1

Isabel Figuerola-FerrettiΨ

Prices and Production Cost in Aluminium Smelting in the Short and

the Long run

Abstract

The main objective of this paper is to reflect the institutional changes that have

characterized the aluminium industry as a result of the introduction of London’s

Metal Exchange (LME) trading. In doing this, I show that product prices are taken

exogenously and linked to input prices via risk sharing agreements. This forces

producers, in a competitive environment, to minimize costs. The latter is completed

with a description of their investment decision-making mechanism, in which

investment is determined by cost, and a measure of Tobin´s q.

The main contributions of this paper are: i) the use of a proprietary and complete

industry data set that allows me ii) to set up the short run input and output price

relationships iii) to model the optimising behaviour of the sector via a flexible cost

function (translog) allowing scale economies and non-constant factor substitution and

iv) to describe the investment-process that has emerged with the introduction of LME

trading.

Ψ Isabel Figuerola-Ferretti: Departamento de Economía de la Empresa. Universidad Carlos III de Madrid. C/Madrid 126, 28903 Getafe, Madrid. E-mail ifgarrig@emp.uc3m.es

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1. Introduction:

The standard microeconomic paradigm envisages a direct link between cost and

prices which firms set on a variable mark-up basis in relation to the position and slope

of the product demand curve. This paradigm applies most directly to manufacturing

industry. It cannot be applied without modification to raw materials producing

industries in which prices are set on competitive exchanges. In such markets,

commercial contracts for the supply of the commodity are priced at a premium or

discount over an exchange price at (or around) the delivery date. The result is that

firms have no direct control over prices and the relationship between production cost

and prices must therefore be indirect. In this paper, I attempt to characterize the

changes in the price-cost determination and investment decisions, which have taken

place in the aluminium industry as a result of the introduction of exchange trading.

Historically, the aluminium industry was dominated by a small group of

producers, which competed on an olygopolistic market and set prices on cost class

basis. The limited number of sellers and the apparent price stability made the metal

unsuitable for exchange trading. In the economic environment of the 1970’s mainly

driven by the two oil price shocks, producers were forced to adjust their listed prices

more frequently and in line with independent market quotations. This resulted on the

introduction of the nickel and aluminium contracts on the LME on October 1978.1

1 The crude oil industry has been subject to the same structural changes. The industy was highly concentrated and over 1980s the OPEC discipline broke down and the crude oil contract was introduced on NYMEX (1983) and in the international petroleum exchange in 1988).

3

During this period concentration diminished significantly2 and the major producers

lost their ability to directly control prices.

By the mid 1980's aluminium was effectively sold world-wide on the basis of

LME quotations even if the metal was not physically sold in the exchange. Over this

period the prerequisites for oligopolistic co-ordination were gradually removed with

the entries of new “fringe producers”. The major producers had big difficulties in

responding to the new situation having to invest in new technologies to reduce costs

and search for new patterns of growth based on mergers, acquisitions and

technological improvements to facilities. Since then there has been significant change

in the price and cost determination. Producers are forced to set prices in line with

LME quotations and adjust costs accordingly through the investment in new

technologies.

Other resulting institutional changes arising with the introduction of LME

trading include the introduction risk-sharing agreements linking the metal price to the

input price. The major cost components in aluminium production are the cost of the

raw material and the cost of electricity required to release aluminium metal from the

alumina feed. Aluminium smelters frequently draw their power from dedicated (often

hydro) electricity generations plants which do not have alternative buyers of their

power. For this reason smelters, electricity generators and aluminium refineries are

often linked by risk sharing contracts, with the consequence that input prices vary

with the LME aluminium price.3 This system benefits the metal producers by

protecting their margins. It also secures input providers with long term demand.

In this paper I look at the changes brought by the centralization of aluminium

2 For figures and discussion in concentration and market power, see Figuerola-Ferretti 2002 p.11-15. 3 Up to the late nineties the price of alumina and power was linked to the aluminium price in about half of the contracts. With the increase of Chineese aluminium production over the last three years the

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LME trading by analyzing its effects on the industry price, cost and investment

determination. This is done in three stages:

1. I establish that aluminium producers have become price takers as they cannot

longer control prices. I justify this argument by showing that there is stronger

evidence of Granger-causality from output prices to input prices than in the

opposite direction. This allows me to model input prices as a function of the

metal price and an error correction term reflecting the prevalent industry risk

sharing agreements.

