How Important Is the Permanent Component of Price Shocks?

As noted earlier, the design and feasibility of stabilization and hedging strategies depend very much on the nature of the shock. At the risk of oversimplifying, income stabilization policies and hedging are useful in dealing only with temporary and, preferably, short‐lived shocks. Permanent shocks require adjustment and, possibly, the implementation of structural policies. To determine how important a role, if any, permanent shocks play in explaining the variability in commodity prices, we proceed in two steps. First, we establish the time‐series properties of the various commodity indices via the standard Augmented Dickey‐Fuller (ADF) and the Phillips‐Perron (PP) unit root tests under two alternative hypotheses: the first of these assumes no structural breaks occurred within the sample; the second allows for a one‐time break in both the mean and the trend at a pre‐specified point in time (see Perron (1989)).⁴ If the series is stationary, all shocks are temporary and the null hypothesis of a unit root is rejected. If the null hypothesis is not rejected, the series has a permanent component of unknown size. Second, to determine the size of the permanent component we employ Cochrane’s (1988) methodology, which provides a measure of the persistence of shocks to a variable by examining the variance of its long differences.

The form of the ADF test employed, given by equation (1), allows for both the presence of a constant (nonzero mean) and a constant deterministic drift. To ensure that the regression residuals are serially uncorrelated, past differences of the variable (denoted by Δ) are also included. As suggested by Campbell and Perron (1991), we begin by including a generous number of lags; if the past differences do not enter significantly, these lags are dropped sequentially. The PP test, which allows for more general forms of heteroskedasticity, also allows for constant and drift terms:

The results of the unit root tests, which are summarized in Table 3, uniformly indicate that, when no breaks are assumed, for the log of the price series examined the null hypothesis of a unit root could not be rejected at standard confidence levels.⁵ Perron (1989), however, has suggested that it is important to model large “shocks” that may result in a one‐time break in either the level or the slope (or both of these) of macroeconomic time‐series when testing for unit roots. He shows that standard unit root tests have little power to distinguish between nonstationarity and stationarity around a broken trend. The 1973 oil price shock, for instance, may have had persistent effects on real commodity prices.

Table 3.

Unit Root Tests, 1957:I–1993:II

^aThe critical values are taken from Guilkey and Schmidt (1989). The number of observations in the sample period is 146.

^bThese are taken from Perron (1989). Figure A.1 plots the fitted broken trends to the data.

Table 3.

Unit Root Tests, 1957:I–1993:II

Alternative hypothesis: no structural breaks
Regression: $\begin{array}{c}\mathrm{\Delta }{y}_t=\mu +\beta t+{\alpha y}_{t-1}+\underset{i=1}{\overset{k}{\mathrm{\Sigma }}}{\delta }_i\mathrm{\Delta }{y}_{t-i}+e_t\end{array}$
Series		k		t‐statistic on a (ADF statistic)		Phillips‐Perron statistic
All commodities		5		–2.1353		–2.6112
Beverages		5		–2.5308		–1.4472
Food		3		–1.8665		–2.4743
Metals		1		–3.3555		–3.2849
Critical values (percent)		1		5		10
150 observationsa		–3.73		–3.46		–3.16
Alternative hypothesis: one‐time structural break occurring at TB
Alternative Hypothesis: $y_t={\mu }_1+{\beta }_{1}t+({\mu }_2-{\mu }_1){DU}_t({\beta }_2-{\beta }_1)D{T}_1+e_t$
where DU = DT = 0 if $t\le T_B$ and DU = 1, DT = t if $t>T_B$
Regression: $\begin{array}{c}\mathrm{\Delta }{\hat{y}}_t={\alpha \hat{y}}_{t-1}+\underset{i=1}{\overset{k}{\mathrm{\Sigma }}}{\delta }_i\mathrm{\Delta }{\hat{y}}_{t-i}+e_t\end{array}$
Series	TB	T‐statistic α (ADF)	Phillips‐Perron	λ	Critical values (percent) b
					1	5	10
All commodities	73:1	–6.449	–3.659	0.4	–4.81	–4.22	–3.95
Beverages	76:1	–3.353	–3.955	0.5	–4.90	–4.24	–3.96
Food	73:1	–4.082	–3.949	0.4	–4.81	–4.22	–3.95
Metals	74:111	–4.558	–4.306	0.5	–4.90	–4.24	–3.96

^aThe critical values are taken from Guilkey and Schmidt (1989). The number of observations in the sample period is 146.

^bThese are taken from Perron (1989). Figure A.1 plots the fitted broken trends to the data.

View Table

Table 3.

