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Market efficiency, spot metals prices and cointegration
Ma.rket efficiency, spot metals prices and cointegration Evidence for the USA, 1964-87
Jonathan D. Jones and Noel D. Uri
This paper investigates the efficiency of three primary metals markets in the USA using both static cointegration and dynamic error correction tests. The spot prices of lead, tin and zinc over the period January 1964 to December 1987 have served as the basis of the analysis. The results show that spot prices for lead and both tin and zinc are cointegrated at the 1% level. This means that these markets are not efficient in the semistrong form sense since causality must run in at least one direction. There is also evidence of a weaker (in a statistical sense) cointegrating relationship between the spot prices for tin and zinc. Jonathan D. Jones is with the US Securities and Exchange Commission, Washinaton. DC 20549. USA. Noel D. Uri is with t?e bS Department of Agriculture, Washington, DC, 20005, USA. The views expressed are those of the authors and do not necessarily represent the policies of the organizations with which they are affiliated. They would like to thank an anonymous referee for useful suggestions. ‘No attempt will be made here to review the literature. Rather for this review the interested reader is referred to eg K. Chu and T. Morrison, ‘World non-oil primary commodity markets: a medium term framework of analysis’, Staff Papers, International Monetary Fund, Vol 33, 1986, pp 139-184; 6. Goss, ‘The forward pricing function of the London Metal Exchange’, Applied Economics, Vol 13, 1981, pp 133continued on p 262
0301-4207/90/040261-08
0
The nature and extent of the primary metals markets’ response to new information about economic conditions (ie the efficiency of the primary metals markets) has been one of the more intensely debated issues among resource economists in recent years.’ Thus, for example, whether the fluctuations in spot metals prices are due in part to efficiently functioning markets or whether these fluctuations are primarily dependent upon other (non-economic) factors has been the topic of several investigations (see eg Chan and Mountain, Slade, Smith, Soladay, Tilton and Vogely and the studies cited therein).’ The issue of the efficiency of the primary metals markets has significant consequences. It has been suggested that the spot prices of primary metals are related to the efficient functioning of the primary metals markets. Thus, the prices of the primary metals should capture all of the information that is available about the future uses of the primary metal of interest and the prices and availability of substitute metals (ie demand considerations should be incorporated) as well as the cost of production and the availability of the metal of interest (ie the supply considerations ought to be reflected) (see eg Morrison and Wattleworth, and Tauchen and Pitts).’ When new information becomes available the primary metals markets will adjust quickly to the new equilibrium levels if they are efficient. If the markets are efficient buyers cannot use available information to generate profits in excess of a normal return on any risk they bear. The fundamental efficient markets model predicts that the returns from buying or selling a specific primary metal depend on buyers’ and sellers’ expectations of such things as the future price of that primary metal and the amount of undiversifiable risk attached to their expectations.4 The efficient markets model makes the additional assumption that buyers and sellers are equally well informed and that their expectations of future metals needs, uses and availability are rational. This being the case, if some news changes these expectations, buyers and sellers are assumed to bid up or down (depending on the
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Market efficiency. spot metal prices and cointegrarion continued from p 261 150; 6. Goss, ‘The semi-strong term efficiency of the London Metal Exchange’, Applied Economics, Vol 15, 1983, pp 681698: M. Hannan and W. Labys, ‘Quantitative analysis of mineral market structure’, a paper presented at the International Commodity Market Modelling Conference, Washington, DC, 1988; D. Hsieh and N. Kulatilaka, ‘Rational expectations and risk premia in forward markets: primary metals at the London Exchange’, The Journal of Finance, Vol 37, 1982, pp 1199-1207; R. MacDonald and M. Taylor, ‘Testing rational expectations and efficiency in the London Metal Market,’ Oxford Bulletin of Economics and Statistics, Vol 50, 1988, pp 41-52; and A. Maizels, ‘A conceptual framework for analysis of primary commodity markets’, World Development, Vol 12, 1984, pp 25-41. ‘M. Chan and D. Mountain, ‘The interactive and causal relationships involving precious metal price movements’, Journal of Business and Economic Statistics, Vol 6, 1988, pp 69-77; M. Slade, ‘Trends in natural-resource commodity prices: an analysis of the time domain’, Journal of Environmental Economics and Management, Vol 9, 1982, pp 122-137; V. Smith, Scarcity and Growth Reconsidered, Johns Hopkins University Press, Baltimore, MD, 1979; J. Soladay, ‘Structural change in the metals industry: a quantitative assessment’, Natural Resources Forum, Vol 12, 1988, pp 315337; and J. Tilton and W. Vogely, ‘Market instability in the metals industries’, Materials and Society, Vol 5, 1981, pp 243-346. 3T. Morrison and M. Wattleworth, The 1984- 1986 Commoditv Recession: An Analysis of the Underking Causes, IMF Working Paper, 1987; and G. Tauchen and M. Pit&, ‘The price variability-volume relationship on speculative markets’, Econometrica, Vol 51, 1983, pp 485-505. 4The efficient markets hypothesis presumes risk aversion on the part of economic agents. Additionally, it assumes that excess returns are rapidly arbitraged away given that transactions costs are low. See E. Fama, ‘Forward rates as predictors of future spot rates’, Journal of Financial Economics, Vol 3. 1976, pp 361-377 for an elaboration of this. 5For example, there is no pattern, or serial correlation, in primary metals prices that individuals could base their buying or selling decisions on. The weak form efficient markets model asserts that any such pattern would be quickly identified and would therefore be eliminated. 60p tit, Ref 1, Goss. ‘00 cit. Ref 1, MacDonald and Tavlor. To date there has been no attempt td reconcile these and other differences. Gilbert (oo tit, Ref 8), however, casts some doubt about the efficacy of the results of Goss. *G. Canarella and S. Pollard, ‘The efficiency of the London Metal Exchange: a test with overlapping and non-overlapping continued on p 263
262
news) the price of the primary metal of concern to a new equilibrium. This process is presumed to occur quickly. It is generally the case that a distinction is made between various types of market efficiency, including weak form, semistrong form, and strong form. A primary metals market is said to be weak form efficient if there is no pattern of past prices that would allow buyers and/or sellers to earn above normal returns on their transactions.” A primary metals market is said to be semistrong form efficient if buyers and/or sellers cannot use publicly available information to realize above normal returns. Finally, a market is strong form efficient if no information (including inside information) can be used to capture above normal returns. Of these, the third is the least tractable, partly because there is little reason to suppose inside information will be discounted in pricing primary metals and also because it is very difficult to test this version of the hypothesis. Weak form efficiency is likewise not very interesting. The information set used in the analysis is limited to solely historical (spot and forward) data on the price series of interest. This being the case, in what follows only semistrong form efficiency will be investigated.