2. On the basis of this result (which implies exogenously-taken output prices), I

can estimate costs using the translog framework, assuming that producers are

price-takers and minimize production costs. This technique was previously

applied for the aluminium industry by Lindquiest (1998). She estimated the

cost structure of six Norwegian aluminium plants with four variable inputs

(labour, raw materials, and electricity) and one predetermined (capital). This

study differs from Lindquiest (1998) in that i) it looks at the long run cost

determination (all inputs are variable), and ii) it applies aggregate industry

data instead of panel data. The use of the translog is motivated by the fact that

earlier studies on the aluminium industry (see Rosebaum 1987 Froem Gewe

1987 and Donowitz et al. 1987) assumed fixed input coefficients and constant

returns to scale. As a consequence the standard way to calculate margins,

involved a measure of average variable cost, often not reliable due to the lack

of accuracy of production cost reports. The estimation of the long run cost

structure applying the translog function to aggregate industry data is therefore

a major contribution of this paper.

amount of contracts priced under this arrangement has been reduced to a third of the world supply.

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3. I establish that producers have responded to the increased international

competition by focusing on cutting costs through investment in economies of

scale, mergers acquisitions and technological improvement. On the basis of

this argument I estimate investment as a function of cost and a measure of

Tobin’s q, reflecting the fact that it will be optimal for a smelter to invest until

the marginal cost of capital equals the marginal return. Output price is then

related to investment, via changes in the output gap between consumption and

capacity. This framework allows me to set up the long relationship between

input cost and product prices.

.

This study illustrates the institutional changes that have taken place in the industry.

It allows me to determine the relationship between cost pricing and investment

decisions. It is made possible through the availability of a proprietary set of

aluminium production cost capacity data provided by the consulting company

Anthony Birds associates.

The remainder of this chapter falls into seven sections. Section 2 provides a

full description of the data. In section 3 I set up the firm level framework consisting of

a series of price-cost relationships describing the short run price setting behaviour

and cost determination. This includes Granger-causality test and the estimation of the

translog function. In section 4 I estimate investment in order to illustrate that

producers react to the increased competition by investing in new smelting capacity as

means of lowering the cost of production. This relationship allows me to link the firm

level framework to the market environment by illustrating the long relationship

between costs and prices. In section 5 I set up the demand and supply schedules for

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aluminium smelting, linking the metal price to the balance between production

capacity and consumption. I conclude in section 6.

2. Data description

I have a complete set of aluminium annual cost data covering the period 1982-1998.

This includes data for total weighted average variable cost, power cost, power use,

alumina price, alumina cost and capacity. These data were provided by the consulting

firm Anthony Birds Associates. Annual data on aluminium consumption and

production were obtained from the World Bulletin of Metal Statistics (WBMS)

To estimate the aluminium investment structure I have used

• Aluminium share price yearly data for the major aluminium producers: Alcan

(Canada), Alcoa (USA), and Reynolds (USA) for the period 1975 to 2000

(Datastream).

• US capital equipment US yearly data for the period 1970-1999 (IMF,

International Financial Statistics, September 2000)

• Annual average data on the nominal interest rates: US 3 year government bond

rate ( IMF, International Financial Statistics, September 2000)

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3. The firm level framework: price and cost

determination

In this section I set up a framework to establish the price-cost setting structure in

the aluminium industry. I first analyze the extent to which aluminium producers can

be regarded as price takers. The underlying argument is that with the centralization of

LME trading all aluminium in the world is sold on the basis of LME quotations. As a

result producers do not longer have the power to set prices as a mark up over their

cost. Under this arrangement most LME traded contracts link the input price to the

metal price via risk sharing agreements. I argue that the result is that in the short run,

metal prices mainly determine power and alumina prices. In the second part of this

section I estimate the traslog cost function in a framework were product prices are

taken exogenously and producers minimize their cost.

3.1. Short run price cost relationships

In order to test whether the direction of causality goes from input prices to output

prices or vice versa I have performed a series of Granger-non-causality tests relating

input prices to output prices using price levels logs and price returns.4 Table 1

presents test output for the alumina-aluminium relationships. Table 2 presents test

results for the power-aluminium relationships. Generally, our findings suggest

stronger evidence of causality from output prices to input prices than in the reverse

4 Dickey Fuller tests results were inconclusive. Results can be provided by the author under request.

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direction.5 This result (more evident in table 1 than in table 2), suggests that output

prices determine input prices by a greater extent that input prices determine output

prices, reflecting the common industry use of risk sharing agreements linking power

and alumina price to the metal price. It also show that producers have no direct

control over prices so that in the long run they can be seen as price takers minimizing

their cost through investment in new capacity. Short term Granger-causality test

therefore validate the use of long term minimizing behaviour captured by the translog

function.

