Division of Economics and BusinessWorking Paper Series

Dahl Mineral Elasticity of Demand and SupplyDatabase (MEDS)

Carol A. Dahl

Working Paper 2020-02http://econbus-papers.mines.edu/working-papers/wp202002 v2.pdf

Colorado School of MinesDivision of Economics and Business

1500 Illinois StreetGolden, CO 80401

April 2020

c©2020 by the listed author(s). All rights reserved.

Colorado School of MinesDivision of Economics and BusinessWorking Paper No. 2020-02April 2020

Title:Dahl Mineral Elasticity of Demand and Supply Database (MEDS)

Author(s):Carol A. DahlDivision of Economics and BusinessPayne Institute for Public PolicyColorado School of MinesGolden, CO 80401cadahl@mines.edu

ABSTRACTMinerals and metals are critical materials in advanced industrial economies as well as for those onthe path to industrializing. Their criticality, capital intensity, and cyclicity all point to the needfor those involved along the supply chain to understand the drivers in these markets and the sizeand speed of response to them. Since demand and supply elasticities can be valuable summaries tohelp us understand these responses, this database is an ongoing effort to collect and catalogue theavailable estimates. Most of the elasticities are derived from econometric work and the databasecontains elasticities as well as information on the sample (what, where, when), included variablesand equations, statistical techniques and statistical properties of the estimates.

JEL classifications: L7, Q31Keywords: Demand, Supply, Elasticity, Metals and Minerals, Mineral Industries

Introduction

From use in skyscrapers and jet planes to toasters and bicycles, minerals and metals across the globe

provide basic building blocks of modern life. The boom and bust nature of these markets in a rapidly

industrializing world, the concentration of some of these resources in unstable areas of the world, worries

that we are depleting these non-renewable resources, and the critical need for some of them for national

defense goods and rapidly increasing renewable energy production has again put them in a spotlight. This

is not a particularly new phenomenon. Figure 1 shows a metal price index for almost a century and other

periods with price spikes and supply uncertainties.

Figure 1 Historical Real

Commodity Metal Price

Index with Forecast to 2025.

Source: Dahl (2020a), p. 7.

The three most notable price run ups – the decade after World War II, 1975 to 1985 and again from 2005-

2015 all caused concern and interest in minerals and mineral policy to increase. Of interest to all

concerned is how responsive quantity demanded and supplied of these products are to these increases in

price. The responsiveness to price is often measured by price elasticities (the percentage change in

quantity (Q) demanded or supplied as the result of a percentage change in price (P), which can be written

as

p

Q

Q  

P

P

=

For modeling purposes, this expression is usually rearranged and converted to one of the following partial

derivatives:

p

Q P log Q or

P Q log P

=

Consumption and production may respond to price, while these price run ups may be caused by shifts in

other variables that increase demand for mineral products or decrease their supply. Many of the models in

the database measure elasticities with respect to these other variables of influence. (e.g. We get the

elasticity of supply or demand for variable X by replacing P with X in the above formulas.) From mine

mouth, stockpiles, smelting, transportation, fabrication, through to the final consumer and scrap recover,

such elasticities are of interest to decision makers along the supply chain of these products, those studying

0

20

40

60

80

100

120

140

160

180

1925 1935 1945 1955 1965 1975 1985 1995 2005 2015 2025

Commodity Metals Price Index (Real)

the supply chain as well as to governments making policy relating to these markets. Thus, dozens of

studies have been conducted to investigate elasticities relating to demand and supply for various minerals.

For example, Fallyand Sayre (2018) survey the literature and present ranges of short and long run price

elasticities of demand and supply for 20 metals from 30 studies. They use these and other commodity

elasticities in a computable general equilibrium model to measure gains from trade. I build on their

ambitious literature review by adding more detail on the studies they present and adding new studies. My

intent is for this to be an ongoing public database as an appendix to this paper. As more studies are

located they will be added to the database and subsequently more critical analysis will be done. Favored

results will be noted in and across studies. In this initial draft of the paper, the current database will be

summarized and patterns will be noted that can be followed up in subsequent survey work and new

analysis.

Including the studies in Fallyand Sayre (2018), I have found more than 60 studies and more than 1400

sets of elasticity estimates to date relating to supply and/or demand for more than two dozen metals and

minerals. I only include studies that report elasticities or for which there is enough information to

compute elasticities. Most are econometric studies but a few are based on expert judgement or other

techniques. Figure 2 shows the distribution of these studies across time by publication date.