Background The notion that the primary metals markets in general are efficient has been the subject of numerous studies. For example, in looking at monthly spot metals prices on the London Metal Exchange, Goss concludes that the markets for lead, tin, and zinc are not efficient.6 MacDonald and Taylor, on the other hand, using monthly data but a different sample period, conclude that they are.’ In rejecting the efficient markets hypothesis Goss puts forward the suggestion that price movements in metals markets reflect short-run speculative waves of optimism and pessimism that are only weakly tied to forecasts of profit opportunities. Doubt about the efficiency of primary metals markets has been bolstered by several recent studies of the efficient markets model (see eg Canarella and Pollard, Gilbert, and Hall and Taylor).8 The majority of these studies that have looked at the efficiency of the primary metals markets have examined whether forward metals prices are unbiased predictors of future spot prices, instead of testing for market efficiency directly. Thus, for example, Hsieh and Kulatilaka, Gilbert, Goss, and MacDonald and Taylor all use this approach.” The major shortcomings of this approach are that if there is a bias in the forward price then there is no reason for it to be related to the price level and if prices have generally risen over the sample period then one will be implicitly testing for time dependence in the bias. Alternative approaches for investigating market efficiency that do not suffer from the shortcomings associated with using forward metals prices are cointegration tests. (The studies cited above avoid the use of cointegration tests.)“’ A cointegration test is ideally suited for testing the efficient market hypothesis because prices in efficient markets cannot be cointegrated (see below for a definition) because cointegration implies that Granger causality runs in at least one direction. (A complete elaboration on this argument is found in Granger.)” For the analysis in this study, both static cointegration and dynamic error correction tests will be used. When certain conditions hold for the cointegrating residuals (see below) it is possible to draw different
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Marker efficiency, spof metal prices and cointegrarion
continued from p 262 data’, Journal of Banking and Finance, Vol 10, 1986, pp 575-593; C. Gilbert, ‘Testing the efficient markets hypothesis on averaged data’, Applied Economics, Vol 18, 1986, pp 1149-l 166; and S. Hall and M. Taylor, ‘Modelling risk premia in commodity forward prices’, a paper presented at the International Commodity Modelling Conference. Washinaton. DC, 1988. gOp cit,‘Ref 1, Hiieh and Kulatilaka; op tit, Ref 8, Gilbert; op tit, Ref 1, Goss; B. Goss, ‘Rejection of unbiasedness is not rejection of market efficiency’, Applied Economics, Vol 18, 1986, pp 1167-l 178; and op tit, Ref 1, MacDonald and Taylor. ‘OAn exception is the paper by MacDonald and Taylor that uses static cointegration tests: R. MacDonald and M. Taylor, ‘Metals prices, efficiency and cointegration: some evidence from the London Metal Bulletin of Economic ReExchange’, search, Vol 40, 1988, pp 235-239. “C. Granger, ‘Developments in the study of cointegrated economic variables’, Oxford Bulletin of Economics and Statistics, Vol 48, 1986, pp 213-228; and C. Granger, ‘Some recent developments in the concept of causality’, Journal of Econometrics, Vol 39, 1988, pp 199-211. ‘qhere are further implications as well. These, however, will not be explored. The interested reader is referred to M. Aoki, ‘Cointegration error correction, and aggregation in dynamic models’, Oxford Bulletin of Economics and Statistics, Vol 50, 1988, pp 89-95. 13For a further discussion of cointegration and of alternative testing procedures, the interested reader is referred to the excellent collection of papers in the Oxford Bulletin of Economics and Statistics, Vol 38, No 3, 1986. ‘%tock shows that the estimates in relationship (2) will be superconsistent if cointegration holds: J. Stock, ‘Asymptotic properties of least squares estimators of cointegrating vectors’, mimeo, Harvard University, 1984. 15T. Jenkinson, ‘Testing neoclassical theories of labor demand: an application of cointegration techniques’, Oxford Bulletin of Economics and Statistics, Vol 48, 1986, pp 241-251. ‘%ince the error correction term is a function of the levels of the spot prices, lagged values of the other spot price are significant in explaining movements in the spot price that serves as the dependent variable when the lagged error correction term is significant. “Op cit. Ref 11. “C. Granger and A. Weiss, ‘Time series analysis of error-correction models’, in S. Karlin, T. Amemiya and L. Goodman, eds, Studies in Econometrics, Time Series, and Multivariate Statistics, Academic Press, New York, 1983; R. Engle and C. Granger, ‘Co-integration and error correctron: representation, estimation and testing’, Econometrica, Vol 55, 1987, pp 251-276.
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inferences about the existence of cointegration (and hence market efficiency) depending upon which of the test procedures is employed.”
Methodology Semistrong form efficiency imples that not just past metals prices but any information that is publicly available should be uncorrelated with subsequent movements in metals prices. The cointegration tests are convenient analytical tools for making such a determination. Cointegration exists between two non-stationary time series (a non-stationary time series is one whose mean and/or variance change over time and whose covariance between values at two time points of the same distance vary when alternative time points are considered) that are both integrated of the same order, I(d), if there is a linear combination of the two series which is itself stationary. By definition, a variable (eg a metals price) is integrated of order d if a dth difference of the series is stationary. A stationary series is denoted as Z(0). Two spot prices for primary metals, s, and s,,, are cointegrated if the relationship between the two can be written as 2, = SX1- (YSy,
(1)
where z, is I(O) and (Yis the cointegrating constant. The equilibrium error process, z,, represents the deviation of the spot prices for x and )j away from the long-run equilibrium.” One test for cointegration involves ordinary least squares (OLS) estimation of the following static cointegrating regression: SYr
=
a
+
b
s,,
+
u,
(2)
where a and b are coefficients to be estimated and u, is the stochastic term. The null hypothesis of no cointegration is rejected if both b is statistically significant and if u, is Z(O).‘” This test is not very powerful, however, in the event that U, is stationary but highly serially correlated. (See Jenkinson for a discussion of this issue.)15 Error correction models provide a second test for cointegration. This approach models both the short-run dynamics and the long-run equilibrium between variables suggested by economic theory. It is also possible to draw causal inferences on the basis of error correction models. For two spot metals prices that are cointegrated, causality must run in at least one direction since one spot price can be used to help forecast the other.16 (As noted above, Granger discusses the causal implications of cointegration.)*’ According to the Granger representation theorem (Granger and Weiss, Engle and Granger, and Engle and Yoo).” if two spot prices are cointegrated, then there is an error correction model (ECM) of the following form: (1 - L) $1 =
-PI
z,-1
+ A(L)
(1-L)
s,, +
B(L)
(1-L)
s,, + ~1,
(3)
(1 - L) s,, =
-P2
21-l
+
(1-L)
sx,
D(L)
(1-L)
s,,
(4)
C(L)
+
+
U2,
where z,-r = s,(,_r) - (Ys~(,_~), p1 and p2 are non-zero parameters and ul, and u2, are both I(0). The one-sided lag polynomials A(L), B(L), C(L) and D(L) are stable so that the roots of the associated polynomial are outside the unit circle. (A one-sided lag polynomial is defined such that the current value of the variable of interest is solely a function of the past values of that variable plus, perhaps, a constant.) L is the lag 1990
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Market efficiency, spot metal prices and cointegrarion 19Granger (op tit, Ref 11) discusses the possibility of viewing the causal impact of the error correction term as occurring at low frequencies (ie in the long run). For example, p, different from zero would indicate long-run causality from the spot price of x to the spot price of y, while B(L) different from zero would indicate short-run causality. While such an interpretation is attractive, Granger warns that it is unclear whether such a view is justified until analysis similar to that in J. Geweke, ‘Measurement of linear dependence and feedback between time series’, Journal of the American Statistical Association, Vol 77, 1982, pp 304-324, is completed for the error correction test being considered here. Such an effort would explore the frequency decomposition of the error correction term. “In 1987 amost 19% of the zinc that was produced was from zinc-lead ore while approximately 94% of the lead produced was from lead-zinc (- and copper) ore. See Bureau of Mines, Minerals Yearbook: Metals and Minerals, US Government Printing Office, Washington, DC, 1989, for more on the production of lead and zinc (as well as tin). “On the production side, tin and lead-zinc are not related, except incidentally (eg similar equipment is used in the mining operations). On the demand side, tin has very limited substitution possibilities for lead (in solder) and none for zinc. Both tin-lead alloys and tin-zinc alloys, however, are desired for strengthening and reducing friction (in the case of tin-lead) and for electroplating (for tin-zinc). Hence, tin, lead and zinc are complements for some applications (on the demand side). See R. Ross, Metal Materials Specification Handbook, E. and F. N. Sport, London, 1980, for more on the substitutability and complementarity of tin and lead and zinc. ‘This point needs a little more elaboration. Because the efficient markets hypothesis argues that market forces are driving the prices of the various primary metals, factors impacting the primary metals markets can be expected to affect the profitability of buying and selling these metals. Since production considerations are an integral part of each of the markets and since the production of lead and zinc are inexorably intertwined, anything affecting the production of one of the metals (at the mining stage) would be expected to impact the market (eg price) of the other. ‘3For example, the development of the flotation process for the treaiment of complex lead-zinc ores had this effect. See Metals Handbook Committee, Metals Handbook, American Society for Metals, Metals Park, OH, 1975, for more on this example. “‘This issue of market interdependency is elaborated upon in N. Uri, J. Howell, and E. Rifkin, ‘On defining a geographic market’, Awlied Economics, Vol 17, 1985, DD 9599ib. 25American Metal Market, Vol 98, No 108, 1990, pp 9-l 3.
264
operator such that LkW, = W,_,. If two spot primary metals prices are cointegrated. the colfficient on the error correction term, z,_,, must be statistically significant in at least one of the error correction equations (ie Equations (3) and (4)). Causal inferences are based on the statistical significance of p, and p2 and the elements in B(L) and D(L). For example, p, and the elements in B(L) equal to zero support the conclusion that the spot price of x does not Granger cause the spot price of y.19 The foregoing, then, describes the methodology that will be used to investigate whether the primary metals markets are semistrong form efficient. The information sets considered contain past values of p.\- and py and consequently the tests are more general than tests which look solely at a single market. To reduce the problem to manageable proportions only a limited number of primary metals will be considered. These are briefly discussed in what follows.
