination of formal tests of parameter stability and out-of-sample forecasts were then employed.

The results obtained from the exercise allowed us to reach the following conclusions. First, there was clearly a shift in the demand for international reserves by industrial countries when the move to the floating rate system occurred. However, the change was not sudden and appears to have taken place toward the end of 1973, rather than in the earlier part of the year when the actual change to floating occurred. Insofar as non-oil developing countries were concerned, the move toward more flexibility in exchange rates did not appear to affect their behavior in any significant manner. This group of countries seems to have had a shift in their demand function in the period 1971–72 rather than at the time of the inception of managed floating. That they did not change their basic behavior pattern in a statistically significant manner can perhaps be attributed to the fact that for most of them the exchange rate regime did not change, as they continued generally to follow a policy of pegging their currency to another major currency. (See Heller (1978).)

Second, we found that after the structural change in 1973, the function explaining reserves behavior continued to be stable in the period of managed floating. This was observed for industrial countries as well as developing countries. ³⁰ However, since the period of floating is too short to perform formal tests, this conclusion should be viewed as only a preliminary one. On the other hand, the results of Frenkel (1978) provide further support for this conclusion.

Finally, it was observed that there was some empirical evidence supporting the hypothesis that the demand for reserves should be reduced as exchange rates became more flexible in the case of industrial countries. On the other hand, surprisingly, the reverse seems to hold true for non-oil developing countries. Their holdings of reserves during the floating rate period have tended to be higher than the levels that would have been implied by their behavior during the fixed rate period. The greater degree of uncertainty and variability in their payments balances resulting from being pegged to a floating currency may well be the explanation for this.

One important caveat that should be explicitly made in regard to our study is the use of the broad country groupings. Clearly, all the countries in the group do not have the same behavior patterns, and in some cases the actions of one, or a few, within any grouping may bias the results in a particular direction. While some allowance was made for this, namely, by excluding the oil exporting countries and the United States, it is obvious that some aggregation problems will continue to remain. Short of studying each country individually, there does not seem to be any simple method to completely eliminate the errors introduced by aggregation.

APPENDICES

I. The Demand for International Reserves, 1964–72

To provide forecasts for the period 1973–76, both the ARIMA models and the behavioral demand for reserve functions were estimated up to the last quarter of 1972. For both cases, the models were of the same form as the ones that were estimated through 1976.³¹ The results are shown in Tables 5 and 6 for the ARIMA estimates and the demand equations, respectively. The projections from both these types of model were then obtained for the period 1973–76. The resulting values were transformed into the level of international reserves, and it is these that are reported in Charts 2–7.

Table 5.

ARIMA Model Estimates for Reserves, Second Quarter 1960 – Fourth Quarter 1972 ¹

^¹t-values in parentheses below coefficients. SSR = sum of squared residuals; DF = degrees of freedom.

Table 6.

Demand for Reserves, First Quarter 1964-Fourth Quarter 1972 ¹

^¹t-values in parentheses below coefficients.

Table 6.

Demand for Reserves, First Quarter 1964-Fourth Quarter 1972 ¹

Country Grouping	$\log R_{t} = a_{0} + a_{1} \log {(I / Y)}_{t} + a_{2} \log I_{t} + a_{3} \log σ_{t}^{2}$
Country Grouping	a₀	a₁	a₂	a₃	ρ₁	ρ₂	SEE	${\bar{R}}^{2}$	D-w
World	2.878 (2.69)	–0.366 (2.45)	0.457 (2.85)	1.400 (5.17)	1.519 (10.69)	–0.608 (4.28)	0.024	0.599	2.35
World (excluding oil exporting countries)	3.045 (2.74)	–0.345 (2.24)	0.423 (2.56)	1.440 (5.20)	1.486 (10.22)	–0.578 (3.99)	0.025	0.595	2.32
World (excluding oil exporting countries and the United States)	3.739 (3.85)	–0.261 (1.81)	0.325 (1.93)	1.575 (4.79)	1.563 (11.30)	–0.616 (4.66)	0.028	0.413	2.32
Industrial countries	–0.392 (0.19)	–0.693 (2.07)	0.886 (2.86)	1.352 (2.76)	0.936 (16.68)	—	0.037	0.379	1.65
Industrial countries (excluding the United States)	1.377 (0.86)	0.442 (1.48)	0.678 (2.58)	1.329 (3.15)	0.911 (12.42)	—	0.049	0.430	1.58
Less developed areas	–1.862 (5.59)	–0.605 (5.89)	1.330 (16.91)	0.668 (0.65)	0.735 (3.91)	–0.138 (0.69)	0.041	0.896	1.88