Figure 2: Histogram of collected studies by year of publication

The metal price spikes in the mid 1970s through the early 1980s and the mood of resource insecurity

spawned the most studies. With the more recent price run up beginning in 2004, the studies have been

picking up as well. The elasticities in these studies have been collected from the primary source where

possible, otherwise any available secondary source has been used. The earliest study found is Charles

River Associates (1970) with estimates for demand and supply of copper. The most recent is Baffes,

Kabundi, and Nagle (2020) with world demand for aluminum, copper, lead, nickel, tin, zinc, and an

aggregate of all six metals. The next two sections provide more detailed summary information for supply

and demand elasticities in the database.

Supply Elasticities

So far 36 studies with supply elasticities have been located. The earliest study is Charles River Associates

(1970) for copper and the most recent is Polli (2016) for indium. Figure 3 shows a histogram of supply

0

5

10

15

20

25

Fre

qu

ency

Number of Mineral Demand and Supply Studies

with Elasticities Found as of January 27, 2020

studies by year of publication. Supply elasticities were most studied back in the 1970s with a dearth of

studies in the 1980s and 90s, with interest again trending upward after 2000.

Figure 3: Histogram of collected studies by year of publication

To get a flavor for the elasticities collected so far, the following histograms display the range of the

estimates. Visual inspection of the short run price elasticities from dynamic models and prices elasticities

from static models did not find them to be too dissimilar. Also the means and medians of short run

elasticities from dynamic models, so they are combined in Figure 4 (a). You can see the bulk of these

shorter term supply price elasticities are between 0 and 0.4, with a median of 0.23, while the bulk of the

long term elasticities are between 0 and 1 with a median of 0.65.

Almost all of the studies that contain both long and short run price elasticities used lagged endogenous

models. Figure 4, panel (c) show the coefficients on the lagged endogenous. We can also compute how

long α*100 percent of the adjustment to long run occurs in such models. If the coefficient on the lagged

endogenous is equal to λ then the adjustment time is ln(1-α)/ln(λ). About half of the coefficients on these

lagged endogenous models are below 0.6 suggesting that 50% of the adjustment occurs in less than

ln(0.5)/ln(0.6)=1.36 years and that 90% of the adjustments occurs in less than ln(0.5)/ln(0.6)=1.36 years

and that 90% of the adjustment to long run occurs in less than ln(0.9)/ln(0.6) = 4.51 years. Given how

capital intensive mining is this seems like a rather short time frame and will be considered as these

models are more critically reviewed. Perhaps the lagged endogenous model may not accurately capture

the dynamics in these markets.

0

2

4

6

8F

req

ue

ncy

Histogram of Mineral Supply

Elasticity Studies by Year of

Publication

Figure 4: Mineral Supply Price Elasticities

Source: Dahl Mineral Elasticity Demand and Supply Database, Appendix (latest version is at

http://dahl.mines.edu/MEDS,xlsx.)

To date the database has supply price elasticity estimates relating to the following metals: aluminum,

cobalt, copper, gold, indium, iron, lead, magnesium, manganese, mercury, nickel, platinum, tin, tungsten,

uranium, and zinc. Table 1 provides more detailed summary statistics by metal. Copper supply is the most

studied (9 studies) followed by uranium and zinc (6 studies each) and gold, iron, lead, nickel, tin, and zinc

(3 studies each). The remainder are considered in 1 or 2 studies.

Table 1 Summary of Supply Elasticities by Material from Dahl Mineral Elasticity of Demand and Supply

Database

Psr Pstat Plr Ysr Ystat Y lr Qt-1

aluminum average 0.359 0.403 0.962 0.835 0.910 1.529 0.479

studies median 0.235 0.170 0.580 0.869 0.910 1.348 0.516

#=6 stdev 0.417 0.449 1.061 0.195 – 0.954 0.299

oldest: 1975 minimum 0.050 0.117 0.073 0.570 0.910 0.570 0.005

newest: 2000 maximum 1.190 0.921 3.290 1.030 0.910 2.850 0.806

count 6 3 8 4 1 4 6

cobalt average 0.230 – 0.395 – – – 0.560

studies median 0.230 – 0.395 – – – 0.430

#=6 stdev 0.028 – 0.064 – – – 0.279

(a) (b)

(c)

