# Is there a common metals demand curve?

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Resources Policy 28 (2002) 95–104www.elsevier.com/locate/resourpol

Is there a common metals demand curve?

M. Evans∗, Andrew C. LewisMaterials Research Centre, School of Engineering, University of Wales, Singleton Park, Swansea SA2 8PP, Wales, UK

Received 3 September 2002; received in revised form 1 October 2002; accepted 6 June 2003

Abstract

Previous studies have identified a single, stable and strong correlation between the price of metals and their consumption, suchthat low priced metals are always used in large amounts and visa versa. Some have interpreted this as evidence that metals sharea common demand curve so that a single price elasticity of demand exists. This paper reviews and tests this hypothesis against anumber of other possible explanations, including the idea that the relationship is an empirical curiosity. Modifications to the demandcurve were tested by allowing metals to have different intercepts and price elasticities. The results from this analysis suggest thatmetals do not share a common demand curve and that the correlation identified between the price of metals and their level ofconsumption is an empirical curiosity. As such, the singular price elasticities published in past papers should not be used forassessing future rates of metals substitution. 2003 Elsevier Ltd. All rights reserved.

Keywords: Common metals demand; Price elasticity; Over/under pricing

Introduction

The choice of which metal to use in the manufactureof a product is governed to a large extent by the materialproperties of the metal in relation to the application, buta dominant if not overriding factor is the primary metalprice. For example, material costs can account for up to60% of the total production cost of an average passengercar manufactured in the UK (Takechi, 1996; Johnson,1997). Currently, the price of aluminium is up to sixtimes more expensive than steel per tonne and this hashelped the steel industry to protect its market share inthe automotive sector. A switch to aluminium wouldinvolve a considerable reinvestment in new productionlines that have relatively long lives and so it is importantfor automotive companies to have some idea on likelyfuture price movements for competing materials.

Therefore, and over the past 25 years, a variety ofdifferent approaches to the study of metals demand andtheir prices have been used. This paper concentrates onthose approaches that have combined cross-sectional and

∗ Corresponding author. Tel.:+44-1792-295-699; fax:+44-1792-295-244.

E-mail address: [email protected] (M. Evans).

0301-4207/$ - see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0301-4207(03)00026-6

time series data. Such studies have identified an inversecorrelation between a number of metal prices and theirlevel of consumption

Pit � atCbtit (1)

where Pit is the price of metali in year t (in $/tonne)and Cit is the annual world consumption of metali inyear t (in thousands of tonnes).bt is the inverse of theprice elasticity of demand and its value depends uponthe ease with which substitution of one metal by anothermetal can occur. Ifbt is low, this may reflect easy substi-tution, but if bt is high, this may reflect more difficultsubstitution. Further, past studies have found thebt

changes little over time so that this empirical relationshipalso appears to be very stable over time. However, whythere should be such an overall relationship for a widevariety of metals is difficult to understand. This paperreviews a number of possible explanations, including theidea that such metals share a common demand curve andthat the above relationship could simply be an empiricalcuriosity. To ensure that the above overall relationshipfor metals is not inappropriately used for demand andprice forecasting these interpretations need to be for-mally tested. This paper therefore proposes and carriesout a number of tests for the hypothesis of a commonmetals demand curve.

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In order to meet these objectives, the paper is struc-tured as follows. The next section reviews a number ofapproaches to the study of metals demand and theirprices. Emphasis is placed on those studies that haveestimated (1) and a number of different explanations forsuch an overall relationship are given. The followingsection then proposes a number of tests to help differen-tiate between these opposing explanations. This is thenfollowed by a section describing the origins of the dataused in this paper. The results of various tests of thecommon metals demand hypothesis are then given in thepenultimate section. Conclusions are then drawn.

Past approaches to studying metals demand andtheir prices

Time series and other studies

Where data are available, detailed input–output analy-sis has been carried out (Myers, 1986) to identify theinfluence of materials substitution and new technologyon metals demand. When data are less disaggregated,authors such as Tilton (1990), Tilton et al. (1996), Tiltonand Fanyu (1999), Valdes (1990), and Evans (1996)have made use of the intensity of use technique toexplain metals demand in terms of movements in thematerial composition of products and the product com-position of national income. The former of these is inturn related to technological change and material priceswhilst the latter is related to structural changes takingplace within a given economy.

A more common approach to analysing metalsdemand is through the estimation and specification ofeither production functions (Slade, 1981) or demandfunctions. In the latter category, Bozdogan and Hartman(1979) assumed that copper demand was a function ofthe copper price, the price of substitutes (mainlyaluminium) and gross domestic product. In a more recentstudy, Figuerola-Ferretti and Gilbert (2001) modelled,using time series techniques, copper, tin and zinc con-sumption as a function of technological change, changesin industrial production, changes in real prices and pricevolatility. In a study by Labson and Crompton (1993),the intensity of use and demand function approacheswere brought together using the cointegration method-ology.

