Chile: Selected Issues

This Selected Issues paper examines a number of potential factors that may have influenced the short-term behavior of the exchange rate between the Chilean peso and the U.S. dollar during the period of floating exchange rate, including the possible impact of developments in Argentina during 2001. The paper investigates whether copper prices can be successfully forecasted over medium-term horizons, emphasizing the properties of copper prices most relevant in the Chilean context, including for fiscal policymaking. The paper also provides a snapshot of the Chilean banking and corporate sectors.

Abstract

This Selected Issues paper examines a number of potential factors that may have influenced the short-term behavior of the exchange rate between the Chilean peso and the U.S. dollar during the period of floating exchange rate, including the possible impact of developments in Argentina during 2001. The paper investigates whether copper prices can be successfully forecasted over medium-term horizons, emphasizing the properties of copper prices most relevant in the Chilean context, including for fiscal policymaking. The paper also provides a snapshot of the Chilean banking and corporate sectors.

III. Forecasting copper prices in the Chilean context 30

A. Introduction

71. The future evolution of copper prices is a matter of interest in the case of Chile. While it is possible to exaggerate the “dependence” of Chile, and of the Chilean government finances, on copper export revenue, such revenue has represented 7–10 percent of GDP and 35–40 percent of exports in recent years. Transfers to the government from CODELCO, the state-owned copper company, have ranged from less than 2 percent of central government revenue (1998 and 1999) to more than 10 percent of such revenue (as recently as 1995), depending mainly on the state of world copper prices. Indeed, copper prices are highly volatile.

72. The Chilean economy as a whole copes with this volatility in a number of ways, including not only a floating exchange rate regime but also a high degree of foreign ownership of copper mines (which dampens the impact of copper price fluctuations on Chilean national income and wealth, and on the external current account balance). In the case of the government, there is the longstanding mechanism of the copper stabilization fund; more recently, the government’s new target for the structural fiscal balance includes an adjustment for copper price fluctuations. In general, such schemes make most sense if the price in question has a component that is temporary and forecastable and does not have a steep trend.31

73. This paper asks what expectations can we reasonably have about copper prices in the medium to long run; that is, over horizons of say, five-ten years ahead. Is there a basis to have any expectations at all, other than whatever is today’s price? These questions are of special interest currently, since real copper prices are near historical lows: is it reasonable to think of this situation as temporary, to make medium-term forecasts for the Chilean economy, and fiscal plans for the government, on the presumption that prices must eventually rise? Is it reasonable to presume that “copper risk” is mainly on the upside? We emphasize that the objective is not to know with confidence the precise level of copper prices five or ten years from now, but rather, to ask whether there is a reasonable basis for expecting them to be significantly higher than they have been recently. If the answer is yes—that large temporary copper price shocks do exist, as this paper concludes—it becomes worth asking another question: what is the typical duration of such temporary shocks?

74. We have two rationales for focusing so much beyond the short run. First, since in the Chilean case neither the government nor the economy as a whole is liquidity constrained, having an accurate idea of copper prices a short period ahead—even if desirable for some purposes—is not critical. Second, we suppose that temporary price shocks might be rather long lived (Cashin, Liang, and McDermott (1999) suggest a typical half life of more than six years).

75. This study considers, and evaluates out-of-sample, a number of forecasts. One group comprises several very simple time-series models, using only information on past copper prices to generate forecasts. We build on the recent study by Engel and Valdes (2001), who evaluate a wide range of time-series models but find that most have essentially no forecasting power at all over horizons of one to five years. Engel and Valdes do find that a simple AR(1) model has some forecasting power, but its margin of victory over a naïve alternative forecast is not great. We investigate whether the limited success of the AR(1) model is related to the long—and perhaps variable—duration of copper price shocks. Indeed, when we consider forecast horizons of six to ten years, the AR(1) model’s margin of victory widens. We also examine the performance of several other simple forecasting alternatives. The object is not to identify a true model of copper prices, nor to find the best possible forecasting tool, but rather to draw useful conclusions about the nature of copper price behavior from the relative forecasting success of alternative approaches.

76. Rather than using past copper prices, a much different forecasting approach would be to use futures market prices as a basis for medium- and long-term forecasts. Since the longest futures contract regularly traded is only 2¼ years, we investigate whether their prices might be used to draw inferences about (market expectations of) the level of copper prices over a longer horizon. We show that these futures prices do have some forecasting power (over a 2¼-year horizon) and that such futures prices have behaved as if the market believed that most copper price fluctuations were temporary. These findings suggest that futures prices should be considered seriously, at least as an indicator of the likely direction of copper price movements over a longer horizon. On the other hand, though futures prices do seem to be related to a market view of the level to which copper prices will eventually converge, we find evidence that this view has changed over time.

77. The chapter is organized as follows. Section B provides background, with a descriptive look at how copper prices have behaved in the past. It also describes some basic aspects of the world copper market, including how it is analyzed by industry experts. Section C evaluates the out-of-sample forecasting performance of several models, as well as London Metals Exchange (LME) futures prices, in relation to a naive benchmark forecast.

78. Section D demonstrates that 2¼-year copper futures prices—although quite volatile themselves—have systematically pointed to copper price increases (declines) when copper prices have been low (high). In fact, the level of the spot price alone explains a very large part of the gap between futures and spot prices observed on a given day. We investigate the stability of this relationship over time, and the prospects for using it to infer market views of a “long-run” level of copper prices and the expected duration of temporary shocks.

79. Section E summarizes the findings of the previous sections and goes on to consider their possible implications for Chile, focusing mainly on the government’s structural balance target and its adjustment for copper price fluctuations. Inevitably, there will be uncertainty not only over the level (if any) to which copper prices are converging, but also over the time needed to reach that level. This section seeks to put these two sources of uncertainty in quantitative perspective with some illustrative simulations, taking account of the relative size of copper in the Chilean economy, as well as key aspects of the government’s overall fiscal position.