The short run relationship between the alumina price and the aluminium price is

represented by the following equation:6

, 10 1 1 2

, 1

lo g lo g lo g a ta t y t

y t

pp p

p−

−−

∆ = α + α ∆ + α

(1)

Regression results and diagnostics are given in table 3. They show that equation (1)

provides a good representation of alumina price determination.

The relationship between the output and electricity prices is specified as

0 1 2 , 1 3 , 1lo g lo g lo g lo gE y E t y tp p p p− −∆ = β + β ∆ + β + β (2)

The results from estimating (2) show that changes in current power prices are highly

dependent on current aluminium prices and lagged discrepancies from their long run

relationship (see table 4).

5 Fora detailed discussion on these results see Figuerola-Ferretti (2002) 6 Note that we justify our modeling of alumina, power and aluminium price relationships by showing that the three set of prices are cointegrated. Johansen-test cointegration results are in Fiquerola-Ferretti (2002). They can also be provided by the author under request.

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3.2. Estimating cost: The translog function:

Following my results I estimate the cost of production using the translog function in a

framework where every firm is a price taker and minimizes production cost for given

prices.

3.2.1Theoretical considerations

The non-homothetic transcendental logarithmic (translog) cost function7 is a second

order approximation to an arbitrary production function, which does not impose any

restrictions on the substitution possibilities among the inputs of production. It also

allows scale economies to vary with the level of output and, more importantly, it

allows input shares to vary over time. This is of particular importance for the

aluminium production process since evidence shows that input demands have not

been constant over time. For instance in 1950's it took on average around the world

about 21 kWh to produce a single kilogram of aluminium from alumina. In 1997 it

took one of the newest smelters just 14kWh. Figures A.1.1-A.3.3 plot alumina and

power input share values as well as estimated cross and own elasticities of

substitution for the 1982-1998 period. The graphs show that neither input demands

nor the substitution elasticities within aluminium production have been constant

through my sample period. I therefore adopt the translog framework to allow input

demands, substitution and price elasticities to change over time.

The translog cost function may be written as:

7 For a theoretical discussion see Paraskevopopoulos, I (2000)

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( ) yppppyyC i

n

i

n

j

n

iiyjijii

n

iiyyy lnlnlnln

21lnln

21lnln

1 1 1,

1

20 ∑ ∑ ∑∑

= = ==

+++++= γγαααα (3)

where:

C is Weighted Average Variable Cost obtained by adding alumina cost and power

cost8

pi is the input i price where i= A,E are alumina and power electricity prices.

Y is output measured as production in the aluminium industry

In order to be well behaved the cost function must satisfy the following conditions

1) Monotonicity: the cost function should be non negative for every

0),( >∈ ipyVy it and it must be non-decreasing in input prices

),(),( 10 ypcypc ≤ when 10 pp ≤

2) Concavity: )()1(),(),)1(( , ypCtyptCypttpC EaEa −+≥−+

I impose the symmetry and homogeneity of degree one restrictions, which allow the

integration of the cost function into the production function:

3) Symmetry

EAAE γγ =

(4)

AEEA γγ =

4) Homogeneity of degree one

000

1

=+=+=+

=+

YEyA

EAEE

AEAA

EA

γγγγγγ

αα

(5)

8 The Weighted Average Variable Cost also includes a small residual cost which I do not model. Instead I choose to model the sum of alumina and power costs. Fitted Weighted Average Variable Cost, is referred to as Cf.

11

Applying Shephard’s lemma to (3) gives the cost share equation for each variable

input noting that the first equation in system (5) implies that the cost shares have to

meet the restriction

11

=∑=

n

iiS

(6)

I estimate the following system:

( ) ypppppyyC AAYAAAEAAEAAyyy lnln)ln(21lnlnlnln

21lnln 22

0 γγγαααα ++++++=

)log()log()log( yppS AYEAEAAAAA γγαα +++= (7)

subject to restrictions (4), (5), and (6) which have been imposed.

3.2.2 Estimation method

I perform all estimations using Iterated Three Stage Least Squares (I3SLS) on the

sub-system consisting of production and the factor shares. Systems estimation allows

consideration of the nonlinearities and cross symmetry conditions. Additional

instruments are the one and two period lagged values of aluminium and input price

returns, and the one period lagged production and capacity variables. Use of these

instruments is justified in terms of the presence of these variables in the reduced

forms for input prices and production.