Cross-section and time series studies

Recently, a number of studies have been carried outthat involve the estimation of demand functions frompanel data sets that contain a combination of time seriesand cross-section date. The first appeared in 1972, whenHughes (1972) identified the following inverse corre-lation between the price, in 1972, of 14 different metals

(aluminium, copper, chrome, gold, iron, lead, niobium,nickel, platinum, silver, tin, titanium, vanadium, andzinc) and their levels of consumption in 1972

ln(Pi) � ln(a) � bln(Ci) (2)

Later, Nutting (1977) supplemented the data ofHughes (1972) with his own for the year 1977 and ident-ified exactly the same relationship. Like Hughes beforehim, the price elasticity of demand for these 14 metalswas estimated to be around 1.5 (i.e. b = 0.66). As antici-pated for a cross-section model of this nature, Nuttingfound that the value for a in 1977 was higher than thatestimated by Hughes reflecting the influence of worldinflation over this period. However, the value of bchanges little between the two years.

Jacobson and Evans (1985) extended this type ofanalysis. They collected data for 16 different commercialmetals (tellurium, antimony, magnesium, lead, zinc, pigiron, aluminium, cadmium, cobalt, copper, gold, mer-cury, nickel, selenium, silver and tin) over a period of20 years—from 1961 to 1980. They found that the firstsix of these metals fell consistently close to a series ofstraight lines given by

ln(Pit) � ln(at) � btln(Cit) (3)

for each of the 20 years. They also found that the slopesof these lines remained virtually constant from year toyear. The mean value for bt was estimated to be �0.357(with a standard error of 0.026). Taking 1980 as an illus-tration, Jacabson and Evans’s estimate of (3) was

ln(Pi) � 5.43(0.10)54.3

� 0.369ln(Ci)(0.017) Standard error21.71 t statistic

R2 = 99.2%.

This relationship between the average price and theannual consumption of metals was further studied byGeorgentalis et al. (1990) over a nine-year period from1975 to 1983 using the same 14 metals that Nutting stud-ied. They also found that the slopes of these linesremained virtually constant from year to year. The meanvalue for bt in (3) was estimated to be �0.698 (with astandard error of 0.092). Their estimate of (3) for1980 was

ln(Pi) � 5.693(0.323)17.63

� 0.714ln(Ci)(0.105) Standard error

6.80 t statistic

R2 = 79.6%, DW = 1.83.

They also found that over this period, the value forln(at) in (3) could be explained using measures of worldinflation and industrial activity

ln(at) � 1.249ln(Pt) � 1.582ln(It)

where Pt was taken to be the wholesale price index forall countries and It, world economic activity. Indeed,

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these two variables accounted for 99.9% of the variationin the estimated values for ln(at). (The authors did notsupply standard errors and t statistics for eachparameter.)

MacAvoy (1988) carried out a study over the period1960–1986 for seven metals (copper, lead, aluminium,zinc, iron, nickel and molybdenum). The price level equ-ation used by MacAvoy took the form

(Pit) � b0i � b1(Pt) � b2(It) � b3(Sit�1) � b4(ERt), (4)

where ER is the exchange rate and S is the metal stocklevel. Such an equation is obtained as the competitiveequilibrium solution to a system of supply anddemand equations.

Interpretations

What stands out from these panel data studies is thatlow priced metals are used in large amounts and highpriced metals are used in small amounts and this inversecorrelation appears to be remarkably stable over time.Indeed, Nutting found it extremely surprising that sucha correlation should hold over five orders of magnitudein relation to price and over eight orders of magnitudein relation to consumption. The observations led him topropose Nutting’s first law—“As the price of a metalincreases relative to other metals by a factor of two, theconsumption decreases relative to other metals by a fac-tor of three” . Such a law implies causation and that met-als have a common price elasticity of demand so thatone interpretation of the above overall relationship is thatall metals have a common demand curve.

This is visualised in Fig. 1 for the simpler case ofthree metals, labelled A–C, in any one year. Each metalhas a different level of supply, but a common demandcurve, giving the three equilibriums that determine theobserved price–consumption pairings for each metal.Note that in this illustration, the world supply or pro-duction of a metal is predetermined by exogenous factors

Fig. 1. A common metals demand curve.

such as mining conditions and the economic consider-ations of previous periods. In such a case, the world mar-ket price adjusts to a predetermined level of metal pro-duction so that price, rather than consumption, is thecorrect dependent variable.