Primary metals and the data Three primary metals are selected for study - lead, tin, and zinc. These metals are chosen for a couple of reasons. First, a number of previous studies (eg those cited previously) have tested the efficient markets hypothesis for these primary metals although these studies have used data from the London Metal Exchange. (The efficiency of the markets for these metals for the USA will be the focus here.) Second, there are characteristics of the three metals that make their markets interrelated and hence potentially not efficient. For example, the markets for lead and zinc are interrelated on the production (supply) side20 while the market for tin is interrelated with the other two metals on the demand side.‘l Therefore, a priori, the markets for lead and zinc (when compared pairwise) might not be efficient.22 (Note that the previous studies ignore this fact.) Hence, any change in the profitability of lead and zinc due to, eg technological innovations in mining or processing operations, should be reflected in the price of both metals.2” This being the case, the price series for these metals would be cointegrated if such factors are important market considerations and if no other elements have affected one or the other markets independently and obfuscated the effects of production changes or other factors that the metals (lead and zinc) have in common.24 A similar argument holds for tin and lead and zinc on the demand side. For example, the development of new tin-lead and/or tin-zinc alloys will affect the price of each of the metals by shifting the demand for each. An important concern in focusing on lead, tin and zinc bought and sold in the USA is whether the analysis is biased because none of the metals is sold on organized commodity exchanges. That is, an exchange comparable to the London Metal Exchange does not formally operate in the USA. Does the absence of such an exchange necessarily (ie a priori) preclude the metals markets (or the market for any commodity for that matter) from operating efficiently? Clearly not. For example, over the period when tin was suspended from being traded on the London Metal Exchange (March 1986-June 1989) no apparent inefficiencies were encountered. (For a discussion of this, see the 4 June 1990 issue of American Metal Market.)25 Second, information on the spot prices and availability of the metals being considered here is readily available to all potential buyers and sellers through the daily publication of the
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Market efficiency, spot metal prices and cointegration
a Critical values for the ADF test with trend are -3.43 and -3.99 at the 5% and 1% significance levels respectively. Without trend the cribcal values are -2.86 and -3.43 at the 5% and 1% significance levels respectively.
Table 1. ADF unit root tests for differencing:
Lead Tin Zinc
Levels With trend
Without trend
First difference With trend
Without trend
-2.48 -0.59 -2.60
-1.69 -1.31 -1.11
-4.13 -4.81 -4.57
-4.13 -4.65 -4.56
Metal Market. Third, there are many buyers and sellers of the metals of interest. That is, the market is not concentrated. For example, Metal Statistics (published by American Metal Market, Fairchild, New York), lists at least ten large buyers and/or sellers for each of the metals. Hence, in the absence of any collusive agreements among buyers and/or sellers (either tacit or explicit), which nominally seems to be the case, prices should follow the dictates of market forces. These facts in concert suggest that, consistent with investigations found in industrial organization research (see eg Scherer, Uri, and Weiss,26 the characteristics of the primary metals markets under scrutiny are sufficient to permit the markets to operate efficiently. Whether they do, however, is another matter and one which the empirical component of this paper addresses, at least for lead, tin and zinc. The price data for lead, tin and zinc are taken from various issues of Metals Week. The observations are monthly covering the period January 1964 to December 1987 and are expressed in cents per pound. The lead prices are for pig lead (common corroding), New York delivery. The tin prices are for Straits tin in New York, prompt delivery. The zinc prices are for Prime Western zinc in New York. Note that in the empirical analysis to follow, all tests are conducted on untransformed, nominal price data.27
American
Testing for efficient markets
since the DF test is frequently used in applied econometric work and reporting the DF statistic affords the reader an opportunity to compare the two tests (the DF and ADF) in detecting unit roots. In recent work Hall, MacDonald and Murphy, and Nachane et al, among others, employ both to test for stationarity in cointegrating regression residuals: see S. Hall, ‘An application of the Granger and Engle twostep estimation procedure to the United Kingdom wage data’, Oxford Bulletin of Economics and Statistics, Vol48, 1986, pp 229-239; R. MacDonald and P. Murphy, ‘Testing for the long run relationship between nominal interest rates and inflation using cointegration techniques’, Applied Economics, Vol 21, 1989, pp 439-447; and D. Nachane, R. Nadkarni and A. Karnik, ‘Co-integration and causality of the energy-GDP relationship: a cross country study’, Applied Economics, Vol 20, 1988, pp 1511-1531. 3’G. Ljung and G. Box, ‘On a measure of lack of fit in time series models’, Biometrika, Vol66, 1978, pp 297-303. RESOURCES
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Table 1 reports augmented Dickey-Fuller (ADF) tests conducted to investigate for autoregressive unit roots in the three primary metals spot price series. The regressions include a constant and 12 lags of the dependent variable to adjust for higher order autoregressive or mixed ARMA (autoregressive moving average) processes. These were estimated both with and without a time trend. Schwert has shown that the ADF test performs adequately in Monte Carlo comparisons with tests proposed by Phillips, Phillips and Perron2s and others which correct for conditional heteroscedasticity and weak dependence of the cointegrating regression residuals. The test results find that all three spot metals prices are difference stationary and must be differenced only once to induce stationarity. Summary results for the static cointegrating regressions (ie relationship (2)) are presented in Table 2 and Table 3. Provided in Table 3 are the cointegrating regression Durbin-Watson statistics (as proposed by Sargan and Bhargava)29 as well as the t-statistics for both DickeyFuller (DF) and agmented Dickey-Fuller tests for stationarity of the regression residuals.30 The OLS estimates of cointegrating constants, presented in Table 3, are statistically significant and positive. In addition the Ljung-Box modified Q-statistic (Ljung and Box)~~ for each regression (presented in Table 3) is very large with marginal significance levels less than 0.001% in each case. (The same result was obtained when Gnger lag lengths (of 24 and 36) of the dependent variable were considered.) 1990
265
Market
efficiency,
spot metal prices and coimegration Table 2. Static cointegrating
’ Critical for the CRDW statistic are 0.386 and 0.511 at the 5% and 1% levels respectively. (The critical values are taken from R. Engle and C. Granger, ‘Co-integration and error correction: representation, estimation and testing’, Econometrica, Vol 55, 1987, p 269.)
Table 3. Static cointegrating regressions cointegrating constants and the Ljung-Box modified O-statisGcs.-
Regression
Cointegrating
Tin on zinc
0.0297 (2.1423) 11.0304 (2.0103) 0.0355 (2.9845) i7.051 i (2.7658) 2.1645 (3.0124) 0.3616 (2.9770)
Zinc on tin Tin on lead Lead on tin Lead on zinc Zinc on lead
Ljung-Box O-statistic 45.31 56.22 46.38 52.97 50.04 59.56
BThe absolute
values of the associated tstatistics of the cointegrating constants are given in parentheses below the estimates. The Q-
statistics are computed based on 48 degrees of freedom.
320p 330p
tit, Ref 10. tit, Ref 15.
34These values are computed from the expression for the CRDW statistic given as CRDW = 2 (1 -p). This is solved for p. 350p tit, Ref 29. 36Note that the E, are assumed to be identically and independently distributed with a mean of zero and a finite variance.
regressions - Dickey-Fuller
tests.*
Regression
CRDW value
DF test
ADF test
0.037 0.036 0.053 0.066 0.036 0.021
-1.07 -0.69 -1.10 -1.03 -1.35 -1.40
-1.25 -1.15 -1 45 -2.06 -2.45 -1.96
The relatively small values for the CRDW statistic as well as the low DF t-statistics indicate a lack of cointegrating relationships between the spot prices for lead, tin and zinc. These results are consistent with those of MacDonald and Taylor for lead, tin and zinc price data from the London Metal Exchange.32 Therefore, based on the results of the static cointegration tests, we conclude that the markets for lead, tin and zinc in the USA are semistrong form efficient. That is, it is not possible to use information concerning tin and zinc, for example, to improve the returns associated with buying or selling lead. A closer examination, however, of the results (in Table 3) from the static cointegration tests lead us to be concerned with the relatively large computed Q-statistics. These values suggest the possibility that the inability to reject the null hypothesis of no cointegration may be due to the low power of the test because of autocorrelated residuals. Jenkinson notes the low power of the CRDW test as well as of both the DF and ADF tests when the residuals in static cointegrating regressions display stationarity by exhibiting an autoregressive pattern. For example, the values of the CRDW statistic in Table 2 imply a first order autoregressive coefficient that is very close but not equal to one in each of the cointegrating regressions. These values range from 0.967 to 0.985 and show the autoregressive nature of the residuals.j4 Sargan and Bhargava” find that the power of the CRDW test for random walk behaviour (the null hypothesis) against the alternative hypothesis that u, = PU,-~ + E, becomes very low as p approaches one.‘761As an alternative to the cointegrating regression, Jenkinson suggests using an error correction models to test for cointegration in the presence of autoregressive residuals. This is done in what follows. Table 4, Table 5 and Table 6 present the final, restricted error correction models for lead, tin and zinc. Both error correction equations for each pairwise relationship are estimated in order to draw correct inferences regarding cointegration. Included in the tables are OLS parameter estimates with absolute values for the associated t-statistics in
(1 -L)
lead, =
0.022 constant + 0.478 (1-L) (8.380) (0.025) + 0.179 (3.03)
266
Dickey-Fuller
Tin on zinc Zinc on tin Tin on lead Lead on tin Lead on zinc Zinc on lead
Table 4. Final restricted joint ECM representations
a The values in parentheses beneath the coefficient estimates are absolute values of the associated t-statistics. SEE denotes the standard error of the regression. Q is the computed Ljung-Box modified Q-statistic with the number of degrees of freedom in parenthesis. The value in brackets, [ 1, is the marginal level of significance of the Q-statistic. L is the lag operator where L* W, = IJV_~. Lead and tin denote the price series for lead and tin respectively. See the text for a discussion of the data. EC is the error correction term.
