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 P_t and R_t are the original (non-stationary) levels of prices and international reserves, respectively, then transforming them into Δ log P_t (the rate of inflation) and Δ log R_t, (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 u_Pt and u_Rt are white noise errors, and theγ_ij(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 R_t does not cause Δlog P_t if, and only if, the lag function γ₁₂ (L) is equal to zero. Conversely, if γ_2l(L) is zero, then Δ log P_t does not cause Δlog R_t. 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 γ_l2 (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, û_Pt and û_Rt, 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 ${r^2}_{{\hat{u}}_P{\hat{u}}_R}$ (k) is the squared correlation coefficient between û_P and the k th lag of û_R.

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 û_R. 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 β_i = 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 R_t

The hypothesis to be tested is that $\underset{i=1}{\overset{m}{\mathrm{\Sigma }}}{\delta }_i\text{=0}$ 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 R_t 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 (a_i) 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

¹t-values in parentheses below coefficients.

Table 1.

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

Country Grouping	Constant	Seasonal Dummies			$\underset{i=1}{\overset{17}{\mathrm{\Sigma }}}{a}_i\mathrm{\Delta }\log R_{t-i+1}$	R 2	D-W	Mean Lag (Quarters)
		I	II	III
World	0.008 (7.10)	0.002 (1.21)	0.001 (0.90)	–0.002 (1.46)	0.534 (15.59)	0.869	1.13	11.7
Industrial countries	0.007 (4.51)	0.002 (0.97)	0.001 (0.55)	–0.002 (1.11)	0.465 (7.31)	0.551	0.55	10.9
Developing countries	0.022 (4.09)	–0.001 (0.09)	0.004 (0.68)	0.005 (0.82)	0.741 (4.77)	0.279	0.55	9.7

¹t-values in parentheses below coefficients.

View Table

Table 1.

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

Country Grouping	Constant	Seasonal Dummies			$\underset{i=1}{\overset{17}{\mathrm{\Sigma }}}{a}_i\mathrm{\Delta }\log R_{t-i+1}$	R 2	D-W	Mean Lag (Quarters)
		I	II	III
World	0.008 (7.10)	0.002 (1.21)	0.001 (0.90)	–0.002 (1.46)	0.534 (15.59)	0.869	1.13	11.7
Industrial countries	0.007 (4.51)	0.002 (0.97)	0.001 (0.55)	–0.002 (1.11)	0.465 (7.31)	0.551	0.55	10.9
Developing countries	0.022 (4.09)	–0.001 (0.09)	0.004 (0.68)	0.005 (0.82)	0.741 (4.77)	0.279	0.55	9.7

¹t-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

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

Table 2.

ARIMA Models, Quarterly, 1957–77

Country Grouping	Dependent Variable	Autoregressive Parameters			Moving- Average Parameters	Seasonal Autoregressive Parameters	Mean	Box-Jenkins Q-Statistic	SSR
		Order
	Rate of growth of				Order	Period
		1	3	6	1	4		(DF)	(x 10-2)
World	Consumer prices	0.665 (7.71)	0.280 (3.25)				0.015 (2.90)	11.22 (9)	0.105
	Reserves	0.635 (7.0)				0.314 (2.84)	0.019 (2.92)	4.48 (9)	2.021
Industrial countries	Consumer prices	0.942 (22.99)			0.347 (2.97)		0.011 (2.86)	9.34 (9)	0.124
	Reserves	0.592 (6.13)				0.334 (3.02)	0.017 (2.14)	7.29 (9)	3.191
Developing countries	Consumer prices	0.947 (23.68)			0.440 (3.86)		0.038 (3.92)	8.23 (9)	0.905
	Reserves	0.626 (7.73)		−0.224 (3.06)		0.196 (1.79)	0.021 (3.52)	10.56 (8)	5.328

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

View Table

Table 2.