For a common demand curve to exist between metals,all the metals placed on it must be equally good substi-tutes in each of their main end use markets. Georgentaliset al. understood that this in part may be true for theystated “ if gold were as cheap as copper, it would be usedin place of copper” . Even more striking is the case ofaluminium over the last 130 years. Prior to the introduc-tion of the Hall–Heroult process for the production ofaluminium in 1876, aluminium was actually moreexpensive than gold and the corresponding productionof aluminium was less than that of gold (147 tonnes ofgold compared to 1 ton of aluminium in 1870). Nowaluminium is the second most widely used metal and itsprice is just about that to be expected from the substi-tution of the annual consumption in Nutting’s law.

However, and at the theoretical level, it seemsunlikely that all the 14 metals considered by Nutting areequally good substitutes in all their main markets. Con-sider, for example, aluminium. Its main markets arepackaging (30% in 1994), building (17%) and transpor-tation (26%). In all these markets, steel is a very closesubstitute, but titanium is only a close substitute in trans-portation. Apart from copper, that competes with alu-minium in the electronics sector, none of the other 14metals studied by Nutting can be considered as a substi-tute for aluminium. Consider also the example of copper.Its main markets are electrical (22% in 1994), construc-tion (42%) and transport (13%). Whilst aluminium andgold are close substitutes in electrical applications, theyare not for construction, where plastics would be a pre-ferred substitute in plumbing due to weight consider-ations. The main market for gold is jewellery (73% in1994), and here, the close substitutes are platinum andsilver. In the other main markets for gold (electronics at14%), the only close substitutes are tin and nickel. As afinal example, consider lead. In 1994, 84% of lead usewere in batteries with the only close substitutes beingnickel and zinc.

It is clear from the above examples, that whilst somemetals might be easily interchangeable with some othermetals if the price was right, it is not clear, at the theor-etical level, whether the actually substitutional possi-bilities are strong enough to generate a common metalsdemand curve—even for such metals.

Another possible explanation for the stable inverserelationship between metal price and consumption is thatthe value for bt in (1) is an average value of the exponentin year t for each individual metal, that is to say, anoverall index of the ease of substitution within the familyof metals considered. Some support for this view isgiven by the Jacobson and Evans study mentioned

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above, where a value for bt of about 1/3 was found forthe select group of six base metals. This result may rep-resent the lower bound solution.

This average interpretation for bt in (1) can be lookedat from a slightly different perspective, namely that ofa statistical curiosity. This is illustrated in Fig. 2 againfor the simpler case of three metals, labelled A–C, inany one year. Unlike Fig. 1, there is no longer a commonmetals demand curve. Each metal has its own price elas-ticity of demand that is different from the other metals.Each metals supply and demand function determines thethree equilibriums that generate the observed price–con-sumption pairings for each metal. When a best fit lineis then put through the observed price–consumption data,a line similar to the shown mongrel function will beobtained. Such a function is neither a demand nor a sup-ply curve but a mixture of the two—even though it looksfor all the world as if a common demand function hasbeen estimated. Eq. (2) can be interpreted as such a mon-grel function, so that the results of Nutting, Jacobsonand Evans and Georgentalis et al. can be considered asspurious regressions. Indeed, the slope of such a mongrelfunction may well turn out to be the average for all theindividual metal demand functions. Then, if the slopesof the individual demand curves are not too differentfrom the mongrel function, the slope of this latter func-tion may provide a reasonable estimate of substitutionrates for all metals following price changes.

A final interpretation for the observed stable inversecorrelation between metal price and consumption is thatsuch a relationship actually identifies a minimum econ-omic price for metal production at a given level of con-sumption. As briefly described above, Jacobson andEvans estimated (3) using data for six metals (tellurium,antimony, magnesium, lead, zinc, pig iron), which theycalled the base metals. Over time they observed thatthese six metals consistently lay close to such a fittedline with bt = �0.357. They called this the base line.This overriding stability of the base metals they put

Fig. 2. A mongrel function.

down to their common characteristics of being subjectto a steady demand, mainly from long established appli-cations such as in heavy engineering and construction,and the fact that their commercial ores are widely distrib-uted and contain these metals in concentrates between1% and 20%. As such, their extraction presents no realproblems. They suggest that all these factors combine toproduce lacklustre associations and help to encouragetheir stable position in the market. They also explainwhy these metals appear to establish the minimum econ-omic price for metal production at a given level of con-sumption.

As further evidence for this theory they noted that themetals aluminium, cobalt, copper, gold, nickel, silverand tin always had prices above the base line. Theyaccounted for this by showing that all these metals(except aluminium) are obtained from ores with concen-trates well below 1%. The extent to which prices lieabove the base line was therefore attributed to ease orotherwise of extraction. Prices below the base line werethen interpreted as unstable prices which betray majormarket weaknesses.