and augmented
(1-L)
+ 0.008 (I-L) (1.983)
- lead and tin.’
lead,_, + 0.119 (1-L) (2.061)
lead,_,
lead,. B + 0.001 (1-L) tin,_, + 0.005 (1-L) tin,_* (1.110) (0.190) tin,_. - 0.007 (1 -L) m- ,o + 0.006 (1 -L) tin,_, (1.452) (1.575)
,
- 0.042 EC, _ , (2.768) SEE = 1.46 (1 -L)
tin, =
SEE = 19.13
Q (48) = 46.71 [OS21 0.629 constant + 0.275 (1 -L) tin, _ , + 0.094 (1 -L) tin,_ 2 (4.749) (1.630) (0.544) - 0.028 EC,_, - 0.202 (1 -L) tin, 6 - 1.080 (1-L) lead,_,, (3.011) (3.594) (1.377) Q (48) = 59.68 [0.12]
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Market efficiency, spar metal prices and cointegration Table 5. Final restricted joint ECM representations (1 -L)
fin, =
0.122 constant + 0.310 (1-L) (5.522) (0.101) + 0.102 (1-L) (0.999)
fJfl,_l
+ 2.694 (l-L)zinc,_3 (3.249) a The values in parentheses beneath the coefficient estimates are absolute values of the associated t-statistics. SEE denotes the standard error of the regression. Q is the computed Ljung-Box modified Q-statistic with the number of degrees of freedom in parenthesis. The value in brackets, [ 1, is the marginal level of significance of the O-statistic. L is the lag operator where L*W, = W,_,. Lead and tin denote the price series for lead and tin respectively. See the text for a discussion of the data. EC is the error correction term.
370p tit, Ref 18. 3BNote that it would be tempting to use data based criteria like the Akaike Information Criterion (AK) (A. Akaike, ‘A new look at statistical model identification’, IEEE Transactions on Automatic Control, Vol 19, 1974, pp 71 S-723) for selecting the model specification. Such a procedure, however, is likely to result in reduced power of the test. See op tit, Ref 18, Engle and Granger for a discussion of this. 39R. Engle and B. Yoo, ‘Forecasting and testing in co-integrated systems’, Journal of Econometrics, Vol 35, 1987, pp 143160. 40A one-tailed test appears appropriate since the error correction term must be negative (and not of indeterminate sign) for a cointegrating relationship to hold.
- 2.030 zinc, _, 0 (1.965)
tin,_,
0.230 (1-L) (4.024)
-
- tin and zinc.’
Q (48) = 49.79 [0.40]
(1 -L) zinc, =
0.056 constant (0.944)
3.551 (1-L)zinc,_. (2.783)
+ 4.294 (1 -L) (3.723)
z,nc,
5
0.107 (1 -L) .r~lc,_~ (1.932)
tin,_, -
+ 0.004 (1-L) (1.683)
0.011 (I-L) (3.934)
tifl,.a
- 0.014 EC,_, (1.740) SEE = 0.99
Q (48) = 54.64 [0.24]
parentheses, Ljung-Box Q-statistics, and the standard errors of the regressions, SEE. The basic model building strategy delineated by Granger and Weiss and Engle and Granger3’ was followed in deriving the final parsimonious error correction models (ECMs) from the initial overparametrized specifications.“* This procedure involves dropping all insignificant lagged values of both variables and imposing the restrictions implied by the lagged error correction term, EC,_ 1. The initial error correction models were specified so that they included a constant, 12 lags of both differenced dependent and independent variables, and lagged values of the level (ie untransformed values of the prices) of each variable. For all three sets of error correction models estimated, the error correction term is negative. This must be the case for cointegration to hold (see eg Engle and Yoo).~~ The results from using the error correction model specification are completely different from those obtained when the static cointegration regression specification was used. Based on the significance level of the estimated coefficient on the error correction term in the previous period, the spot prices of lead and tin and the spot prices of lead and zinc are shown to be cointegrated at better than the 1% level. The error correction model results also indicate a somewhat weaker, although still statistically identifiable, cointegrating relationship between the spot prices for tin and zinc. (This latter relationship is statistically significant at the 5% level for a one-tailed test.)40 These results suggest that the markets for lead, tin and zinc are not
0.014 constant + 0.423 (1-L) (0.161) (7.699) (1-L)
(0.999)
December
+
+ 0.501 (1 -L) zinc,_, (9.666)
- 0.104 (I-L)~inc,_,~ (1.891)
+ 0.174
POLICY
thm8
0.008 EC, - , (0.912)
SEE = 18.51
(1 -L) lead, =
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tin,_,
tinlme + 0.122 (1-L) (2.178)
Table 6. Final restricted joint ECY representations
a The values in parentheses beneath the coefficient estimates are absolute values of the associated t-statistics. SEE denotes the standard error of the regression. Q is the computed Ljung-Box modified Q-statistic with the number of degrees of freedom in parenthesis. The value in brackets, [ 1, is the marginal level of significance of the Q-statistic. L is the lag operator wehere L” W, = W,_*. Lead and tin denote the price series for lead and tin respectively. See the text for a discussion of the data. EC is the error correction term.
- 0.061 (1-L) (1.060)
(1 -L) zinc, =
lead,_, + 0.078 (1-L)
B - 0.030 EC, (2.742)
zinc,_,
Q (48) = 51.06 [0.33]
- 0.080 constant + 0.474 (1 -L) zinc, ~I (8.685) -0.111 (I-L)zinc,.,,+0.128(1-L)lead,_1 (2.020) (3.111) - 0.094 (1 -L) lead,_, (2.314)
1990
- 0.080 (1-L) (1.027)
~,
(1.331)
SEE = 0.98
lead,_,
(1.412)
tead,_8 + 0.076 (1-L)zinc,.z (0.999)
+ 0.065 (1 -L) zinc, (0.775) SEE = 1.47
- lead and zinc.*
Q (48) = 59.47 IO.121
- 0.077 (1 -L) (2.000)
-
1.333 (1 -L) zinc, 5 (2549) -0.097 (1-L)/ead,_? (2.400) lead,. ,2 - 0.011 EC,_, (1.727)
Market efficiency, spot metal prices and coinregrarion
semistrong form efficient with respect to the information sets used in the analysis, contrary to the implications of the results from the static cointegration tests. Hence, based on the results from the error correction model estimation, it should be possible to use information on the prices (and implicitly any factor affecting the markets) for any two of the metals considered here to enhance the returns associated with buying and selling the third metal.4’ Hence, for example, publicly available information on new uses for one of the metals (eg tin) can be used when making purchase or sale decisions in lead and tin. Additionally, any explicit attempt to control the price of one of the metals (as the International Tin Council tries to do for the international price of tin)” will have an impact on the markets for the other metals. 41Note that because of the way the problem has been formulated, it is not possible to directly infer that other factors besides those explicitly considered are cointegrated with the various primary metals price series. Hence, for example, it is not possible to offer any insights into whether and how speculative waves of optimism might impact the price for these primary metals. 42Note that the International Tin Council financially collapsed in early 1986. Its predecessor was established in mid-l 989 but it not certain yet whether it will be a viable entity. 43Although it is beyond the scope of this study, the findings by MacDonald and Taylor (op cif, Ref 10) that the spot prices for lead, tin, and zinc are not cointegrated could be due to the fact that only static cointegrating regressions were considered in their analysis.
266
Conclusion This paper has investigated the efficiency of three primary metals markets in the USA using both static cointegration and dynamic error correction tests. The spot prices of lead, tin and zinc over the period January 1964 to December 1987 have served as the basis of the analysis. The results show that spot prices for lead and both tin and zinc are cointegrated at the 1% level. This means that these markets are not efficient in the semistrong form sense since causality must run in at least one direction. There is also evidence of a weaker (in a statistical sense) cointegrating relationship between the spot prices for tin and zinc. Finally, this study does highlight the importance of using not just a static cointegration approach to investigating semistrong form market efficiency. Clearly, dynamic tests should become an integral part of any such investigations. This is especially true, as was the case in this study. when the residuals from the cointegration regressions are stationary but highly autoregressive.