0

10

20

30

40

Fre

qu

en

cy

Histogram of Mineral Supply Price

Elasticities: Long Run

0

10

20

30

40

Fre

qu

en

cy

Histogram of Coefficients on Lagged

Endogenous Variables

oldest: 1980 minimum 0.210 – 0.350 – – – 0.370

newest: 1985 maximum 0.250 – 0.440 – – – 0.880

count 2 – 3 – – – 3

copper average 0.247 0.134 1.048 – 0.970 – 0.754

studies median 0.188 0.100 0.719 – 0.930 – 0.795

#=9 stdev 0.241 0.080 0.955 – 0.115 – 0.246

oldest: 1970 minimum 0.007 0.050 0.052 – 0.870 – 0.210

newest: 1990 maximum 1.200 0.254 3.800 – 1.150 – 1.070

count 25 9 18 – 8 – 21

gold average -0.355 -0.425 0.617 0.989

studies median -0.422 -0.400 0.738 0.980

#=3 stdev 0.143 0.222 0.377 0.023

oldest: 1983 minimum -0.522 -0.700 0.090 0.960

newest: 1999 maximum -0.140 -0.200 1.049 1.020

count 11 4 8 9

indium average 0.066 -0.003 0.122 0.006 0.010 0.041 0.462

studies median 0.066 -0.003 0.122 0.006 0.006 0.041 0.462

#=1 stdev 0.014 0.123 0.025 0.018 0.004

oldest: 2014 minimum 0.056 -0.090 0.104 0.006 -0.006 0.041 0.459

newest: 2014 maximum 0.076 0.084 0.140 0.006 0.029 0.041 0.464

count 2 2 2 1 3 1 2

iron average 0.203 0.382 0.539 0.746 1.140 1.446 0.481

studies median 0.160 0.318 0.422 0.700 1.045 1.298 0.470

#=3 stdev 0.153 0.309 0.455 0.361 0.587 0.613 0.200

oldest: 1979 minimum 0.040 0.040 0.060 0.210 0.180 0.774 0.120

newest: 2011 maximum 0.550 0.885 1.625 1.560 2.190 2.943 0.920

Includes

bauxite count 14 10 13 14 10 14 20

lead average 0.160 0.187 0.928 – – – 0.514

studies median 0.169 0.187 0.700 – – – 0.752

#=3 stdev 0.054 0.058 0.624 – – – 0.521

oldest: 1975 minimum 0.086 0.109 0.470 – – – -0.264

newest: 1995 maximum 0.217 0.271 1.840 – – – 0.817

count 4 5 4 – – – 4

manganese

ore average 0.104 0.558 0.316 – – – 0.690

studies median 0.104 0.558 0.316 – – – 0.672

#=6 stdev – – – – – – 0.118

oldest: 1985 minimum 0.104 0.558 0.316 – – – 0.582

newest: 1985 maximum 0.104 0.558 0.316 – – – 0.817

count 1 1 1 – – – 3

mercury average 1.000 – 3.000 – – – –

studies median 1.000 – 3.000 – – – –

#=1 stdev – – – – –

oldest: 1974 minimum 1.000 – 3.000 – – – –

newest: 1974 maximum 1.000 – 3.000 – – – –

count 1 – 1 – – – –

nickel average 0.718 – 2.922 – – – 0.676

studies median 0.750 – 2.015 – – – 0.766

#=3 stdev 0.434 – 2.027 – – – 0.324

oldest: 1975 minimum 0.133 – 1.200 – – – 0.247

newest: 1990 maximum 1.280 – 5.500 – – – 0.990

count 6 – 6 – – – 6

tellurium average 0.016 – 0.034 – – – 0.533

studies median 0.016 – 0.034 – – – 0.533

#=1 stdev 0.026 – 0.057 – – – 0.016

oldest: 2014 minimum -0.003 – -0.006 – – – 0.521

newest: 2014 maximum 0.034 – 0.075 – – – 0.544

count 2 – 2 – – – 2

tin average 0.400 – 1.024 – – – 0.472

studies median 0.300 – 0.910 – – – 0.465

#=3 stdev 0.356 – 0.609 – – – 0.155

oldest: 1990 minimum 0.032 – 0.180 – – – 0.230

newest: 1990 maximum 1.110 – 2.090 – – – 0.710

count 7 – 7 – – – 6

tungsten average 0.122 – 0.614 – – –

studies median 0.110 – 0.500 – – –

#=2 stdev 0.024 – 0.296 – – –

oldest: 1974 minimum 0.107 – 0.393 – – –

newest: 1977 maximum 0.150 – 0.950 – – –

left out China count 3 – 3 – – –

uranium average 0.102 0.363 2.473 – – – 0.383

studies median 0.102 0.630 0.160 – – – 0.304

#=7 stdev 0.034 0.488 4.993 – – – 0.297

oldest: 1975 minimum 0.060 -0.200 0.128 – – – 0.110

newest: 2011 maximum 0.142 0.660 11.400 – – – 0.848

count 6 3 5 – – – 6

zinc average 0.257 0.110 0.595 0.451

studies median 0.181 0.110 0.509 0.408

#=3 stdev 0.191 0.535 0.159

oldest: 1975 minimum 0.085 0.110 0.000 0.248

newest: 1990 maximum 0.642 0.110 1.750 0.744

count 7 1 8 7

all average 0.189 0.185 0.934 0.725 0.898 1.389 0.603

studies median 0.151 0.129 0.628 0.700 0.920 1.313 0.601

#=36 stdev 0.349 0.329 1.456 0.363 0.521 0.729 0.278

oldest: 1970 minimum -0.522 -0.700 -0.800 0.006 -0.006 0.041 -0.264

newest: 2014 maximum 1.280 0.921 11.400 1.560 2.190 2.943 1.070

count 97 41 90 19 24 19 99

Source: Summarized from studies in Appendix (http://dahl.mines.edu/MEDS.xlsx, worksheet MEDS)

Notes: # under studies shows the number of studies for the material, while oldest and newest indicate the

dates of the oldest and newest studies. Stdev= standard deviation for the elasticities for each material and

