Journal Issue

Inflation and International Reserves: A Time-Series Analysis

International Monetary Fund. Research Dept.
Published Date:
January 1979
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In a Frequently Cited Paper investigating the relationship between the growth of international reserves and worldwide inflation during the period of fixed exchange rates, Heller (1976, p. 62) concludes that

… the recent increase in international reserves helped to precipitate the world-wide monetary expansion that was an important causal factor in the world-wide inflation of the early 1970s.

The model that Heller utilized to obtain this conclusion contains two basic elements. First, there is the relationship between international reserves and the money supply. An expansion in international reserves increases the monetary base and, given a stable money multiplier, results in an expansion in the total money supply. Second, relying on a simple extension of the quantity theory of money to the world as a whole, the growth of money would, after some delay, cause prices to rise.

Heller’s tests provide empirical support for both these relationships, and his conclusions are consistent with the evidence provided by, among others, Meiselman (1975), Genberg and Swoboda (1977), and Parkin (1977). 1 It can, therefore, be accepted that a statistically significant relationship has existed between reserve growth and inflation. However, the method of testing used in these various studies does not warrant the stronger conclusion that changes in international reserves “caused” inflation. Fairly plausible models could be constructed that argue that international reserves simply responded to inflation while at the same time remaining consistent with the result that the two variables are closely related. 2 At this stage the evidence shows only that variations in international reserves are statistically related to variations in the rate of inflation.

The main purpose of this paper is to examine the empirical relationship between the two variables, employing statistical methodology that is better suited to testing the degree of association and the direction of causation. These methods, developed by Granger (1969), Sims (1972), Haugh (1976), and Pierce and Haugh (1977), and generally referred to in the literature as “tests of causality,” have been applied in a number of recent empirical studies. The tests are designed essentially to detect the existence of leads and lags between time series, and the results are interpreted to imply causality. Whether or not the presence of leads or lags generally satisfy the notion of “causality” as economists understand it, 3 it is sufficient here to determine whether the growth of international reserves led inflation, as Heller and others argue, or lagged behind. 4 Furthermore, within the framework of the tests employed, greater confidence can be attached to any contemporaneous relationship that may exist, since these tests greatly reduce the possibility of spurious correlation that may arise from, say, the relevant time series following a common trend.

A secondary purpose of this paper is to go further than previous studies and extend the analysis into the period of floating exchange rates to determine whether the relationship changed. If exchange rates are completely market-determined, then one could argue that reserves would not be a causal factor in the inflationary process, since the connecting link through the money supply would be broken. That is, any payments imbalances would be absorbed through exchange rate changes without any effect being felt on the monetary base. At the same time there would also be no reason for countries to hold international reserves, so that the alternative causal chain going from inflation to reserves would also be cut. However, it is clear that the period since 1973 cannot be characterized as one of free floating, because countries have intervened systematically in the exchange market for a variety of reasons, and the effects of reserve movements on the monetary base have not been completely sterilized. Also, countries have not only continued to hold assets in the form of foreign reserves but have in fact added significantly to their real stocks. 5 Given these facts, one would expect that reserves and inflation would continue to be related. However, as exchange rates now move more freely, the relationship would be somewhat weaker and the direction of causation less clear than in the fixed rate period.

Performing the tests for the floating rate period also has some implications for the current international monetary situation, as well as for the near-term future. It would be quite useful to determine if the expansion in reserves that resulted from, among other factors, recent U. S. current account deficits, and the planned future increases in reserves through the Fund’s actions, can be considered the cause, or potential cause, of current and future inflation.

The empirical tests in this exercise cover three aggregate country groupings—the world, industrial countries, and developing countries (excluding oil exporting countries)—for the period 1957–77. In order to consider the impact of floating, the reserve-inflation relationship during the period 1973–77 is examined separately.

Section I describes the basic hypothesis, and the form in which it is tested, and briefly discusses the methodology underlying the statistical procedures employed. Section II contains the results obtained for the various aggregates. Some of the implications of the examination are considered in Section III.

I. Basic Model and Testing Procedure

To test the relationship between the growth in reserves and inflation, the simplest and most direct formulation is to relate the percentage change in prices to the percentage changes in current and lagged values of international reserves: 6

where P is the rate of inflation and R is the percentage change in international reserves.