Unit Root Tests, 1957:I–1993:II

Alternative hypothesis: no structural breaks
Regression: $\begin{array}{c}\mathrm{\Delta }{y}_t=\mu +\beta t+{\alpha y}_{t-1}+\underset{i=1}{\overset{k}{\mathrm{\Sigma }}}{\delta }_i\mathrm{\Delta }{y}_{t-i}+e_t\end{array}$
Series		k		t‐statistic on a (ADF statistic)		Phillips‐Perron statistic
All commodities		5		–2.1353		–2.6112
Beverages		5		–2.5308		–1.4472
Food		3		–1.8665		–2.4743
Metals		1		–3.3555		–3.2849
Critical values (percent)		1		5		10
150 observationsa		–3.73		–3.46		–3.16
Alternative hypothesis: one‐time structural break occurring at TB
Alternative Hypothesis: $y_t={\mu }_1+{\beta }_{1}t+({\mu }_2-{\mu }_1){DU}_t({\beta }_2-{\beta }_1)D{T}_1+e_t$
where DU = DT = 0 if $t\le T_B$ and DU = 1, DT = t if $t>T_B$
Regression: $\begin{array}{c}\mathrm{\Delta }{\hat{y}}_t={\alpha \hat{y}}_{t-1}+\underset{i=1}{\overset{k}{\mathrm{\Sigma }}}{\delta }_i\mathrm{\Delta }{\hat{y}}_{t-i}+e_t\end{array}$
Series	TB	T‐statistic α (ADF)	Phillips‐Perron	λ	Critical values (percent) b
					1	5	10
All commodities	73:1	–6.449	–3.659	0.4	–4.81	–4.22	–3.95
Beverages	76:1	–3.353	–3.955	0.5	–4.90	–4.24	–3.96
Food	73:1	–4.082	–3.949	0.4	–4.81	–4.22	–3.95
Metals	74:111	–4.558	–4.306	0.5	–4.90	–4.24	–3.96

^aThe critical values are taken from Guilkey and Schmidt (1989). The number of observations in the sample period is 146.

^bThese are taken from Perron (1989). Figure A.1 plots the fitted broken trends to the data.

To examine this possibility, the deterministic component was modeled to incorporate a single structural break, at which time both the level and the slope of the deterministic component changed; the dummy variables DU and DT capture the shifts in the average price and the slope of the time trend, respectively. As in Perron (1989), the sample behavior of the data was allowed to indicate where the “potential” break (denoted in Table 3 by T_B) occurred. These breaks are timed closely with the oil shock for all commodities, food, and metals. For beverages, the coffee boom that was caused by frost damage came to an end in 1977 and appears the best candidate for a behavioral change. The exact time of the break is shown in the first column of the bottom panel of Table 3. Under the alternative hypothesis, DU = DT = 0 if $t\le T_B$ and DU = 1, DT = t if $t>T_B$. Prices and their respective deterministic broken trends are plotted in Figure A.1.

The Perron test proceeds in two steps: the first estimates the parameters associated with the deterministic components (the (β_i and μ_i); in the second step the ADF (drift and trend terms are omitted) is performed on the de‐trended series, denoted by $\hat{y}$ in Table 3. The appropriate critical value will depend on the time of the break relative to total sample size, λ. As Table 3 shows, the results of the Perron unit root tests indicate that the metal index is stationary around the broken trend whereas for the food and beverages indices, the unit root hypothesis cannot be rejected. The results for all commodities are ambiguous, but the more powerful Phillips‐Perron tests indicate nonstationarity. However, the power of the Perron tests has recently come into question (see Zivot and Andrews (1992)), and these results should therefore be interpreted with care. Given (1) the ambiguities about the exact time‐series properties of some of the commodity price indices (all commodities and metals), (2) the more general concerns about the power of the Perron test, (3) the lack of consensus in the literature about the existence and timing of breaks, we proceed under the hypothesis that the series in question has a unit root component.⁶

However, as the unit root tests are silent on the size and relative importance of the permanent component, we proceed to shed light on this issue by employing the methodology proposed by Cochrane (1988). Specifically, if the variable y has the following representation,

if δ = 1 and the disturbance term, ∈, is white noise, then y follows a random walk and the variance of its k‐differences grows linearly with the difference

If $\delta >1$, so y is a stationary process, the variance of its k‐differences is given by

Therefore, the ratio $(1/k)\mathrm{var}(y_t-y_{t-k})/\mathrm{var}(y_t-y_{t-k})$ is equal to one if y is a random walk. If y is stationary, all shocks eventually die out, so the variance ratio converges to zero. If y is a more general I(1) process, which has both permanent and temporary (stationary) components, the ratio will converge to the ratio of the variance of the permanent shock to the total variance of y. Thus, the closer that ratio is to unity, the larger is the size of the unit root component, and the lower is the relative importance of temporary shocks. In the limiting case, where the ratio converges to unity, there would be no scope for stabilization policies, since all shocks are permanent. The presence of an important temporary component, however, does not guarantee that price and/or income stabilization policies will be feasible, since persistence in the temporary component may be so high as to make stabilization extremely costly. Hence, as regards stabilization policies, “temporariness” is a necessary but not sufficient condition.