^¹t-values in parentheses below coefficients.

Table 6.

Demand for Reserves, First Quarter 1964-Fourth Quarter 1972 ¹

Country Grouping	$\log R_{t} = a_{0} + a_{1} \log {(I / Y)}_{t} + a_{2} \log I_{t} + a_{3} \log σ_{t}^{2}$
Country Grouping	a₀	a₁	a₂	a₃	ρ₁	ρ₂	SEE	${\bar{R}}^{2}$	D-w
World	2.878 (2.69)	–0.366 (2.45)	0.457 (2.85)	1.400 (5.17)	1.519 (10.69)	–0.608 (4.28)	0.024	0.599	2.35
World (excluding oil exporting countries)	3.045 (2.74)	–0.345 (2.24)	0.423 (2.56)	1.440 (5.20)	1.486 (10.22)	–0.578 (3.99)	0.025	0.595	2.32
World (excluding oil exporting countries and the United States)	3.739 (3.85)	–0.261 (1.81)	0.325 (1.93)	1.575 (4.79)	1.563 (11.30)	–0.616 (4.66)	0.028	0.413	2.32
Industrial countries	–0.392 (0.19)	–0.693 (2.07)	0.886 (2.86)	1.352 (2.76)	0.936 (16.68)	—	0.037	0.379	1.65
Industrial countries (excluding the United States)	1.377 (0.86)	0.442 (1.48)	0.678 (2.58)	1.329 (3.15)	0.911 (12.42)	—	0.049	0.430	1.58
Less developed areas	–1.862 (5.59)	–0.605 (5.89)	1.330 (16.91)	0.668 (0.65)	0.735 (3.91)	–0.138 (0.69)	0.041	0.896	1.88

^¹t-values in parentheses below coefficients.

The differences in the estimates of the ARIMA models based on the periods 1960–72 and 1960–76 are not particularly striking. However, substantial differences in the estimated elasticities for the reserve demand equation do emerge, as would be indicated by the tests of parameter stability discussed in the body of the paper.

II. Data Definitions and Sources

All the data used in this study have been obtained from the International Monetary Fund Data Fund and correspond to those reported in the Fund’s International Financial Statistics (IFS).

The country groupings we worked with are classified according to the standard Fund categories. The Fund country codes are reported in Table 7.

The definitions of the variables that were used are as follows:

Reserves = gold, foreign exchange held by monetary authorities, SDRs, and reserve position in the Fund in billions of U. S. dollars. The data are identified as line 1..d in IFS.

Imports = in billions of U. S. dollars. The data are identified as line 71..d.

Income = This variable was first calculated as the sum of gross national product (or gross domestic product) of the countries comprising the group defined in Table 7, converted into U. S. dollars at the prevailing exchange rate. Second, the annual figures were converted to a quarterly basis using a simple linear interpolation procedure. The data were constructed by the Fund and are available from the authors upon request. Please address inquiries to Mr. Mohsin S. Khan, Research Department, International Monetary Fund, Washington, D.C. 20431.

Table 7.

Fund Country Group Definitions and Country Codes

Source: International Monetary Fund, International Financial Statistics.

Table 7.

