Commodities as Final Goods

This subsection discusses a basic dynamic model of the interaction of commodity and industrial prices in which the two are final goods entering the CPI, and commodity prices are determined in flexible markets with forward-looking expectations. The model can he interpreted as one country with two sectors, or as two countries, one producing commodities and the other a perishable industrial output. The model includes a monetary sector, in which expectations of commodity price movements are important, and an industrial sector, in which prices adjust gradually following excess demand. To focus attention on price dynamics, the level of real output in the industrial sector is held constant. The model is an extension of Frankel (1986), which applies the Dornbusch (1976) overshooting model to the case of commodity price dynamics. In Boughton and Branson (1990b), the model is extended to the two-country case, with the exchange rate as an additional flexible response variable.

Equilibrium in the money market is characterized by equation (1):

where m, p_m, p_c and y are the logarithms of the nominal money stock, the price of the manufactured good, the price of commodities, and real output; i is the nominal short-term interest rate; and α is the share of manufactures in the CPI. The interest rate is related to commodity price inflation by the arbitrage condition:

where b is the real return to holding commodities for final use, net of storage costs, and ${\dot{p}}_c$ is the expected rate of change of the commodity price.

Combining equations (1) and (2) yields the following dynamic equation:

The locus of points where ${\dot{p}}_c$ = 0 is shown in Figure 1; its slope is – (1 – α)/α < 0.

Commodity and Manufactures Prices; Market Equilibrium and Dynamics

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Commodity and Manufactures Prices; Market Equilibrium and Dynamics

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Commodity and Manufactures Prices; Market Equilibrium and Dynamics

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For a point above the p_c = 0 line to be consistent with money market equilibrium, p_c must be expected to rise. This is because above the line the CPI is higher, and real balances lower, than on it. This makes the interest rate higher than b above the p_c = 0 line, so commodity prices must be expected to rise. If expectations exhibit perfect foresight, p_c must actually be rising above the p_c = 0 line. In other words, a commodity price level above that consistent with zero expected inflation must be supported by a positive rate of commodity price inflation. Similarly, at any point below the p_c = 0 line, commodity prices would be falling. These dynamics of p_c are shown by the horizontal arrows in Figure 1.

The supply of the industrial good (y_m) is given exogenously in this model. Demand is an increasing function of the price of commodities relative to industrial goods, p_c/P_m, and a decreasing function of the real interest rate in terms of the industrial good. This demand function may be written as

In contrast to the rapidly adjusting commodity price, the price of the industrial good is assumed to adjust slowly to eliminate excess demand:

Consolidation of the terms on ${\dot{p}}_m$ yields a second dynamic equation:

where η = π/(1 – πσ). If, as expected, a stimulus to excess demand is to raise the price of the industrial good, η must be positive.

The p_m = 0 locus in Figure 1 shows the relationship between the two prices that would maintain zero excess demand in the market for industrial goods for a given value of the money stock. The slope of the line is positive because an increase in the commodity price creates excess demand for industrial output, requiring an increase in the industrial price to eliminate it. The slope is less than unity because as prices rise, the interest rate also rises, reducing the demand for industrial goods.⁴ So as the price of commodities rises, the increase in industrial goods prices needed to eliminate excess demand is less than proportional. At points above the p_m = 0 line, there is excess supply of industrial goods and the price is falling, assuming η > 0. Below the line, there is excess demand and the price is rising. The dynamics of adjustment of the industrial price are summarized by the vertical arrows in Figure 1.

The two equilibrium lines in Figure 1 show the equilibrium pair of prices at E₀ for a given money stock and real commodity supply conditions. The dynamic adjustment to equilibrium is along the stable saddle path ss. This path has two essential properties. It leads to the equilibrium, and along it the expected rate of change of the commodity price is realized. All other paths explode away from the equilibrium; they are speculative bubbles. The assumption that the market seeks out the stable ss path is equivalent to assuming that speculative bubbles are unsustainable. Eventually they collapse, and the market moves back to the stable path.

The model of Figure 1 can be used to illustrate two properties of commodity price behavior that are important for constructing a leading indicator for inflation: following an unanticipated increase in the money supply, commodity prices overshoot, and they lead the adjustment in prices of industrial goods. In a situation in which the signals from the various monetary aggregates are unclear, the movements in commodity prices can be interpreted as distilling the information in the aggregates into a clearer signal.

The role of commodity prices as a leading indicator of the inflationary effects of a monetary disturbance is illustrated in panel (a) of Figure 2, which shows the effects of an unanticipated increase in the money supply. If the model is interpreted as representing two countries, this would involve a proportional increase in both countries’ money supplies. The original equilibrium from Figure 1 is at E₀ in Figure 2. An increase in the money supply shifts both the p_c = 0 and p_m = 0 lines, and the new long-run equilibrium moves proportionately out to E₁. In the long run, both prices rise by the same proportion as the money supply. In the short run, the gradually adjusting industrial price does not move, but the flexible commodity price jumps to the new ss path at E₀^’. Then gradually the industrial price rises and the commodity price falls along the ss path to the new Equilibrium at E₁. In response to an unanticipated monetary shock, commodity prices jump and overshoot, and lead the subsequent inflation in industrial prices.

Price Adjustment with Commodities as Final Goods

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Price Adjustment with Commodities as Final Goods

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Price Adjustment with Commodities as Final Goods

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The initial jump in the commodity price is consistent with an initial decline in the interest rate. In the original equilibrium at E₀, the expected rate of commodity price increase is zero, and the interest rate is equal to b. The rise in the money supply increases real balances initially, reducing the interest rate below b. This is consistent with equilibrium only if commodity prices are expected to fall. So initially the commodity price must rise by enough to create the expectation that it will fall during the adjustment period. This generates the jump onto the new ss path, along which the commodity price falls as expected as the economy moves toward E₁. At that point, real balances and the interest rate are back to their original levels, and the expected rate of commodity price inflation is again zero.