Table 4 summarizes the main results. The values of k range between 1 and 20 years. For each of the four commodity indices, permanent shocks play a role in explaining the variance of commodity prices. However, their relative importance varies considerably across commodity groupings and just as much within groupings (see Cuddington (1992)). Permanent shocks are least important for metals (29 percent of the variance of yearly changes) and most important for beverages (85 percent). The index for all commodities, reflecting the differing characteristics of its components, falls in the middle of the range, with permanent shocks accounting for about 45 percent of the variance of yearly changes.⁷ For the two price indices with the largest unit root component—beverages and food—the ratio took the longest number of years to converge, possibly indicating that even the temporary component of these series exhibits a high degree of persistence.

As this methodology is based entirely on the univariate behavior of the variable, it does not discriminate among types or sources of temporary shocks. For example, it does not distinguish between a temporary shock owing to a recession in the industrial countries and a temporary shock owing to a bumper crop. Such a distinction would require a structural model of commodity prices (see Borensztein and Reinhart (1994)).

Table 4.

1/k Times the Variance of k‐Differences, 1957–92 ^a

^aAnnual data were used. All commodity price indices are deflated by the export unit values of manufactures. Standard errors are in parentheses. The standard errors were tabulated from Monte Carlo simulations (600 replications) for n = 35 and k = 10, 12, and 20 under the null hypothesis of a random walk.

Table 4.

1/k Times the Variance of k‐Differences, 1957–92 ^a

$1/k({\sigma }_k^2/{\sigma }_1^2)$ for various k (years)
2	4	8	10	12	20
All commodities
1.032	0.465	0.524	0.448
(0.007)	(0.013)	(0.022)	(0.026)
Beverages
1.176	1.220	0.904	0.998	1.260	0.846
(0.007)	(0.013)	(0.025)	(0.029)	(0.033)	(0.039)
Food
1.188	0.816	0.682	0.613	0.731
(0.007)	(0.013)	(0.021)	(0.024)	(0.027)
Metals
1.099	0.481	0.333	0.287
(0.007)	(0.013)	(0.022)	(0.026)

^aAnnual data were used. All commodity price indices are deflated by the export unit values of manufactures. Standard errors are in parentheses. The standard errors were tabulated from Monte Carlo simulations (600 replications) for n = 35 and k = 10, 12, and 20 under the null hypothesis of a random walk.

View Table

Table 4.

1/k Times the Variance of k‐Differences, 1957–92 ^a

$1/k({\sigma }_k^2/{\sigma }_1^2)$ for various k (years)
2	4	8	10	12	20
All commodities
1.032	0.465	0.524	0.448
(0.007)	(0.013)	(0.022)	(0.026)
Beverages
1.176	1.220	0.904	0.998	1.260	0.846
(0.007)	(0.013)	(0.025)	(0.029)	(0.033)	(0.039)
Food
1.188	0.816	0.682	0.613	0.731
(0.007)	(0.013)	(0.021)	(0.024)	(0.027)
Metals
1.099	0.481	0.333	0.287
(0.007)	(0.013)	(0.022)	(0.026)

^aAnnual data were used. All commodity price indices are deflated by the export unit values of manufactures. Standard errors are in parentheses. The standard errors were tabulated from Monte Carlo simulations (600 replications) for n = 35 and k = 10, 12, and 20 under the null hypothesis of a random walk.

Rising Volatility of Commodity Prices

In addition to assessing whether a commodity price is driven primarily by permanent or transitory shocks, other aspects of the nature of the shocks have to be considered when designing policy. For instance, even if the price is stationary around a deterministic trend (so all shocks are temporary), there are relatively few gains from setting up a stabilization fund and/or hedging if the variance of prices is small and large shocks are rare. The benefits to be obtained from stabilization funds, or, more generally, from precautionary savings will increase in a more volatile and uncertain environment, because greater uncertainty in a country’s export revenue stream increases the value to that country of accumulating assets to insure itself against future shocks (Ghosh and Ostry (1994)). Similarly, hedging strategies acquire greater importance as volatility increases and the probability of large destabilizing shocks is high. To examine these issues, we focus on the sample moments of the price series of interest.

Table 5.

Changing Variance of Commodity Prices: Tests for Heteroskedasticity, 1959:I–1993:II ^a

^aOwing to the nonstationarity of the data, the tests were performed on the log‐differences of the real all‐commodity price index.

Table 5.

Changing Variance of Commodity Prices: Tests for Heteroskedasticity, 1959:I–1993:II ^a

ARCH test	X2(1) = 7.683 (0.005)
Breusch‐Pagan test	X2(3) = 6.377 (0.095)
White’s test	X2(5) = 11.034 (0.051)

^aOwing to the nonstationarity of the data, the tests were performed on the log‐differences of the real all‐commodity price index.

View Table

Table 5.