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3.3 Estimation results

Table 5 shows the results from estimating the system.9. The cost function is well

behaved if it satisfies the monotonicity and concavity conditions. In order to test for

monotonicity, I look at the fitted shares. The predicted average shares are 57.58% for

alumina and 42.43% for power, fitted average variable cost and conditional input

share values suggest that the translog cost function is monotonic.10

Concavity requires that the matrix of substitution elasticities is negative semi-

definite. The estimated values for price and substitution elasticities suggest that the

concavity property is not violated. 11 The mean Allen own price elasticities εAA (-

1.2371) and εEE (-1.0458) are negative. The mean cross price elasticities εAE (0.1019)

and εEA (0.1360) are positive indicating that alumina and power are substitutes.12

Since some of our estimated output parameters are insignificant, I have looked

for possible parsimonious simplifications. Table 6 shows results of these tests.13

Whereas it can be argued that there is weak evidence supporting homotheticity, our

model strongly rejects any further simplification.

9 For a discussion on the parameter estimates see Figuerola Ferretti (2002) 10 Figure A.1.1 shows that fitted weighted average variable cost values ( C ) are positive at all points and highly correlated with the true values. Figures A.1.2 and A.1.3 show that fitted alumina and power input share values ( AS and ES respectively) are also positive at all points over the sample period and highly correlated with the true values suggesting that the translog cost function is monotonic. 11 As can be seen in figures A.2.1 and A.3.3 in, own price and substitution elasticities are negative at all points, and cross substitution and price elasticities are positive at all points, demonstrating that the concavity property is not violated. 12 This is verified by the eigenvalues of the mean Allen price elasticity matrixes which are both negative (-1.5402, -0.7427) indicating that the matrix is negative semidefinite. 13 See Paraskevopoulos 2000 p. 45-46 for discussion on restrictions for testing different models.

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4. The long term link between cost and prices: the

investment determination

In this section I set up an investment relation where the change in capacity (my

proxy for investment) is determined by cost through profitability. My purpose is to

illustrate how the increase in competition in the aluminium industry has forced

producers to compete internationally and seek for lower costs in processing

operations. I illustrate how this process drives the push to bigger and more

modernized and automated smelters to gain the efficiency of scale needed to compete

on a global basis.

This argument allows me to establish that lower cost of production, and therefore

higher profits, leads to higher investment in efficiency improving technologies.

Investment is also related to a measure of Tobin’s q (see Tobin 1987 and Shiller

1990). It is optimal for the firm to invest until the marginal cost equals the marginal

return. I estimate q as the ratio a weighted average of the share prices of the major

aluminium producers, to the cost of capital in the industry. Share prices directly

reflect current and anticipated prices of the aluminium metal, so the expectation of a

high future price-cost margin translates directly into higher investment. An increase in

the exogenous component of costs reduces q and thus eventually results in lower

supply and higher prices.

Investment is therefore and increasing function of q also denoted as the

‘shadow price of capital’.

Investment is modelled in a rational expectations framework14 where

14 I assume that investors make their decisions on the basis of current share prices which in turn are

14

132110 −− +∆+Π+= tttt IqI γγγγ (8)

where :

CkSq = (8.1)

S = average share price

Ck = cost of capital and

Cp Al

t ˆ=π 15 (8.2)

The cost of capital is defined as

e

cmK m Rm

∆= + δ −

where (8.3)

m is the cost of machinery

R is the nominal interest rate (US 3 year government bond rate, IMF, International

Financial Statistics, September 2000)

δ is the depreciation rate which we assume to be constant at 5%,16 and

∆= +

•

t

te

mm

Em 1 (8.4)

is an estimate for the rate of inflation in the price of machinery.

I have used ∆q as explanatory variable instead of q as the consequence of apparent

non-stationarity of q arising out of the trend in nominal interest rates over the sample

period -see Figuerola-Ferretti (2002 p.122). The change in machinery price em

m∆ is

based on rational expectations of future corporate cashflows. 15 This is a variable measuring profit determined by the ratio of aluminium price to fitted cost. We expect profits to be significant in explaining investment, and be able to derive a long run relationship from cost to prices. 16 This figure was reported by an aluminium industry consultant who estimated that the depreciation

15

modelled adaptively so that the expected rate of inflation for machinery is explained

on the basis of the discrepancy between the last years predicted and current inflation

value and the actual outcome – see Harvey (1981, pp.229-30).

1 1ln ln (1 ) lne et t tm m m− −∆ = α∆ + − α ∆ (8.5)

which may be written as

1ln (1 ) lne i

t t ii

m m∞

−=

∆ = − α α ∆∑ (8.6)

I take the value α=0.5 truncating the distribution at 6. The cost of capital is thus

estimated using the calculated values from equation 9.3 a depreciation rate of 5%.

In order to get an estimate of the average share price in the aluminium industry, I

have averaged share prices of Alcoa, Alcan and Reynolds. 17 Taken together, these

three firms control 30% of the world aluminium production -see I. Figuerola –Ferretti

(2002 table 1.3 p11). I have weighted each of the quoted share prices by the inverse of

their volatilities. Higher volatility of share prices indicates that investors expect

higher risk over future earnings, which suggests a lower degree of precision in the

estimates (see Parakevopoulos, 2000).