Fund Country Group Definitions and Country Codes

Country Grouping	Country Code
World	001
World (excluding oil exporting countries)	001–(999)
World (excluding oil exporting countries and the United States)	001–(999)–(111)
Industrial countries	110
Industrial countries (excluding the United States)	110–(111)
Less developed areas	201

Source: International Monetary Fund, International Financial Statistics.

Table 7.

Fund Country Group Definitions and Country Codes

Country Grouping	Country Code
World	001
World (excluding oil exporting countries)	001–(999)
World (excluding oil exporting countries and the United States)	001–(999)–(111)
Industrial countries	110
Industrial countries (excluding the United States)	110–(111)
Less developed areas	201

Source: International Monetary Fund, International Financial Statistics.

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Mr. Heller, Chief of the Financial Studies Division of the Research Department when the paper was prepared, is now at the Bank of America, San Francisco. He holds degrees from the University of Minnesota and the University of California at Berkeley, and has taught at the University of California at Los Angeles and the University of Hawaii. He is the author of International Trade, International Monetary Economics, The Economic System, Japanese Investment in the United States, and a number of articles in professional journals.

Mr. Khan, Assistant Chief of the Financial Studies Division of the Research Department, holds degrees from Columbia University and the London School of Economics and Political Science.

This ratio is sometimes taken as a rough indicator of “reserve adequacy.” See Williamson (1973).

Since the United States can be viewed as a major supplier of reserves.

During the period 1963–77.

See Williamson (1974). Haberler (1977) attributes this argument to Harrod (1965)

For a theoretical discussion of the assumptions necessary for this to occur, see Ripley (1974).

See Ishiyama (1976) and Suss (1976).

This is recognized by Frenkel (1978). To our knowledge, only Iyoha (1976) attempts to include lags even in a cross-section framework.

Discussions of this relationship and the studies utilizing it are contained in the surveys by Grubel (1971), Williamson (1973), Claassen (1974), and Cohen (1975).

Conditional liquidity consists of the potential of borrowing of reserves through swaps or the credit tranches in the Fund.

See Heller (1966) and Williamson (1973) for a discussion.

See Heller (1966) and Williamson (1973).

See Williamson (1973, p. 695) for a list of the studies that use various measures for the opportunity cost variable.

This was achieved by taking logarithmic first-differences of reserves, that is,

$R_{t}^{*} = \log R_{t} - \log R_{t - 1}$

In the logarithmic form of equation (2), it is immaterial whether we use ${\hat{v}}_{t}^{2}$ or its squared root $\sqrt{{\hat{v}}_{t}^{2}}$ as the variability concept. The result for the latter can be derived from our estimates as 2a₃.

For some applications of the tests, see Khan (1978) and Heller and Khan (1978). The Quandt test is also one of the tests used by Frenkel (1978).

For forecasting purposes, the ARIMA model requires no information other than on the past values of the series in question.

In the sense of goodness-of-fit, significance of the coefficients, and serial independence of the residuals.

The test for serial independence in the errors is made on the basis of the x² statistic that is reported.

So as to ensure that positive and negative values will have the same effect.

See Heller (1966) and Kreinin and Heller (1974).

Or, that the required domestic adjustment to achieve a level of reserves would be larger.

This is done in order to avoid any confusion that a changing autocorrelation coefficient may cause in the tests.

Recall our earlier mention of the fact that the cusums test is better able to detect gradual changes in parameters, while the cusums-squared test is more powerful when changes are erratic.

The shift observed does, however, anticipate the oil price increase, so that one can reasonably assume that the cause of the change is identified.

The estimates of both the reserve demand equations and the ARIMA models through 1972 are shown in Appendix I.

They were also slightly lower in the first quarter of 1974.

Recent data show that this growth continued into 1977 as well.

This also conforms to the evidence of increased Eurodollar borrowing undertaken by members of this group in recent years.

This is clearly why no instability was indicated.

For developing countries, this conclusion held from 1972 onward.