Changing Variance of Commodity Prices: Tests for Heteroskedasticity, 1959:I–1993:II ^a

ARCH test	X2(1) = 7.683 (0.005)
Breusch‐Pagan test	X2(3) = 6.377 (0.095)
White’s test	X2(5) = 11.034 (0.051)

^aOwing to the nonstationarity of the data, the tests were performed on the log‐differences of the real all‐commodity price index.

To examine the issue of rising volatility, we first test for the presence of heteroskedastic disturbances and then review the descriptive statistics of commodity prices over different sample periods. The tests for heteroskedasticity on the log‐differences of real commodity prices (the results for all commodities are reported in Table 5) uniformly reject the null hypothesis that the shocks to commodity prices are identically distributed during the sample period.⁸

These results are consistent with the picture that emerges from Table 6, which presents the evolution of the basic descriptive statistics of the real commodity indices over three subsamples. Several features are worth noting. First, the average price is markedly lower during the most recent sample, consistent with the presence of a negative trend. Second, there is a sustained and sharp increase in the variance of commodity prices.⁹ This increase is evident in all the indices but is most pronounced in the all commodities and food groupings.¹⁰ The coefficient of variation rises sharply as prices become more volatile around a falling mean; for food the increase in the coefficient of variation is sixfold. Figure 2, which plots the coefficients of variation (based on a moving 15–year sample) for 1972:I–1993:II, also highlights the marked rise in volatility. Not surprisingly, the sharpest increases in volatility appear to have taken place during the early 1970s following the breakdown of the Bretton Woods exchange system and on the heels of the first oil shock. However, volatility has remained high during the 1980s and 1990s. Stuctural models often link oil prices and the U.S. real exchange rate to real commodity prices (see, for instance, Borensztein and Reinhart (1994)). Hence, the changing structure of the oil industry since the early 1970s—which has contributed to sharp increases in the volatility of oil prices—and the switch to a floating exchange rate regime—which has increased the volatility of other key relative prices such as real exchange rates (see Mussa (1986))— are likely to be important factors in explaining the more volatile behavior of commodity prices since the early 1970s. Last, the evidence on the probability of large shocks is mixed; the distributions of commodity prices were characterized by excess kurtosis (fat tails) during the 1970s, as large shocks became more commonplace.¹¹ However, the more recent sample is characterized by relatively infrequent realizations of large shocks.

Table 6.

Descriptive Statistics, 1957:I–1993:II^a

^aThe variables are the logs of the commodity index deflated by the export unit value of manufactures. The statistics are sample moments; owing to potential nonstationarity, the population moments may not be well defined. The numbers in parentheses are probability values under the null hypothesis of normality.

Table 6.

Descriptive Statistics, 1957:I–1993:II^a

Sample period	1957:I–1969:IV	1970:I–1979:IV	1980:I–1993:II
Number of observations	52	40	54
All commodities
Mean	4.714	4.705	4.386
Variance	0.001	0.017	0.031
Coefficient of variation	0.789	2.806	4.036
Skewness	1.275	1.291	–0.061
	(0.000)	(0.001)	(0.859)
Kurtosis	1.939	1.019	–1.386
	(0.008)	(0.229)	(0.052)
Beverages
Mean	4.573	4.668	4.203
Variance	0.018	0.112	0.199
Coefficient of variation	2.974	7.178	10.611
Skewness	1.152	0.979	–0.411
	(0.001)	(0.015)	(0.230)
Kurtosis	0.083	0.396	–1.254
	(0.909)	(0.640)	(0.078)
Food
Mean	4.766	4.789	4.341
Variance	0.002	0.042	0.053
Coefficient of variation	0.839	4.280	5.300
Skewness	0.428	1.129	0.138
	(0.221)	(0.005)	(0.687)
Kurtosis	–0.096	0.338	–1.526
	(0.901)	(0.690)	(0.032)
Metals
Mean	4.819	4.677	4.412
Variance	0.008	0.016	0.024
Coefficient of variation	1.868	2.737	3.490
Skewness	0.619	1.299	–0.250
	(0.039)	(0.001)	(0.467)
Kurtosis	–0.280	1.638	–0.802
	(0.700)	(0.053)	(0.260)

^aThe variables are the logs of the commodity index deflated by the export unit value of manufactures. The statistics are sample moments; owing to potential nonstationarity, the population moments may not be well defined. The numbers in parentheses are probability values under the null hypothesis of normality.

View Table

Table 6.