In response to repeated monetary shocks, jumps in the level of commodity prices would lead changes in the rate of inflation of industrial prices. This should produce a positive correlation between the level of world commodity prices and the subsequent rate of inflation of manufactures prices if repeated monetary disturbances are empirically important. Cointegration of the level of commodity prices and the rate of inflation in consumer prices is not rejected in the statistical tests in the following section.

The reaction of the model to a real disturbance that alters the equilibrium relative price of commodities is shown in panel (b) of Figure 2. As one would expect, it is substantially different from the reaction to a monetary disturbance. Suppose that a supply shock raises the equilibrium relative price of commodities. This shifts the p_m = 0 line down along the p_c = 0 line to a new long-run equilibrium at E₂, which lies on a ray from the origin that characterizes the new higher ratio of commodity prices to industrial prices. With no monetary accommodation, the p_c = 0 line does not move. The result is that commodity prices jump onto the new ss path at E₀^’ and then continue to rise, gradually, as industrial prices fall toward the new equilibrium E₂. As is usual in this type of model, the commodity price undershoots in response to a real disturbance. The industrial price must fall if there is no monetary accommodation. So in this case commodity prices lead, but industrial prices move in the opposite direction.

It could appear from this analysis that commodity prices would not be a useful indicator of future inflation in the presence of unaccommodated supply shocks. In fact, in this model, as long as these are not accommodated, there is no general inflation. As one price rises, the other fails to keep the weighted CPI constant. Thus a stochastic series of aggregate supply shocks would produce stochastic behavior of the commodity price with no general inflation. If in empirical implementation we use an index of a variety of commodity prices, supply shocks would come from differing sources, depending on the commodity. To the extent that these are independent, offsetting negative and positive disturbances at the individual commodity level would minimize the contribution of supply shocks to the variance of the index. Thus the path of the index would be dominated by monetary disturbances, with real disturbances producing noise around that path. The contribution of supply shocks to the variance of the index would be minimized to the extent that they are uncorrelated. This would improve the usefulness of the index as an inflation indicator.

Commodities as Inputs

The case of commodities as inputs can be discussed more briefly, since only two minor modifications need to be made to the model, and the results are essentially the same. In the money market, the deflator is now simply the price of industrial goods, so the dynamic equation (3) reduces to

This change makes the ${\dot{p}}_c$ = 0 line in the top panel of Figure 3 horizontal at the level of the industrial price that clears the money market with zero expected commodity price inflation.⁵ At points above the p_c = 0 line, real balances are lower than on it. so the interest rate is higher than b, and commodity prices are expected to rise. Below the p_c = 0 line, commodity prices are falling. These dynamics are illustrated by the horizontal arrows in the top panel of Figure 3.

Price Adjustment with Commodities as Inputs

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Price Adjustment with Commodities as Inputs

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Price Adjustment with Commodities as Inputs

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The market for industrial output is slightly more complicated. The demand for industrial goods is a decreasing function of the real interest rate. The supply of industrial goods is an increasing function of their price relative to commodities. Therefore, excess demand is a decreasing function of the relative price of industrial goods and the real interest rate. This gives a new equation for p_m:

Here β represents the supply effect, and η is defined as before.

The ${\dot{p}}_m$ = 0 locus is the positively sloped line in the top panel of Figure 3. To hold excess demand equal to zero in the market for industrial goods with a given increase in the commodity price, the industrial price would increase less than proportionately because the interest rate rises. Thus, the p_m = 0 line along which excess demand for the industrial good is zero has a slope less than unity in the top panel of Figure 3. Above this line, there is excess supply and P_m is falling. Below it, P_m is rising. The stable dynamic adjustment path is ss in Figure 3, as in the case of commodities as final goods.

The analysis following an unanticipated increase in the money supply is the same as that in panel (a) of Figure 2, discussed above. Adjustment to a supply shock that raises the equilibrium price of commodities relative to that of industrial output is illustrated in the bottom panel of Figure 3. The p_m = 0 line shifts out to intersect the p_c = 0 line at the new equilibrium price ratio. The commodity price rises, but, with no monetary accommodation, the price of industrial goods remains unchanged. The price of value added in the industrial sector or country falls. As before, it may be noted that a broad index of commodity prices might essentially average out supply shocks, leaving monetary disturbances to dominate movements of the index.

In these two models, commodity prices play the role of an inflation hedge. With gradual adjustment of industrial prices, agents can protect themselves against an anticipated inflation by buying commodities or, more generally, commodity futures contracts. The result falls naturally out of an analysis with two prices, one that adjusts gradually and one that can jump. The latter becomes the hedge against inflation in the former. A richer model would include more prices, such as foreign exchange or domestic equities, that can adjust instantaneously to inflationary expectations. In such a model, several variables can play the role of inflation hedge, with a wide variety of over-shooting and under-shooting behavior. This was shown in Frenkel and Rodriguez (1982). Then which price is the best indicator of future inflation becomes an empirical question. The conclusion to be drawn from the analysis in this section is that commodity prices are a reasonable candidate.

Construction of Data

The first empirical task is to construct a data series for the aggregate CPI for the large industrial countries. How best to do this is not obvious, because national price data are in different currencies. One approach would be to convert the time series data on price levels into a common currency (say, U.S. dollars or SDRs) and then construct an average index using GNP, consumption, or some other set of weights. One would then have a direct estimate of the aggregate price level measured in that currency. An alternative would be to average the logarithms of the price levels in local-currency terms. This procedure would give a more accurate measure of the average inflation experience in the countries concerned. Which procedure to choose depends on the intended purpose, but in the present case the choice is complicated because of the diverse international structure of the markets for primary commodities.

The problem may be illustrated as follows. If the national price indexes are averaged directly, the aggregate price level is described by

where p is the logarithm of the aggregate CPI, p_i is the logarithm of the CPI for country i (denominated in the currency of that country), and the w_i are the weights. Alternatively, if the aggregate CPI is to be denominated in the currency of (say) the first country, then the formula may be written as

where e_i is the logarithm of the exchange rate for country i, expressed as the cost of local currency in terms of the currency of country 1.