This, in the case of the ARIMA models, implies that the same order autoregressive and moving average processes are applicable. Insofar as the behavioral model is concerned, it simply means using the same set of explanatory variables.

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IMF Staff papers: Volume 25 No. 4

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1978: Issue 004

Publisher:: International Monetary Fund

ISBN:: 9781451930443

ISSN:: 1020-7635

Pages:: 234

DOI:: https://doi.org/10.5089/9781451930443.024

Keywords
I. Specification of the Model
- theoretical formulation
- empirical specification
  - Estimating equation
  - Stability tests
II. Results
III. Conclusion
- APPENDICES
  - I. The Demand for International Reserves, 1964–72
  - II. Data Definitions and Sources
REFERENCES

View raw image

Ratios of Aggregate Reserves to Aggregate Imports, 1971–771

(In per cent)

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Reserves: World, 1973–76

(In billions of U.S. dollars)

View raw image

Reserves: World (Excluding On. Exporting Countries), 1973–76

(In billions of U.S. dollars)

View raw image

Reserves: World (Excluding Oil Exporting Countries and the United States), 1973–76

(In billions of U.S. dollars)

View raw image

Reserves: Industrial Countries, 1973–76

(In billions of U.S. dollars)

View raw image

Reserves: Industrial Countries (Excluding the United States), 1973–76

(In billions of U.S. dollars)

View raw image

Reserves: Less Developed Areas, 1973–76

(In billions of U.S. dollars)

Foresee

Table 7.

Fund Country Group Definitions and Country Codes

Country Grouping	Country Code
World	001
World (excluding oil exporting countries)	001–(999)
World (excluding oil exporting countries and the United States)	001–(999)–(111)
Industrial countries	110
Industrial countries (excluding the United States)	110–(111)
Less developed areas	201

Source: International Monetary Fund, International Financial Statistics.

World	$\begin{array}{l} \underset{S S R = 0.044}{\underset{(8.52)}{(1 - 0.867 L)}} \underset{x^{2} = 9.65}{\underset{(\begin{matrix} 2.25 \end{matrix})}{[(1 - L) \log R_{t} - 0.022]}} = \underset{D F =10}{\underset{(\begin{matrix} 3.19 \end{matrix})}{(1 + 0.548 L)} u_{t}} \end{array}$
World (excluding oil exporting countries)	$\begin{array}{l} \underset{S S R = 0.045}{\underset{(7.89)}{(1 - 0.857 L)}} \underset{x^{2} = 12.89}{\underset{(\begin{matrix} 2.00 \end{matrix})}{[(1 - L) \log R_{t} - 0.019]}} = \underset{D F = 10}{\underset{(2.99)}{(1 + 0.536 L)}} u_{t} \end{array}$
World (excluding oil exporting countries and the United States)	$\begin{matrix} \underset{(7.75)}{(1 - 0.841 L)} [(1 - L) \log R_{t} - \underset{(\begin{matrix} 2.27 \end{matrix})}{0.026}] = \underset{(2.55)}{(1 + 0.459 L)} u_{t} \\ S S R = 0.054 x^{2} = 16.74 D F = 10 \end{matrix}$
Industrial countries	$\begin{matrix} \underset{(4.74)}{(1 - 0.818 L)} [(1 - L) \log R_{t} - \underset{(1.95)}{0.017}] = \underset{(2.54)}{(1 + 0.607 L) u_{t}} \\ S S R = 0.075 x^{2} = 11.25 D F = 10 \end{matrix}$
Industrial countries (excluding the United States)	$\begin{matrix} \underset{(5.22)}{(1 - 0.794 L)} [(1 - L) \log R_{t} - \underset{(2.16)}{0.025}] = \underset{(2.28)}{(1 + 0.400 L)} u_{t} \\ S S R = 0.110 x^{2} = 13.22 D F = 10 \end{matrix}$
Less developed areas	$\begin{matrix} \underset{(5.03)}{(1 - 0.530 L} - \underset{(3.67)}{0.417 L^{4}} + \underset{(4.09)}{0.462 {L^{5})}^{}} [(1 - L) \log R_{t} - \underset{(3.84)}{0.030]} = u_{t} \\ S S R = 0.067 x^{2} = 7.56 D F = 9 \end{matrix}$