ARIMA Models, Quarterly, 1957–77

Country Grouping	Dependent Variable	Autoregressive Parameters			Moving- Average Parameters	Seasonal Autoregressive Parameters	Mean	Box-Jenkins Q-Statistic	SSR
		Order
	Rate of growth of				Order	Period
		1	3	6	1	4		(DF)	(x 10-2)
World	Consumer prices	0.665 (7.71)	0.280 (3.25)				0.015 (2.90)	11.22 (9)	0.105
	Reserves	0.635 (7.0)				0.314 (2.84)	0.019 (2.92)	4.48 (9)	2.021
Industrial countries	Consumer prices	0.942 (22.99)			0.347 (2.97)		0.011 (2.86)	9.34 (9)	0.124
	Reserves	0.592 (6.13)				0.334 (3.02)	0.017 (2.14)	7.29 (9)	3.191
Developing countries	Consumer prices	0.947 (23.68)			0.440 (3.86)		0.038 (3.92)	8.23 (9)	0.905
	Reserves	0.626 (7.73)		−0.224 (3.06)		0.196 (1.79)	0.021 (3.52)	10.56 (8)	5.328

¹t-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

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

²Significant at the 10 per cent level.

Table 3.

Tests of Independence Between Inflation and Growth of International Reserves, Quarterly, 1957–77

Country Grouping	Number of Lags (Quarters)	S*-Statistic1
World	12	39.552
	16	45.952
Industrial countries	12	33.762
	16	44.292
Developing countries	12	28.00
	16	36.01

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

²Significant at the 10 per cent level.

View Table

Table 3.

Tests of Independence Between Inflation and Growth of International Reserves, Quarterly, 1957–77

Country Grouping	Number of Lags (Quarters)	S*-Statistic1
World	12	39.552
	16	45.952
Industrial countries	12	33.762
	16	44.292
Developing countries	12	28.00
	16	36.01

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

²Significant 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

¹Degrees of freedom are (12, 59).

²Significant at the 10 per cent level.

Table 4.

Sims Tests of Causality Between Inflation and Growth of International Reserves, Quarterly, 1957–77

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth In reserves causes inflation
World	1.33	2.012
Industrial countries	0.64	1.952
Developing countries	1.18	0.52

¹Degrees of freedom are (12, 59).

²Significant at the 10 per cent level.

View Table

Table 4.

Sims Tests of Causality Between Inflation and Growth of International Reserves, Quarterly, 1957–77

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth In reserves causes inflation
World	1.33	2.012
Industrial countries	0.64	1.952
Developing countries	1.18	0.52

¹Degrees of freedom are (12, 59).

²Significant 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

¹Degrees of freedom are (12, 46).

²Significant at the 10 per cent level.

Table 5.

Direct Granger Tests of Causality Between Inflation and Growth of International Reserves, Quarterly, 1957–77

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth in reserves causes inflation
World	1.04	5.162
Industrial countries	0.72	3.612
Developing countries	1.30	1.46

¹Degrees of freedom are (12, 46).

²Significant at the 10 per cent level.

View Table

Table 5.

Direct Granger Tests of Causality Between Inflation and Growth of International Reserves, Quarterly, 1957–77

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth in reserves causes inflation
World	1.04	5.162
Industrial countries	0.72	3.612
Developing countries	1.30	1.46

¹Degrees of freedom are (12, 46).

²Significant 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

¹Significant at the 10 per cent level. DF = degrees of freedom.

Table 6.

Values of Q-Statistic for Autocorrelation

Country Grouping	Dependent Variable	Estimation Period 1952–72	Forecast Period, 1973–77
	Rate of growth of:	(DF)	(DF)
World	Consumer prices	9.39 (9)	4.53 (5)
	Reserves	4.24 (9)	4.69 (5)
Industrial countries	Consumer prices	9.48 (9)	16.781 (5)
	Reserves	4.88 (9)	6.80 (5)
Developing countries	Consumer prices	8.67 (9)	2.68 (5)
	Reserves	5.02 (8)	17.87 (4)1

¹Significant at the 10 per cent level. DF = degrees of freedom.

View Table

Table 6.

Values of Q-Statistic for Autocorrelation

Country Grouping	Dependent Variable	Estimation Period 1952–72	Forecast Period, 1973–77
	Rate of growth of:	(DF)	(DF)
World	Consumer prices	9.39 (9)	4.53 (5)
	Reserves	4.24 (9)	4.69 (5)
Industrial countries	Consumer prices	9.48 (9)	16.781 (5)
	Reserves	4.88 (9)	6.80 (5)
Developing countries	Consumer prices	8.67 (9)	2.68 (5)
	Reserves	5.02 (8)	17.87 (4)1

¹Significant 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

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

Table 7.