Empirical tests for differentiating betweencompeting theories

Over- and underpricing

If (3) represents a common metals demand curve, thena metal whose price is above such a common demandcurve can be interpreted as a metal that is overpriced(i.e. supply exceeds demand). Likewise, a metal whoseprice is below the common demand curve could be inter-preted as a metal that is underpriced (i.e. demandexceeds supply over such a time span). However, suchover- or underpricing should not persist for prolongedperiods of time. Eventually, the forces of supply anddemand will ensure that markets equilibriate and soprices should tend towards the common demand curveover time. Unless, of course, (3) is a mongrel curve andeach metal has its own demand curve. Then prices canbe persistently above or below (3) depending upon eachmetals supply and demand conditions.

Thus a simple test for a common demand curve, asopposed to a mongrel function, is to plot the extent ofover- and underpricing over time and observe the tend-ency (or lack there of) for such pricing to dissipate overtime. A tendency for a metals price to be continuouslyabove or below (3) is evidence to indicate that that thereis no common demand curve amongst metals.

Another test for a common metals demand curvewould be to generalise (3) and test the validity of sucha generalisation. For example, the following is a moregeneral specification for (3):

ln(Pit) � ln(ait) � btln(Cit). (5)

99M. Evans, A.C. Lewis / Resources Policy 28 (2002) 95–104

Under this specification, each metal has a commonprice elasticity of demand but each metals demand curvehas a different intercept term. This specification is verysimilar to a model estimated by MacAvoy (1988).Another generalisation for (3) is

ln(Pit) � ln(at) � bitln(Cit) (6)

Under this specification, each metal has a differentprice elasticity of demand but each metals demand curvehas the same intercept term. Combining the above gener-alisations leads to a specification in which each metalhas a different price elasticity and intercept term

ln(Pit) � ln(ait) � bitln(Cit) (7)

The parameters of (5)–(7) can be estimated in a var-iety of ways. If the aim is to make inferences about thepopulation of metals and minerals, then ai and bi shouldbe treated as random variables and the random effectsmodel of Balestra and Nerlove (1966) used. However,in this paper, the authors are interested in making infer-ences about only this set of 14 metals and so ai and bi

are treated as fixed. In such a fixed effects model, esti-mation is carried out by introducing (see Maddala, 2001for the econometric background and MacAvoy, 1988 foran application to seven metals) dummy variables foreach metal. Under any of these generalisations, a test fora common metals demand curve is now straight forward.First the specification given by (5)–(7) must be esti-mated. In this paper, this is done by letting

ln(ait) � a0 � a1ln(Pt) � a2ln(It)

and by assuming that b is fixed over time (as all thereviewed evidence above suggests). Of course, furthergeneralisation is then possible by allowing a1 and a2 tovary by metal but such generalisations are not consideredin this paper.

(5) can now be estimated by applying the least squaresprocedure to

(Pit) � a01 � �q

i � 2

a0iDi � a1lnPt � a2lnIt (8)

� bln Cit

where Di takes on a value of 1 when it refers to metali and zero otherwise. Thus, a0i measure the extent towhich a metals demand curve is shifted up or down rela-tive to the first i = 1 metal, which is taken to be alu-minium in this study. In total, there are q = 14 suchmetals. Similarly, (6) can now be estimated by applyingthe least squares procedure to

(Pit) � a0 � a1lnPt � a2lnIt � b1 lnCit (9)

� bi �q

i � 2

DilnCit

Then, (7) can be estimated by applying the least squaresprocedure to

(Pit) � a01 � a0i �q

i � 2

Di � a1lnPt � a2lnIt

� b1 lnCit � bi �q

i � 2

DilnCit (10)

The Student t statistic associated with each a0i in (8)or the Student t statistic associated with each bi in (9),or the t statistic associated with each a0i and bi in (10)then provides a simple test for a common metalsdemand. Under specification (8), those metals with t stat-istics for a0i below the 5% critical value can be takento have a metals demand curve whose intercept is thesame as that for aluminium. Under specification (9),those metals with t statistics for bi below the 5% criticalvalue can be taken to have a metals demand curve thatis the same as that for aluminium, i.e. such metals havethe same price elasticity of demand as that for alu-minium. Under specification (10) those metals with tstatistics for a0i and t statistics for bi below the 5% criti-cal value can be taken to have a metals demand curvethat is the same as that for aluminium.