each elasticity category. Psr indicates short run price elasticity, Pstat indicates price elasticities from static

models, and Plr indicates long run price elasticities from dynamic models. Ysr, Ystat, and Ylr are similar

elasticities for income or activity elasticities. Qt-1 is the coefficient on a lagged endogenous model for

those models that estimate dynamics in a model using one lagged endogenous model. Count is the

number of elasticity estimates for each material and elasticity category.

A few patterns emerge in the above table. The medians and averages for the most part appear to be well

behaved. For the long run supply price elasticities, all are positive and most of the short run and those

from static models are positive with only a couple of exceptions (gold and indium). Where there are more

than 3 elasticities per price category, the means tend to be about 20% higher suggesting the distributions

of elasticity are skewed in the positive direction. However, on average the difference between the means

and medians for the coefficient on the lagged endogenous model is small. Medians and averages from

static models are larger than short run categories in half the cases and smaller in the other half. More

reassuring is that the medians and averages are always larger in the long run than in the short run. To

come to conclusions about initial suggested elasticities for individual metals will require more careful

consideration of the quality and timing of the studies in each category.

Demand Elasticities

Demand for minerals has been more heavily studied econometrically. I have currently identified 56

studies and catalogued more than 1300 sets of demand elasticities for 30 categories of metals or

materials– aluminum, chromium, cobalt, copper, gold, heavy rare earth elements, indium, iron, lead, light

rare earth elements (heavy and light), lithium, magnesium, manganese, mercury, metals, nickel, niobium,

palladium, plastic, platinum, rare earth elements, silver, steel, tellurium, tin, titanium, tungsten, uranium,

vanadium, and zinc. The earliest study found with demand elasticities is again Charles River Associates

(1970) for copper and the most recent is Baffes, Kabundi (2020) for aluminum, copper, lead, nickel, tin,

zinc, and an aggregate of these metals. The elasticities are divided into those that come from dynamic

models and yield both long and short run elasticities in panels (a) and (c) and those that come from static

models panel (b).

For the short run, there are more than 500 elasticity estimates from 37 studies with a histogram of their

values shown in figure 5 panel a. They vary across mineral, time, location, and methodology and range

from -1.76 to 1.26. More than a third have a positive price elasticity with the bulk of the rest between 0

and -0.2. The median is -0.03 with the average a bit more elastic at -0.06. With one-tailed tests, all the

positive elasticities would not be significantly different from zero and we might conclude the short run

elasticity is quite small if not often zero. However, there are some flags that will require more scrutiny in

the future. With a two tailed test about a quarter of the positive elasticities are significant at a 10% or

better significance level. A possibility to consider is whether these demand equations are identified. Might

they not really be supply equations. Almost all the positive elasticities are from lagged endogenous

models. For a quarter of them, the coefficient on the lagged endogenous model is an implausibly negative

but less than 1 in absolute value, which makes adjustment in the long less than adjustment in the short run

with a cyclical adjustment path. Again, a further look will be taken investigate whether the lagged

endogenous model is able to represent dynamic adjustment in material markets. Further over 90% of the

positive price elasticities use the London Metal Exchange price London Metal Exchange (2020) with

many of these elasticities at the country level. Further investigating should be done to see if these prices

are good price proxies at the local level.