Equation (1) can be viewed essentially as a reduced form equation derived from two underlying structural relationships—first, the relationship between international reserves and monetary growth linked through the monetary base, and, second, between money and prices relying on a quantity theory of money model. With the introduction of lags and certain simplifying assumptions, such as constancy in the growth rates of the money multiplier, the domestic component of the monetary base, real income, and velocity, one can obtain equation (1).

Estimates by Heller of equation (1) using annual data (1950–74) for world aggregates of the percentage changes in consumer prices and international reserves (defined in terms of U. S. dollars) yielded a statistically significant relationship. 7 Since lagged values of the independent variable (R) appeared to have a relatively stronger weight than the current value, Heller concluded that his evidence pointed to the existence of a causal link between the growth of international reserves and the increase in worldwide inflation.

This important result does not appear to depend on the particular simplifying assumptions necessary to obtain the bivariate model represented by equation (1). Genberg and Swoboda (1977) also reached a similar conclusion in the context of a complete structural model that relaxed the various assumptions implicit in the Heller framework.

An empirical relationship between the two variables seems to be now fairly well established, at least for the fixed exchange rate period. However, the methodology used in the various studies cannot exclude the possibility of spurious correlation resulting from, say, both variables following a common trend. 8 Furthermore, tests of the type conducted by Heller do not allow for strong conclusions to be drawn on the causal nature of the relationship. The hypothesis that growth in international reserves “causes” inflation may be adequately tested by a model similar to equation (1), but the alternative hypothesis, namely, that inflation “causes” growth in reserves, is not tested. 9 Without the results of the latter test, the picture is obviously incomplete. Genberg and Swoboda impose a similar one-sided distributed lag structure on the relationship running from international reserves to inflation, and thus their study has the same shortcoming as Heller’s.

In this paper the relationship is tested using recently developed statistical methods that are more powerful and better suited to detecting correlation between time series than is standard regression analysis. These tests also enable one to determine the direction of the relationship, or, in other words, its causal structure. Both the contemporaneous and causal relationships are examined in the context of the definitions proposed by Granger (1969). In the Granger framework, the absence of correlation between the current value of a variable, say, inflation, and the current value of another variable, growth in international reserves (once account has been taken of the effects of past values of inflation and growth in international reserves on their respective current values), implies the absence of a significant contemporaneous relationship. The lack of correlation between the past values of the adjusted growth of reserves and the adjusted current value of inflation is interpreted as an absence of causation running from the growth in reserves to inflation. Similarly, if there is no correlation in the reverse direction, then inflation does not cause the growth in reserves.

In essence, the Granger concept can be viewed in a forecasting framework, namely, does it help in predicting inflation if information is available on the current and lagged values of international reserves as well as on the past values of inflation? While this definition may not conform closely to the concept of “causality” as economists generally use the term, it nevertheless represents one particular way to give this logical concept some operational content. 10

Specific econometric tests involving the Granger methodology have been proposed by Sims (1972), Haugh (1976), Pierce (1977), and Pierce and Haugh (1977), and these tests have been applied in recent studies to a variety of economic relationships. 11 The remainder of this section describes, in a somewhat heuristic manner, the methods proposed by Pierce and Haugh (1977) and Sims (1972).

The first step in the exercise is to ensure that the respective means and variances of the time series are constant over time, that is, they are covariance stationary. Pierce (1977) has suggested that for most economic series the elimination of trends can be achieved through transforming the relevant series into logarithmic first-differences. If Pt and Rt are the original (non-stationary) levels of prices and international reserves, respectively, then transforming them into Δ log Pt (the rate of inflation) and Δ log Rt, (the growth in international reserves) will generally satisfy the stationary requirement. 12

In discussing the Sims (1972) and Pierce (1977) tests of the Granger procedure, first, each of the time series can be described as a distributed lag function of serially uncorrelated random errors, and then each of the series can be related to a distributed lag function of the other. In matrix notation this system can be expressed as

where uPt and uRt are white noise errors, and theγij(L)s are general polynomials in the lag operator, L. γ11(L) and γ22(L) are the lag functions that relate the current value of the variable to its past values.

Sims (1972) shows that in the framework of equation (2) Δ log Rt does not cause Δlog Pt if, and only if, the lag function γ12 (L) is equal to zero. Conversely, if γ2l(L) is zero, then Δ log Pt does not cause Δlog Rt. Moreover, the two series are said to be “causally” independent if both the lagfunctionsr γ12(L) and γ21(L) are equal to zero. Since the case of independence is simpler, it is useful to test this hypothesis first and then, if it is rejected, proceed toward determining the causal direction of the relationship.