Descriptive Statistics, 1957:I–1993:II^a

Sample period	1957:I–1969:IV	1970:I–1979:IV	1980:I–1993:II
Number of observations	52	40	54
All commodities
Mean	4.714	4.705	4.386
Variance	0.001	0.017	0.031
Coefficient of variation	0.789	2.806	4.036
Skewness	1.275	1.291	–0.061
	(0.000)	(0.001)	(0.859)
Kurtosis	1.939	1.019	–1.386
	(0.008)	(0.229)	(0.052)
Beverages
Mean	4.573	4.668	4.203
Variance	0.018	0.112	0.199
Coefficient of variation	2.974	7.178	10.611
Skewness	1.152	0.979	–0.411
	(0.001)	(0.015)	(0.230)
Kurtosis	0.083	0.396	–1.254
	(0.909)	(0.640)	(0.078)
Food
Mean	4.766	4.789	4.341
Variance	0.002	0.042	0.053
Coefficient of variation	0.839	4.280	5.300
Skewness	0.428	1.129	0.138
	(0.221)	(0.005)	(0.687)
Kurtosis	–0.096	0.338	–1.526
	(0.901)	(0.690)	(0.032)
Metals
Mean	4.819	4.677	4.412
Variance	0.008	0.016	0.024
Coefficient of variation	1.868	2.737	3.490
Skewness	0.619	1.299	–0.250
	(0.039)	(0.001)	(0.467)
Kurtosis	–0.280	1.638	–0.802
	(0.700)	(0.053)	(0.260)

^aThe variables are the logs of the commodity index deflated by the export unit value of manufactures. The statistics are sample moments; owing to potential nonstationarity, the population moments may not be well defined. The numbers in parentheses are probability values under the null hypothesis of normality.

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Rising Volatility in Real Non–Oil Commodity Prices

(Coefficients of variation)

Citation: IMF Staff Papers 1994, 002; 10.5089/9781451947168.024.A001

Sources: IMF, International Financial Statistics, and the authors.Note: The coefficient of variation is based on 15–year moving averages and 15–year standard deviations that are backward looking; the observation for 1972:I, for instance, is based on data from 1957:II–1972:I.

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Trend‐Cycle Decompositions

If a unit root is present, admissible ways of disentangling trend from cycle are either by the methodology proposed by Beveridge and Nelson (1981) or by the structural time‐series approach associated with Harvey (1985), as both of these approaches allow for the presence of a stochastic trend. We next apply, in turn, both of these approaches.

First, employing the Beveridge‐Nelson (B‐N) technique (Beveridge and Nelson (1981)) as modified by Miller (1988), we decompose the real commodity price into its “permanent” (or steady‐state) component and its “temporary” (or cyclical component), denoted by z and c, respectively. As discussed above, the identifying criteria for this technique is that the former captures the nonstationary component of the variable, while the latter captures its stationary element. Hence,

The evolution of the permanent component is given by

where θ and Φ are the parameters describing the ARMA process. Using the estimates of θ, Φ, and ϵ, the path of the permanent component is constructed. The cyclical component is calculated residually as the difference between the estimated permanent component, z, and the actual values of y.¹²

Using the Box–Ljung Q statistic as a guideline, the ARMA processes were selected to whiten the error. In general the longer ARMA processes provided the best fit.¹³ At the quarterly frequency, an ARMA(20,4) process was fitted to the all commodities and beverages groupings, while food and metals were characterized by ARMA(16,4) processes. Table 7 reports the full estimation results for the annual frequency and the main diagnostics of the quarterly estimation. Figure 3 plots the actual series along with the estimated permanent component. For example, large deviations from trend were evident in the indices for all commodities, food, and metals during 1973, at the time of the first oil shock. For beverages, the largest deviations from trend during the sample took place during 1977 and are associated with a supply shock.¹⁴ As Figure 3 illustrates, except for the metals basket, for which the actual price has been below trend since late 1990, actual prices for all other indices are close to their permanent trend component. Figure 3 also illustrates that the evolution of the permanent component changes considerably during the course of the sample. Whereas during the 1960s and up to the first oil shock all prices were relatively stable, the trend has become markedly negative since the mid–1970s (somewhat later for beverages).

Table 7.

Beveridge‐Nelson Decompositions Modeling Change in Permanent Component as an RMA Process ^a

^aAll commodity price indices are deflated by the export unit values of manufactures. Standard errors are in parentheses. The models were estimated using log‐differences. All series were allowed to have a break in their rates of change in 1973. The Q statistic tests whether the regression residuals are white noise. The significance level is the probability that the actual Q statistic value will be observed under the null hypothesis that the residuals are white noise.

Table 7.

Beveridge‐Nelson Decompositions Modeling Change in Permanent Component as an RMA Process ^a