There are somewhat more demand price elasticities from static models coming from 27 studies. A

histogram of their values is shown in Figure 5, panel b. They range from -5.14 to 3.19 with a median of -

0.08 and a mean of -0.20. More than 30% of them are positive, but only about 10% of these are

significantly positive. More than 80% of the positive price elasticities use the London Metal Exchange

price. Yet again a call for further work to investigate if and how these USD prices were converted to local

real prices and whether it matters. More than one half of the positive elasticities are from Fernandez

(2018). In this study, the variables are differenced and two lagged price differences were included.

Although the author labeled these elasticities as long run, their small size led me to down grade them to

the static category. This specification also should be further scrutinized as it seems unlikely to me that this

specification is capturing the long run either. Large negative elasticities that might be considered outliers

tend to pair with large income elasticities, while some of the large positive price elasticities pair with

large negative income elasticities.

The histogram of long run price elasticities is shown in figure 5, panel c. Their median value is -0.11 and

their average value is -0.20. Their range is an even more exciting 11.69 to -21.8. For these two extremes

one comes from a lagged endogenous model with a coefficient near one, and another comes from an error

correction model with the estimated error correction term negative but very near zero. Again more than

30% are positive. Since most come from lagged endogenous models, the same arguments and suggestions

made earlier for further work hold. Many come from lagged endogenous models with small or negative

coefficients on the lagged endogenous variable. A sizeable number of the positive price elasticities are

paired with negative income elasticities. The bulk of the negative elasticities are well behaved with

estimates less elastic than -0.5. Over half of the long run price elasticities that more elastic than -1 come

from models with distributed lags on price but not on income. Further work comparing the patterns on

these distributed lag models with lagged endogenous models would likely improve our knowledge of the

dynamics in these markets.

Figure 5 The above histograms summarize the range of demand price elasticities from Dahl Mineral

Elasticity Demand and Supply Database (http://dahl.mines.edu/MEDS,xlsx, worksheet MEDS, columns

N, P, Q).

Moving on, let's consider the income or activity elasticities. I would expect these to vary more than for

price as the activity variables vary more. In many cases, it is GDP or GDP per capita. When this variable

is used the elasticity tends to fall as GDP per capita rises and countries shift away from goods towards

services (Baffes, Kabundi (2020)). When industrial productions is used, the elasticities are likely to be

less elastic as countries get richer and their metal and material demand shifts as their economies shift

away from industrial production towards more services. Elasticities may also change as technologies

become more efficient and there is substitution across raw materials. Some of the studies contain cross

price elasticities and they are contained in the database and will be studied further as this project moves

forward.

There are more than 700 estimates of short run income elasticities from 55 studies. The histogram of their

values is shown in figure 6, panel a. The median value is 0.6 and the mean is 0.80. The range is -7.768 to

16.198. Less than 15% of the elasticities are negative and only a quarter of these are significantly negative

for a two tailed test at a 10% significant level or better. Again the most extreme of the negative and

positive values come from models where the coefficient on the lagged endogenous model is very small or

even negative. The histogram does show more variation in income elasticities as was suspected and

further work will be done to try to isolate and explain these differences. Again the elasticities are

clustered but over a wider range. More than 35% are between 0 and 0.6, more than 60% from 0 to 1.2,

and another 11% from 1.2 to 1.8.

(b)

Figure 6 Histograms that summarize the range of demand income elasticities and coefficient on a lagged

endogenous variable from Dahl Mineral Elasticity Demand and Supply Database

(http://dahl.mines.edu/MEDS,xlsx, worksheet MEDS, with these statistics taken from columns R, T, U,

V)

There are close to 350 income elasticities from static models from 56 studies summarized in figure 6,

panel b. Their median is 0.80 and their mean is 0.93 with a range from -6.41 to 15.70. These elasticities

seem better behaved than the short run alluding to the difficulties in teasing out the dynamics in

complicated markets. Less than 2% have negative income elasticities and there is no statistical evidence

that they are significantly different from zero. More than half of the elasticities fall in the range from 0.5

to 1 and around another 18% are between 1 and 1.5.

The histogram for long run income elasticities is shown in figure 6, panel c. About 550 elasticities have a

median of 0.9 and a mean of 1.14. They are not as well behaved as the elasticities from the static models.