The difference between these two measures of the aggregate CPI constitutes an exchange rate between the currency of country 1 and the weighted geometric average of the other countries as a group:

For the tests in this paper, the aggregate CPI is constructed according to equation (7); for convenience, the implicit currency basket in which the data are thereby denominated will be referred to as the “group currency unit” or GCU.⁷

The difficulty posed by this choice is that the relationship between commodity and consumer prices is not invariant with respect to the currency in which the data are denominated.⁸ In order to isolate the effects of commodity price movements on inflation from those of exchange rate changes, it is desirable not only that commodity and consumer prices be denominated in the same currency or basket, but also that that denomination correspond as closely as possible to the currency or basket that is most relevant for the various markets concerned. This last concept, however, is quite vague and difficult to judge empirically. Most commodity prices are quoted in U. S. dollars, but a number of them are quoted in other currencies, including notably pounds sterling, deutsche marks, and Japanese yen. Furthermore, the currency in which prices are quoted does not necessarily indicate the currency that is most relevant for that particular market; for a price quoted in U. S. dollars, for example, it is possible that movements in the effective exchange rate for the dollar could systematically induce corresponding changes in the dollar price.

The consequences of choosing an inappropriate denomination may be demonstrated by reference to a simple bivariate model. First, letting _c denote an index of commodity prices, note that the dollar-denominated index (c’) may be converted into GCUs:

corresponding to the relationship described for the aggregate CPI in equation (8). Now suppose that the “true” relationship between commodity and consumer prices, free of exchange rate effects, holds when the data are denominated in GCUs, expressed as

Obviously, if one were to estimate, instead of equation (10), a regression in which commodity prices were denominated in dollars (or another currency), a spurious exchange rate effect would be introduced. Perhaps less obviously, a spurious effect would be introduced even if both indexes were denominated in dollars. Suppose one were to estimate

which is equivalent to

unless β = 1, the exchange rate would enter the implicit equation in GCUs, in contrast to equation (10).

Commodity Prices: Nominal and Real, 1960–89¹

(In GCUs; 1980 = 100)

¹ The real price is obtained by deflating by the seven-country consumer price index.

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Commodity Prices: Nominal and Real, 1960–89¹

(In GCUs; 1980 = 100)

¹ The real price is obtained by deflating by the seven-country consumer price index.

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Commodity Prices: Nominal and Real, 1960–89¹

(In GCUs; 1980 = 100)

¹ The real price is obtained by deflating by the seven-country consumer price index.

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In the absence of detailed knowledge about the nature of the individual markets, the best that one can do is to use a broad index of major currencies and to be sure that all data are measured commensurately. Since the aggregate CPI is constructed according to equation (7), it is appropriate to measure commodity prices in GCUs, converting dollar prices by the implicit exchange rate described in equation (8).

The commodity price index to be used for these tests uses a total of 40 prices, weighted according to 1979–81 shares in world exports.⁹ This is the same weighting system that is used in the World Economic Outlook, as noted in the Introduction. Preliminary tests suggested that similar results (though generally not quite as favorable) would obtain using other weighting methods such as imports or consumption rather than exports. A major decision is whether to include oil prices, since in 1979–81 oil accounted for roughly 50 percent of world exports of primary commodities. The inclusion of oil did somewhat improve the statistical properties in preliminary tests, and it was therefore included in the final index used in this study.

Long-Run Relationships

The first empirical question to be analyzed is whether there exists a stable long-run relationship between the level of commodity prices and the level of consumer prices. If so, then it may be possible to make quantitative inferences about future CPI inflation from observations of commodity prices. In the absence of a long-run levels relationship, there may still be qualitative linkages between changes in inflation rates in the two data series, but one would want to avoid arguing that any given change in commodity prices would be expected to be followed (eventually) by a specified change in consumer prices.

A very simple heuristic approach to this question is to examine the stationarity of the relative price of commodities. As may be seen from Chart 3, there has been a general downward trend in this relative price; the extent of the drift, however, has not been uniform, and it was starkly interrupted by a sudden and large rise in 1972–73. The hypothesis that the relative commodity price is unbounded in the long run would seem to be a reasonable one to entertain.

Table 1.

Stationarity Tests for Commodity and Consumer Prices¹

¹The numbers in this table are t-statistics from estimates of equation (11) over the indicated sample periods using monthly data. The distribution of these statistics is not standard; the 95 percent confidence level for the rejection of nonstationarity (^*) is approximately –3.78, and the 99 percent level (^**) is approximately –4.35. See Engle and Yoo (1987).

²Commodity price index deflated by the consumer price index.

³These tests are relevant only where the hypothesis of first-order nonstationarity has not been rejected.

Table 1.

Stationarity Tests for Commodity and Consumer Prices¹

		Commodity Prices	Consumer Prices	Relative Prices2
Tests for zero-order stationarity
	1960–89	1.24	4.76	–0.50
	1972–89	1.02	3.52	–0.16
	1974–89	0.41	3.31	–0.87
Tests for first-order stationarity
	1960–89	–9.31**	–2.24	–9.69**
	1972–89	–7.06**	–1.70	–7.37**
	1974–89	–7.02**	–1.94	–7.12**
Tests for second-order stationarity3
	1960–89		–16.26**
	1972–89		–12.47**
	1974–89		–11.64**

¹The numbers in this table are t-statistics from estimates of equation (11) over the indicated sample periods using monthly data. The distribution of these statistics is not standard; the 95 percent confidence level for the rejection of nonstationarity (^*) is approximately –3.78, and the 99 percent level (^**) is approximately –4.35. See Engle and Yoo (1987).

²Commodity price index deflated by the consumer price index.

³These tests are relevant only where the hypothesis of first-order nonstationarity has not been rejected.

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Table 1.