Testing the null hypothesis of independence using the procedures suggested by Haugh (1976) and Pierce and Haugh (1977) requires first setting the lag polynomials γl2 (L) and γ21(L) equal to zero. This results in two univariate time-series processes:

These two processes can be estimated efficiently by methods proposed by Box and Jenkins (1970). In the Box-Jenkins framework, these general lag functions can be written as ratios of two simple polynomial lag functions, that is,

where the functions Φ1(L) and Φ2(L) correspond to autoregressive (AR) processes and θ1(L) and θ2 (L) to moving average (MA) processes. Equations (5) and (6) are described as general autoregressive integrated moving average (ARIMA) models.

After estimating equations (5) and (6), the resulting residuals, ûPt and ûRt, are then checked for (a) own serial independence and (b) mutual contemporaneous and serial independence. Insofar as own serial independence is concerned, a test based on the calculation of the Box-Jenkins Q-statistic is used. This statistic is defined as

where N is the number of observations, m the number of lags considered, and r2 (i) the squared value of the autocorrelation coefficient at lag i. This statistic is distributed asymptotically as X2 with (m - n) degrees of freedom, and n is the number of AR and MA parameters estimated.

The Pierce-Haugh test for mutual independence, which is analogous to the Q-test, involves calculating the statistic: 13

which is also distributed as X2 with (2m + 1) degrees of freedom, and r2u^Pu^R (k) is the squared correlation coefficient between ûP and the k th lag of ûR.

By going through this two-step procedure of first eliminating the effects of past values of the variables on their respective current values, that is, prewhitening the series, and then correlating them, the Granger concept of incremental forecasting improvement is satisfied. At the same time, the possibility of spurious correlation is also greatly reduced once the variables are put through the estimated Box-Jenkins filter.

Pierce and Haugh (1977) argue that if the null hypothesis of independence is rejected, the S*-statistic can be used to determine the direction of causation. However, since this cannot be formally tested, 14 when independence is rejected it is preferable to employ the method proposed by Sims (1972) to test for the direction of the relationship. Working with the residuals from the ARIMA models (equations (5) and (6)), the Sims procedure involves first regressing ûP on present and past values of ûR. 15 The null hypothesis that Δ log P does not cause Δ log R is accepted if the addition of future values of ûR into the regression does not lead to a significant improvement in the goodness-of-fit of the regression. This procedure can be written in terms of the following regression relationship:

The null hypothesis that Δ log P does not cause Δ log R is accepted if βi = 0 for all i. This can be statistically tested by an F-test on the nested models. 16

The same test is performed in the reverse direction to test the hypothesis that Δ log R does not cause Δ log P.

On the basis of the results obtained from the two tests, three possible outcomes can be distinguished:

(1) If the tests result in a rejection of both the hypotheses, a feedback relationship between the two variables is indicated.

(2) If one test results in acceptance of the null hypothesis and the other in a rejection, unidirectional causality is indicated.

(3) If the tests result in accepting both the hypotheses, a possible contemporaneous relationship would be indicated. 17

Another alternative method for testing causality, which Pierce and Haugh (1977, pp. 288–89) argue follows directly from the Granger definition, is to simply regress Δ log P on its own past values, that is,

and then add in past values of Δlog Rt

The hypothesis to be tested is that Σi=1mδi=0 and this can be done by using a standard F-test. If this null hypothesis is rejected, then it can be argued that growth in international reserves causes inflation. Performing the test in the reverse direction with Δlog Rt as the dependent variable can allow a test of the hypothesis that inflation causes growth of reserves.

While this direct Granger test is certainly simpler to perform than the two-stage procedure of prewhitening the relevant series and then doing the regressions such as equation (9), one has to be careful to select an adequate number of lags to eliminate possible serial correlation in the errors. Provided that sufficient caution is exercised, and that one is not overly concerned with “parsimony” in the number of parameters to estimate, 18 this procedure should be adequate to test for Granger causality.

In summary, then, the strategy in this paper is to first check the ARIMA residuals for mutal independence by performing the Pierce-Haugh test and, second, apply the Sims test and the direct Granger test to determine the causal nature of the relationships. The direct Granger test is utilized essentially to provide additional support for the Sims test.