Around 13% are negative but there is no statistical information to determine if any are significantly

negative. More than forty percent of the long run income elasticities are between 0 and 1 and more than

70% are between 0 and 2. For outliers greater than 4, more than half come from a lagged endogenous

model with an included time trend that has a negative coefficient. Although time trends are quite common

in time series work, they are an admission of ignorance and more work could be done to try to isolate

what they are picking up and identify better proxies for these effects.

The last summary histogram is for coefficients on lagged endogenous variables, when it is the only

variable added to capture dynamics. More than 20% are a disappointing negative value but only about a

(a) (b)

(c) (d)

050

100150200250300

Fre

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cy

Histogram of Mineral Demand

Income Elasticities: Short Run

0

50

100

150

200

250

Fre

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Histogram of Mineral Demand

Income Elasticities from Static

Models

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Fre

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Histogram of Mineral Demand

Income Elasticities: Long Run

0

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Histogram of Coefficients on Lagged

Endogenous Variables

quarter of these are significantly negative. If we conclude these are equal to zero, it suggests that the long

run and short run are the same as in the static models or adjustment is completed within one time period,

which seems unlikely in very capital and material intensive industries. Again computing how long α*100

percent of the adjustment to long run occurs in such models with the coefficient on the lagged

endogenous of λ (ln(1-α)/ln(λ)), about half of the coefficients on these lagged endogenous models are 0.5

or below suggesting that a half or more of the adjustment to long run occurs in the first time period and

90% or more occurs within 3-4 years. In mature economies, where a larger percent of durable good

purchase is replacement, this seems a bit short. Although some consumer durables may only last 3 to 4

year, many last considerably longer while material intensive capital goods and infrastructure may last for

decades. As in supply, the lagged endogenous model invites greater scrutiny and a search for other ways

to capture dynamics. A first place to look is the few newer studies that apply newer time series techniques

(unrestricted error correction models) and do co-integration analysis.

Estimates of total value for most of the materials with demand estimates in the database are shown in

table 2. Steel tops the list with over a trillion dollars a year in sales followed by plastic, iron, copper,

aluminum, and gold all with sales greater than 100 billion. All the markets studied have sales in the

billions except for mercury, manganese, tellurium and indium. Rare earth elements, much in the news

these days, have a market estimated at less than $3 billion, which is rather small compared to most of the

other materials. Summary statistic for the demand elasticities for each of these materials with overall

summaries at the bottom are shown in Table 3.

Table 2 Sales value for global minerals and materials markets in 2014 (in $106)

Material Sales Source

aluminum 120,238 Tiltonand Guzmán (2016)

chromium 6,467 Tilton and Guzman (2016)

cobalt 3,457 Tilton and Guzman (2016)

copper 129,862 Tilton and Guzman (2016)

gold 116,778 Tilton and Guzman (2016)

indium <1 Tilton and Guzman (2016)

iron 325,220 Tilton and Guzman (2016)

lead 10,352 Tilton and Guzman (2016)

lithium 1,265 Tilton and Guzman (2016)

magnesium 4741 U.S. Bureau of Mines, Price from Kelleyand Matos (2014)

manganese 36 Tilton and Guzman (2016)

mercury 100 Tilton and Guzman (2016)

nickel 40,471 Tilton and Guzman (2016)

niobium 3,812 Tilton and Guzman (2016)

palladium 5,070 Tilton and Guzman (2016)

plastic 478,830 Grand View Research (2020) extrapolated back from 2019 with growth rate

of 3.5%

platinum 7,454 Tilton and Guzman (2016)

REE 2,304 Production growth (2015 to 2016 = 5%) from Zhou, Li, and Chen (2017), to

extrapolate back value 2018 (2.8 billion in 2018) from Grand View Research

(2019)

silver 15,969 Tilton and Guzman (2016)

steel 1,126,575

Price (HRC) Berezowsky (2014) , quantity from World Steel Institute (2019)

tellurium 33

Price is from U.S. Geological Survey (2015) Quantity is from Benzinga

(2014).

tin 6,395 Tilton and Guzman (2016)

titanium 4,982 Tilton and Guzman (2016)

tungsten 3,637 Tilton and Guzman (2016)

uranium 6,727 Price times quantity with price (U3O8) from U. S. EIA (2014) and quantity

from World Nuclear Organization (2019)

vanadium 1,780 Tilton and Guzman (2016)

zinc 28,881 Tilton and Guzman (2016)