B. Background: Consensus Views of the Copper Market and a Look at the Data

80. This section provides an initial, descriptive look at how copper prices have behaved in the past. This turns out to be enough to illustrate a number of key points, and to give some intuition for the results presented later. As additional background, this section first describes some basic aspects of the global copper market, including how it is viewed by industry analysts and how experts on the copper industry make their own long-term price forecasts.

A consensus view of the copper market

81. Though it is widely acknowledged that copper prices are difficult to forecast accurately, there is broad agreement among analysts of the industry about how to frame an analysis of the market, how copper prices can be expected to behave over time, and how best to generate medium-term forecasts.

82. This consensus holds that copper price shocks are often temporary in nature. In turn, this belief implies the potential to forecast movements in copper prices on the basis of the expected decay of already-observed temporary shocks. This is not to say that permanent price shocks are not also possible; however, except over the very long run (when only permanent shocks matter, by definition) movements driven by short-term factors tend to be large relative to those from permanent shocks, or possible long-run “trends.”

83. Such a view is consistent with the use of a copper adjustment in the Chilean fiscal balance target. Its strong contrast to a possible alternative should be emphasized. One might suspect instead that a commodity such as copper should be analyzed as an asset, for which intertemporal arbitrage would play a dominant role in price determination, in the extreme ruling out any forecastable temporary component to copper prices (essentially, because any expectations of a future change in price would only cause that change to materialize immediately). However, the consensus is that such intertemporal arbitrage in practice does not play such a dominant role, and it is considered misleading to think of copper simply as an asset, a stock in finite supply. In that case, Hotelling’s theory would predict that the price would over time tend to increase at the rate of interest (i.e., enough to compensate holders of copper for not selling, while not creating above-normal returns), which is clearly at odds with the evidence. Instead, the consensus analyzes the supply of the copper as a flow; indeed, the idea is that the long run supply curve is rather flat.32

84. In the consensus view, the difficulty of forecasting the price of copper does not arise from a predominance of unanticipated permanent shocks, but rather from the difficulty of forecasting temporary shocks to the variables influencing copper supply and demand. Moreover, because both supply and demand are thought to be inelastic to price changes in the short run33 shocks to either side can require the price of copper to move substantially to clear the market. Shocks shifting the short-run demand curve are considered especially important, with a key factor being the state of the world economy in the business cycle (e.g., because much of copper demand arises from construction and other investment activity sensitive to the business cycle).

85. Even if temporary shocks do predominate in the short run, is there a long-run trend—in one direction or the other—underneath all the noise? As noted, the positive Hotelling effect is absent. One might suspect instead a downward trend, perhaps on the (Prebisch-Singer) notion that primary goods would have a low income elasticity of demand or that in time substitutes would inevitably be developed. However, the consensus view does not seem to include a particular expectation about the direction of demand shifts over time, other than the positive effect arising from growth of the world economy.34 If the consensus sees an important trend, it is on the supply side, with ongoing technological progress pushing down the cost of production, and thus the supply curve and market price of copper. As will be seen shortly, however, it is difficult to detect a significant positive or negative trend from the historical record of (real) copper prices. At least so far, it seems that supply and demand shocks have tended to offset each other over long periods.

86. How then do industry experts go about making their own medium to long term copper price forecasts? Reflecting the above, attention focuses on the supply side, constructing a world supply curve by aggregating the individual cost curves of mines in existence or in the pipeline. Assumptions about the evolution of demand (beyond the period of business cycle fluctuations) tend to be essentially neutral and play a lesser role in projecting the market-clearing price. It seems that there is considerable information sharing among industry gurus, and a half-dozen or so groups tend to generate forecasts in the same ballpark. Unfortunately, forecasts of this kind are not amenable to rigorous, systematic evaluation of their predictive accuracy.

A long look at the data: copper prices since 1908

87. Figure 1 shows the evolution of (real) copper prices since 1908. For our purposes, a few basic points can be noted:

  • No steep trend, either upward or downward, is obvious over this long period. It is true that the most recent observation (for 2001) is very near the sample’s minimum level, but the minimum in fact occurred 65 years earlier. Similarly, the sample’s maximum (in 1966) is separated from the next-highest value (1916) by 50 years. Statistically, we find no significant trend or drift in the series.35

  • Despite the absence of a steep trend, tremendous variation in the period is seen. The sample maximum is more than four times the sample minimum. Even disregarding, say, the ten most outlying observations, the range of the remaining observations is still wide, in economic terms: from about 60 to 180 U.S. cents per pound (in 1999 prices).

  • Though the price series is obviously autocorrelated, the sample is long enough to see the series cross over the sample mean and median values quite a few times.36 However, the time spent between such crossings can be considerable (e.g., about ten years for the boom that began in 1964, and even longer for the crash after about 1930.)

  • The price data are skewed upward, with a few very high outliers. This skewness could suggest asymmetry in the price adjustment process, with positive shocks decaying more quickly than negative ones. (As seen in the bottom panel of Figure 1, the log transformation results in a much less skewed series.37)

Figure 1.
Figure 1.

Annual Real Copper Prices

(1908-2001)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: CODELCO.1/ Copper price deflated by U.S.wholesale price index.

88. Figure 2 provides a finer view of the second half of the sample, with monthly data (available from 1957). It is interesting to note that the current episode of (historically) very low prices (defined say, as below about 75 cents/lb., in 1999 prices) is now approaching in duration the only other longish period of low prices seen in the last 45 years: the five years after mid-1982.

Figure 2.
Figure 2.

Monthly Real Copper Prices

(January 1957 - March 2002)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: IMF, International Financial Statistics.1 Copper price deflated by U.S.wholesale price index.

89. Such eyeballing of the data seems to support the conventional wisdom of large temporary shocks to copper prices. But it also gives the impression that such shocks may take many years to decay.