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Jonathan D. Jones and Noel D. Uri
This paper investigates the efficiency of three primary metals markets in the USA using both static cointegration and dynamic error correction tests. The spot prices of lead, tin and zinc over the period January 1964 to December 1987 have served as the basis of the analysis. The results show that spot prices for lead and both tin and zinc are cointegrated at the 1% level. This means that these markets are not efficient in the semistrong form sense since causality must run in at least one direction. There is also evidence of a weaker (in a statistical sense) cointegrating relationship between the spot prices for tin and zinc. Jonathan D. Jones is with the US Securities and Exchange Commission, Washinaton. DC 20549. USA. Noel D. Uri is with t?e bS Department of Agriculture, Washington, DC, 20005, USA. The views expressed are those of the authors and do not necessarily represent the policies of the organizations with which they are affiliated. They would like to thank an anonymous referee for useful suggestions. ‘No attempt will be made here to review the literature. Rather for this review the interested reader is referred to eg K. Chu and T. Morrison, ‘World non-oil primary commodity markets: a medium term framework of analysis’, Staff Papers, International Monetary Fund, Vol 33, 1986, pp 139-184; 6. Goss, ‘The forward pricing function of the London Metal Exchange’, Applied Economics, Vol 13, 1981, pp 133continued on p 262
0301-4207/90/040261-08
0
The nature and extent of the primary metals markets’ response to new information about economic conditions (ie the efficiency of the primary metals markets) has been one of the more intensely debated issues among resource economists in recent years.’ Thus, for example, whether the fluctuations in spot metals prices are due in part to efficiently functioning markets or whether these fluctuations are primarily dependent upon other (non-economic) factors has been the topic of several investigations (see eg Chan and Mountain, Slade, Smith, Soladay, Tilton and Vogely and the studies cited therein).’ The issue of the efficiency of the primary metals markets has significant consequences. It has been suggested that the spot prices of primary metals are related to the efficient functioning of the primary metals markets. Thus, the prices of the primary metals should capture all of the information that is available about the future uses of the primary metal of interest and the prices and availability of substitute metals (ie demand considerations should be incorporated) as well as the cost of production and the availability of the metal of interest (ie the supply considerations ought to be reflected) (see eg Morrison and Wattleworth, and Tauchen and Pitts).’ When new information becomes available the primary metals markets will adjust quickly to the new equilibrium levels if they are efficient. If the markets are efficient buyers cannot use available information to generate profits in excess of a normal return on any risk they bear. The fundamental efficient markets model predicts that the returns from buying or selling a specific primary metal depend on buyers’ and sellers’ expectations of such things as the future price of that primary metal and the amount of undiversifiable risk attached to their expectations.4 The efficient markets model makes the additional assumption that buyers and sellers are equally well informed and that their expectations of future metals needs, uses and availability are rational. This being the case, if some news changes these expectations, buyers and sellers are assumed to bid up or down (depending on the
1990 Butterworth-Heinemann
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261
Market efficiency. spot metal prices and cointegrarion continued from p 261 150; 6. Goss, ‘The semi-strong term efficiency of the London Metal Exchange’, Applied Economics, Vol 15, 1983, pp 681698: M. Hannan and W. Labys, ‘Quantitative analysis of mineral market structure’, a paper presented at the International Commodity Market Modelling Conference, Washington, DC, 1988; D. Hsieh and N. Kulatilaka, ‘Rational expectations and risk premia in forward markets: primary metals at the London Exchange’, The Journal of Finance, Vol 37, 1982, pp 1199-1207; R. MacDonald and M. Taylor, ‘Testing rational expectations and efficiency in the London Metal Market,’ Oxford Bulletin of Economics and Statistics, Vol 50, 1988, pp 41-52; and A. Maizels, ‘A conceptual framework for analysis of primary commodity markets’, World Development, Vol 12, 1984, pp 25-41. ‘M. Chan and D. Mountain, ‘The interactive and causal relationships involving precious metal price movements’, Journal of Business and Economic Statistics, Vol 6, 1988, pp 69-77; M. Slade, ‘Trends in natural-resource commodity prices: an analysis of the time domain’, Journal of Environmental Economics and Management, Vol 9, 1982, pp 122-137; V. Smith, Scarcity and Growth Reconsidered, Johns Hopkins University Press, Baltimore, MD, 1979; J. Soladay, ‘Structural change in the metals industry: a quantitative assessment’, Natural Resources Forum, Vol 12, 1988, pp 315337; and J. Tilton and W. Vogely, ‘Market instability in the metals industries’, Materials and Society, Vol 5, 1981, pp 243-346. 3T. Morrison and M. Wattleworth, The 1984- 1986 Commoditv Recession: An Analysis of the Underking Causes, IMF Working Paper, 1987; and G. Tauchen and M. Pit&, ‘The price variability-volume relationship on speculative markets’, Econometrica, Vol 51, 1983, pp 485-505. 4The efficient markets hypothesis presumes risk aversion on the part of economic agents. Additionally, it assumes that excess returns are rapidly arbitraged away given that transactions costs are low. See E. Fama, ‘Forward rates as predictors of future spot rates’, Journal of Financial Economics, Vol 3. 1976, pp 361-377 for an elaboration of this. 5For example, there is no pattern, or serial correlation, in primary metals prices that individuals could base their buying or selling decisions on. The weak form efficient markets model asserts that any such pattern would be quickly identified and would therefore be eliminated. 60p tit, Ref 1, Goss. ‘00 cit. Ref 1, MacDonald and Tavlor. To date there has been no attempt td reconcile these and other differences. Gilbert (oo tit, Ref 8), however, casts some doubt about the efficacy of the results of Goss. *G. Canarella and S. Pollard, ‘The efficiency of the London Metal Exchange: a test with overlapping and non-overlapping continued on p 263
262
news) the price of the primary metal of concern to a new equilibrium. This process is presumed to occur quickly. It is generally the case that a distinction is made between various types of market efficiency, including weak form, semistrong form, and strong form. A primary metals market is said to be weak form efficient if there is no pattern of past prices that would allow buyers and/or sellers to earn above normal returns on their transactions.” A primary metals market is said to be semistrong form efficient if buyers and/or sellers cannot use publicly available information to realize above normal returns. Finally, a market is strong form efficient if no information (including inside information) can be used to capture above normal returns. Of these, the third is the least tractable, partly because there is little reason to suppose inside information will be discounted in pricing primary metals and also because it is very difficult to test this version of the hypothesis. Weak form efficiency is likewise not very interesting. The information set used in the analysis is limited to solely historical (spot and forward) data on the price series of interest. This being the case, in what follows only semistrong form efficiency will be investigated.