ARIMA Models, Monthly, 1973–77 ¹

Country Grouping	Dependent Variable	Autoregressive Parameters		Seasonal Autoregressive Parameters		Mean	Box-Jenkins Q-Statistic	SSR
	Rate of growth of	Order		Periods
		1	3	6	12		(DF)	(x10–2)
World	Consumer prices	0.691 (7.65)		0.178 (1.74)	0.602 (5.94)	0.008 (4.36)	8.11 (8)	0.200
	Reserves		0.379 (3.24)			0.009 (4.38)	12.80 (10)	0.680
Industrial countries	Consumer prices	0.517 (4.64)	0.236 (2.04)			0.007 (6.39)	9.67 (9)	0.170
	Reserves	0.209 (1.64)	0.262 (2.21)	0.414 (3.56)		0.008 (1.36)	9.71 (8)	0.980
Developing countries	Consumer prices	0.397 (3.48)				0.022 (19.32)	13.39 (10)	0.160
	Reserves					0.014 (0.70)	12.61 (12)	—

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

View Table

Table 7.

ARIMA Models, Monthly, 1973–77 ¹

Country Grouping	Dependent Variable	Autoregressive Parameters		Seasonal Autoregressive Parameters		Mean	Box-Jenkins Q-Statistic	SSR
	Rate of growth of	Order		Periods
		1	3	6	12		(DF)	(x10–2)
World	Consumer prices	0.691 (7.65)		0.178 (1.74)	0.602 (5.94)	0.008 (4.36)	8.11 (8)	0.200
	Reserves		0.379 (3.24)			0.009 (4.38)	12.80 (10)	0.680
Industrial countries	Consumer prices	0.517 (4.64)	0.236 (2.04)			0.007 (6.39)	9.67 (9)	0.170
	Reserves	0.209 (1.64)	0.262 (2.21)	0.414 (3.56)		0.008 (1.36)	9.71 (8)	0.980
Developing countries	Consumer prices	0.397 (3.48)				0.022 (19.32)	13.39 (10)	0.160
	Reserves					0.014 (0.70)	12.61 (12)	—

¹t-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

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

²Significant at the 10 per cent level.

Table 8.

Test of Independence Between Inflation and Growth of International Reserves, Monthly, 1973–77

Country Grouping	Number of Lags (Months)	S*-Statistic1
World	12 24	29.05 69.312
Industrial countries	12 24	25.73 54.90
Developing countries	12 24	21.42 56.60

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

²Significant at the 10 per cent level.

View Table

Table 8.

Test of Independence Between Inflation and Growth of International Reserves, Monthly, 1973–77

Country Grouping	Number of Lags (Months)	S*-Statistic1
World	12 24	29.05 69.312
Industrial countries	12 24	25.73 54.90
Developing countries	12 24	21.42 56.60

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

²Significant 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

¹Degrees of freedom are (12, 36).

²Significant at the 10 per cent level.

Table 9.

Sims Tests of Causality Between Inflation and Growth of International Reserves, Monthly, 1973–77

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth in reserves causes inflation
World	1.47	0.95
Industrial countries	2.232	1.43
Developing countries	1.04	1.43

¹Degrees of freedom are (12, 36).

²Significant at the 10 per cent level.

View Table

Table 9.

Sims Tests of Causality Between Inflation and Growth of International Reserves, Monthly, 1973–77

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth in reserves causes inflation
World	1.47	0.95
Industrial countries	2.232	1.43
Developing countries	1.04	1.43

¹Degrees of freedom are (12, 36).

²Significant 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

¹Degrees of freedom are (12, 22).

Table 10.

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

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth in reserves causes inflation
World	1.18	1.27
Industrial countries	0.98	1.37
Developing countries	0.78	1.74

¹Degrees of freedom are (12, 22).

View Table

Table 10.

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

	F-Statistic1
Country Grouping	Inflation causes growth in reserves	Growth in reserves causes inflation
World	1.18	1.27
Industrial countries	0.98	1.37
Developing countries	0.78	1.74

¹Degrees 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.