II. Results

The tests described in the previous section were conducted for three basic country groupings—the world, industrial countries, and developing countries (excluding oil exporting countries). The countries included in each of these groupings correspond to the aggregates defined in the Fund’s International Financial Statistics (IFS). 19 For each aggregate the price variable is taken to be the consumer price index (IFS, line 64), and the reserves variable is defined as gross reserves in terms of special drawing rights (SDRs) and includes gold, SDRs, foreign exchange holdings of monetary authorities, and reserve positions in the Fund (IFS, line 1s).

Tests for Complete Period, 1957–77

After transforming the relevant series from their level form to rates of growth, equation (1) was directly estimated, namely, by relating the growth in prices to the current and lagged values of the growth in international reserves. Using a second-degree polynomial (with no end-point constraints) for the lag function, and 16 lags, the results shown in Table 1 were obtained. Since the data are not seasonally adjusted, three seasonal dummies were introduced into the specification. In Table 1 are shown the estimated coefficients and their respective t-values, the adjusted coefficients of determination (R2), and the Durbin-Watson test statistics (D-W). For economy, only the sums of the individual weights (ai) attached to each lag are presented. Also shown are the mean lags (in quarters) calculated from these weights.

Table 1.Inflation as a Function of Growth of International Reserves, Quarterly, 1957–771

ConstantSeasonal DummiesΣi=117aiΔlogRti+1R2D-WMean Lag



















t-values in parentheses below coefficients.

t-values in parentheses below coefficients.

Clearly, from these results there appears to be a significant relationship between the two variables. The lag pattern consistently showed that the weights attached to the current and the first four lagged values of Δlog R were not significantly different from zero. Both this result and the size of the average lag obtained would tend, at least initially, to confirm Heller’s findings for the world aggregate. Note, however, the fairly severe degree of first-order autocorrelation present in the residuals of the estimated equations. This signals the clear possibility of spurious correlation between the two variables, 20 and thus one should be somewhat cautious of the conclusions that could be drawn from Table 1.

Turning now to the other test procedures that reduce this danger of spurious correlation, appropriate ARIMA models to each of the stationary series were identified and fitted. The results of these ARIMA estimates are shown in Table 2. In this table the estimates, and corresponding t-values, of the autoregressive and moving-average parameters are reported. Since the series are not seasonally adjusted, seasonal autoregressive parameters, when necessary, are included in the table. Also shown is the Box-Jenkins Q-statistic calculated over 16 quarters.

Table 2.ARIMA Models, Quarterly, 1957–77
Country GroupingDependent VariableAutoregressive



Seasonal Autoregressive ParametersMeanBox-Jenkins

Rate of

growth of
13614(DF)(x 10-2)































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

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

The results in Table 2 indicate that fairly simple models were adequate to achieve the principal purpose of the exercise, which was to obtain residuals that can be considered relatively free from serial correlation. In every case the calculated value of the Q-statistic allowed easy acceptance of the hypothesis of independent residuals. One feature worth noting in the results is the apparent absence of any seasonal variation in the rates of inflation for the three groupings. 21 Since seasonality is commonly observed in the inflation rates of individual countries, it can only be surmised that the aggregation over countries somehow manages to eliminate it. The international reserves series, on the other hand, do display distinct seasonal fluctuations.

Using the residuals from the ARIMA models, the Pierce-Haugh cross-correlation tests for independence were performed. The S*-statistics, calculated over 12 and 16 quarters, are shown in Table 3.

Table 3.Tests of Independence Between Inflation and Growth of International Reserves, Quarterly, 1957–77
Country GroupingNumber of Lags

Industrial countries1233.762
Developing countries1228.00

Degrees of freedom are (2m+ 1), where m is the number of lags.

Significant at the 10 per cent level.

Degrees of freedom are (2m+ 1), where m is the number of lags.

Significant at the 10 per cent level.

For both the world and industrial country aggregates, the value of the S*-statistic leads to a rejection of the null hypothesis that the two series are independent at the 10 per cent level. More confidence can be placed in the relationship between the two variables than was possible on the basis of the results in Table 1, since in this test most of the serial correlation present in the two series has been eliminated. While the test statistic in the developing country aggregate did not permit rejection of the null hypothesis at the 10 per cent level, its value was still fairly large. In such a situation it is advisable to be conservative and view the relationship as if it were related.