Origins of data

The 14 metals used for this study are the same as thoseused by Georgentalis et al. They therefore ranged fromiron, the cheapest, to platinum, the most expensive, giv-ing a wide range of prices and consumption. At theworld level, the annual consumption of a particular metalin year t, Cit, was measured as

Cit � Prodit � �Sit, (11)

where Prodit is the production of metal i in year t and�Sit, the addition to the stock of metal i in year t. Suchconsumption data, measured in metric tonnes, were col-lected for each of the 14 metals over the period 1980–1999 from annual issues of Metals Bulletin, MineralsHandbook and Platinum. However, for iron, no con-sumption data were available and so the production ofiron ore (Fe content) was used instead. Metal prices weremeasured in US dollars per metric ton and were obtainedfrom various issues of International Financial StatisticsYearbook (1980–1989), Metals Bulletin (1980–1989),Minerals Handbook (1980–1989), and Platinum (1980–1989).

World inflation, Pt, was taken to be the wholesaleprice index for all countries as published in variousissues of International Financial Statistics Yearbook andIt, world economic activity, was taken to be the indexfor industrial production (at constant value terms) for theindustrialised nations, again as published in International

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Financial Statistics Yearbook. Both these indices werebased at 1995.

Empirical results

Comparisons with previous results

Fig. 3 contains price and consumption data for the 14metals mentioned above for the year 1999. Also shownis the fit given by (3) to this set of data. The full set ofregression results for this year is

ln(Pi) � 19.9531.68411.84

� 0.855ln(Ci)(0.121) Standard error

7.07 t statistic

R 2 = 80.48%.

It can be seen that after some 16 years since Georgen-talis et al. first published their results, there is still a verystrong inverse correlation between metal price and metalconsumption—with some 80.48% of the variation inmetal prices being explained by variations in metals con-sumption. However, the estimated value for bt appearsto be a little higher than the average value obtained byGeorgentalis et al. Table 1 gives the ln(at) and bt valuesobtained for each of the remaining years from 1980 to1999 (together with their standard errors and R2 values).As can be seen, and in line with other studies in thisarea, they observed very little variation in the value forbt over time and in fact none of the estimated bt valueswere significantly different from each other.

Fig. 4 compares the results shown in Table 1 with thebt estimates made by Georgentalis et al. It can be seenthat for the overlap years 1980–1983, the currentauthors’ estimates for bt are higher than those obtainedby Georgentalis et al. Reasons for this are difficult tofind because the original data used by Georgentalis etal. are no longer available. It is interesting to note thata similar observation was made by Jacobson and Evanswhen comparing their work to that of Nutting. Recallthat for 1977, Nutting estimated bt to be �0.67, butJacobson and Evans found the average value for bt to

Fig. 3. Metal price v. world consumption for 14 metals in 1999.

Table 1Values obtained by the current authors for the parameters ln(at) andbt of (3) for the years 1980–1999

Year ln(at) at R2

1980 20.720 (1.478) –0.908 (0.109) 85.261981 20.216 (1.409) –0.884 (0.104) 85.741982 19.778 (1.421) –0.866 (0.105) 84.891983 19.735 (1.569) –0.863 (0.117) 82.051984 19.643 (1.535) –0.856 (0.113) 82.621985 19.635 (1.542) –0.858 (0.113) 82.661986 19.828 (1.619) –0.872 (0.119) 81.741987 19.832 (1.712) –0.861 (0.126) 79.651988 20.033 (1.731) –0.855 (0.126) 79.241989 19.876 (1.653) –0.838 (0.121) 80.121990 19.715 (1.672) –0.833 (0.122) 79.551991 19.607 (1.680) –0.837 (0.123) 79.471992 19.520 (1.730) –0.834 (0.127) 78.331993 19.527 (1.803) –0.843 (0.132) 77.271994 19.714 (1.809) –0.846 (0.132) 77.401995 20.027 (1.716) –0.853 (0.125) 79.641996 19.945 (1.682) –0.848 (0.122) 80.051997 19.990 (1.653) –0.848 (0.120) 80.761998 20.220 (1.577) –0.870 (0.114) 82.941999 19.953 (1.684) –0.855 (0.121) 80.48

1980–1999 19.876 (1.633) –0.856 (0.120)(mean)

R2 is the coefficient of determination measuring the percentage vari-ation in ln(Pit) explained by variations in ln(Cit). Standard errors areshown in parentheses.

be closer to �0.74 over the period 1961–1980. Havingsaid that, when the two sets of bt values are plottedalongside their respective and approximate 95% confi-dence intervals, as in Fig. 4, it becomes clear that theobserved differences are not statistically significant. Thatis, the confidence intervals for the two separate estimatesof bt over the period 1980–1983 overlap and so there isnot enough evidence to conclude that these two estimatesare actually different.