World	$\begin{array}{l} \underset{S S R = 0.044}{\underset{(8.52)}{(1 - 0.867 L)}} \underset{x^{2} = 9.65}{\underset{(\begin{matrix} 2.25 \end{matrix})}{[(1 - L) \log R_{t} - 0.022]}} = \underset{D F =10}{\underset{(\begin{matrix} 3.19 \end{matrix})}{(1 + 0.548 L)} u_{t}} \end{array}$
World (excluding oil exporting countries)	$\begin{array}{l} \underset{S S R = 0.045}{\underset{(7.89)}{(1 - 0.857 L)}} \underset{x^{2} = 12.89}{\underset{(\begin{matrix} 2.00 \end{matrix})}{[(1 - L) \log R_{t} - 0.019]}} = \underset{D F = 10}{\underset{(2.99)}{(1 + 0.536 L)}} u_{t} \end{array}$
World (excluding oil exporting countries and the United States)	$\begin{matrix} \underset{(7.75)}{(1 - 0.841 L)} [(1 - L) \log R_{t} - \underset{(\begin{matrix} 2.27 \end{matrix})}{0.026}] = \underset{(2.55)}{(1 + 0.459 L)} u_{t} \\ S S R = 0.054 x^{2} = 16.74 D F = 10 \end{matrix}$
Industrial countries	$\begin{matrix} \underset{(4.74)}{(1 - 0.818 L)} [(1 - L) \log R_{t} - \underset{(1.95)}{0.017}] = \underset{(2.54)}{(1 + 0.607 L) u_{t}} \\ S S R = 0.075 x^{2} = 11.25 D F = 10 \end{matrix}$
Industrial countries (excluding the United States)	$\begin{matrix} \underset{(5.22)}{(1 - 0.794 L)} [(1 - L) \log R_{t} - \underset{(2.16)}{0.025}] = \underset{(2.28)}{(1 + 0.400 L)} u_{t} \\ S S R = 0.110 x^{2} = 13.22 D F = 10 \end{matrix}$
Less developed areas	$\begin{matrix} \underset{(5.03)}{(1 - 0.530 L} - \underset{(3.67)}{0.417 L^{4}} + \underset{(4.09)}{0.462 {L^{5})}^{}} [(1 - L) \log R_{t} - \underset{(3.84)}{0.030]} = u_{t} \\ S S R = 0.067 x^{2} = 7.56 D F = 9 \end{matrix}$