Results from estimating equation (8) are reported in table (7). These show that

current changes in q and the price-cost margin are very significant in explaining

investment. They therefore support the claim that lower cost leads to higher

investment in new smelting capacity and, that the investment process continues as

long as the shadow value of capital is greater than its cost.

rate for aluminum smelters is linear on a 20 year basis. 17 Six dominant players Alcoa (USA) Alcan (Canada), Pechiney (France), Reynolds (USA), Kaiser (USA) and Alusuisse (Switzerland) have traditionally dominated the industry. These produced 60% of the world total in 1975 50% in 1984 and 42.4% in 1990. I was not able to find share price data for Aussuise , Kiser and Pechiney . This si why I do not use their share prices to

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5. The demand and supply relationships

I have established that in the face of higher competition producers seek to gain

efficiency through the investment in scale economies. In this section I describe the

process by which investment (defined as the change in capacity) determines prices,

illustrating in this way the relationship between the firm level framework and the

market environment.

I set up the inverse demand function where the metal price is defined as a function of

its own lag and the output gap between consumption on the one hand and capacity

and lagged production on the other.

1,413210 loglogloglog)log( −− ++++= tytttty pkykcapconsp κκκ (9)

Regression results are reported in table 8. They show that all the estimated

coefficients are highly significant. The inverse demand equation may be interpreted

with the investment equation 8; lower cost leads to greater investment in more

efficient techniques, which cause more competitive prices. For a 1% increase in

capacity we expect prices to drop by 3.17%. Lower current consumption also leads to

lower prices and higher levels of past production also lead to a downwards price

pressure.

The consumption variable is endogenised in equation (10) where it is modelled as

a function of industrial production and lagged output prices. Aluminium is an

intermediate product used as an input mainly in the construction, electricity, transport

calculate the industry average. See Figuerola-Ferretti (2002) for a more detailed explanation.

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and packaging industry. Aluminium consumption therefore is highly dependent on

industry output production. Consumption is also determined by lagged and not current

aluminium prices, since industrial producers need a long time lead to build new

capacity. The consumption equation is specified as,

)log()log()log( 1,210 −++= tALpinprodCons λλλ (10)

Estimation results are reported in table 9. Both estimated coefficients are significant

and have the expected sign. They imply that for every 1% increase in industrial

production aluminium consumption rises by 1.53%. Conversely if prices rise by 1%

consumption next will be expected to drop by 0.13% in the next period.

Finally I set up the supply schedule in which production is restricted to be

autoregressive, and also dependent on capacity and one period lagged prices.

1,21110 loglog)1(loglog −− +−++= tyttt pycapy µµµµ (11)

Results from estimating (11) are presented in table 9. Production increases when

capacity is expanded. For every 1% increase in smelter’s capacity we should expect

aluminium production to increase by 0.53%. If aluminium prices rise by 1% we

production is expanded in the next period by 0.10%.

The purpose of this section has been to provide a framework illustrating the

aluminium demand and supply schedules using a complete set of price, consumption

and production variables. The link between the market environment and the firm

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level model has been provided through investment , which is determined by Tobin´s

q and a measure of profitability.

6. Concluding remarks

The introduction of the aluminium LME trading in the aluminium industry has

brought important changes in the industry price-cost and investment determination.

Producers have lost their ability to control prices and have to operate in an

competitive environment. Margins are in many cases protected through the use of risk

sharing agreements linking the LME quoted metal price to the input price. As a result

in the short run output prices mainly determine the input prices so that if the price for

the metal falls so does the raw material cost. Cost is an important determinant of the

investment process investment as producers have responded to the increased

international competition by investment in economies of scale, technological

improvement in order to gain efficiency of production.

The main contribution of this paper has been to apply an exclusive set of

proprietary industry data to analyze the effects of the introduction of LME aluminium

trading in the price cost and investment determination. Results may be summarised as

follows:

1. There is stronger evidence of Granger-causality from output prices to input prices

than in the reverse direction. Input prices are ultimately driven by demand for the

metal.

2. In a framework where aluminium producers act as price takers in variable input

markets, the translog function gives best fitting estimates of the average variable

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cost and the conditional input demands. It does not appear possible to restrict

factor substitution patterns.

3. The long term link between cost and output prices in the aluminium is given by

investment in new smelter capacity. Costs have indeed decreased over the last

decade, as a result of greater investment in new technologies and economies of

scale.