Stationarity Tests for Commodity and Consumer Prices¹

		Commodity Prices	Consumer Prices	Relative Prices2
Tests for zero-order stationarity
	1960–89	1.24	4.76	–0.50
	1972–89	1.02	3.52	–0.16
	1974–89	0.41	3.31	–0.87
Tests for first-order stationarity
	1960–89	–9.31**	–2.24	–9.69**
	1972–89	–7.06**	–1.70	–7.37**
	1974–89	–7.02**	–1.94	–7.12**
Tests for second-order stationarity3
	1960–89		–16.26**
	1972–89		–12.47**
	1974–89		–11.64**

¹The numbers in this table are t-statistics from estimates of equation (11) over the indicated sample periods using monthly data. The distribution of these statistics is not standard; the 95 percent confidence level for the rejection of nonstationarity (^*) is approximately –3.78, and the 99 percent level (^**) is approximately –4.35. See Engle and Yoo (1987).

²Commodity price index deflated by the consumer price index.

³These tests are relevant only where the hypothesis of first-order nonstationarity has not been rejected.

A preliminary examination of the long-run relationship between consumer and commodity prices can be made by testing whether each series is stationary in first differences and whether the relative price level is stationary. For this purpose, augmented Dickey-Fuller regressions have been run on first differences of each price series and on the relative price level:

where x is the difference of order j (for a test of stationarity of order j) in the logarithm of the variable, and the null hypothesis (no stationarity) is that β = 0. As shown in Table 1, the tests have been conducted over three sample periods, all ending in 1989. In addition to the full-sample estimates, regressions have been run for samples beginning in 1972, when commodity prices first began to show substantial fluctuations; and beginning in 1974, after the apparently unique jump in commodity prices that occurred in 1972–73. The regressions have been run with 2 lags on Δx.¹⁰

In the case of commodity prices, the null hypothesis is rejected, regardless of the sample period. For consumer prices, however, the hypothesis that β = 0 cannot be rejected, although the second differences appear to be stationary. The implication of these tests is that commodity prices are integrated of order 1, whereas consumer prices are integrated of order 2; that is, the first differences in commodity prices are stationary, whereas only the second differences of consumer prices are stationary. In these circumstances, the levels of the two data series cannot be cointegrated, and the standard cointegration tests are not applicable (see, for example, Granger (1986)).¹¹

One interpretation of the different stationarity properties of consumer and commodity prices is that consumer prices have a more persistent tendency toward inflation, so that the real (or relative) price of commodities is nonstationary with a negative trend. Such drift is at least weakly evident in Chart 3, and nonstationarity is confirmed in the tests summarized in the final column of Table 1. Another interpretation, however, is that the relative stationarity of commodity prices may reflect their role as a jump variable, as discussed in the previous section. That is, even though the tendency for the relative commodity price to return to a fixed level is fairly weak, there does seem to be a strong relationship between high levels of commodity prices and high inflation rates for consumer prices, following positive monetary shocks (and conversely, following negative shocks). Indeed, standard test results are consistent with the hypothesis that the level of commodity prices is cointegrated with the average CPI inflation rate for the seven major countries.¹²

Short-Run Relationships

The next step is to evaluate the relationship between shorter-run movements in commodity and consumer prices. For this purpose, it is necessary to render the data stationary, which may he accomplished simply by taking second differences of the data. As noted above, commodity prices are reasonably stationary in first differences, but second differencing is required to make the full data set stationary.¹³ In addition, in order to reduce the importance of seasonal fluctuations, inflation rates have been calculated as 12-month changes. Thus, the following tests relate to monthly changes in 12-month inflation rates:

Table 2.

Commodity Prices and Industrial-Country Inflation: Granger Causality Tests¹

¹For the test of whether commodity prices Granger-cause the CPI, the CPI has been regressed on 18 lagged monthly values of the commodity price index plus 18 lagged values of itself. For the test of reverse causation, the two series are switched. Industrial-country inflation is measured by the average change in consumer prices for the seven largest countries; the construction of the data is described in the text. All data have been made stationary by taking monthly changes in 12-month inflation rates. The double asterisk indicates that the null hypothesis—that the aggregate effect of the lagged values of the independent variable is zero—is rejected with 99 percent confidence.

Table 2.

Commodity Prices and Industrial-Country Inflation: Granger Causality Tests¹

		Non-oil Commodities		All Commodities
		Commodity prices cause CPI	CPI causes commodity prices	Commodity prices cause CPI	CPI causes commodity prices
With data in U.S. Dollars:
	1960–89	—	**	**	—
	1972–89	—	—	—	—
	1974–89	—	—	—	—
With data in GCUs:
	1960–89	**	—	**	**
	1972–89	—	—	**	**
	1974–89	—	—	**	**

¹For the test of whether commodity prices Granger-cause the CPI, the CPI has been regressed on 18 lagged monthly values of the commodity price index plus 18 lagged values of itself. For the test of reverse causation, the two series are switched. Industrial-country inflation is measured by the average change in consumer prices for the seven largest countries; the construction of the data is described in the text. All data have been made stationary by taking monthly changes in 12-month inflation rates. The double asterisk indicates that the null hypothesis—that the aggregate effect of the lagged values of the independent variable is zero—is rejected with 99 percent confidence.

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Table 2.

Commodity Prices and Industrial-Country Inflation: Granger Causality Tests¹

		Non-oil Commodities		All Commodities
		Commodity prices cause CPI	CPI causes commodity prices	Commodity prices cause CPI	CPI causes commodity prices
With data in U.S. Dollars:
	1960–89	—	**	**	—
	1972–89	—	—	—	—
	1974–89	—	—	—	—
With data in GCUs:
	1960–89	**	—	**	**
	1972–89	—	—	**	**
	1974–89	—	—	**	**

¹For the test of whether commodity prices Granger-cause the CPI, the CPI has been regressed on 18 lagged monthly values of the commodity price index plus 18 lagged values of itself. For the test of reverse causation, the two series are switched. Industrial-country inflation is measured by the average change in consumer prices for the seven largest countries; the construction of the data is described in the text. All data have been made stationary by taking monthly changes in 12-month inflation rates. The double asterisk indicates that the null hypothesis—that the aggregate effect of the lagged values of the independent variable is zero—is rejected with 99 percent confidence.

where x is the logarithm of the relevant index and z is the “whitened” form of the data.