Dependent variable	All commodities	Beverages	Food	Metals
Annual: 1964–92
ARMA(p, q)	ARMA(5,1)	ARMA(4,1)	ARMA(4,1)	ARMA(5,1
Constant	0.003	0.017	0.002	0.007
	(0.008)	(0.026)	(0.013)	(0.007)
AR(1)	–0.880	–0.567	–0.646	–1.203
	(0.351)	(0.146)	(0.646)	(0.191)
AR(2)	–0.912	–0.128	–0.535	–0.832
	(0.266)	(0.298)	(0.247)	(0.278)
AR(3)	–0.629	–0.167	–0.420	–0.942
	(0.371)	(0.271)	(0.476)	(0.263)
AR(4)	–0.374	–0.195	–0.295	–0.645
	(0.269)	(0.101)	(0.149)	(0.288)
AR(5)	–0.118	******	******	–0.315
	(0.253)			(0.236)
MA(1)	0.817	1.352	0.754	1.476
	(0.333)	(0.386)	(0.554)	(0.439)
R2	0.469	0.341	0.311	0.617
Q statistic	9.085	5.981	13.842	6.267
Significance level	(0.826)	(0.967)	(0.461)	(0.959)
Quartely: 1962:I–1993:II
ARMA(p, q)	ARMA(20,4)	ARMA(20,4)	ARMA(16,4)	ARMA(16,4)
R2	0.465	0.454	0.393	0.371
Q statistic	8.567	10.966	14.183	15.560
Significance level	(0.999)	(0.999)	(0.998)	(0.996)

^aAll commodity price indices are deflated by the export unit values of manufactures. Standard errors are in parentheses. The models were estimated using log‐differences. All series were allowed to have a break in their rates of change in 1973. The Q statistic tests whether the regression residuals are white noise. The significance level is the probability that the actual Q statistic value will be observed under the null hypothesis that the residuals are white noise.

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Table 7.

Beveridge‐Nelson Decompositions Modeling Change in Permanent Component as an RMA Process ^a

Dependent variable	All commodities	Beverages	Food	Metals
Annual: 1964–92
ARMA(p, q)	ARMA(5,1)	ARMA(4,1)	ARMA(4,1)	ARMA(5,1
Constant	0.003	0.017	0.002	0.007
	(0.008)	(0.026)	(0.013)	(0.007)
AR(1)	–0.880	–0.567	–0.646	–1.203
	(0.351)	(0.146)	(0.646)	(0.191)
AR(2)	–0.912	–0.128	–0.535	–0.832
	(0.266)	(0.298)	(0.247)	(0.278)
AR(3)	–0.629	–0.167	–0.420	–0.942
	(0.371)	(0.271)	(0.476)	(0.263)
AR(4)	–0.374	–0.195	–0.295	–0.645
	(0.269)	(0.101)	(0.149)	(0.288)
AR(5)	–0.118	******	******	–0.315
	(0.253)			(0.236)
MA(1)	0.817	1.352	0.754	1.476
	(0.333)	(0.386)	(0.554)	(0.439)
R2	0.469	0.341	0.311	0.617
Q statistic	9.085	5.981	13.842	6.267
Significance level	(0.826)	(0.967)	(0.461)	(0.959)
Quartely: 1962:I–1993:II
ARMA(p, q)	ARMA(20,4)	ARMA(20,4)	ARMA(16,4)	ARMA(16,4)
R2	0.465	0.454	0.393	0.371
Q statistic	8.567	10.966	14.183	15.560
Significance level	(0.999)	(0.999)	(0.998)	(0.996)

^aAll commodity price indices are deflated by the export unit values of manufactures. Standard errors are in parentheses. The models were estimated using log‐differences. All series were allowed to have a break in their rates of change in 1973. The Q statistic tests whether the regression residuals are white noise. The significance level is the probability that the actual Q statistic value will be observed under the null hypothesis that the residuals are white noise.

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Real Non‐Oil Commodity Prices: Trends and Cycles Beveridge‐Nelson Decomposition

Citation: IMF Staff Papers 1994, 002; 10.5089/9781451947168.024.A001

Sources: IMF, International Financial Statistics, and the authors.

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An alternative approach to decomposing a time‐series into its stochastic trend and cycle is associated with Harvey (1985). This structural time‐series approach relies on the Kalman filter. In this trend plus cycle model, the stochastic trend or permanent component, z_t can be modeled as¹⁵

where η_t and ϵ_t are mutually independent, normally distributed white‐ noise disturbances. The cycle is given by

where, as before, c_tis the cyclical component, ω_t, and ${\omega }_t^{*}$ are uncorrelated white‐noise disturbances, and $c_t^{*}$ appears by construction (see Harrison and Akram (1983)). The parameters λ and ρ describe the frequency of the cycle and the damping factor on the amplitude of the cycle, respectively. Using the Kalman filter, the parameters $(\lambda ,\rho ,{\sigma }_{\eta }^2,{\sigma }_{ϵ}^2,{\sigma }_{\omega }^2)$ are estimated by maximum likelihood (ML) in the time or frequency domains.

The estimates of the structural time‐series model present a similar scenario to the B‐N decomposition. Figure 4 plots the permanent component produced by this technique alongside the actual price series; as before, the bulk of the recent price weakness is associated with the secular component and there is no evidence of an abnormally large cycle. The most substantive differences between the results from the two methods are that (1) the Kalman‐filter approach produces smoother trend components for the beverages and food groupings, and, hence, a somewhat more volatile cycle, and (2) metals prices during 1993 are closer to trend using the structural time‐series approach than using the B‐N decomposition. However, even giving the results of the Perron tests a higher weight and treating the indices for all commodities and metals as stationary about a broken trend, the main implications about trends and cycles remain. As Figure A.1 in the appendix indicates, the recent weakness does not appear to be of a primarily cyclical nature.