Results of testing for a common metals demand curveusing over- and underpricing

Fig. 5 shows the extent of over- and underpricingassuming a common metals demand curve. Under suchan assumption, a metal is said to be overpriced when itsprice is consistently in excess of

ln(Pit) � ln(at) � btln(Cit),

and underpriced when it is consistently below such aprice. In Fig. 5, the percentage difference between a met-als actual price and that given by (3) is plotted againsttime. The values for at and bt in (3) that are used forsuch calculations in each year are those shown inTable 1.

If the assumption of a common metals demand curve

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Fig. 4. Values for βt as obtained by Goergentalis et al. for the period 1975–1983 and by present authors for 1980–1999.

Fig. 5. (a) Extent of overpricing for aluminium, copper, iron and gold assuming a common metals demand curve. (b) Extent of overpricing fornickel, zinc, silver and platinum assuming a common metals demand curve. (c) Extent of overpricing for titanium, vanadium, niobium and chromiumassuming a common metals demand curve. (d) Extent of overpricing for tin and lead assuming a common metals demand curve.

is correct, then the prices given by (3) can be interpretedas market clearing prices. Overpricing then correspondsto excess supply and underpricing, excess demand. Fig.5a,c shows that the metals aluminium, copper, iron andgold are all “overpriced” to a considerable extent for thewhole length of the sample, whilst the metals titanium,vanadium, niobium and chromium are “underpriced” toa considerable extent for the whole length of the sample.Fig. 5b shows that the metals nickel, zinc, silver andplatinum also remained “overpriced” during the fulllength of the sample period but to a lesser extent thanthose metals shown in Fig. 5a. Whilst it is believed that

product markets rarely clear instantaneously following achange in demand or supply conditions, it is highlyunlikely that the prices of all the metals shown in Fig.5a,c could remain so far away from market clearing lev-els for such long periods of time. It would thereforeappear that Fig. 5 provides some evidence to suggestthat these metals do not have a common demand curve.Put differently, the prices given by (3) are not marketclearing prices. Tin and lead remained overpriced for thefirst half of the 1980s, but since then have remained mar-ginally underpriced (Fig. 5d).

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Results of testing for a common metals demand curveusing individual demand curves

The first possible generalisation of (3) is to allow eachmetals demand curve to have a different intercept valueas in (8). Table 2 shows the result obtained from estimat-ing (8) using ordinary least squares. Some of the a0i

coefficients were found to be insignificantly differentfrom zero and so a simplification search procedure wasimplemented. Here, the coefficient with the smallestStudent t value was removed and (8) then reestimated.This procedure was continued until all remaining coef-ficients were statistically significant at the 5% signifi-cance level. The results are shown in Table 3. The inter-cept term of the demand curve for aluminium is

a01 � 5.5167,

whilst the intercept term of the demand curve for ironore (i = 7) is

a01 � a07 � 5.5167�2.6619 � 2.8548.

Under this specification, the iron ore demand curve isparallel to the aluminium demand curve but lies signifi-cantly below it. Table 4 shows the estimated demandcurves for the remaining metals. It can be seen from thistable that the demand curves for copper, nickel, gold,silver and platinum lie above that for aluminium, withthe remaining metals having demand curves lying belowthat for aluminium.

The Student t values in Table 2 suggest that only twometals share a common intercept—aluminium and tin(metal i = 1 and i = 5). This may again be an empiricalcuriosity or it may reflect the competition between alu-minium and tin plate in the packaging sector. All the

Table 2Ordinary least squares estimate of the coefficients of (8)

Metal Coefficient Estimated value t-value

Aluminium a01 5.2460 1.38Copper a02 0.1344 0.81Lead a03 –1.3618 –3.46∗

Nickel a04 0.3985 0.40Tin a05 0.1112 0.08Zinc a06 –0.7133 –2.23∗

Iron ore a07 –2.7435 –2.54∗

Gold a08 5.8441 2.02∗

Silver a09 2.4755 1.11Platinum a010 4.8764 1.26Chromium a011 –3.7918 –7.95∗

Titanium a012 –1.9868 –4.03∗

Vanadium a013 –0.8264 –0.41Niobium a014 –0.7916 –0.35– a1 –0.2781 –4.34∗

– a2 1.9998 2.49∗

– b –0.3554 –1.11

∗ Coefficient significant at the 5% significance level.

Table 3Ordinary least squares estimate of the simplified version of (8)

Metal Coefficient Estimated value t-value

Aluminium a01 5.5167 2.23∗

Copper a02 0.1204 10.2∗

Lead a03 –1.3932 –199.0∗

Nickel a04 0.3209 54.0∗

Tin a05a a

Zinc a06 –0.7391 –86.0∗

Iron ore a07 –2.6619 –69.2∗

Gold a08 5.6207 121.0∗

Silver a09 2.3028 71.1∗

Platinum a010 4.5789 68.2∗

Chromium a011 –3.8296 –729.0∗

Titanium a012 –2.0259 –413.0∗

Vanadium a013 –0.9877 –35.8∗

Niobium a014 –0.9657 –29.5∗

– a1 –0.2790 –4.49∗

– a2 2.0324 3.41∗

– b –0.3801 –55.4∗

∗ Coefficient significant at the 5% significance level.a Coefficient constrained to zero.