An interesting extension to this study lies on the investigation of the effects of the

recent ongoing consolidation taking place within the aluminium industry. In the year

2000 three important mergers have been completed reflecting the industry move

towards a highly “reconcentrated” structure - see Figuerola-Ferretti (2002 p. 85). Two

important questions arise which I hope to answer in future research.

• Is the “re-concentration” process going to change the system of cost-

cutting incentives enforced by the centralization of LME trading?

• Given that the main players will no longer be able to control prices

directly, will they choose to play output setting games in order to

indirectly set prices?

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Table 1 : Granger Causality test on the alumina and aluminium prices lag length

Levels Logs Returns

ay pp →

ya pp → ay pp → ya pp → ay pp → ya pp →

1 F16,15=19.24 (0.074%)**

F16,15=8.39 (1.24%)*

F15,14=39.40 (0.00%)**

F15,14=14.95 (0.2%)**

F15,14=7.82 (1.61%)*

F15,14=5.82 (3.27%)*

2 F15,13=5.81 (2.11%)*

F15,13=3.79 (5.95%)

F14,12=5.44 (2.82%)*

F14,12=3.25 (8.64%)

F14,12=5.32 (2.98%)*

F14,12=2.39 (14.68%)

3 F14,11=3.37 (8.37%)

F16,15=1.82 (23.12%)

F13,10=2.20 (18.81%)

F13,10=1.42 (32.17%)

F13,10=2.96 (11.94%)

F13,10=3.31 (9.87%)

4 F13,9=2.53 (19.47%)

F13,9=1.85 (28.28%)

F12,8=1.79 (32.87%)

F12,8=1.66 (35.13%)

F12,8=0.95 (53.76%)

F12,8=1.69 (34.69%)

The table gives the outcome of Granger-causality tests on the aluminium and alumina prices. Tail probabilities are given in brackets. Significant outcomes at the 95% level are indicated in bold face. *denotes statistical significance at the 95 percent level of confidence ** denotes statistical significance at the 99 level of confidence

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Table 2: Granger causality results power and aluminium price

lag length

Levels Logs Returns

Ey pp → yE pp → Ey pp → yE pp → Ey pp → yE pp →

1 F16,15=1.14 (30.48%)

F16,15=0.88 (36.42%)

F15,14=3.55 (8.37%)

F15,14=4.41 (5.73%)

F15,14=0.06 (93.5%)

F15,14=0.02 (86.67%)

2 F15,13=0.95 (41.62%)

F15,13=2.93 (9.92%)

F14,12=0.44 (65.51%)

F14,12=1.51 (27.13%)

F14,12=0.56 (58.76%)

F14,12=0.32 (73.30%)

3 F14,11=0.59 (63.78%)

F16,15=5.14 (3.44%)*

F13,10=0.19 (89.41%)

F13,10=2.41 (16.50%)

F13,10=0.44 (72.85%)

F13,10=1.74 (25.70%)

4 F13,9=1.93 (26.84%)

F13,9=4.64 (8.31%)

F12,8=0.68 (64.95%)

F12,8=2.73 (21.74%)

F12,8=0.63 (67.19%)

F12,8=2.84 (20.84%)

The table gives the outcome of Granger-causality tests on the aluminium and alumina prices. Tail probabilities are given in brackets. Significant outcomes at the 95% level are indicated in bold face. *denotes statistical significance at the 95 percent level of confidence ** denotes statistical significance at the 99 level of confidence

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Table 3: The Estimated Alumina Equation

Variable log pa Coefficient Std. Error t-Statistic Prob. α0 -0.860469 0.138750 -6.201581 0.0000 α1 0.251991 0.072820 3.460486 0.0042 α2 -0.450013 0.072736 -6.186905 0.0000 SE of regression 0.060101 LM test (F-

statistic) Prob(F-statistic)

Heteroskedast. (Fstatistic) Prob(F-statistic)

0.15224 (0.8661)

R-squared 0.774267 0.9597 0.4669

Durbin-Watson stat 1.502508 Prob(F-statistic) 0.000063 The table gives the OLS estimates of the alumina demand equation (4.6). are given in parentheses.

23

Table 4: the power price equation

Variable Log pE Coefficient Std. Error t-Statistic Prob. β0 -0.153187 0.383686 -0.399249 0.6967 β1 0.285026 0.042327 6.733886 0.0000 β2 0.211959 0.047380 4.473618 0.0008 β3 -0.472453 0.142966 -3.304657 0.0063 SE of regression 0.03201 LM test (F-statistic)18

Prob(F-statistic) 0.131275 0.08785

R-squared 0.854083 Heterosked. (F-statistic)Prob (F-statistic)

1.8992 0.1858

Durbin-Watson stat 2.027171 Prob(F-statistic) 0.000026 The table gives the OLS estimates of the electricity demand equation (4.7). Probability values are given in parentheses.