Having established the existence of a statistical relationship between the two series, the direction of causality using the Sims test was examined. The F-statistics calculated from the four regressions for each of the country groups are shown in Table 4. 22 The hypothesis that the growth in international reserves has not caused inflation is rejected at the 10 per cent level for both the world and industrial country aggregates, while the reverse hypothesis that inflation has not caused the growth in international reserves is accepted with the same confidence. Causality, thus, appears to have been unidirectional for the period 1957–77, that is, running from growth in international reserves to inflation. This result confirms both the Heller conclusion for the world aggregate and the Genberg and Swoboda (1977) one relating to industrial countries. However, the average lags between changes in the growth in international reserves and resulting changes in inflation turn out to be shorter than the average lags implied in the earlier studies. For the world aggregate, the average lag was about 8 quarters and for the industrial countries was between 7 and 8 quarters. 23

Table 4.Sims Tests of Causality Between Inflation and Growth of International Reserves, Quarterly, 1957–77
Country GroupingInflation causes

growth in reserves
Growth In reserves

causes inflation
Industrial countries0.641.952
Developing countries1.180.52

Degrees of freedom are (12, 59).

Significant at the 10 per cent level.

Degrees of freedom are (12, 59).

Significant at the 10 per cent level.

For the group of developing countries, both hypotheses regarding causation were accepted, since neither F-statistic was significant. The acceptance of both hypotheses is interpreted as implying a contemporaneous, rather than causal, relationship. Changes in the one variable have been accompanied by a simultaneous change in the other. This result should not be taken to imply the complete absence of a lagged relationship between the two variables, since it could simply be a consequence of a major part of the effects occurring within the same period. 24

The F-statistics obtained from the direct Granger test are shown in Table 5. For the necessary regressions, the number of lags was limited to 12, in keeping with the number utilized in the Sims test.

Table 5.Direct Granger Tests of Causality Between Inflation and Growth of International Reserves, Quarterly, 1957–77
Country GroupingInflation causes

growth in reserves
Growth in reserves

causes inflation
Industrial countries0.723.612
Developing countries1.301.46

Degrees of freedom are (12, 46).

Significant at the 10 per cent level.

Degrees of freedom are (12, 46).

Significant at the 10 per cent level.

The Sims test results reported in Table 4 are confirmed by the results shown in Table 5, with growth of international reserves causing inflation in the world and industrial country categories and no evidence of any causal relationship in the developing country grouping.

Tests for Floating Rate Period, 1973–77

While the results so far indicate a certain relationship, causal or contemporaneous, between the two variables, the period over which the tests were undertaken covers two distinct exchange rate regimes. It would not be a surprise if the move to floating rates in 1973 resulted in a fundamental change in the relationship between inflation and the growth in international reserves. Therefore, it will now be determined whether the type of empirical relationship obtained continued to be unchanged in the post-floating period.

Examining the stability of causal relationships essentially involves the testing for constancy over time of the ARIMA models from which the prewhitened series were obtained. Only if the null hypothesis of constant parameters of the estimated models is rejected is it necessary to go into directly investigating the causal relationships themselves. For the purpose here, a general evaluation of the stability of the relevant ARIMA models is not really required. It is sufficient to simply divide the sample into the fixed and floating subperiods, that is, pre-1973 and post-1973, and ascertain if the parameters were different.25 The method used to evaluate the stability of the ARIMA model parameters is based on the out-of-sample behavior of the forecasts of the model. After an ARIMA model has been fitted to a series, any change in the parameters will cause autocorrelation in the forecast errors.26 Therefore, testing these forecast errors for serial correlation is equivalent to testing for stability of the parameters.

For the tests, the ARIMA models were fitted up to the fourth quarter of 1972, and these models were used to generate forecasts from 1973 through 1977. The autocorrelation in the out-of-sample forecast errors was examined through the use of the Box-Jenkins Q-statistic. The results of the test are shown in Table 6. For comparison, the values of the Q-statistic for the estimated models during the period 1957–72 are also shown.

Table 6.Values of Q-Statistic for Autocorrelation

Dependent VariableEstimation Period

Forecast Period,

Rate of growth of:(DF)(DF)
WorldConsumer prices9.39





Consumer prices9.48





Consumer prices8.67





Significant at the 10 per cent level. DF = degrees of freedom.

Significant at the 10 per cent level. DF = degrees of freedom.

Of the six possible results, there are two where the value of the Q-statistic would reject the hypothesis that the errors are independent, namely, inflation in industrial countries and reserve growth in developing countries. Some instability in the parameters of the ARIMA models for these variables would be indicated. No such instability is apparent for either of the two variables at the world level. It would thus be necessary to look further into the empirical relationships for the floating rate period for industrial countries and developing countries. Although it is not strictly necessary from the stability test to consider the world aggregates, these are included in the analysis to maintain comparability.