Post-Sample Tests

Table 3 presents information on the out-of-sample predictive ability of commodity prices, with broad-money equations also included for comparison. For this exercise, regressions such as those in equations (12) and (13) were run over a series of six sample periods, starting with 1968–77 and then extending by two years up to 1968–87. In each case, the estimated equations were used to generate dynamic predictions for the aggregate CPI inflation rate over the 24 months following the end of the sample. During the prediction period, commodity price inflation and broad-money growth were projected on the basis of their own prior history. As shown in the table, three comparisons were made. First, did the inclusion of commodity prices reduce the standard error of the estimate within the sample period? Second, did the equations that include commodity prices reduce the forecast error for the average inflation rate over the two-year horizon? Third, did they reduce the root mean squared error (RMSE) for the 24 monthly inflation forecasts?

Table 3.

Inflation Predictions, 1976–89¹

(In percent)

¹Post-sample 24-month dynamic predictions of the aggregate CPI from equations as described in the text. The estimation sample is from February 1968 (plus prior lagged data) to December of the year preceding the listed forecast period.

²In percentage points.

Table 3.

Inflation Predictions, 1976–89¹

(In percent)

			1976–77	1978–79	1980–81	1982–83	1984–85	1986–87	1988–89
Actual inflation			7.5	9.5	10.3	4.9	3.7	2.1	3.7
Baseline prediction			8.2	7.7	11.0	6.6	4.9	2.8	3.2
Baseline prediction error			0.7	-1.8	0.7	1.7	1.2	0.7	-0.5
Predictions using commodity prices:
	Predicted inflation		9.0	5.4	11.2	8.0	5.0	3.6	2.6
	Reduction in:
		In-sample error	18.2	16.3	10.8	11.6	11.7	11.5	11.0
		Prediction error2	—	—	—	—	—	—	—
		RMSE	—	—	—	—	1.1	—	—
Prediction using broad money balances:
	Predicted inflation		7.9	7.4	10.1	7.4	5.4	2.9	3.0
	Reduction in:
		In-sample error	2.9	2.6	1.7	1.5	1.3	1.0	1.5
		Prediction error2	0.3	—	0.5	—	—	—	—
		RMSE	—	7.8	95.5	—	—	20.1	—

¹Post-sample 24-month dynamic predictions of the aggregate CPI from equations as described in the text. The estimation sample is from February 1968 (plus prior lagged data) to December of the year preceding the listed forecast period.

²In percentage points.

View Table

Table 3.

Inflation Predictions, 1976–89¹

(In percent)

			1976–77	1978–79	1980–81	1982–83	1984–85	1986–87	1988–89
Actual inflation			7.5	9.5	10.3	4.9	3.7	2.1	3.7
Baseline prediction			8.2	7.7	11.0	6.6	4.9	2.8	3.2
Baseline prediction error			0.7	-1.8	0.7	1.7	1.2	0.7	-0.5
Predictions using commodity prices:
	Predicted inflation		9.0	5.4	11.2	8.0	5.0	3.6	2.6
	Reduction in:
		In-sample error	18.2	16.3	10.8	11.6	11.7	11.5	11.0
		Prediction error2	—	—	—	—	—	—	—
		RMSE	—	—	—	—	1.1	—	—
Prediction using broad money balances:
	Predicted inflation		7.9	7.4	10.1	7.4	5.4	2.9	3.0
	Reduction in:
		In-sample error	2.9	2.6	1.7	1.5	1.3	1.0	1.5
		Prediction error2	0.3	—	0.5	—	—	—	—
		RMSE	—	7.8	95.5	—	—	20.1	—

¹Post-sample 24-month dynamic predictions of the aggregate CPI from equations as described in the text. The estimation sample is from February 1968 (plus prior lagged data) to December of the year preceding the listed forecast period.

²In percentage points.

Perhaps the most striking feature of Table 3 is that the RMSE is reduced by the inclusion of commodity prices in only one of the seven forecast periods: 1984–85. In that period, the prior weakness in commodity prices provided useful information about how rapidly consumer prices would decelerate. In the other periods, however, the predictions are worsened somewhat in comparison with those made only on the basis of the CPl’s own history. In all periods other than 1984–85, the equations using broad money do somewhat better than the equations using commodity prices.

Overall, the inclusion of neither commodity prices nor broad money could be said to have improved the post-sample inflation forecasts. In contrast, within each sample period, there is a substantial improvement in the fit when commodity prices are included, and only a small improvement when money balances are included. It thus appears that the quantitative linkages between commodity and consumer prices are significant, but are not stable enough to permit one to draw quantitative inferences about the extent to which consumer prices might respond to a given change in commodity prices.

Estimation of Indexes

Two basic approaches have been used to estimate commodity price indexes on the basis of their relationship with the aggregate CPI. One is to allow the data to determine the weights freely, with all commodity prices as contenders for inclusion in the index. The other involves constraining the data, by eliminating negative weights and, in the final set of estimates, by initially aggregating commodities that have small weights in industrial-country trade or consumption into somewhat broader categories. The second approach was intended to check whether the efficiency of the estimates might be improved by the constraints.

Estimation Using All Available Commodity Price Data

The objective of the first approach is to allow the maximum freedom for the data to “speak” in determining the “best” weights for commodities for the purpose of predicting CPI inflation. This approach uses the prices that are incorporated into the available IMF commodity price indexes, plus the prices of gold and petroleum, in an unconstrained regression framework. There are 32 years of monthly observations on the 40 commodity price series, extending from January 1958 through December 1989. With a forecast horizon chosen to run from 1 to 36 months, the problem is to devise a procedure that narrows quickly to the most important explanatory variables over different forecast horizons with a minimum of loss in efficiency in utilizing the information in the data.