I was somewhat surprised that the number of studies and the size of the market were not correlated with a

correlation coefficient of less than 0.1. The large copper and aluminum markets have the most demand

studies (20 and 14). They are followed by the considerably smaller markets for tin and zinc markets (12

studies each), lead (8 studies), and nickel (7 studies). Somewhat surprisingly the huge steel market only

has 7 studies). Nor is the large iron market near the top of the list with only 4 studies. Cobalt comes in

with 5 studies all prior to 1985. However, with applications in solar energy and wind turbines it is likely

to come under increasing scrutiny. Uranium has 4 studies, and lithium, platinum and tungsten have 3

studies each. The remainder are considered in 1 or 2 studies. The large gold market (large by value not by

tonnes) only saw two studies. The importance of gold for investment purposes may not lend itself well to

statistical analysis. The one study that looked at gold demand by category Sherman (1986) combined

visual inspection of historical data with expert judgment and concluded that the demand for gold bullion

and coins, likely for investment purposes, was upward sloping.

Table 3 Summary of Demand Elasticities by Material

aluminum average -0.087 -0.120 -0.123 1.167 0.780 1.610 0.178

studies median -0.047 -0.032 -0.121 0.842 0.815 1.396 0.138

#=15 stdev 0.359 0.322 0.761 1.236 0.301 1.195 0.361

oldest: 1971 minimum -1.760 -0.856 -2.135 -2.011 0.159 -2.005 -0.787

newest: 2020 maximum 1.133 0.507 6.020 7.681 1.720 6.332 0.948

count 78 73 94 114 30 92 68

chromium average -2.622 10.337

studies median -2.622 10.337

#=2 stdev 3.567

oldest: 1984 minimum -5.144 10.337

newest: 2002 maximum -0.100 10.337

count 2 1

cobalt average -0.165 -0.601 -1.734 0.937 1.598 1.513 0.381

studies median -0.070 -0.590 -0.542 0.937 1.040 1.513 0.381

#=5 stdev 0.274 0.228 4.443 2.738

oldest: 1971 minimum -1.375 -0.920 -21.810 0.937 0.280 1.513 0.381

newest: 1984 maximum -0.012 -0.200 0.134 0.937 15.697 1.513 0.381

count 26 8 24 1 30 1 1

copper average -0.029 -0.138 -0.135 0.701 0.712 0.900 0.273

studies median -0.014 -0.083 -0.146 0.508 0.769 1.046 0.275

#=20 stdev 0.330 0.341 0.580 1.131 0.282 1.871 0.374

oldest: 1970 minimum -1.410 -0.863 -2.880 -3.198 0.124 -8.825 -0.516

newest: 2020 maximum 1.257 1.610 2.061 7.648 1.720 13.232 0.968

count 85 89 126 116 46 116 75

gold average -0.413 1.042

studies median -0.600 1.042

#=2 stdev 1.520

oldest: 1986 minimum -2.500 1.042

newest: 2002 maximum 2.500 1.042

count 9 1

indium average -0.151 2.618

studies median -0.151 2.618

#=1 stdev 0.149 0.881

oldest: 2014 minimum -0.256 1.995

newest: 2014 maximum -0.045 3.241

count 2 2

iron average -0.184 -0.186 -0.247 0.761 1.117 1.088 0.304

studies median -0.145 -0.070 -0.214 0.770 1.030 1.021 0.280

#=3 stdev 0.180 0.299 0.262 0.325 0.377 0.402 0.195

oldest: 1987 minimum -0.640 -0.856 -0.901 0.300 0.540 0.685 -0.100

newest: 2011 maximum -0.040 -0.030 0.000 1.330 1.720 2.078 0.630

count 10 7 11 11 9 11 11

lead average 0.008 -0.163 -0.009 0.538 0.611 0.777 0.402

studies median 0.019 -0.054 0.015 0.352 0.674 0.537 0.418

#=8 stdev 0.183 0.340 0.261 0.730 0.383 1.164 0.347

oldest: 1996 minimum -0.888 -0.856 -1.281 -0.839 0.070 -2.640 -0.537

newest: 2020 maximum 0.438 0.621 0.702 3.740 1.720 4.442 0.968