90. Of course, the existence of temporary shocks would not rule out a role for permanent shocks occurring alongside. We find it helpful to think of the copper price series, in principle, as the sum of two components: one stationary, driven by shocks that eventually disappear entirely, and the other with a unit root. A priori, one would suppose that at least some permanent shocks would exist alongside temporary shocks to copper prices. But for many purposes, what matters is not the existence but rather the relative size of these two components.38

91. On this question, it is interesting that the (net) accumulation of any permanent shocks over the last 90-some years has not carried the real price of copper off more strongly, in one direction or the other, than seen in Figure 1. Even a random walk without drift might have been expected to carry the price further over long horizons—indeed, this is essentially the result of the variance ratio analysis conducted by Engel and Valdes (2001). They apply Cochrane’s variance ratio statistic to virtually the same data shown in our Figure 1. Taking account of the finite sample properties of this statistic, they find evidence of a large temporary component. Indeed, Engel and Valdes find a striking correspondence between the actual variance ratio statistics and those which would be generated by a simple AR(1) process having no permanent component at all.39

C. Evaluation of the Accuracy of Alternative Copper Price Forecasts

92. In this section we examine the forecasting accuracy of several simple forecasting methods, comparing the track record of each to that of a benchmark forecast based simply on a random walk. These forecasts are assessed according to the conventional criterion of minimizing root mean squared error (RMSE),

93. We first consider accuracy, over horizons as long as 10 years, of forecasts from the AR(1) model for which Engel and Valdes (2001) found some support, as well as others based on averages of past prices (historical and rolling means). We then analyze the forecast accuracy of futures market prices, where data limitations force us to consider horizons no longer than 2¼ years.

Forecast accuracy over long horizons: AR(1) and past averages, 1970–2001

94. In analyzing the track records of forecasts generated using AR(1) estimates or historical or rolling means, we are not suggesting that these kinds of forecasts might be the best possible. Rather, we evaluate them because their relative forecasting performance illustrates—in simple terms—some essential points. Moreover, these forecasts are amenable to repeated out-of-sample evaluation.

95. The forecasts are evaluated over ten horizons, ranging from one to ten years, drawing on annual data for real copper prices from 1908-2001. The basic period of forecast evaluation is 1970-2001, nearly identical to that used by Engel and Valdes. We also report results for 1940-2001.

96. Table 1, and its companion Figure 3 and 4, allow comparison of different forecasts’accuracy over each of the ten horizons. In Table 1, the results are reported first as RMSEs (times 100) and then as ratios of RMSEs to that of the random walk benchmark (i.e., Theil’s U statistic).40 Figure 3 and 4 allow a visual comparison of these Theil’s U values.

Table 1

Comparisons of Real Copper price Forecast Accuracy: RMSEs, Theil’s U, and Diebold-Mariano Statistics

(errors defined as LN(actual)-LN(forecast))

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Source: IMF staff estimates.Notes: Figures in bold lettering correspond to best forecasting performance at a given horizon and evaluation period. Based on annual data for real copper prices, as obtained from Codelco for 1908-1999, and extended to 2001 using IFS. D-M statistics using the Harvey, Leybourne and Granger (1997) modification of the the statistic proposed by Diebold and Mariano (1995). The null hypothesis is that the mean “loss differential” (defined as the squared errors of the forecast in question minus the squared error of the random walk forecast) is zero. The statistic can be evaluated using the 1-dtstribution, with n-1 degrees of freedom, but it is known to be somewhat oversized in small samples.
Figure 3.
Figure 3.

Relative Accuracy of Alternative Forecasts of Real Copper Price Theil’s U for Horizons of 1-10 years.

(Evaluation Period: 1970 to 2001)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: IMF staff estimates.
Figure 4.
Figure 4.

Relative Accuracy of Alternative Forecasts of Real Copper Price Theil’s U for Horizons of 1-10 years.

(Evaluation Period: 1940 to 2001)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: IMF staff estimates.

97. The essential results are most readily seen in Figure 3. For very short horizons of only 1 or 2 years, forecasts derived from past prices seem to be of no use, performing either much worse, or only slightly better, than the random walk benchmark. For longer horizons, however, these forecasts have some success, and indeed, the longer the horizon considered, the greater is their margin of victory over the benchmark. More specifically:

98. Are these results significant, in economic or statistical terms? For horizons of five years or longer, many of the Theil’s U values in Table 1, imply a reduction in forecast RMSE of about 20 percent or more; in our judgment, this qualifies as “economic” significance. Regarding statistical significance, we use a form of the Diebold-Mariano (1995) statistic to see whether the track record of the best performers in Table 1 is statistically different from that of the random walk alternative.43 The results, shown in Table 1, are not strong, especially for the shorter horizons, where the null hypothesis of equal forecasting performance cannot be rejected. For horizons longer than three years, the results tend to be borderline. Many of the Diebold-Mariano statistics exceed in absolute value, or are very near, the 10 percent critical value (about-1.7 in samples of these sizes). However, the modified Diebold-Mariano test is known to be over-sized in small samples; i.e., rejecting the null hypothesis somewhat too often.44

99. In light of the (relative) out-of-sample success of the AR(1) and historical mean forecasts, it is interesting to see how estimates of the AR(1) model’s implied steady-state value, and calculations of the historical mean, would have evolved during the sample period (i.e., as each year of new data became available). Figure 5’s top panel shows this, along with the actual spot price series. Note that for many years, both the steady-state estimates and the historical mean have been rather stable, around 4.7 or 4.8 in log terms, or about 110 or 120 U.S. cents/lb. in constant prices of 1999. Such levels are far above the actual prices observed in the last several years, and considerably above the reference price recently used in the Chilean structural balance adjustment (about U.S. 90 cents). Of course, these observations should be interpreted with caution; one should not conclude from this that 110-120 cents is “the” long-run price. We note especially that the AR(1) model, whatever its relative forecasting success in the past, is a crude device, and will be slow to pick up any permanent shocks that may have hit lately.