The procedure that was employed to estimate “optimum” indexes was as follows. First, the aggregate CPI and all 40 series, expressed as logarithms of GCU-denominated indexes, were transformed by taking the first differences of their 12-month differences (i.e., changes in inflation rates). Second, the 40 principal components were extracted from the data matrix of the transformed commodity price data, to produce orthogonal regressors. Third, a multiple regression was estimated over the period February 1962 to December 1984 with the transformed CPI as the dependent variable and the 40 principal components as independent variables (with the constant suppressed) separately at each lag length from 1 to 36 months. The termination of the sample at the end of 1984 was chosen so as to leave a reasonably long post-sample period for testing the stability of the results.

These regression results were used to select significant principal components for the remaining analysis. Two selection criteria were used to narrow the set of principal components. The first was to rank them by average absolute t-ratio across lags. The second was to select principal components with coefficients that were significant at the 1 percent level at at least four different lags, of which at least one was longer than 12 months. The second criterion yielded eight principal components, of which seven coincided with those in the highest ten on the average absolute t-ratio criterion. Thus the two criteria together yielded a list of 11 candidate principal components for the next stage.

Next, a regression was estimated with the transformed CPI as the dependent variable, and fourth-order PDLs with length 36 months (constrained to zero at the far end only) on the candidate principal components as independent variables along with a similar PDL on the lagged transformed CPI. This regression (over the 1962–84 period) had an adjusted R² of .55, compared with .31 for a regression of the transformed CPI only on its own lags. Each of the 11 selected principal components contributed significantly to this regression. Finally, the coefficient on the weighted (and normalized) lag distribution on each principal component was taken as an estimate of the contribution of that component to the index being derived.

The lag distributions on the 11 principal components in the final regression differ in length and shape. Therefore, when the implied weights on the commodity prices are retrieved, a weighting matrix is obtained, which in principle would have a different set of weights for each lag length. Thus the distributed lag coefficients on the final principal components equation could be used to estimate a different set of weights for the commodity prices at each forecast horizon, reflecting differences in the information in the various commodity prices for explaining aggregate CPI inflation at different forecast horizons. This step was not taken at this stage. Instead, a single set of weights was calculated, reflecting the average information in the commodity price series across forecast horizons. These are the weights shown in the first column of Table 4.

Table 4.

Econometrically Estimated Weights for Commodity Price Indexes¹

(In percent)

¹Detail may not add to totals, owing to rounding.

²Several of the listed commodities are divided into two or more components in the full data set. When negative weights were reset to zero for the second index, the calculations were made at that disaggregated level.

³Based on 1979–81 data. Source: IMF, Commodities Division.

Table 4.

Econometrically Estimated Weights for Commodity Price Indexes¹

(In percent)

Commodity2		Unconstrained	Eliminating Negative Weights	Using Prior Aggregation	Memorandum: World Exports Weights3
Cereals		79.6	17.6	16.8	10.6
	Wheat	34.2	7.6	8.1	5.1
	Maize	36.7	8.1	6.1	3.8
	Rice	8.7	1.9	2.6	1.6
Vegetable oils		–36.3	10.2	0.1	5.7
	Soybeans	–46.6	2.4	0.1	4.5
	Other	10.4	7.9	—	1.2
Meat		80.8	17.8	—	3.3
	Beef	29.7	6.6	—	2.8
	Lamb	51.1	11.3	—	0.5
Sugar		18.0	5.8	—	1.6
Bananas		67.3	14.9)	—	0.4
Beverages		–19.6	6.1	—	6.0
	Coffee	27.7	6.1	—	3.8
	Cocoa	–7.3	—	—	1.6
	Tea	–39.9	—	—	0.6
Agricultural raw materials		–60.3	4.9	62.7	12.0
	Timber	–9.1	—	14.7	5.4
	Cotton	–36.9	—	—	2.0
	Wool	–3.4	0.7	—	1.2
	Rubber	19.1	4.2	11.0	1.3
	Tobacco	–5.2	—	37.0	1.3
	Other	–24.8	—	—	0.7
Metals		–3.4	22.7	1.9	14.9
	Copper	5.1	1.1	0.4	3.0
	Aluminum	16.2	3.6	0.3	2.3
	Gold	–38.6	—	0.5	3.7
	Iron ore	44.9	9.9	0.3	2.1
	Other	–31.1	8.0	0.5	3.8
Petroleum		–26.0	—	18.5	45.5
Total		100.0	100.0	100.0	100.0

¹Detail may not add to totals, owing to rounding.

²Several of the listed commodities are divided into two or more components in the full data set. When negative weights were reset to zero for the second index, the calculations were made at that disaggregated level.

³Based on 1979–81 data. Source: IMF, Commodities Division.

View Table

Table 4.

Econometrically Estimated Weights for Commodity Price Indexes¹

(In percent)

Commodity2		Unconstrained	Eliminating Negative Weights	Using Prior Aggregation	Memorandum: World Exports Weights3
Cereals		79.6	17.6	16.8	10.6
	Wheat	34.2	7.6	8.1	5.1
	Maize	36.7	8.1	6.1	3.8
	Rice	8.7	1.9	2.6	1.6
Vegetable oils		–36.3	10.2	0.1	5.7
	Soybeans	–46.6	2.4	0.1	4.5
	Other	10.4	7.9	—	1.2
Meat		80.8	17.8	—	3.3
	Beef	29.7	6.6	—	2.8
	Lamb	51.1	11.3	—	0.5
Sugar		18.0	5.8	—	1.6
Bananas		67.3	14.9)	—	0.4
Beverages		–19.6	6.1	—	6.0
	Coffee	27.7	6.1	—	3.8
	Cocoa	–7.3	—	—	1.6
	Tea	–39.9	—	—	0.6
Agricultural raw materials		–60.3	4.9	62.7	12.0
	Timber	–9.1	—	14.7	5.4
	Cotton	–36.9	—	—	2.0
	Wool	–3.4	0.7	—	1.2
	Rubber	19.1	4.2	11.0	1.3
	Tobacco	–5.2	—	37.0	1.3
	Other	–24.8	—	—	0.7
Metals		–3.4	22.7	1.9	14.9
	Copper	5.1	1.1	0.4	3.0
	Aluminum	16.2	3.6	0.3	2.3
	Gold	–38.6	—	0.5	3.7
	Iron ore	44.9	9.9	0.3	2.1
	Other	–31.1	8.0	0.5	3.8
Petroleum		–26.0	—	18.5	45.5
Total		100.0	100.0	100.0	100.0

¹Detail may not add to totals, owing to rounding.