Characteristics of the Cycle

Figure 5 plots the cycles generated by the two methods; as noted earlier, the similarities are strong. In effect, the pairwise correlations between the cycles generated by the two approaches are quite high: 0.95 for all commodities, 0.87 for beverages, 0.90 for food, and 0.87 for metals. ¹⁶ It is also evident from these figures that the cycles are correlated across commodity groupings, showing the high degree of co‐movement in commodity prices. Cycles in all commodities are highly correlated (correlations above 0.80) with cycles in food and metals. Beverages exhibit the most idiosyncratic behavior, as cycles appear to be primarily driven by supply shocks.

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Real Commodity Prices: Trends and Cycles

Structural Time‐Series Decomposition

Citation: IMF Staff Papers 1994, 002; 10.5089/9781451947168.024.A001

Sources: IMF, International Financial Statistics, and the authors.

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Real Commodity Prices: Cycles

(Beveridge‐Nelson Cycle (left panel) versus Kalman Filter Cycle (right panel))

Citation: IMF Staff Papers 1994, 002; 10.5089/9781451947168.024.A001

Sources: IMF, International Financial Statistics, and the authors.

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As noted earlier, the temporary shocks that drive the cycle can exhibit differing degrees of persistence. Stabilization funds are better suited to smoothing out short‐lived shocks; the more persistent the shock, the greater are the costs of maintaining an “artificially” high internal price (assuming the shock had tended to depress prices). To examine this issue, we first fit an AR process to the cyclical component.¹⁷ The estimated model was then used to generate impulse responses that allow us to visualize the time it takes for the effects of the shock to disappear (or become arbitrarily small). Figure 6 plots the impulse responses based on the estimated AR processes.¹⁸ Although the full effects of the shock may take longer to disappear, for practical purposes we will focus on the time it takes for these effects to become smaller than some arbitrary cutoff, say plus/minus 0.02 of a unitary shock, after which the impact of the shock is minimal. Based on these considerations, shocks are the least persistent for metals (reaching the cutoff in 6 to 7 quarters) and the most persistent for beverages (12 to 13 quarters).¹⁹

General Observations on the Time‐Series Properties of Commodity Prices

A series of recent papers, including Cuddington and Urzua (1989), Powell (1991), Ardeni and Wright (1992), and Deaton and Laroque (1992), analyze the behavior of real commodity prices. These papers, which give careful consideration to modeling the time‐series properties of commodity prices (usually for long‐run annual data—see Figure 1), often present contradictory results. There is little consensus on whether real commodity prices are stationary or not or when, if any, structural breaks have taken place.

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Impulse Responses: Persistence in the Cycle

Beveridge‐Nelson Cycle (left panel) versus Kalman Filter Cycle (right panel)

Citation: IMF Staff Papers 1994, 002; 10.5089/9781451947168.024.A001

Note: These impulse responses are based on the estimated AR processes.

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Similar ambiguities arise from the analysis of the quarterly postwar data used in this study. There is, however, one robust finding in the empirical work—real commodity prices exhibit a high degree of persistence, and the high autocorrelation in the data is well documented. Although ambiguities about the exact time‐series properties of real commodity prices remain, a number of practical implications still emerge from an analysis of their time‐series behavior. First, whether the trend component is modeled by a simple broken deterministic linear trend (Figure A.1 in the appendix) or by a stochastic process using alternative methodologies (this section), the recent decline in commodity prices appears to be primarily secular (Figures 3, 4, and A.1 all illustrate this point). Contrary to the findings of Boughton (1991), no evidence in any of the decompositions indicates that the recent price weakness is part of an anomalous cycle, which suggests that the prospects for a sharp recovery in real commodity prices to pre–1980 levels are somewhat dim. Second, irrespective of the technique used, the downward trend has obviously steepened in recent years, implying that the design of stabilization efforts should incorporate this feature of commodity price behavior. Third, whereas for some of the indices (all commodities and metals) the results on stationarity are not clear cut, from a practical policy standpoint this distinction may not be relevant. As noted earlier, the success of stabilization funds requires shocks to be temporary. However, if a shock is temporary, but its effects persist for many years, price stabilization may be equally costly.