Figure 5.
Figure 5.

Real Copper Prices: AR(1)Estimation Results

(Samples beginning 1908 and ending 1930 - 2001)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: CODELCO; and IMF staff estimates.

100. It is natural to also consider the AR(1) estimates for hints about the typical duration of temporary copper price shocks. Figure 5’s bottom panel shows how the estimate of autoregressive coefficient has evolved over time. The implied half-life estimate has tended to be about four years. The latest estimate, with an autoregressive coefficient of 0.848, implies a half life of 4.2 years for the (log) real copper price. Again, caution is in order, as such a result could reflect some potentially strong sources of bias. One possibility is an upward bias arising from temporal aggregation of prices into annual values.45 To illustrate the point, when we re-estimate the AR(1) using monthly data instead, the estimated autoregressive coefficient implies a half life of less than 2.7 years, compared to four years in the annual data.46 On the other hand, downward bias is also possible. If copper prices have a unit root component, then OLS estimates of the autoregressive coefficient, and the associated half life, will be biased downward. Cashin, Liang, and McDermott (1999) concern themselves with this potential problem and advocate using instead a “median-unbiased” estimator of the autoregressive coefficient in analyzing commodity prices. For the case of copper, their results do indeed imply a much longer half life, at 6.6 years, even when estimated using monthly data. The confidence interval associated with this estimate is however very wide, ranging from slightly under two years to infinity. The authors interpret such a large confidence interval as indicating that copper price shocks vary considerably in their duration.

Accuracy over shorter horizons: futures prices and AR(1)

101. We turn next to the accuracy of forecasts directly based on copper futures prices. In particular, we want to learn whether 2¼- year futures—the longest regularly traded—have any predictive power. For this question, we compare errors from futures prices with errors from a random walk benchmark. Since it turns out that the futures are relatively successful, we then go on to check how their performance compares to that of an AR(1) alternative used to generate forecasts for the same horizon, during the same sample period.

102. Recall that the above analysis was based on annual observations, with forecasts evaluated over periods of several decades, and forecasts horizons as long as 10 years, reflecting our interest in the medium- to long-run behavior of copper prices. In contrast, here we are forced, by data availability limitations, to analyze shorter evaluation periods, to begin the analysis in the mid-1990s, and to consider forecast horizons no longer than 2¼ years. The analysis is conducted using monthly data.47 (A further difference, the significance of which is discussed shortly, is that here we work with nominal rather than real prices, since futures prices are set in nominal terms.)

103. The evaluation period is determined by the availability of LME 2¼ year futures data on a consistent basis starting only in July 1993. With monthly data through March 2002, we have 8¾ years of futures data (105 monthly observations), of which we can compare forecasts and outcomes for a period of 6½ years (78 observations, October 1995- March 2002). Although a longer evaluation period would be desirable, the available period has been a rich one for our purposes, with copper prices swinging widely. (Section D presents and discusses aspects of LME futures data in more detail.) Again, the evaluation criterion is RMSE.

104. Table 2 presents the results not only for 2¼ year (27 month) futures, but also for the two shorter horizons for which futures data are available from the LME web site (15 months and 3 months). Here again we see a pattern in which the longer the forecast horizon, the more successful are the forecasts considered in comparison to the random walk benchmark. At the three month horizon, futures prices essentially do no better than the random walk, with a Theil’s U very close to one. At the 15-month horizon, however, Theil’s U falls to around 0.8, while the 27-month futures do better yet, with a Theil’s U of about 0.7, signifying a 30 percent reduction in RMSE.48

Table 2

Forecast Accuracy of Futures Prices Relative to Random Walk Benchmark

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Source: IMF Staff estimates.RMSE calculations are based on monthly data in log form, multiplied by 100. For the random walk forecasts, variant (a) is the current spot price. Variants (b) and (c) adjust this for expected inflation. Variant (b) is calculated using expected inflation of 0.98 percent per year, equal to average U.S. PPI inflation during July 1993-March 2002. Variant (c) uses the actual U.S. PPI change over each forecast horizon, thereby assuming perfect foresight of inflation.

105. These findings continue to hold when the futures forecasts are compared to enhanced versions of the random walk benchmark that take into account expected inflation. In principle, the simple random walk benchmark is at some disadvantage in this competition, since the nominal futures prices analyzed presumably incorporate expected inflation over the forecast horizon; whereas a forecast based simply on today’s (nominal) spot copper price does not. To gauge the extent of this problem, we construct alternative benchmark forecasts of the nominal spot rate based on the current spot rate, but adjusted for the inflation expected over the forecast horizon. For expected inflation, we use either a (generous) perfect foresight assumption or simply the average rate of actual inflation over the entire sample period. Table 2 shows that Theil’s U ratios are barely affected by considering these alternative benchmarks. Such a result is not surprising, given the low rate of inflation within the evaluation period.

106. Given the forecasting success of futures prices relative to random walk benchmarks, it is worth asking whether the AR(1) model analyzed earlier could do as well, for forecasts of the same horizon and in the same evaluation period. To find out, we re estimate the AR(1) using monthly real copper price data from the IFS, beginning in January 1957, and then use the results to generate a 27-month ahead forecast of the real copper price.49 It turns out that the AR(1) does not do well at this horizon. Whereas the futures-based forecasts had achieved a 30 percent reduction in RMSE relative to a random walk, in the same evaluation period the AR(1) does worse than a random walk, with a Theil’s U ratio of 1.11 (RMSEs of 31.5 and 28.3, respectively.)