Background The notion that the primary metals markets in general are efficient has been the subject of numerous studies. For example, in looking at monthly spot metals prices on the London Metal Exchange, Goss concludes that the markets for lead, tin, and zinc are not efficient.6 MacDonald and Taylor, on the other hand, using monthly data but a different sample period, conclude that they are.’ In rejecting the efficient markets hypothesis Goss puts forward the suggestion that price movements in metals markets reflect short-run speculative waves of optimism and pessimism that are only weakly tied to forecasts of profit opportunities. Doubt about the efficiency of primary metals markets has been bolstered by several recent studies of the efficient markets model (see eg Canarella and Pollard, Gilbert, and Hall and Taylor).8 The majority of these studies that have looked at the efficiency of the primary metals markets have examined whether forward metals prices are unbiased predictors of future spot prices, instead of testing for market efficiency directly. Thus, for example, Hsieh and Kulatilaka, Gilbert, Goss, and MacDonald and Taylor all use this approach.” The major shortcomings of this approach are that if there is a bias in the forward price then there is no reason for it to be related to the price level and if prices have generally risen over the sample period then one will be implicitly testing for time dependence in the bias. Alternative approaches for investigating market efficiency that do not suffer from the shortcomings associated with using forward metals prices are cointegration tests. (The studies cited above avoid the use of cointegration tests.)“’ A cointegration test is ideally suited for testing the efficient market hypothesis because prices in efficient markets cannot be cointegrated (see below for a definition) because cointegration implies that Granger causality runs in at least one direction. (A complete elaboration on this argument is found in Granger.)” For the analysis in this study, both static cointegration and dynamic error correction tests will be used. When certain conditions hold for the cointegrating residuals (see below) it is possible to draw different
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Marker efficiency, spof metal prices and cointegrarion
continued from p 262 data’, Journal of Banking and Finance, Vol 10, 1986, pp 575-593; C. Gilbert, ‘Testing the efficient markets hypothesis on averaged data’, Applied Economics, Vol 18, 1986, pp 1149-l 166; and S. Hall and M. Taylor, ‘Modelling risk premia in commodity forward prices’, a paper presented at the International Commodity Modelling Conference. Washinaton. DC, 1988. gOp cit,‘Ref 1, Hiieh and Kulatilaka; op tit, Ref 8, Gilbert; op tit, Ref 1, Goss; B. Goss, ‘Rejection of unbiasedness is not rejection of market efficiency’, Applied Economics, Vol 18, 1986, pp 1167-l 178; and op tit, Ref 1, MacDonald and Taylor. ‘OAn exception is the paper by MacDonald and Taylor that uses static cointegration tests: R. MacDonald and M. Taylor, ‘Metals prices, efficiency and cointegration: some evidence from the London Metal Bulletin of Economic ReExchange’, search, Vol 40, 1988, pp 235-239. “C. Granger, ‘Developments in the study of cointegrated economic variables’, Oxford Bulletin of Economics and Statistics, Vol 48, 1986, pp 213-228; and C. Granger, ‘Some recent developments in the concept of causality’, Journal of Econometrics, Vol 39, 1988, pp 199-211. ‘qhere are further implications as well. These, however, will not be explored. The interested reader is referred to M. Aoki, ‘Cointegration error correction, and aggregation in dynamic models’, Oxford Bulletin of Economics and Statistics, Vol 50, 1988, pp 89-95. 13For a further discussion of cointegration and of alternative testing procedures, the interested reader is referred to the excellent collection of papers in the Oxford Bulletin of Economics and Statistics, Vol 38, No 3, 1986. ‘%tock shows that the estimates in relationship (2) will be superconsistent if cointegration holds: J. Stock, ‘Asymptotic properties of least squares estimators of cointegrating vectors’, mimeo, Harvard University, 1984. 15T. Jenkinson, ‘Testing neoclassical theories of labor demand: an application of cointegration techniques’, Oxford Bulletin of Economics and Statistics, Vol 48, 1986, pp 241-251. ‘%ince the error correction term is a function of the levels of the spot prices, lagged values of the other spot price are significant in explaining movements in the spot price that serves as the dependent variable when the lagged error correction term is significant. “Op cit. Ref 11. “C. Granger and A. Weiss, ‘Time series analysis of error-correction models’, in S. Karlin, T. Amemiya and L. Goodman, eds, Studies in Econometrics, Time Series, and Multivariate Statistics, Academic Press, New York, 1983; R. Engle and C. Granger, ‘Co-integration and error correctron: representation, estimation and testing’, Econometrica, Vol 55, 1987, pp 251-276.
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inferences about the existence of cointegration (and hence market efficiency) depending upon which of the test procedures is employed.”
Methodology Semistrong form efficiency imples that not just past metals prices but any information that is publicly available should be uncorrelated with subsequent movements in metals prices. The cointegration tests are convenient analytical tools for making such a determination. Cointegration exists between two non-stationary time series (a non-stationary time series is one whose mean and/or variance change over time and whose covariance between values at two time points of the same distance vary when alternative time points are considered) that are both integrated of the same order, I(d), if there is a linear combination of the two series which is itself stationary. By definition, a variable (eg a metals price) is integrated of order d if a dth difference of the series is stationary. A stationary series is denoted as Z(0). Two spot prices for primary metals, s, and s,,, are cointegrated if the relationship between the two can be written as 2, = SX1- (YSy,
(1)
where z, is I(O) and (Yis the cointegrating constant. The equilibrium error process, z,, represents the deviation of the spot prices for x and )j away from the long-run equilibrium.” One test for cointegration involves ordinary least squares (OLS) estimation of the following static cointegrating regression: SYr
=
a
+
b
s,,
+
u,
(2)
where a and b are coefficients to be estimated and u, is the stochastic term. The null hypothesis of no cointegration is rejected if both b is statistically significant and if u, is Z(O).‘” This test is not very powerful, however, in the event that U, is stationary but highly serially correlated. (See Jenkinson for a discussion of this issue.)15 Error correction models provide a second test for cointegration. This approach models both the short-run dynamics and the long-run equilibrium between variables suggested by economic theory. It is also possible to draw causal inferences on the basis of error correction models. For two spot metals prices that are cointegrated, causality must run in at least one direction since one spot price can be used to help forecast the other.16 (As noted above, Granger discusses the causal implications of cointegration.)*’ According to the Granger representation theorem (Granger and Weiss, Engle and Granger, and Engle and Yoo).” if two spot prices are cointegrated, then there is an error correction model (ECM) of the following form: (1 - L) $1 =
-PI
z,-1
+ A(L)
(1-L)
s,, +
B(L)
(1-L)
s,, + ~1,
(3)
(1 - L) s,, =
-P2
21-l
+
(1-L)
sx,
D(L)
(1-L)
s,,
(4)
C(L)
+
+
U2,
where z,-r = s,(,_r) - (Ys~(,_~), p1 and p2 are non-zero parameters and ul, and u2, are both I(0). The one-sided lag polynomials A(L), B(L), C(L) and D(L) are stable so that the roots of the associated polynomial are outside the unit circle. (A one-sided lag polynomial is defined such that the current value of the variable of interest is solely a function of the past values of that variable plus, perhaps, a constant.) L is the lag 1990
263
Market efficiency, spot metal prices and cointegrarion 19Granger (op tit, Ref 11) discusses the possibility of viewing the causal impact of the error correction term as occurring at low frequencies (ie in the long run). For example, p, different from zero would indicate long-run causality from the spot price of x to the spot price of y, while B(L) different from zero would indicate short-run causality. While such an interpretation is attractive, Granger warns that it is unclear whether such a view is justified until analysis similar to that in J. Geweke, ‘Measurement of linear dependence and feedback between time series’, Journal of the American Statistical Association, Vol 77, 1982, pp 304-324, is completed for the error correction test being considered here. Such an effort would explore the frequency decomposition of the error correction term. “In 1987 amost 19% of the zinc that was produced was from zinc-lead ore while approximately 94% of the lead produced was from lead-zinc (- and copper) ore. See Bureau of Mines, Minerals Yearbook: Metals and Minerals, US Government Printing Office, Washington, DC, 1989, for more on the production of lead and zinc (as well as tin). “On the production side, tin and lead-zinc are not related, except incidentally (eg similar equipment is used in the mining operations). On the demand side, tin has very limited substitution possibilities for lead (in solder) and none for zinc. Both tin-lead alloys and tin-zinc alloys, however, are desired for strengthening and reducing friction (in the case of tin-lead) and for electroplating (for tin-zinc). Hence, tin, lead and zinc are complements for some applications (on the demand side). See R. Ross, Metal Materials Specification Handbook, E. and F. N. Sport, London, 1980, for more on the substitutability and complementarity of tin and lead and zinc. ‘This point needs a little more elaboration. Because the efficient markets hypothesis argues that market forces are driving the prices of the various primary metals, factors impacting the primary metals markets can be expected to affect the profitability of buying and selling these metals. Since production considerations are an integral part of each of the markets and since the production of lead and zinc are inexorably intertwined, anything affecting the production of one of the metals (at the mining stage) would be expected to impact the market (eg price) of the other. ‘3For example, the development of the flotation process for the treaiment of complex lead-zinc ores had this effect. See Metals Handbook Committee, Metals Handbook, American Society for Metals, Metals Park, OH, 1975, for more on this example. “‘This issue of market interdependency is elaborated upon in N. Uri, J. Howell, and E. Rifkin, ‘On defining a geographic market’, Awlied Economics, Vol 17, 1985, DD 9599ib. 25American Metal Market, Vol 98, No 108, 1990, pp 9-l 3.
264
operator such that LkW, = W,_,. If two spot primary metals prices are cointegrated. the colfficient on the error correction term, z,_,, must be statistically significant in at least one of the error correction equations (ie Equations (3) and (4)). Causal inferences are based on the statistical significance of p, and p2 and the elements in B(L) and D(L). For example, p, and the elements in B(L) equal to zero support the conclusion that the spot price of x does not Granger cause the spot price of y.19 The foregoing, then, describes the methodology that will be used to investigate whether the primary metals markets are semistrong form efficient. The information sets considered contain past values of p.\- and py and consequently the tests are more general than tests which look solely at a single market. To reduce the problem to manageable proportions only a limited number of primary metals will be considered. These are briefly discussed in what follows.