²Several of the listed commodities are divided into two or more components in the full data set. When negative weights were reset to zero for the second index, the calculations were made at that disaggregated level.

³Based on 1979–81 data. Source: IMF, Commodities Division.

The most notable feature of the weights in the unconstrained index is that about half of the commodities have negative weights. In particular, within most groups, some commodities have positive and some negative weights. The reason for the negative weights is not that a rise in the price of a particular commodity, by itself, would be expected to lead to a fall in consumer prices; it is rather that the regression essentially computes the weights for an optimal portfolio of commodity prices that minimizes the residual error vis-à-vis the CPI. This procedure assigns negative weights to some prices that have positive covariance with the others. Small changes in specification could easily reverse the signs on individual commodities. The individual weights therefore should not be assigned any intrinsic value.¹⁶

The time path of this index is shown in the upper left panel of Chart 4. It is apparent that this is a much more volatile index than the others. Nonetheless, a moving average of this index would have a time profile reasonably similar to those of the other indexes shown in the chart. A regression of the transformed aggregate CPI on its own history plus a 36-month PDL on this first index yielded an adjusted R² of .33. The reduction from .55 is a measure of the cost of time aggregation into a single index; in fact, it may be seen that most of the improvement over equation (12) has been lost through time aggregation. The out-of-sample performance of this index is examined in the next subsection.

Econometrically Estimated Indexes, Consumer Prices, Export-Weighted Index, and Broad Money, 1960–89

(In GCUs: 1980 = 100)

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Econometrically Estimated Indexes, Consumer Prices, Export-Weighted Index, and Broad Money, 1960–89

(In GCUs: 1980 = 100)

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Econometrically Estimated Indexes, Consumer Prices, Export-Weighted Index, and Broad Money, 1960–89

(In GCUs: 1980 = 100)

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Evaluation of the Estimated Indexes

The properties of a leading indicator are, of course, not well defined by how well they fit within the sample period. This subsection therefore examines the post-sample properties of the estimated indexes. These properties are summarized in Table 5, which may be compared with the results presented above in Table 3.

Table 5.

Inflation Predictions Using Estimated Commodity Price Indexes, 1976–89¹

(In percent)

¹Post-sample 24-month dynamic predictions of the aggregate CPI from equations as described in the text. The estimation sample is from February 1962 (plus prior lagged data) to December of the year preceding the listed forecast period.

Table 5.

Inflation Predictions Using Estimated Commodity Price Indexes, 1976–89¹

(In percent)

			1976–77	1978–79	1980–81	1982–83	1984–85	1986–87	1988–89
Actual inflation			7.5	9.5	10.3	4.9	3.7	2.1	3.7
Baseline prediction			8.2	7.7	11.0	6.6	4.9	2.8	3.2
Baseline prediction error			0.7	–1.8	0.7	1.7	1.2	0.7	–0.5
Predictions using first (unconstrained) index:
	Predicted inflation		6.0	9.6	11.2	6.5	5.7	3.1	3.9
	Reduction in:
		In-sample error	3.7	4.8	3.2	1.8	2.3	1.8	0.6
		Prediction error	—	1.7	—	0.1	—	—	0.3
		RMSE	—	86.5	55.2	14.4	—	—	81.3
Prediction using second (positive weight) index:
	Predicted inflation		13.0	6.4	11.8	7.6	5.3	3.5	4.5
	Reduction in:
		In-sample error	7.6	8.2	8.0	7.8	6.2	5.7	4.3
		Prediction error	—	—	—	—	—	—	—
		RMSE	—	—	—	—	—	—	—
Prediction using third (prior-aggregation) index:
	Predicted inflation		8.5	5.5	11.1	9.1	4.6	3.7	2.7
	Reduction in:
		In-sample error	21.0	19.4	15.6	16.2	13.2	13.3	12.4
		Prediction error	—	—	—	—	0.4	—	—
		RMSE	—	—	—	—	51.4	—	58.8

¹Post-sample 24-month dynamic predictions of the aggregate CPI from equations as described in the text. The estimation sample is from February 1962 (plus prior lagged data) to December of the year preceding the listed forecast period.

View Table

Table 5.

Inflation Predictions Using Estimated Commodity Price Indexes, 1976–89¹

(In percent)

			1976–77	1978–79	1980–81	1982–83	1984–85	1986–87	1988–89
Actual inflation			7.5	9.5	10.3	4.9	3.7	2.1	3.7
Baseline prediction			8.2	7.7	11.0	6.6	4.9	2.8	3.2
Baseline prediction error			0.7	–1.8	0.7	1.7	1.2	0.7	–0.5
Predictions using first (unconstrained) index:
	Predicted inflation		6.0	9.6	11.2	6.5	5.7	3.1	3.9
	Reduction in:
		In-sample error	3.7	4.8	3.2	1.8	2.3	1.8	0.6
		Prediction error	—	1.7	—	0.1	—	—	0.3
		RMSE	—	86.5	55.2	14.4	—	—	81.3
Prediction using second (positive weight) index:
	Predicted inflation		13.0	6.4	11.8	7.6	5.3	3.5	4.5
	Reduction in:
		In-sample error	7.6	8.2	8.0	7.8	6.2	5.7	4.3
		Prediction error	—	—	—	—	—	—	—
		RMSE	—	—	—	—	—	—	—
Prediction using third (prior-aggregation) index:
	Predicted inflation		8.5	5.5	11.1	9.1	4.6	3.7	2.7
	Reduction in:
		In-sample error	21.0	19.4	15.6	16.2	13.2	13.3	12.4
		Prediction error	—	—	—	—	0.4	—	—
		RMSE	—	—	—	—	51.4	—	58.8

¹Post-sample 24-month dynamic predictions of the aggregate CPI from equations as described in the text. The estimation sample is from February 1962 (plus prior lagged data) to December of the year preceding the listed forecast period.