107. To summarize the main points of this section, we found that very simple forecasts, based only on past copper prices, have some success at forecasting copper prices at long horizons—indeed, the longer the horizon, the better the relative performance. We interpret this as evidence that temporary but long-lasting shocks are an important part of the story. Futures prices are found to have predictive power, outperforming a random walk at a horizon of 2¼ years. Since futures prices are not available for horizons longer than 2¼ years, we explore in the next section whether these data might nevertheless be used to infer market beliefs about where copper prices are heading over longer horizons.

108. Before proceeding, however, we note some further results on the accuracy of forecasts based directly on copper futures prices. Above, we evaluated such forecasts only in terms of the size of their errors, relative to those of a random walk benchmark, since our aim was to learn whether futures prices had some predictive power. The positive results found, of course, do not necessarily mean that such forecasts are highly accurate, nor that they are the best forecasts available, nor that they are efficient in the statistical sense. In a further analysis, we also conducted tests related to several other standard forecast evaluation criteria. The following results refer to a data set, obtained from Professor Christopher Gilbert, of LME spot and 3-month futures prices, spanning more than 25 years: 50

D. Copper Futures Prices: What Is the Market Telling Us?

109. Two considerations motivate our further investigation of futures prices here. One is that they have some predictive power, as shown in the last section, at least over a horizon of about two years. Second, from an operational perspective, using readily observed futures prices might be an easy—and transparent—way of generating and updating frequently forecasts needed for policy purposes. Of course, a particular time-series model could be selected and then used repeatedly to provide forecasts on an ongoing and transparent basis. However, futures prices should provide a much richer base than mechanically utilizing past copper price movements, in principle, synthesizing all information available to markets, and in particular being quicker to respond to structural breaks or other permanent shocks.

110. We are interested in two questions: (i) do futures prices behave in a way that supports the underlying premise of the Chilean structural balance’s copper revenue adjustment, and that could be useful in that context? and (ii) if so, is it possible to make inferences useful for policy purposes?

111. Regarding (i), the question is whether futures prices suggest that the market believes that there is an important temporary component to spot copper prices and that it can identify temporary fluctuations as they occur (not merely ex post). Here, an “important” temporary component means not only that temporary fluctuations are of an economically interesting magnitude, but also that such fluctuations are large in relation to any permanent movements that are likely to occur (that is, over the medium-term horizon of policy interest). Put another way, does the market have a fairly stable view of where copper prices will be over the medium term? Regarding (ii), the objective is to infer market beliefs about the duration of a “typical” temporary price shock, and about the level (if any) to which spot prices are expected to converge over the medium term.

112. We examine the behavior of forward prices for 27-month contracts, the longest for which data are available.52 Importantly, the analysis does not need to presume that temporary shocks will have completely, or even mostly, dissipated over a horizon of only 27 months, only that the process of decay will have begun.

113. Figure 6 provides a first look at the data, a time series plot of almost nine years of daily LME data for both spot and 27-month prices, from July 1993 to March 2002. From this perspective, futures prices seem to move closely with spot prices; it is not obvious that futures prices might point to a stable view of where spot prices will be in the years ahead.

Figure 6.
Figure 6.

LME Copper Spot Prices and 27-Month Futures Prices.

(July 1993 - March 2002)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: London Metals Exchange; and IMF staff estimates.

114. A closer look, however, shows that futures prices have not merely followed spot prices, but in fact have differed from spot prices in a systematic manner. The bottom panel of Figure 6 presents the same data, but this time with the futures price plotted against the spot. While the level of the futures price is strongly positively correlated with the spot price, this pattern could simply mean that the 27 month horizon is not long enough to include the expected complete decay of temporary shocks. Indeed, the relationship suggested by this chart has a slope clearly much less than one, suggesting expectations of such decay. Note also that on virtually every day when the nominal spot price was below about 80 (higher than about 90) U.S. cents/lb., the futures price was higher (lower) than the spot price.

115. Inspired by Figure 6, we set out to study the relationship between future and spot prices more carefully, using regression analysis. For this, the basic model we analyze, along with a number of variants, is the following:

(1)In(f27t)In(st)=a+BIn(st/USWPIt)+et

where t refers to monthly observations (LME data for the third Wednesday of each month) for the period July 1993 to March 2002.

116. Here, we interpret In (f27) - In (s), the log difference of the 27-month future and spot prices, as a measure of the expected average rate of change of the spot price over the coming 2¼ years.53 This variable we regress on a constant and the log of the current real spot price. The idea is that the market’s view of an “equilibrium” or steady-state price—if any—would be conceived in real terms. As is conventional in analyses of copper prices, we measure the real price by deflating by the US WPI.54 (Performing this deflation makes little difference to the results, since the cumulative increase in the US WPI over these nine years was minimal. For this reason, we do not concern ourselves with inflation that might be expected over the 2¼-year horizons of the futures contracts, and that in principle would call for an adjustment for expected inflation on the LHS of eq. (1).)

117. Taking the log of the real spot price reduces the heteroskedasticity in the sample (readily apparent in the raw data in Figure 6) and reflects our hypothesis that the speed of adjustment to real copper price shocks will be greater in response to positive shocks than to negative ones. To further explore this possibility, we also estimate a variant of eq. (1) that allows for a possible “kink” in the estimated relationship. In particular, by adding a spline term, we can estimate separately the coefficients Blow and Bhigh, which apply when the real spot price is below and above, respectively, a threshold of 85 U.S. cents/lb. (a value suggested by Figure 6).

118. We consider the absolute value of the estimated coefficient B as an indicator of the expected speed of adjustment, or rate of decay, of temporary copper price shocks. Assuming a constant rate of decay, the estimated half life of such shocks is ln(0.5)/ln(1+B)-2.25 years. In addition, solving the estimated equation for a steady-state real copper price—at which the difference between the future and spot price would be zero—may provide an indication of market beliefs about an “equilibrium” copper price (-a/B, in log terms). In this way, we hope to use the 2¼ year futures data to infer beliefs about copper prices over a horizon longer than 2¼ years.