Primary metals and the data Three primary metals are selected for study - lead, tin, and zinc. These metals are chosen for a couple of reasons. First, a number of previous studies (eg those cited previously) have tested the efficient markets hypothesis for these primary metals although these studies have used data from the London Metal Exchange. (The efficiency of the markets for these metals for the USA will be the focus here.) Second, there are characteristics of the three metals that make their markets interrelated and hence potentially not efficient. For example, the markets for lead and zinc are interrelated on the production (supply) side20 while the market for tin is interrelated with the other two metals on the demand side.‘l Therefore, a priori, the markets for lead and zinc (when compared pairwise) might not be efficient.22 (Note that the previous studies ignore this fact.) Hence, any change in the profitability of lead and zinc due to, eg technological innovations in mining or processing operations, should be reflected in the price of both metals.2” This being the case, the price series for these metals would be cointegrated if such factors are important market considerations and if no other elements have affected one or the other markets independently and obfuscated the effects of production changes or other factors that the metals (lead and zinc) have in common.24 A similar argument holds for tin and lead and zinc on the demand side. For example, the development of new tin-lead and/or tin-zinc alloys will affect the price of each of the metals by shifting the demand for each. An important concern in focusing on lead, tin and zinc bought and sold in the USA is whether the analysis is biased because none of the metals is sold on organized commodity exchanges. That is, an exchange comparable to the London Metal Exchange does not formally operate in the USA. Does the absence of such an exchange necessarily (ie a priori) preclude the metals markets (or the market for any commodity for that matter) from operating efficiently? Clearly not. For example, over the period when tin was suspended from being traded on the London Metal Exchange (March 1986-June 1989) no apparent inefficiencies were encountered. (For a discussion of this, see the 4 June 1990 issue of American Metal Market.)25 Second, information on the spot prices and availability of the metals being considered here is readily available to all potential buyers and sellers through the daily publication of the
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Market efficiency, spot metal prices and cointegration
a Critical values for the ADF test with trend are -3.43 and -3.99 at the 5% and 1% significance levels respectively. Without trend the cribcal values are -2.86 and -3.43 at the 5% and 1% significance levels respectively.
Table 1. ADF unit root tests for differencing:
Lead Tin Zinc
Levels With trend
Without trend
First difference With trend
Without trend
-2.48 -0.59 -2.60
-1.69 -1.31 -1.11
-4.13 -4.81 -4.57
-4.13 -4.65 -4.56
Metal Market. Third, there are many buyers and sellers of the metals of interest. That is, the market is not concentrated. For example, Metal Statistics (published by American Metal Market, Fairchild, New York), lists at least ten large buyers and/or sellers for each of the metals. Hence, in the absence of any collusive agreements among buyers and/or sellers (either tacit or explicit), which nominally seems to be the case, prices should follow the dictates of market forces. These facts in concert suggest that, consistent with investigations found in industrial organization research (see eg Scherer, Uri, and Weiss,26 the characteristics of the primary metals markets under scrutiny are sufficient to permit the markets to operate efficiently. Whether they do, however, is another matter and one which the empirical component of this paper addresses, at least for lead, tin and zinc. The price data for lead, tin and zinc are taken from various issues of Metals Week. The observations are monthly covering the period January 1964 to December 1987 and are expressed in cents per pound. The lead prices are for pig lead (common corroding), New York delivery. The tin prices are for Straits tin in New York, prompt delivery. The zinc prices are for Prime Western zinc in New York. Note that in the empirical analysis to follow, all tests are conducted on untransformed, nominal price data.27
American
Testing for efficient markets
since the DF test is frequently used in applied econometric work and reporting the DF statistic affords the reader an opportunity to compare the two tests (the DF and ADF) in detecting unit roots. In recent work Hall, MacDonald and Murphy, and Nachane et al, among others, employ both to test for stationarity in cointegrating regression residuals: see S. Hall, ‘An application of the Granger and Engle twostep estimation procedure to the United Kingdom wage data’, Oxford Bulletin of Economics and Statistics, Vol48, 1986, pp 229-239; R. MacDonald and P. Murphy, ‘Testing for the long run relationship between nominal interest rates and inflation using cointegration techniques’, Applied Economics, Vol 21, 1989, pp 439-447; and D. Nachane, R. Nadkarni and A. Karnik, ‘Co-integration and causality of the energy-GDP relationship: a cross country study’, Applied Economics, Vol 20, 1988, pp 1511-1531. 3’G. Ljung and G. Box, ‘On a measure of lack of fit in time series models’, Biometrika, Vol66, 1978, pp 297-303. RESOURCES
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Table 1 reports augmented Dickey-Fuller (ADF) tests conducted to investigate for autoregressive unit roots in the three primary metals spot price series. The regressions include a constant and 12 lags of the dependent variable to adjust for higher order autoregressive or mixed ARMA (autoregressive moving average) processes. These were estimated both with and without a time trend. Schwert has shown that the ADF test performs adequately in Monte Carlo comparisons with tests proposed by Phillips, Phillips and Perron2s and others which correct for conditional heteroscedasticity and weak dependence of the cointegrating regression residuals. The test results find that all three spot metals prices are difference stationary and must be differenced only once to induce stationarity. Summary results for the static cointegrating regressions (ie relationship (2)) are presented in Table 2 and Table 3. Provided in Table 3 are the cointegrating regression Durbin-Watson statistics (as proposed by Sargan and Bhargava)29 as well as the t-statistics for both DickeyFuller (DF) and agmented Dickey-Fuller tests for stationarity of the regression residuals.30 The OLS estimates of cointegrating constants, presented in Table 3, are statistically significant and positive. In addition the Ljung-Box modified Q-statistic (Ljung and Box)~~ for each regression (presented in Table 3) is very large with marginal significance levels less than 0.001% in each case. (The same result was obtained when Gnger lag lengths (of 24 and 36) of the dependent variable were considered.) 1990
265
Market
efficiency,
spot metal prices and coimegration Table 2. Static cointegrating
’ Critical for the CRDW statistic are 0.386 and 0.511 at the 5% and 1% levels respectively. (The critical values are taken from R. Engle and C. Granger, ‘Co-integration and error correction: representation, estimation and testing’, Econometrica, Vol 55, 1987, p 269.)
Table 3. Static cointegrating regressions cointegrating constants and the Ljung-Box modified O-statisGcs.-
Regression
Cointegrating
Tin on zinc
0.0297 (2.1423) 11.0304 (2.0103) 0.0355 (2.9845) i7.051 i (2.7658) 2.1645 (3.0124) 0.3616 (2.9770)
Zinc on tin Tin on lead Lead on tin Lead on zinc Zinc on lead
Ljung-Box O-statistic 45.31 56.22 46.38 52.97 50.04 59.56
BThe absolute
values of the associated tstatistics of the cointegrating constants are given in parentheses below the estimates. The Q-
statistics are computed based on 48 degrees of freedom.
320p 330p
tit, Ref 10. tit, Ref 15.
34These values are computed from the expression for the CRDW statistic given as CRDW = 2 (1 -p). This is solved for p. 350p tit, Ref 29. 36Note that the E, are assumed to be identically and independently distributed with a mean of zero and a finite variance.
regressions - Dickey-Fuller
tests.*
Regression
CRDW value
DF test
ADF test
0.037 0.036 0.053 0.066 0.036 0.021
-1.07 -0.69 -1.10 -1.03 -1.35 -1.40
-1.25 -1.15 -1 45 -2.06 -2.45 -1.96
The relatively small values for the CRDW statistic as well as the low DF t-statistics indicate a lack of cointegrating relationships between the spot prices for lead, tin and zinc. These results are consistent with those of MacDonald and Taylor for lead, tin and zinc price data from the London Metal Exchange.32 Therefore, based on the results of the static cointegration tests, we conclude that the markets for lead, tin and zinc in the USA are semistrong form efficient. That is, it is not possible to use information concerning tin and zinc, for example, to improve the returns associated with buying or selling lead. A closer examination, however, of the results (in Table 3) from the static cointegration tests lead us to be concerned with the relatively large computed Q-statistics. These values suggest the possibility that the inability to reject the null hypothesis of no cointegration may be due to the low power of the test because of autocorrelated residuals. Jenkinson notes the low power of the CRDW test as well as of both the DF and ADF tests when the residuals in static cointegrating regressions display stationarity by exhibiting an autoregressive pattern. For example, the values of the CRDW statistic in Table 2 imply a first order autoregressive coefficient that is very close but not equal to one in each of the cointegrating regressions. These values range from 0.967 to 0.985 and show the autoregressive nature of the residuals.j4 Sargan and Bhargava” find that the power of the CRDW test for random walk behaviour (the null hypothesis) against the alternative hypothesis that u, = PU,-~ + E, becomes very low as p approaches one.‘761As an alternative to the cointegrating regression, Jenkinson suggests using an error correction models to test for cointegration in the presence of autoregressive residuals. This is done in what follows. Table 4, Table 5 and Table 6 present the final, restricted error correction models for lead, tin and zinc. Both error correction equations for each pairwise relationship are estimated in order to draw correct inferences regarding cointegration. Included in the tables are OLS parameter estimates with absolute values for the associated t-statistics in
(1 -L)
lead, =
0.022 constant + 0.478 (1-L) (8.380) (0.025) + 0.179 (3.03)
266
Dickey-Fuller
Tin on zinc Zinc on tin Tin on lead Lead on tin Lead on zinc Zinc on lead
Table 4. Final restricted joint ECM representations
a The values in parentheses beneath the coefficient estimates are absolute values of the associated t-statistics. SEE denotes the standard error of the regression. Q is the computed Ljung-Box modified Q-statistic with the number of degrees of freedom in parenthesis. The value in brackets, [ 1, is the marginal level of significance of the Q-statistic. L is the lag operator where L* W, = IJV_~. Lead and tin denote the price series for lead and tin respectively. See the text for a discussion of the data. EC is the error correction term.