Secular Developments

Institutional Factors: International Commodity Agreements (ICAs)

Part of the blame for weakening commodity prices during the 1980s and 1990s is often attributed to the international community’s failure to abide by and support commodity agreements designed to help stabilize prices and ensure a “fair” return to commodity producers. Several such agreements were in effect during the 1970s and early 1980s. In June 1984 the agreement covering sugar collapsed. Thereafter, other agreements followed suit or became economically moribund: tin (October 1985), cocoa (February 1988), coffee (July 1989), and natural rubber (April 1993). The immediate impact on price of a breakdown in a commodity agreement may have a large “temporary” component as prices spike downward; for instance, beverage prices fell well below trend from mid–1987 to mid–1989 (Figures 3–5).²² However, the effects of the breakdown are likely to have an important “permanent” component as the behavior of exporters adjusts to the more competitive regime. In effect, the evidence suggests that, in addition to agricultural policies in industrial countries and the technological innovations discussed above, the breakdown of the numerous agreements has been a factor behind the sharp expansion in world commodity supplies in recent years. In part, however, the breakdown of a number of agreements reflects the difficulties of trying to influence prices by managing output or other means in the face of developments (such as productivity increases acting to foster an expansion in supplies).

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Cereal Yields by Region

Citation: IMF Staff Papers 1994, 002; 10.5089/9781451947168.024.A001

Source: Food and Agriculture Organization, Production Yearbook.

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Cyclical Factors

Temporary Price Shocks and the Role of Government in Smoothing Income

Temporary shocks to commodity prices affect both the private and public sectors in the commodity producing countries. When facing temporary changes in income, the optimal response by individual consumers is to use saving and borrowing in an attempt to smooth the path of consumption. Similarly, governments facing temporary changes in revenue should adjust their spending to make it consistent with sustainable levels.

A traditional argument for government to absorb the effects of commodity price fluctuations is based on microeconomic considerations relating to the behavior of private agents.²⁴ If private agents bear all the commodity price risk, they will tend to face variable and unpredictable income streams over time, with possibly very limited opportunity to smooth consumption. Therefore, it may be best for the government to intervene to stabilize the prices received by private agents and thus enhance the welfare of risk‐averse individuals by permitting smoother income and consumption streams.

Empirical evidence on savings behavior in developing countries is far from conclusive, but it does suggest that consumption smoothing may well take place more than is traditionally assumed.²⁵ At the microeconomic level, the evidence suggests that agents do react to commodity price instability in a manner consistent with theory. Rice farmers in Thailand, for example, smooth their consumption quite successfully both within and between harvest years.²⁶ Also, an analysis of the coffee boom of 1976–79 in Kenya found that as much as 60 percent of boom income went into private savings; farmers were aware that the boom was due to frost damage in Brazil and that their income gains were largely a windfall.²⁷ In contrast, governments in a number of countries have found it difficult to manage the proceeds of temporary windfall gains well. Thus, the evidence suggests that governments may be well advised to reassess their intervention strategies and the responsibility they assume for managing commodity price risk at the country level.

Intervention Strategies

With fluctuations in international commodity prices affecting the domestic economy, the types of intervention employed have been varied; the strategies most often used and their problems are outlined below.

Government Policies for the Longer Term

As well as international commodity price variability, commodity exporting countries in recent years have also faced a downward trend in real commodity prices. It may well be unwise to base policies on the assumption that the weakness in real commodity prices will be quickly overcome. A stronger economic recovery in the industrial countries would certainly help, as would continuing high rates of growth in the newly industrializing countries. Some supply‐side factors may ease over time (such as recent shocks to metals markets from the former Soviet Union), but other factors (such as structural changes in exporting countries and productivity gains owing to technical progress) seem unlikely to be reversed. The decline in commodity prices poses the question of what—if any—are the appropriate structural policies for exporting countries, in particular with regard to resource allocation and international trade.

The lessons from the experience in Latin America with inward‐looking development strategies are that whereas a negative terms of trade shock is certainly an adverse development from an exporting country’s viewpoint, adding distortions to the domestic economy does not improve the situation. The increasing body of evidence on cross‐country growth performance indicates that distortions to international trade and market-oriented resource allocation can have adverse effects on economic efficiency and growth.

The experience of the fastest growing developing countries shows that their export structures have evolved over time toward greater diversification (Table 1). The recent review of the high‐performing Asian economies provides some guidance on how such diversification was achieved.²⁹

First, whereas agriculture’s share of output and employment in these economies has declined significantly over time, growth in agricultural output and productivity was much higher than in other developing countries. The governments of these high‐performing Asian economies supported the agricultural sector through extension services, agricultural research, pilot schemes, significant investment in irrigation and rural infrastructure (roads, bridges, electricity, and water supplies), and non‐ punitive crop taxation. The experience of these economies indicates that establishing a dynamic agricultural sector is an important phase in the diversification process; for lower‐income countries the message is that failure to attach sufficiently high priority to agriculture in favor of other sectors is likely to be counterproductive.

Second, in addition to policies that generally provided a stable macroeconomic environment, the high‐performing Asian economies facilitated the more general process of diversification by public investment and institution building, by opening up their economies, by dismantling many of the regulatory barriers to resource reallocation, and by adopting policies or reforms that produced fewer distortions than in many other developing countries.