119. The error term in eq. (1) likely represents such factors as mismeasurement of the conceptualized variables, as well as misspecification of the adjustment process. For example, our treatments of nonlinearities may not be adequate; moreover, even if individual shocks were each expected to decay at a constant rate, that rate might plausibly be expected to vary with different types of shocks.55 We must, therefore, interpret the estimated B as some kind of average adjustment speed expected for shocks during the sample period. A more serious concern is that some shocks during the period may not have been expected to decay at all. A positive (negative) permanent shock can be thought of as shifting the simple bivariate relationship in eq. (1) “upward” (“downward”). Our hope is that any such shifts during the sample period were small; more on this shortly.

120. Table 3 presents regression results for eq. (1) and a number of variants. The top half of the table shows results with t-statistics based on Newey-West standard errors, the bottom half repeats the exercise but with estimation that includes a first-order autoregressive error process.56 We highlight the following points:

121. However, even if markets viewed most copper price shocks as temporary, further analysis suggests that the market view of an equilibrium real copper price did not remain perfectly stable over the sample period. As a simple robustness check, we added a time trend regressor to the eq. (1) specification, as well as to the nonlinear (spline) specification. As seen in Table 3 (rows d, e, i, and j), this change does not upset the basic finding that B is negative and statistically significant by a wide margin. However, the time trend regressor is always statistically significant (and negative, in our sample period). Moreover, a visual inspection of the regression errors from eq. (1) suggested some “structural breaks” within the sample period. Indeed, dummies added for the periods July 1993-October 1994 and June 2000-March 2002 also turned out to be statistically significant (results not shown).57 It seems therefore that regressions of eq. (1) may not be able to provide a precise estimate of a stable equilibrium price. Put another way, in forecasting the price of copper, the most recent observations of futures prices deserve to be given more weight than past observations.

Table 3

LME Future-Spot Regression Results

July 1993-March 2002, 105 Monthly observations, 3rd Wednesday of each month

(t-statistics in parentheses)

article image
IMF staff estimate

E. Summary and Some Implications for Chile

122. In this section, we briefly summarize the findings of the chapter, emphasizing the points most relevant for Chile. We go on to consider their possible implications for Chile, focusing on the government’s structural balance target and its adjustment for copper price fluctuations.

Summary and interpretation of results

123. We consider that our findings tend to support the basic validity of the copper adjustment in Chile’s structural balance target, and the more general idea that full and immediate economic adjustment to all copper price shocks is not necessary. Most importantly, the evidence suggests the following about copper prices: the absence of a strong drift or trend; large temporary shocks; and even that most shocks may be temporary. These last two points are supported by our finding that simple forecasting models—using only information from past copper prices—have predictive power especially over long horizons, as well as by Engel and Valdes’ variance ratio analysis. We find also that futures market prices behave as if market participants believe that most copper price fluctuations are temporary (and our finding that futures prices have predictive power suggests that such market beliefs are worth taking seriously).

124. But some cautionary points hold as well. That a strong downward trend in copper prices has not been observed in the past does not mean that such a trend could not start tomorrow (or even have begun already). Moreover, even if no such trend were to develop, there is no reason to rule out the possibility that a significant one-time, permanent shock could occur (or already have occurred recently). For policymaking purposes, the problem is to detect and distinguish any such shock quickly, in the midst of the usual large temporary shocks. Making the task more difficult is the likelihood that temporary copper price shocks are quite long-lived on average, and probably also variable in length. Under such circumstances, techniques using only the time-series of past copper prices will not be up to the job, so it is natural to turn to industry experts with wide-ranging knowledge of copper market fundamentals.

125. Unfortunately, expert forecasts of medium- and long-term copper prices are difficult to systematically evaluate for accuracy, so a certain amount of faith is necessary in choosing to believe one particular expert view. One approach would attempt to utilize the expertise embodied in the market’s determination of futures prices. Though this approach has its problems, the finding that futures prices have some forecasting power suggests that further work on utilizing such prices could be worthwhile.

126. How then can policy decisions be made under such uncertainty? In the case of fiscal policy, the Chilean authorities have recently established a structural balance target that includes an adjustment for copper price fluctuations. Several aspects of its design can be seen as pragmatic ways to cope with the above-mentioned types of uncertainty. In particular, the reference price has been defined not as “the” long-run price, but rather as the average price expected over the next ten years. This approach injects a degree of conservatism (that is, in the current environment of historically low prices and expectations of eventual price recovery). Moreover, since the reference price will be updated annually by a committee of experts, there will be a regular opportunity to revise and correct over time (e.g., if a permanent shock were at first incorrectly identified as being temporary). Note also that the delegation of the question to a committee allows the government to avoid having to subjectively choose among competing forecasts (the reference price is based on the mean forecasts of the individual committee members) and to avoid the loss of regime credibility that might occur if it instead chose the reference price according to its own discretion.

Chile’s structural balance rule: some illustrative simulations58

127. Inevitably, there will be considerable uncertainty not only over the level (if any) to which copper prices are converging, but also over the time needed to reach that level. We seek to put these two sources of uncertainty in quantitative perspective with some illustrative simulations, taking account of the relative size of copper in the Chilean economy, as well as key aspects of the government’s overall fiscal position.

128. For all the simulations, we take 70 U.S. cents per pound (1999 prices) as the initial value, which is close to where actual prices have been in recent years, including in both 1999 and 2001. Since this level is historically low, it may illustrate the implications of an atypically large price shock. From this base, we consider six alternative price recovery scenarios, as follows:

129. Thus, these simulations assume no trend, only a smooth adjustment (in the absence of further shocks) back to a stable equilibrium or steady-state level.