and augmented
(1-L)
+ 0.008 (I-L) (1.983)
- lead and tin.’
lead,_, + 0.119 (1-L) (2.061)
lead,_,
lead,. B + 0.001 (1-L) tin,_, + 0.005 (1-L) tin,_* (1.110) (0.190) tin,_. - 0.007 (1 -L) m- ,o + 0.006 (1 -L) tin,_, (1.452) (1.575)
,
- 0.042 EC, _ , (2.768) SEE = 1.46 (1 -L)
tin, =
SEE = 19.13
Q (48) = 46.71 [OS21 0.629 constant + 0.275 (1 -L) tin, _ , + 0.094 (1 -L) tin,_ 2 (4.749) (1.630) (0.544) - 0.028 EC,_, - 0.202 (1 -L) tin, 6 - 1.080 (1-L) lead,_,, (3.011) (3.594) (1.377) Q (48) = 59.68 [0.12]
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December 1990
Market efficiency, spar metal prices and cointegration Table 5. Final restricted joint ECM representations (1 -L)
fin, =
0.122 constant + 0.310 (1-L) (5.522) (0.101) + 0.102 (1-L) (0.999)
fJfl,_l
+ 2.694 (l-L)zinc,_3 (3.249) a The values in parentheses beneath the coefficient estimates are absolute values of the associated t-statistics. SEE denotes the standard error of the regression. Q is the computed Ljung-Box modified Q-statistic with the number of degrees of freedom in parenthesis. The value in brackets, [ 1, is the marginal level of significance of the O-statistic. L is the lag operator where L*W, = W,_,. Lead and tin denote the price series for lead and tin respectively. See the text for a discussion of the data. EC is the error correction term.
370p tit, Ref 18. 3BNote that it would be tempting to use data based criteria like the Akaike Information Criterion (AK) (A. Akaike, ‘A new look at statistical model identification’, IEEE Transactions on Automatic Control, Vol 19, 1974, pp 71 S-723) for selecting the model specification. Such a procedure, however, is likely to result in reduced power of the test. See op tit, Ref 18, Engle and Granger for a discussion of this. 39R. Engle and B. Yoo, ‘Forecasting and testing in co-integrated systems’, Journal of Econometrics, Vol 35, 1987, pp 143160. 40A one-tailed test appears appropriate since the error correction term must be negative (and not of indeterminate sign) for a cointegrating relationship to hold.
- 2.030 zinc, _, 0 (1.965)
tin,_,
0.230 (1-L) (4.024)
-
- tin and zinc.’
Q (48) = 49.79 [0.40]
(1 -L) zinc, =
0.056 constant (0.944)
3.551 (1-L)zinc,_. (2.783)
+ 4.294 (1 -L) (3.723)
z,nc,
5
0.107 (1 -L) .r~lc,_~ (1.932)
tin,_, -
+ 0.004 (1-L) (1.683)
0.011 (I-L) (3.934)
tifl,.a
- 0.014 EC,_, (1.740) SEE = 0.99
Q (48) = 54.64 [0.24]
parentheses, Ljung-Box Q-statistics, and the standard errors of the regressions, SEE. The basic model building strategy delineated by Granger and Weiss and Engle and Granger3’ was followed in deriving the final parsimonious error correction models (ECMs) from the initial overparametrized specifications.“* This procedure involves dropping all insignificant lagged values of both variables and imposing the restrictions implied by the lagged error correction term, EC,_ 1. The initial error correction models were specified so that they included a constant, 12 lags of both differenced dependent and independent variables, and lagged values of the level (ie untransformed values of the prices) of each variable. For all three sets of error correction models estimated, the error correction term is negative. This must be the case for cointegration to hold (see eg Engle and Yoo).~~ The results from using the error correction model specification are completely different from those obtained when the static cointegration regression specification was used. Based on the significance level of the estimated coefficient on the error correction term in the previous period, the spot prices of lead and tin and the spot prices of lead and zinc are shown to be cointegrated at better than the 1% level. The error correction model results also indicate a somewhat weaker, although still statistically identifiable, cointegrating relationship between the spot prices for tin and zinc. (This latter relationship is statistically significant at the 5% level for a one-tailed test.)40 These results suggest that the markets for lead, tin and zinc are not
0.014 constant + 0.423 (1-L) (0.161) (7.699) (1-L)
(0.999)
December
+
+ 0.501 (1 -L) zinc,_, (9.666)
- 0.104 (I-L)~inc,_,~ (1.891)
+ 0.174
POLICY
thm8
0.008 EC, - , (0.912)
SEE = 18.51
(1 -L) lead, =
RESOURCES
tin,_,
tinlme + 0.122 (1-L) (2.178)
Table 6. Final restricted joint ECY representations
a The values in parentheses beneath the coefficient estimates are absolute values of the associated t-statistics. SEE denotes the standard error of the regression. Q is the computed Ljung-Box modified Q-statistic with the number of degrees of freedom in parenthesis. The value in brackets, [ 1, is the marginal level of significance of the Q-statistic. L is the lag operator wehere L” W, = W,_*. Lead and tin denote the price series for lead and tin respectively. See the text for a discussion of the data. EC is the error correction term.
- 0.061 (1-L) (1.060)
(1 -L) zinc, =
lead,_, + 0.078 (1-L)
B - 0.030 EC, (2.742)
zinc,_,
Q (48) = 51.06 [0.33]
- 0.080 constant + 0.474 (1 -L) zinc, ~I (8.685) -0.111 (I-L)zinc,.,,+0.128(1-L)lead,_1 (2.020) (3.111) - 0.094 (1 -L) lead,_, (2.314)
1990
- 0.080 (1-L) (1.027)
~,
(1.331)
SEE = 0.98
lead,_,
(1.412)
tead,_8 + 0.076 (1-L)zinc,.z (0.999)
+ 0.065 (1 -L) zinc, (0.775) SEE = 1.47
- lead and zinc.*
Q (48) = 59.47 IO.121
- 0.077 (1 -L) (2.000)
-
1.333 (1 -L) zinc, 5 (2549) -0.097 (1-L)/ead,_? (2.400) lead,. ,2 - 0.011 EC,_, (1.727)
Market efficiency, spot metal prices and coinregrarion
semistrong form efficient with respect to the information sets used in the analysis, contrary to the implications of the results from the static cointegration tests. Hence, based on the results from the error correction model estimation, it should be possible to use information on the prices (and implicitly any factor affecting the markets) for any two of the metals considered here to enhance the returns associated with buying and selling the third metal.4’ Hence, for example, publicly available information on new uses for one of the metals (eg tin) can be used when making purchase or sale decisions in lead and tin. Additionally, any explicit attempt to control the price of one of the metals (as the International Tin Council tries to do for the international price of tin)” will have an impact on the markets for the other metals. 41Note that because of the way the problem has been formulated, it is not possible to directly infer that other factors besides those explicitly considered are cointegrated with the various primary metals price series. Hence, for example, it is not possible to offer any insights into whether and how speculative waves of optimism might impact the price for these primary metals. 42Note that the International Tin Council financially collapsed in early 1986. Its predecessor was established in mid-l 989 but it not certain yet whether it will be a viable entity. 43Although it is beyond the scope of this study, the findings by MacDonald and Taylor (op cif, Ref 10) that the spot prices for lead, tin, and zinc are not cointegrated could be due to the fact that only static cointegrating regressions were considered in their analysis.
266
Conclusion This paper has investigated the efficiency of three primary metals markets in the USA using both static cointegration and dynamic error correction tests. The spot prices of lead, tin and zinc over the period January 1964 to December 1987 have served as the basis of the analysis. The results show that spot prices for lead and both tin and zinc are cointegrated at the 1% level. This means that these markets are not efficient in the semistrong form sense since causality must run in at least one direction. There is also evidence of a weaker (in a statistical sense) cointegrating relationship between the spot prices for tin and zinc. Finally, this study does highlight the importance of using not just a static cointegration approach to investigating semistrong form market efficiency. Clearly, dynamic tests should become an integral part of any such investigations. This is especially true, as was the case in this study. when the residuals from the cointegration regressions are stationary but highly autoregressive.
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POLICY
December
1990