Table 4Estimated individual metals demand curves under specification (8)

Metal Intercept, a1 a2 ba0i

Aluminiuma 5.5167 –0.2791 2.0324 –0.3801Copper 5.6371 –0.2791 2.0324 –0.3801Lead 4.1235 –0.2791 2.0324 –0.3801Nickel 5.8376 –0.2791 2.0324 –0.3801Tina 5.5167 –0.2791 2.0324 –0.3801Zinc 4.7776 –0.2791 2.0324 –0.3801Iron ore 2.8548 –0.2791 2.0324 –0.3801Gold 11.1374 –0.2791 2.0324 –0.3801Silver 7.8195 –0.2791 2.0324 –0.3801Platinum 10.0956 –0.2791 2.0324 –0.3801Chromium 1.6871 –0.2791 2.0324 –0.3801Titanium 3.4908 –0.2791 2.0324 –0.3801Vanadium 4.5356 –0.2791 2.0324 -0.3801Niobium 4.5510 –0.2791 2.0324 –0.3801

a1: coefficient in front of variable lnP in (8), a2: coefficient in frontof variable lnI in (8), b: coefficient in front of variable lnC in (8).

a Common metals demand curve.

remaining metals however have an intercept term thatdiffers significantly to that associated with the metal alu-minium and so it is clear that most of the 14 metalsstudied here do not share a common demand curve.

The next possible generalisation of (3) is to allow eachmetal demand curve to have a different slopes or priceelasticity of demand as in (9). Table 5 shows the resultobtained from estimating (9) using ordinary leastsquares. Some of the bi coefficients were found to beinsignificantly different from zero and so the above-men-tioned simplification search procedure was implemented.

103M. Evans, A.C. Lewis / Resources Policy 28 (2002) 95–104

Table 5Ordinary least squares estimate of the coefficients of (9)

Metal Coefficient Estimated value t-value

Aluminium b1 –0.6554 –12.3∗

Copper b2 –0.0013 –0.23Lead b3 –0.1117 –16.0∗

Nickel b4 –0.0390 –2.88∗

Tin b5 –0.0987 –4.90∗

Zinc b6 –0.0643 –9.94∗

Iron ore b7 –0.0865 –8.49∗

Gold b8 0.4067 6.48∗

Silver b9 0.0391 1.01Platinum b10 0.2702 1.98∗

Chromium b11 –0.2781 –36.3∗

Titanium b12 –0.1611 –20.7∗

Vanadium b13 –0.2565 –7.92∗

Niobium b14 –0.2978 –7.61∗

– a0 8.1256 4.02∗

– a1 –0.3185 –3.95∗

– a2 2.5084 4.89∗

∗ Coefficient significant at the 5% significance level.

The results are shown in Table 6. The inverse of theprice elasticity of the demand for aluminium is

b1 � �0.6524,

whilst the inverse of the price elasticity of demand foriron ore (i = 7) is

b1 � b7 � �0.6524�0.0865 � �0.7389.

Aluminium is therefore more price elastic than iron

Table 6Ordinary least squares estimate of the simplified version of (9)

Metal Coefficient Estimated value t-value

Aluminium b1 –0.6524 –12.6∗

Copper b2a a

Lead b3 –0.1108 –18.9∗

Nickel b4 –0.0376 –3.12∗

Tin b5 –0.0968 –5.28∗

Zinc b6 –0.0635 –11.7∗

Iron ore b7 –0.0865 –8.51∗

Gold b8 0.4115 6.98∗

Silver b9 0.0423 1.98∗

Platinum b10 0.2800 2.17∗

Chromium b11 –0.2771 –42.8∗

Titanium b12 –0.1602 –24.3∗

Vanadium b13 –0.2537 –8.44∗

Niobium b14 –0.2946 –8.07∗

– a0 8.0962 4.02∗

– a1 –0.3185 –3.96∗

– a2 2.5014 4.89∗

∗ Coefficient significant at the 5% significance level.a Coefficient constrained to zero.

ore. Table 7 shows the estimated demand curves for theremaining metals. It can be seen from this table that themetals gold, silver and platinum are more price elasticthan aluminium and the metals lead, nickel, tin, zinc,iron ore, chrome, titanium, vanadium and niobium areless price elastic than aluminium.