130. Figure 7 shows the implications of these six scenarios, plotting the paths of the simulated copper spot price (in the two left panels). The implied copper “reference price” is also shown, in the two right panels. In practice, a commission each year will meet to determine/update the reference price as the average price expected for the coming ten years; for these simulations, we simply calculate the reference price as the average of the simulated prices for the next ten years. Note that this reference price changes over time, even in the absence of any new shocks.

131. As intended, the six spot price paths in Figure 7 illustrate a considerable diversity of outcomes. The wide range of adjustment speeds selected plays its role, but over time, of course, what matters most is the level to which the price converges. Turning to the six associated reference price paths, one can get a sense of the degree of conservatism implied by defining the reference price as the one-ten year ahead average (i.e., instead of the steady-state level). Of course, the reference price, at all horizons, lies between the spot and steady-state price levels, but to which is it closer? The answer depends on the assumed speed of adjustment. For our intermediate case—a half life of four years—the reference price falls just about mid-way between the spot and steady-state levels (at all horizons). For the fast adjustment case, the reference price lies closer to the steady-state; for the slow adjustment case, the reference price lies close to the spot price.60

Figure 7.
Figure 7.

Simulated Spot and Reference Price Paths 1/

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: IMF staff estimates. (see text for explanation.)1 Half-life values refer to the evolution of the logarithm of real copper prices. The simulation results have been converted to (real) U.S. cents per pound.

132. Figure 8 tries to put this range of possibilities into some economic perspective, depicting the associated copper “revenue gap” paths implied by each scenario. The revenue gap represent the copper related adjustment that would be made in each year to the central government’s actual fiscal balance, in order to arrive at the structural balance. We simulate this path by simply taking the difference between the simulated (real) spot and reference prices, then scaling the result—under a number of assumptions—to yield the revenue gap as a percent of Chile’s GDP.61

133. It turns out that the role of different speeds of decay depends on the horizon considered. At three or four years out, the speed of adjustment hardly matters. For shorter horizons, a faster speed actually produces a bigger gap (because the forward-looking reference price jumps ahead more quickly); at longer horizons, a faster adjustment speed is associated with a smaller gap.

Figure 8.
Figure 8.

Copper “Revenue Gap” Simulations

(In percent of GDP)

Citation: IMF Staff Country Reports 2002, 163; 10.5089/9781451807554.002.A003

Sources: IMF staff estimates. (see text for explanation.)

134. The essential point of these simulations is that the copper revenue adjustments depicted are neither terribly large, nor so small as to be of no practical consequence. Nearly all the simulated adjustments are less than 1 percent of Chilean GDP, limiting the extent to which the actual fiscal balance would differ from the government’s structural balance target level of+1 percent of GDP. While other factors need to be taken into consideration (such as the target’s adjustment for the output gap and the central bank deficit not included in the target), copper adjustments of this magnitude do not raise questions of the sustainability of public finances, given the current low level of government debt, the level of the fiscal target, and ongoing economic growth. At the same time, the simulated copper adjustments are not trivial in magnitude. The copper price adjustment does give fiscal policy some important space and time for maneuver, even as the government adheres to a point target for the (structural) fiscal balance.

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30

Prepared by Steve Phillips and Andrew Swiston (WHD). The authors thank especially Professor Christopher Gilbert for his advice and expertise on the copper market and for providing certain data. Helpful comments were also received from participants at a seminar hosted by the Central Bank of Chile, including Esteban Jadresic, AlvaroRojas, and Rodrigo Valdes, and at the IMF from Saul Lizondo, Alessandro Rebucci, Marco Espinosa, and Mauricio Villafuerte.

31

As will be discussed later, Chile’s new structural balance system includes a technical innovation that may be seen as a pragmatic approach to a situation in which the ideal answersto these questions do not hold with certainty. Specifically, the reference price used aims not to capture a notional “long-run” price, but rather the average price expected for the coming ten years.

32

That is, flat over the relevant range of copper quantities, as determined by the position of the demand curve, and holding other things constant, such as production technologies.

33

For the supply side, a rule of thumb is that it takes about eight years for an investment in an entirely new copper mine to enter production, and about four years to significantly expand the capacity of an existing mine. Such lags limit the short-run supply response to upward price developments. As for price declines, fixed and sunk costs limit the supply response by existing mines (and, in some countries, environmental regulations requiring land rehabilitation imply costs of shutting down a mine). Still, some mines do cease production during price downturns; indeed, this has happened within the last few years.

34

One demand factor promoting a positive view of demand developments has been copper’s use in electronic devices. The development of fiber optic cable as a substitute in some uses has been a negative factor. See Vial (1989) for a broader view of both supply and demand determinants.

35

Attempting to fit a time trend, or regressing the changes of the data on a constant, both with and without taking logs of the data, did yield negative signs but none of the estimates were significant (the associated probability values were in the range of about 0.40 to 0.70).

36

By this observation we are not claiming that copper prices were always returning to a stable equilibrium value; the point here is just to document the superficial appearance of large temporary—but long-lived—cycles in copper prices.

37

The skewness measure falls from+1.12 to+0.43 for the logged series. Kurtosis is 3.74 in the original data and 2.55 in the logged data. As regards normality, this is strongly rejected in the original data, but cannot be rejected in the logged data (Jarque-Bera statistic of 3.69, with associated probability value of 0.16).

38

Thus, we are not motivated to apply unit root tests to copper price series. Such tests typically have low power to reject a null hypothesis that in turn is not very interesting (mere presence of a unit root, without reference to its relative contribution to observed price fluctuations).

39

Schwartz (1997), using another methodology, also finds strong mean reversion in copper prices.

40

Note that the number of forecast error observations in each RMSE calculation is always the same, either 32 (for the 1970-2001 evaluation period) or 62 (for the 1940-2001 period). Moving left to right across Table 1, what varies instead is the number of years of past data available to generate the forecast.