As with the full-sample results, it may be seen that the third index does much better than the other two estimated indexes, and a little better than the export-weighted index, in terms of reducing the standard error of the estimate for in-sample CPI predictions. Post-sample, however, the unconstrained index does quite a bit better: the average prediction error is reduced in three of the seven periods, and the RMSE is reduced in four of seven cases.

The apparently poor overall quantitative performance of commodity prices as additional inflation predictors is attributable in part to the difficulty of forecasting commodity prices during the forecast period. When actual commodity prices are used in the post-sample period, the prediction errors drop sharply. The use of a 24-month dynamic forecast period is a harsh standard, and the choice is to some extent arbitrary. Given the strong in-sample performance—especially for the third estimated index as well as for the export-weighted index—it is likely that better results would be obtained for shorter horizons.

Qualitative relationships may be as important as quantitative ones if commodity prices are to serve as a leading indicator. That is, one may he at least as interested in predicting turning points in CPI inflation as in predicting the value of the future inflation rate. It was already noted (see Chart 1) that there is an observed tendency for inflation in the export-weighted commodity price index to display cyclical patterns that are similar to those of the aggregate CPI inflation (though with differing amplitudes) and that frequently lead CPI turning points. This tendency is examined more closely in Table 6.

Table 6.

Prediction of Turning Points in Aggregate CPI Inflation

¹A minus sign indicates a late call. x indicates that a false signal preceded the correct one; x(2) indicates 2 consecutive false signals.

— indicates that (a) the index was pointing in the wrong direction at the time of the turning point in the CPI or (b) that the index called the turning point before the preceding turning point.

²False signal in December 1987; peak called in July 1989.

³Peak called in February 1989.

⁴False signal in April 1987.

⁵False signal in January 1988.

⁶False signal in November 1987.

Table 6.

Prediction of Turning Points in Aggregate CPI Inflation

Turning Points in Aggregate CPI Inflation						Lead Time for Prediction1 (in months)
	Date			Peak or Trough	Inflation Rate	Export Weights	First Index	Second Index	Third Index	Broad Money
	September 1			P	3.3	—	1	0x	—	—
	July 1967			T	2.5	–6	5	–19	—	0
	November 1970			P	5.6	25	4x	1	—	—x
	June 1972			T	4.1	—	–1	1	3	—
	November 1974			P	13.5	6	2x(2)	5	6	14
	July 1976			T	7.3	12	—x	5	14	12
	May 1977			P	8.1	—x	—	—x	3	—
	March 1978			T	6.5	—	7	—	–2	—
	May 1980			P	12.0	3x	—x	0x	2	16
	July 1983			T	4.0	13	2x	3	—x	6x
	March 1984			P	4.6	–5	3	0	—	2
	December 1986			T	1.1	2	—x	2x	–1	—x
Memorandum:
	December 1989				3.9	2	3	4	5	6
Summary:
	Number of calls
			On time			6	7	9	5	6
			Late			2	1	1	2	0
			Missed			4	4	2	5	6
	Number of false signals					3	7	5	2	4
	Lead time for correct calls
		(in months)
		Mean				10	3	2	6	8
			Standard deviation			8.6	2.1	2.0	4.9	6.6

¹A minus sign indicates a late call. x indicates that a false signal preceded the correct one; x(2) indicates 2 consecutive false signals.

— indicates that (a) the index was pointing in the wrong direction at the time of the turning point in the CPI or (b) that the index called the turning point before the preceding turning point.

²False signal in December 1987; peak called in July 1989.

³Peak called in February 1989.

⁴False signal in April 1987.

⁵False signal in January 1988.

⁶False signal in November 1987.

View Table

Table 6.

Prediction of Turning Points in Aggregate CPI Inflation

Turning Points in Aggregate CPI Inflation						Lead Time for Prediction1 (in months)
	Date			Peak or Trough	Inflation Rate	Export Weights	First Index	Second Index	Third Index	Broad Money
	September 1			P	3.3	—	1	0x	—	—
	July 1967			T	2.5	–6	5	–19	—	0
	November 1970			P	5.6	25	4x	1	—	—x
	June 1972			T	4.1	—	–1	1	3	—
	November 1974			P	13.5	6	2x(2)	5	6	14
	July 1976			T	7.3	12	—x	5	14	12
	May 1977			P	8.1	—x	—	—x	3	—
	March 1978			T	6.5	—	7	—	–2	—
	May 1980			P	12.0	3x	—x	0x	2	16
	July 1983			T	4.0	13	2x	3	—x	6x
	March 1984			P	4.6	–5	3	0	—	2
	December 1986			T	1.1	2	—x	2x	–1	—x
Memorandum:
	December 1989				3.9	2	3	4	5	6
Summary:
	Number of calls
			On time			6	7	9	5	6
			Late			2	1	1	2	0
			Missed			4	4	2	5	6
	Number of false signals					3	7	5	2	4
	Lead time for correct calls
		(in months)
		Mean				10	3	2	6	8
			Standard deviation			8.6	2.1	2.0	4.9	6.6

¹A minus sign indicates a late call. x indicates that a false signal preceded the correct one; x(2) indicates 2 consecutive false signals.

— indicates that (a) the index was pointing in the wrong direction at the time of the turning point in the CPI or (b) that the index called the turning point before the preceding turning point.

²False signal in December 1987; peak called in July 1989.

³Peak called in February 1989.

⁴False signal in April 1987.

⁵False signal in January 1988.

⁶False signal in November 1987.