18 Note that for the LM test in both equations we use a lag length of 2 and results are robust to an increase of the lag length

24

Table 5: Translog Cost Function Estimates

Coefficient Std. Error t-Statistic Prob. α0 -9.179526 16.43749 -0.558451 0.5819 αy 2.822613 3.428152 0.823363 0.4188 αyy -0.251496 0.360059 -0.698484 0.4919 αA 0.170048 0.407674 0.417117 0.6805 γAE 0.076790 0.004499 17.06671 0.0000 γAA 0.194465 0.031258 6.221216 0.0000 γAY -0.090672 0.048291 -1.877619 0.0732 αE 0.340096 0.407674 0.417117 0.6805 γEE -0.076790 0.004499 17.06671 0.0000 γEY 0.090672 0.048291 -1.877619 0.0732 SE of regression 0.004115 R2

C 0.999234 DWc 0.6976 R2

A 0.608387 DWA 1.320706 The table gives the OLS estimates of the pair of equations defined by (5).

25

TABLE 6: Hypothesis testing

Number of χ2 χ2 Hypotheses restrictions value p value Homotheticity 1 3.5254 0.0604 Homogeneity 2 4.3097 0.1159 CRTS 3 4723.29 0.000 UELST 1 291.272 0.0000 HUELST 2 300.0080 0.0000 Cobb Douglas 4 127.05 0.0000 CRTS Constant Returns to Scale UELST Unitary Elasticity of Substitution HUELAST Homotheticity and Unitary Elasticity of Substitution The table gives the outcomes of the likelihood ratio tests on the restrcitions imposed in the model, estimates of which were reported in Table 4.1.

26

Table 7: The Estimated Investment Relationship Variable Investment Coefficient Std. Error t-Statistic Prob. γ0 -0.069218 0.027446 -2.522002 0.0284 γ1 0.028139 0.011812 2.382356 0.0363 γ2 0.001687 0.000833 2.025699 0.0677 γ3 -2.05E-06 1.12E-05 -0.183771 0.8575 SE of regression 0.020368 LM test19 ( F-statistic)

Prob (F-statistic)

0.1173 0.8907

R-squared 0.493755 Heterosked. (F-statitic) Prob (F-statistic) Prob(F-statistic)

0.8907 0.7721

Durbin-Watson stat 1.882863 0.050398 The table gives the OLS estimates of the investment equation (4.9). Probability values are given in parentheses.

19 The lag length used for the LM residual correlation test is 2. Results are robust to the extension of the lag length.

27

Table 8: The Estimated Aluminium Price Equation Variable log py Coefficient Std. Error t-Statistic Prob. κ0 20.55036 5.446106 3.773404 0.0031 κ1 3.393012 0.858660 3.951522 0.0023 κ2 -3.170838 1.120685 -2.829375 0.0164 κ3 -1.842486 0.756808 -2.434550 0.0331 κ4 0.435922 0.172331 2.529562 0.0280 SE of regression 0.147562 LM (F-statistic)

Prob (F-statistic)

0.5637 0.7721

R-squared 0.690646 0.8366 Durbin-Watson stat 1.538292

Heterosked. (F-statistic) Prob (F-statistic) Prob(F-statistic)

0.007562

The table gives the OLS estimates of the investment equation (4.10). Probability values are given in parentheses.

.

28

Table 9: Estimated Consumption Equation

Variable log cons Coefficient Std. Error t-Statistic Prob. λ0 3.663634 0.349056 10.49583 0.0000 λ1 1.527074 0.090536 16.86695 0.0000 λ2 -0.131037 0.037494 -3.494842 0.0040 SE of regression 0.030516 LM(2) F-statistic20

Prob (F-statistic) 2.0579 0.0278

R-squared 0.961930 Heteroskedast. (F-statistic) 1.3858 0.3012

Adjusted R-squared

0.956073 Prob ( F -statistic) 0.00000

The table gives the OLS estimates of the consumption equation (11). Probability values are given in parentheses.

20 Note that this result is not robust to the extension off lags as LM(5) F=2.0579 (0.1739)

29

Table 10: Estimated Production Equation

Variable log yt Coefficient Std. Error t-Statistic Prob. µ0 -0.964834 0.275043 -3.507941 0.0039 µ1 0.532001 0.131632 4.041589 0.0014 µ2 0.106327 0.034186 3.110228 0.0083 SE of regression 0.030212 LM(2) F-statistic

Prob (F-statistic) 0.3665 0.7013

R-squared 0.937042 Heterosked. (F-statistic) Prb (F-statistic)

9.553536 0.3505

Adjusted R-squared 0.927356 Prob (F-statistic) The table gives the OLS estimates of the production equation (4.12). Probability values are given in parentheses.