World	$\begin{matrix} \underset{\begin{matrix} (9.67) \end{matrix}}{(1 - 0.901 L)} [(1 - L) \log R_{t} \underset{\begin{matrix} (1.56) \end{matrix}}{- 0.022]} = \underset{(2.56)}{(1 + 0.478 L)} u_{t} \\ S S R = 0.022 X^{2} = 10.07 D F = 7 \end{matrix}$
World (excluding oil exporting countries)	$\begin{matrix} \underset{\begin{matrix} (9.06) \end{matrix}}{(1 - 0.899 L)} [(1 - L) \log R_{t} \underset{\begin{matrix} (1.57) \end{matrix}}{- 0.021]} = \underset{(2.62)}{(1 + 0.506 L)} u_{t} \\ S S R = 0.023 X^{2} = 8.79 D F = 7 \end{matrix}$
World (excluding oil exporting countries and the United States)	$\begin{array}{l} \underset{(8.60)}{(1 - 0.872 L)} [(1 - L) \log R_{t} - \underset{(2.00)}{0.029]} = \underset{(2.18)}{(1 + 0.416 L)} u_{t} \\ S S R = 0.030 X^{2} = 11.83 D F = 7 \end{array}$
Industrial countries	$\begin{array}{l} \underset{(4.97)}{(1 - 0.816 L)} [(1 - L) \log R_{t} - \underset{(1.59)}{0.018]} = \underset{(1.96)}{(1 + 0.497 L)} u_{t} \\ S S R = 0.045 X^{2} = 6.08 D F = 7 \end{array}$
Industrial countries (excluding the United States)	$\begin{array}{l} \underset{(5.43)}{(1 - 0.799 L)} [(1 - L) \log R_{t} - \underset{(1.93)}{0.029]} = \underset{(1.81)}{(1 + 0.415 L)} u_{t} \\ S S R = 0.073 X^{2} = 8.08 D F = 7 \end{array}$
Less developed areas	$\begin{matrix} \underset{(2.59)}{(1 - 0.363 L} - \underset{(3.04)}{0.427 L^{4}} + \underset{(2.18)}{0.308 L^{5})} [(1 - L) \log R_{t} - \underset{(3.10)}{0.025]} = u_{t} \\ S S R = 0.041 X^{2} = 2.87 D F = 6 \end{matrix}$

World	$\begin{matrix} \underset{\begin{matrix} (9.67) \end{matrix}}{(1 - 0.901 L)} [(1 - L) \log R_{t} \underset{\begin{matrix} (1.56) \end{matrix}}{- 0.022]} = \underset{(2.56)}{(1 + 0.478 L)} u_{t} \\ S S R = 0.022 X^{2} = 10.07 D F = 7 \end{matrix}$
World (excluding oil exporting countries)	$\begin{matrix} \underset{\begin{matrix} (9.06) \end{matrix}}{(1 - 0.899 L)} [(1 - L) \log R_{t} \underset{\begin{matrix} (1.57) \end{matrix}}{- 0.021]} = \underset{(2.62)}{(1 + 0.506 L)} u_{t} \\ S S R = 0.023 X^{2} = 8.79 D F = 7 \end{matrix}$
World (excluding oil exporting countries and the United States)	$\begin{array}{l} \underset{(8.60)}{(1 - 0.872 L)} [(1 - L) \log R_{t} - \underset{(2.00)}{0.029]} = \underset{(2.18)}{(1 + 0.416 L)} u_{t} \\ S S R = 0.030 X^{2} = 11.83 D F = 7 \end{array}$
Industrial countries	$\begin{array}{l} \underset{(4.97)}{(1 - 0.816 L)} [(1 - L) \log R_{t} - \underset{(1.59)}{0.018]} = \underset{(1.96)}{(1 + 0.497 L)} u_{t} \\ S S R = 0.045 X^{2} = 6.08 D F = 7 \end{array}$
Industrial countries (excluding the United States)	$\begin{array}{l} \underset{(5.43)}{(1 - 0.799 L)} [(1 - L) \log R_{t} - \underset{(1.93)}{0.029]} = \underset{(1.81)}{(1 + 0.415 L)} u_{t} \\ S S R = 0.073 X^{2} = 8.08 D F = 7 \end{array}$
Less developed areas	$\begin{matrix} \underset{(2.59)}{(1 - 0.363 L} - \underset{(3.04)}{0.427 L^{4}} + \underset{(2.18)}{0.308 L^{5})} [(1 - L) \log R_{t} - \underset{(3.10)}{0.025]} = u_{t} \\ S S R = 0.041 X^{2} = 2.87 D F = 6 \end{matrix}$

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Abstract

I. Specification of the Model

theoretical formulation

empirical specification

Estimating equation

Stability tests

II. Results

ARIMA model estimates

behavioral model estimates

stability tests

comparison of forecasts for the managed-floating period

III. Conclusion

APPENDICES

I. The Demand for International Reserves, 1964–72

II. Data Definitions and Sources

REFERENCES

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Inter-American Development Bank

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