In examining the floating rate period independently, there is the constraint of having only 20 quarterly observations for the relevant variables. For this reason, monthly data on the time series for these tests were used. Doing this, however, runs the risk inherent in time-series analysis that, with shorter intervals between observations, “noise” can have a higher variance than the systematic movements in the series in question. This feature can quite easily obscure the basic economic relationship that may exist between the two variables.27 Consequently, it should be acknowledged at the outset that the test results may well be biased toward acceptance of the hypothesis of independence. Also, comparing the monthly results with the quarterly estimates may be inappropriate, since, as pointed out earlier, the character of a particular relationship may be significantly affected by the time unit of observation.

The results of the ARIMA models estimated for 1973–77, on a monthly basis, are shown in Table 7. As in the quarterly results, fairly simple ARIMA processes were found to be sufficient to reach the basic goal of serially uncorrelated errors. 28

Table 7.ARIMA Models, Monthly, 1973–77 1
Country GroupingDependent





Rate of

growth of




























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

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

Using the residuals from the ARIMA models, the cross-correlation tests were performed and the calculated values of the S*-statistic are reported in Table 8.

Table 8.Test of Independence Between Inflation and Growth of International Reserves, Monthly, 1973–77
Country GroupingNumber of Lags



Industrial countries12


Developing countries12



Degrees of freedom are (2m + 1), where m is the number of lags.

Significant at the 10 per cent level.

Degrees of freedom are (2m + 1), where m is the number of lags.

Significant at the 10 per cent level.

From the estimates shown in Table 8, it would have to be concluded that, with one exception, the series were effectively independent. This conclusion must, however, be made cautiously, for two reasons. First, as mentioned earlier, in using monthly data, random movements in the series could possibly disguise the underlying economic relationship. Second, data constraints limited analysis to lags of only two years, and this may be too short a period to pick up the relationship. 29 Because of these possible problems with the cross-correlation tests and the fact that, even though they are not significant, the chi-squared values are fairly large, the decision was made to proceed with both the Sims and direct Granger tests for the three aggregates. The F-statistics calculated for the Sims test are shown in Table 9.

Table 9.Sims Tests of Causality Between Inflation and Growth of International Reserves, Monthly, 1973–77
Country GroupingInflation causes

growth in reserves
Growth in reserves

causes inflation
Industrial countries2.2321.43
Developing countries1.041.43

Degrees of freedom are (12, 36).

Significant at the 10 per cent level.

Degrees of freedom are (12, 36).

Significant at the 10 per cent level.

In conjunction with the results of the tests of independence (see Table 8), the Sims test indicates that the relationship between worldwide inflation and growth of world reserves should be characterized as contemporaneous rather than causal. This represents an apparent change from the unidirectional relationship that resulted when the total period was considered on a quarterly basis. One reason for this conflict could be that in the quarterly estimates the relationship was dominated by what happened prior to 1973. Examining the floating rate subperiod separately presumably allows the proper relationship for this period to emerge.

For industrial countries, a reversal of the earlier conclusions regarding the causal sequence occurs—the growth of international reserves seems to have responded to inflation during the floating rate period rather than having caused it.

The change in the relationship for the world and the industrial country aggregates could be the result of a variety of factors, and their identification is difficult in view of the number of underlying structural models that are consistent with the bivariate representation examined here. However, it would seem that one factor most likely to account for the results peculiar to the floating rate period would be a possibly changed relationship between international reserves and the money supply. As mentioned before, flexibility in exchange rates would be expected to weaken this particular relationship. Therefore, the relevant S*-statistic for these two variables was calculated both for the entire period and for the subperiod 1973–77. It turned out that for the world aggregates there did not seem to be any change—in both periods the S*-statistic indicated that the two series were significantly related. For industrial countries, however, the calculation showed that the relationship between reserves and the money supply was much weaker in the floating rate period than in the fixed rate period. On the basis of these results, it is quite likely that the reversal in the reserve-inflation conclusion for industrial countries occurs because the effect of reserve movements on the monetary base (and the money supply) has been significantly reduced with the advent of floating, since changes in the exchange rate absorb the effects of payments imbalances. 30

For the developing countries, despite the fact that the parameters of the ARIMA model were unstable, there was no change in the underlying relationship. It continued to be simultaneous rather than causal in nature. This conclusion is consistent with the observation that for most developing countries there was no basic change in their exchange rate systems, since they continued to peg their exchange rates to one or a number of other currencies. Therefore, no change in the relationship between inflation and the growth of international reserves would be expected to occur between the pre-1973 and post-1973 periods.