30

AKNOWLEDGEMENTS:

I would like to thank Christopher L. Gilbert and Yannis Paraskevopoulos for their

valuable comments. I am also thankful to my colleagues from Carlos III Josep A.

Tribó and Andrea Fosfuri for their helpful suggestions. Finally I would like to thank

Wayne Wagner for his useful references. I would also like to thank Anthony Birds

Associates for providing me with the data set. Of course all errors are my own.

31

References

Berndt E.R. and Christensen L.R.:(1973) The translog function and the substitution of

equipment, structures, and labour in U.S. manufacturing 1929-68, Journal of

Econometrics, volume 1, pp:81-114.

Christensen, L.R and Greene W.H. (1976), Economies of scale in U.S. electric power

generation, Journal of Political Economy, 84:4/1, pp.655-676.

Domowitz, I., R.G Hubbard and B.C. Petersen (1987) Oligopoly Supergames: Some

Empirical Evidence on Prices and Margins The Journal of Industrial Economics 17,

1-17.

Figuerola-Ferretti, I., and C.L. Gilbert (2001),Price variability and marketing method

in the non-ferrous metals industry, Resources Policy 27, 169-177

Figuerola-Ferretti I., and C.L. Gilbert (2001) Has futures trading affected the volatility

of aluminium transaction prices? 432 Working Paper Series, Economics Department,

Queen Mary, University of London.

Figuerola-Ferretti I. 2002 The Economics of different Marketing Methods in the Non-

Ferrous Metals Industry. Ph.d thesis. Queen Mary, University of London.

Lindquist, Kjersti-Gro (1995) The existence of Factor Substitution in the primary

Aluminum Industry: A Multivariate Error-Correction Approach Using Norwegian

Panel Data'. Journal of Empirical Economics, vol 20, pp361-83

Salinger M.A. (1984) Tobin's q Unionization, and the Concentration-Profits

Relationship RAND Jounal of Economics, vol 15, pp 159-170.

32

Paraskevopulos Y. (2000) Econometirc Models Applied to Productivity Theory Ph.d

Thesis. Queen Mary, University of London

Radetzki M. (1990) A Guide to Primary Commodities in the World Economy.

Blackwell.

Roseabaum, D.I (1989): An Empricical test of the Effects of Exess Capacity in Price

Setting, Capacity-Constraint Supergames, International Journal of Industrial

Organization 7, 231-241

Tobin, James(1987) Essays in Macroeconomics MIT press.

Wold Aluminium Organisation Web Page: www.world-aluminium-org

33

600

700

800

900

1000

82 84 86 88 90 92 94 96 98

C C^

Figure A.1.1:

0.50

0.52

0.54

0.56

0.58

0.60

0.62

0.64

84 86 88 90 92 94 96 98

AS AS

Figure A.1.2

34

-2 .20

-2 .18

-2 .16

-2 .14

-2 .12

-2 .10

-2 .08

84 86 88 90 92 94 96 98

S E A A

F ig ure A .2 .1 :

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

84 86 88 90 92 94 96 98

ES ES

Figure A.1.3

35

-2 .4

-2 .2

-2 .0

-1 .8

-1 .6

-1 .4

8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8

S E E

F ig u re A .2 .2

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

84 86 88 90 92 94 96 98

SE AE

F igure A .2 .3

36

-1 .3 5

-1 .3 0

-1 .2 5

-1 .2 0

-1 .1 5

8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8

P E A A

F ig u re A .3 .1 :

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

84 86 88 90 92 94 96 98

PEEE

Figure A.3.2

37

0.11

0.12

0.13

0.14

0.15

0.16

84 86 88 90 92 94 96 98

PEAE

Figure A.3.3

38

A.1.1. Actual and fitted Weighted Average Variable Cost (C and C )

A.1.2. Actual and fitted alumina conditional input demands (SA and AS )

A.1.3. Actual and fitted power conditional input demands (SE and ES )

A.2.1. Alumina Own Substitution Elasticity (SEAA )

A.2.2. Power Own Substitution Elasticity (SEEE)

A.2.3. Alumina and Power cross substitution Elasticity (SEAE)

A.3.1. Alumina own price elasticity (PEAA)

A.3.2. Power own price elasticity (PEEE)

A.3.3. Alumina and power cross price elasticities (PEAE)

C.1. The Relationship between the Aluminium price and the Alumina price

C.2. The Relationship between the Aluminium price and the Power price

D.1. Time series plot of Tobin´s Q

D.2. US three year Government Bond Yield

39