41

This difference presumably reflects Engel Valdes’ use of fixed span (35-year) rolling regressions to generate forecasts, whereas we “roll” only the sample’s end date, always using all the past data available—back to 1908—to estimate the equation from which the forecasts are derived. That using more past data tends to generate more accurate forecasts is itself interesting, suggesting that structural breaks or other permanent shocks have not been dominant.

42

Note that at the nine- and ten-year horizons the historical mean even beats the AR(1), by a small margin.

43

We use the modification of the Diebold-Mariano statistic proposed by Harvey, Leybourne, and Newbold (1997). See Table 1 for details.

44

See Harvey, Leybourne, and Newbold (1997) for an investigation of this problem.

45

Taylor (2001) emphasizes this problem in the case of mean reversion tests of the law of one price.

46

This result refers to a different sample period, since we have monthly data only after 1957. But it is the difference in frequency of the data, rather than in the sample period, that accounts for the difference in results: when we re-estimate the AR(1) using annual data for 1957-2001 only, the estimated half life is 4.0 years, quite similar to the 1908-2001 results.

47

We use prices from the 3rd Wednesday of each month. Futures prices are available on daily basis, but we use monthly data to facilitate comparison with forecasts from AR(1) estimated using monthly real copper prices.

48

Regarding statistical significance, the modified D M statistics for the 15-month and 27 month horizons are -2.0 and -1.7, respectively. The former is statistically significant, but the latter is borderline. (The power of these tests to reject the null hypothesis is limited by the shortness of the sample period relative to the forecast horizon.)

49

As before, the AR(1) forecasts are evaluated on an out of sample basis. The AR(1) model is re estimated for each new forecast, rolling the estimation sample’s end-date. For example, the first forecast is obtained by estimating the AR(1) over January 1957-July 1993, then applying the results to the actual real copper price of July 1993 to generate a forecast of the real price in October 1995 (27 months ahead). The final forecast, for the March 2002 price, is based on AR(1) estimates from a January 1957-December 1999 sample.

50

This is the longest data set we could find, allowing an evaluation period consisting of over 100 nonoverlapping three-month forecast horizons. Since we use only quarterly observations from this data set, there is no issue of overlapping observations in the statistical results.

51

Of course, this means that the slope coefficient was also not different from zero, suggesting that three-month futures prices may have little explanatory power (and consistent with our earlier finding that three-month futures do not outperform a random walk).

52

The 27-month contract is not the one most traded. However, with shorter contracts—say three months there is the potential problem that if there is a moving average component to price shocks, this may still be building up, in the short run perhaps outweighing the tendency of temporary shocks to decay.

53

We have also investigated separately regressions for shorter futures contracts, of 15 and 3 months. The estimated slope coefficients from these regressions do vary in the expected direction: i.e., the shorter the horizon, the less negative is the slope.

54

Considering that most copper production occurs outside the United States, one might suppose that if the equilibrium spot price were mainly cost-based, then the spot price series in equation (1) would be better measured by adjusting the nominal US$ spot price instead by the U.S. real exchange rate. Recalling that in a bivariate regression measurement error in the regressor will bias the slope coefficient toward zero, we investigated this possibility empirically, but did not find a stronger relationship. In fact, no relationship was found at all.

55

For example, the price effect of a work stoppage in a major copper producer might be expected to be very short-lived, while a permanent positive demand shock might raise prices temporarily, but for many years, given the long gestation period for expanding mining capacity.

56

Preliminary OLS regressions found strong autocorrelation of the regression errors at the one-month lag, but not at longer lags.

57

With a significant positive dummy at the beginning of the sample period, and a significant negative dummy at its end, the time trend regressor loses its statistical significance and in fact turns positive. We, therefore, would warn against concluding that equilibrium copper prices have been following a deterministic downward trend. It would be fair to say, however, that the signs of the coefficients on the time trend regressor, and on the two time dummies mentioned above, indicate that the statistically significant relationship captured by eq. (1) shifted downward within the sample period, in turn implying lowered perceptions of any equilibrium price.

58

See Phillips (2001) for a broad explanation and analysis of Chile’s structural balance target.

59

Using annual data in natural log form, these half-lives correspond to AR(1) coefficients on the lagged real copper price of 0.758, 0.841, and 0.899, respectively.

60

Specifically, for the case with fastest adjustment, the reference price “gap” (i.e., its deviation from the steady-state level) is about 30 percent of the spot price gap. For the case with the slowest adjustment, the reference price gap is about 60 percent of the spot price gap.

61

In practice, the copper adjustment to the fiscal accounts depends not only on the difference between the spot and reference prices. Other factors include Codelco’s production volume and the real exchange rate. The simulations here assume a constant real exchange rate and that Codelco’s volume grows at the same rate as Chile’s real GDP. This allows us to calculate the gap by simply taking the difference in simulated spot and reference prices (in real 1999 U.S. cents per lb.) and then dividing by a factor of 20 (since in 1999, the difference between the actual price and the reference price was about 20 U.S. cents per lb., while the official measure of Chile’s structural balance included a copper price adjustment of 1 percent of GDP).

Chile: Selected Issues
Author: International Monetary Fund
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    Annual Real Copper Prices

    (1908-2001)

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    Monthly Real Copper Prices

    (January 1957 - March 2002)

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    Relative Accuracy of Alternative Forecasts of Real Copper Price Theil’s U for Horizons of 1-10 years.

    (Evaluation Period: 1970 to 2001)

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    Relative Accuracy of Alternative Forecasts of Real Copper Price Theil’s U for Horizons of 1-10 years.

    (Evaluation Period: 1940 to 2001)

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    Real Copper Prices: AR(1)Estimation Results

    (Samples beginning 1908 and ending 1930 - 2001)

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    LME Copper Spot Prices and 27-Month Futures Prices.

    (July 1993 - March 2002)

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    Simulated Spot and Reference Price Paths 1/

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    Copper “Revenue Gap” Simulations

    (In percent of GDP)