The direct Granger tests performed over the shorter monthly period (Table 10) broadly yielded results similar to the Sims test, although it should be mentioned that this second set of causality tests did not confirm the apparent reversal of causality found in the industrial countries’ case. Instead, the tests indicated a contemporaneous relationship, thereby making the overall results consistent across the three groups.

Table 10.Direct Granger Tests of Causality Between Inflation and Growth of International Reserves, Monthly, 1973–77

Inflation causes

growth in reserves
Growth in reserves

causes inflation
Industrial countries0.981.37
Developing countries0.781.74

Degrees of freedom are (12, 22).

Degrees of freedom are (12, 22).

III. Conclusion

This paper has re-examined the empirical evidence on the relationship between inflation and the growth of international reserves that was provided initially by Heller (1976). The methodology followed here differs from earlier studies in several important respects. First, the relationship was tested within the framework of statistical techniques developed by Granger (1969) and Sims (1972). Second, quarterly, as opposed to annual, data were used, and the coverage was not restricted to a single world grouping but included, as separate aggregates, industrial countries and developing countries. Third, an attempt was made to test the relationship in the floating exchange rate period as well as in the fixed exchange rate period. While theoretically there may be good reasons for not considering the relationship between inflation and international reserves as being particularly meaningful when exchange rates are floating, on empirical grounds the question is still an open one and merits investigation.

In summary, while keeping in mind various problems that could arise in the implementation of the Granger-Sims procedures, 31 the tests yielded interesting and useful information. When considering the total period, that is, covering both the fixed and floating exchange rate regimes, it was found that inflation appeared to lag behind the growth in international reserves for the world and industrial country groupings. In other words, it was the growth in reserves that “caused” the inflation witnessed. For developing countries as a group, the relationship between the two variables was apparently contemporaneous rather than causal.

Since the inclusion of data from two distinct exchange rate regimes may lead to a distorted view, particularly with regard to the relationship from 1973 onward, the floating rate period was examined somewhat further.32 Observing that statistically there was some evidence that the relationship had changed with the advent of floating, the tests for the subperiod 1973–77 were repeated with monthly data on the relevant variables. It was found that world inflation and reserve growth should be regarded as contemporaneously related during the more recent years. For industrial countries, there was a fundamental change in the direction of the relationship in the later period, namely, running from inflation to reserve growth rather than the other way around, as had been observed when using the total sample. The relationship continued to be simultaneous for the developing countries, perhaps reflecting the fact that these countries continued to peg their currency to a single currency or a basket of currencies. In other words, there was no real change in the exchange rate regime relevant to this group. Generally speaking, because of data limitations and certain statistical problems that arise in the testing procedure when monthly data are used, the conclusions for the floating rate period should be viewed as highly tentative. Identifying the “true” relationship during the floating rate period with a greater degree of confidence will presumably have to wait until enough time has passed to generate an adequate number of quarterly observations.

In broad terms, the results here tend to support the quantity theory of money approach extended to the world economy. This was clearly evident for the pre-1973 period. Since then, inflation and growth of international reserves have continued to be related, although the causal nature of the relationship is more ambiguous than for the fixed exchange rate period. More flexibility in exchange rates did not seem to eliminate entirely the particular relationship. This could be partly due to the fact that floating was managed, and perhaps also to a high degree of substitutability between currencies. Both these facts would tend to indicate a continued link between domestic price developments and international reserve flows.33 It can, therefore, still be said that, if international reserves are expanded exogenously, this expansion would undoubtedly have some effect on prices, even though it may not be as strong as would be expected under a fixed exchange rate regime.


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Mr. Khan, Assistant Chief of the Financial Studies Division of the Research Department, is a graduate of Columbia University and the London School of Economics and Political Science.

The author is grateful to Edgar L. Feige and H. Robert Heller for helpful comments on this paper.

Genberg and Swoboda’s study is more akin to the Heller one, since it also directly considers the role of international reserves in the price determination mechanism. The other studies focus exclusively on the relationship between monetary growth and inflation.