The Student t values in Table 5 suggest that two met-als appear to share a common price elasticity ofdemand—aluminium and copper (metal i = 1 and i =2). This may reflect the competition between aluminiumand copper in the transport sector (which was around15% of the copper market in 1994) and the electronicssector (which accounted for around 25% of the marketsfor copper). All the remaining metals however have priceelasticities that differ significantly to that associated withthe metal aluminium and so it is clear that most of the14 metals studied do not share a common demand curve.

It would appear that most metals have demand curveswith differing slopes—as in Fig. 2—so that (3) depictsthe mongrel function that is neither a supply nor ademand curve. Yet Table 7 reveals that most metals havea similar, but statistically different price elasticity ofdemand. Gold and platinum appear to be more priceelastic than most, whilst niobium, vanadium and chro-mium are more price inelastic than most. The remainingnine metals have inverse price elasticities close to 0.7.This is a lot lower than the bt values shown in Table 1,and so it would be dangerous to use such values to infersomething on rates of future substitution between metals.

The final generalisation of (3) to be considered in thispaper is to allow each metal demand curve to have adifferent slopes or price elasticities of demand and dif-ferent intercepts as in (10). However, the results obtainedfor such a generalisation were not satisfactory. Table 8shows the simplified estimated demand curve for each

Table 7Estimated individual metals demand curves under specification (9)

Metal Intercept, a0 a1 a2 bi

Aluminiuma 8.0962 –0.3185 2.5014 –0.6524Coppera 8.0962 –0.3185 2.5014 –0.6524Lead 8.0962 –0.3185 2.5014 –0.7632Nickel 8.0962 –0.3185 2.5014 –0.6900Tin 8.0962 –0.3185 2.5014 –0.7492Zinc 8.0962 –0.3185 2.5014 –0.7159Iron ore 8.0962 –0.3185 2.5014 –0.7389Gold 8.0962 –0.3185 2.5014 –0.2409Silver 8.0962 –0.3185 2.5014 –0.6101Platinum 8.0962 –0.3185 2.5014 –0.3724Chromium 8.0962 –0.3185 2.5014 –0.9295Titanium 8.0962 –0.3185 2.5014 –0.8126Vanadium 8.0962 –0.3185 2.5014 –0.9061Niobium 8.0962 –0.3185 2.5014 –0.9470

a1: coefficient in front of variable lnP in (9), a2: coefficient in frontof variable lnI in (9), b: coefficient in front of variable lnC in (9).

a Common metals demand curve.

104 M. Evans, A.C. Lewis / Resources Policy 28 (2002) 95–104

Table 8Estimated individual metals demand curves under specification (10)

Metal Intercept, a0i a1 a2 bi

Aluminium 18.7485 –0.2647 2.0096 –1.1687Coppera 18.5024 –0.2647 2.0096 –1.1687Leadb 18.7485 –0.2647 2.0096 –1.1687Nickel –3.5515 –0.2647 2.0096 0.3134Tinc 18.7485 –0.2647 2.0096 –1.4508Zinc –11.1567 –0.2647 2.0096 0.6362Iron oreb 18.7485 –0.2647 2.0096 –1.1687Gold 11.4154 –0.2647 2.0096 –1.9277Silvera 15.5736 –0.2647 2.0096 –1.1687Platinum 9.6025 –0.2647 2.0096 –0.2649Chromium –1.0923 –0.2647 2.0096 –0.1944Titanium –13.1410 –0.2647 2.0096 1.4497Vanadium 4.8748 –0.2647 2.0096 1.3043Niobium 16.3934 –0.2647 2.0096 –0.4083

a1: coefficient in front of variable lnP in (10), a2: coefficient in frontof variable lnI in (10), b: coefficient in front of variable lnC in (10).

a Common price elasticity with aluminium.b Common intercept and price elasticity with aluminium.c Common intercept with aluminium.

metal under this specification and as can be seen, fourof the metals appear to have a positive price elasticityof demand—nickel, zinc, titanium and vanadium.

Conclusions

A number of conclusions can be drawn from the abovestudy. First, the empirical correlation between a metalsprice and its level of consumption first identified byHughes in 1972 still holds today, with roughly the sameprice elasticity of demand. However, this relationshipshould be interpreted as mongrel function rather than asa stable common metals demand curve. The stabilityover time probably reflects the fact that the same typeof information is being averaged each year. As such, thesingular price elasticities published in past papers shouldnot be used for assessing future rates of metals substi-tution.

Secondly, when price elasticities are allowed to varybetween metals, the resulting estimates suggest that met-als have similar but statistically different rates of substi-tution. Platinum and gold have the highest rates of sub-stitution whilst niobium and chrome have the lowestrates of substitution. Finally, it appears to be the casethat aluminium and copper share a common price elas-

ticity of demand and this is consistent with the fact thatthese metals compete in some of their major markets.

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