One such obvious model would show the demand for international reserves to be a function of prices, among other variables. This fairly standard formulation (see Heller and Khan (1978)) would result in reserves adjusting to, rather than causing, inflation. For other models, see Putnam and Wilford (1978).

See Simon (1952) for various definitions of causality. In a more recent paper, Zellner (1979) discusses the different concepts of causation and causality in economics.

It should be mentioned in this context that the Friedman and Schwartz (1963) conclusion that changes in money caused changes in economic activity in the United States was based essentially on the observation that, historically, changes in money led changes in prices and income.

Defined as the stock of reserves deflated either by international prices or by the value of foreign trade. See Heller and Khan (1978) for evidence on this observation.

This is precisely the form that Heller (1976) used.

Heller also estimated the two underlying equations separately. Here, however, only the composite form (equation (1)) is considered.

The danger of spurious correlation, and the relative frequency with which this problem arises in empirical analysis, is discussed by Granger and Newbold (1974).

For a discussion of this subject, see below.

See Sims (1977 b) and Zellner (1979) for a discussion of how the causal concepts outlined by Simon (1952) can be related to the Granger definition. Schwert (1979) prefers the more accurate definition “incremental predictability” to describe the Granger procedure. In the remainder of this paper, the terms causation and causality will be used in the narrow Granger sense.

See the survey by Pierce and Haugh (1977). More recent papers include those by Feige and Pearce (1976) and (1979), Frenkel (1977), and Brillembourg and Khan (1979).

Heller’s use of percentage changes is equivalent to defining the variables in this form.

The statistic shown in the small-sample version.

See Pierce and Haugh (1977). Further arguments against using this test for establishing causal relationships are contained in Schwert (1979) and Sims (1979).

Using the ARIMA model residuals is only one way of ensuring that the series are suitably prefiltered. Sims (1972) suggests that the time series be prewhitened through the common filter (1-0.75L)2. Since there is no reason to expect this latter filter to convert the series into serially uncorrelated processes, it is best to allow the data to determine the appropriate filter.

Sims (1977 a) has pointed out that use of the independent Box-Jenkins filters for the two variables may result in a bias in the estimates of αi and βi unless the ûRs are orthogonal to the lagged values of Δlog P. For this reason, the tests were performed using the same filter to prewhiten both time series. This filter, which had the form (1-pL), was applied to the rate of inflation and the growth of international reserves. The results, or more strictly the inter-pretations drawn from them, are the same as those reported in this paper using different filters for the two variables. The basic conclusions are apparently independent of the prewhitening procedure.

The Sims test cannot detect certain types of contemporaneous feedback, and thus this last conclusion can be made only in conjunction with the results of the cross-correlation test. See Sims (1972).

It is this aspect that generally leads one to employ ARIMA-type models.

The IFS country codes for these aggregates are 001, 110, and 201, respectively.

This was also evident in Table 1, where the parameters of the seasonal dummies were insignificant.

In running the regressions, 12 lags and 12 leads were used for the right-hand variable.

Heller put the lag at between three and a half and four and a half years, while Genberg and Swoboda found it to be even longer for industrial countries.

Whether a relationship is identified as contemporaneous or causal could depend on the length of the unit of observation. For example, what would be described as a causal relationship on a monthly basis could, if the lags were short, easily appear as contemporaneous if quarterly or annual data were employed. This is clearly a problem with the Granger methodology that must be kept in mind.

For a discussion of more general methods of examining the stability of ARIMA models when the breakpoint is not known a priori, see Brillembourg and Khan (1979).

See Sims (1977 a) and Brillembourg and Khan (1979) for a discussion of this subject.

In fact, the growth of international reserves in developing countries turned out to be a white noise series itself. This implies that (the logarithm of) the level of international reserves would be described by a random walk process.

The calculation of the S*-statistic requires (2m + 1) observations, which in the present case is 49. The total sample is only 60 months.

On a quarterly basis, S*-statistics calculated over 12 quarters for the world and industrial country aggregates were, respectively, 33.79 and 40.87. Both of these are significant at the 10 per cent level. The monthly estimates yielded S*-statistics (for 24 months) of 62.10 and 47.07 for these two groups. Only the former value is significant at the 10 per cent level.

See Feige and Pearce (1976), Schwert (1979), and Zellner (1979) for a discussion of these problems.

The relatively large size of the fixed rate observations in the total sample may weight the overall result to one that is not applicable to the floating rate period.

See Miles (1978) for a discussion on how floating cannot insulate the economy if there is a high degree of currency substitution.

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