count 64 72 78 105 29 79 58

lithium average -0.540

studies median -0.540

#=3 stdev

oldest: 2005 minimum -0.540

newest: 2018 maximum -0.540

count 1

magnesium average -0.400

studies median -0.400

#=1 stdev 0.035

oldest: 2006 minimum -0.425

newest: 2006 maximum -0.375

count 2

manganese average -0.212 -0.120 -0.359 0.408

studies median -0.212 -0.100 -0.359 0.408

#=2 stdev 0.050

oldest: 1984 minimum -0.212 -0.178 -0.359 0.408

newest: 1985 maximum -0.212 -0.083 -0.359 0.408

count 1 3 1 1

mercury average -1.000

studies median -1.000

#=1 stdev

oldest: 1971 minimum -1.000

newest: 1971 maximum -1.000

count 1

metals average -0.234 0.910

studies median -0.260 0.918

#=1 stdev 0.064 0.112

oldest: 2020 minimum -0.300 0.732

newest: 2020 maximum -0.100 1.138

count 16 17

nickel average -0.032 -0.233 -0.054 1.092 0.704 1.863 0.228

studies median -0.030 -0.146 -0.105 0.666 0.830 1.079 0.158

#=7 stdev 0.239 0.602 1.465 2.111 1.164 4.695 0.293

oldest: 1996 minimum -0.712 -1.840 -2.950 -3.536 -6.412

-

10.522 -0.293

newest: 2020 maximum 0.682 3.191 11.690 16.198 1.700 31.241 0.971

count 58 72 79 98 42 69 53

niobium average -1.375 4.922

studies median -1.375 4.922

#=2 stdev 1.520

oldest: 1984 minimum -2.449 4.922

newest: 2002 maximum -0.300 4.922

count 2 1

palladium average -0.200 -0.700

studies median -0.200 -0.700

#=1 stdev –

oldest: 1974 minimum -0.200 -0.700

newest: 1974 maximum -0.200 -0.700

count 1 1

plastic average -0.918 -2.083

studies median -0.918 -2.083

#=1 stdev

oldest: 1991 minimum -0.918 -2.083

newest: 1991 maximum -0.918 -2.083

count 1 1

platinum average -0.458 -2.206 -1.279 0.585 4.103 1.300 0.590

studies median -0.344 -2.206 -1.150 0.585 4.103 1.300 0.590

#=3 stdev 0.210 2.220 0.716 0.474 4.926 0.665 0.156

oldest: 1974 minimum -0.700 -3.775 -2.050 0.250 0.620 0.830 0.480

newest: 2004 maximum -0.330 -0.636 -0.636 0.920 7.586 1.770 0.700

count 3 2 3 2 2 2 2

Rare Earth

Elements

(REE) average -0.400

studies median -0.400

#=1 stdev 0.141

oldest: 2014 minimum -0.500

newest: 2014 maximum -0.300

count 2

REE heavy average -0.300

studies median -0.300

#=1 stdev

oldest: 2016 minimum -0.300

newest: 2016 maximum -0.300

count 1

REE light average -0.500

studies median -0.500

#=1 stdev

oldest: 2016 minimum -0.500

newest: 2016 maximum -0.500

count 1

silver average -0.856 1.720

studies median -0.856 1.720

#=1 stdev

oldest: 2002 minimum -0.856 1.720

newest: 2002 maximum -0.856 1.720

count 1 1

steel average -0.101 -0.151 -0.805 1.167 1.191

studies median -0.017 -0.071 -0.805 1.144 1.071

#=5 stdev 0.141 0.260 0.116 0.683

oldest: 1981 minimum -0.355 -1.000 -0.805 1.026 0.010

newest: 2018 maximum 0.005 0.201 -0.805 1.621 4.050

count 7 62 1 47 49

tellurium average -0.393 -0.260 -0.501 1.016 0.777 1.344 0.288

studies median -0.393 -0.260 -0.501 1.016 0.777 1.344 0.288

#=1 stdev 0.358 0.362 0.690 0.593 0.199

oldest: 2014 minimum -0.646 -0.260 -0.757 0.528 0.777 0.925 0.147

newest: 2014 maximum -0.140 -0.260 -0.245 1.504 0.777 1.763 0.429

count 2 1 2 2 1 2 2

tin average -0.103 -0.161 -0.106 0.474 0.703 0.618 0.345

studies median -0.121 -0.104 0.438 0.773 0.338 0.381

#=11 stdev 0.185 0.470 0.501 0.984 0.232 1.567 0.329

oldest: 1972 minimum -0.550 -1.469 -1.262 -3.962 0.162 -6.021 -0.418

newest: 2020 maximum 0.370 1.262 3.154 3.838 1.385 4.526 1.026

count 67 77 81 103 29 77 64

titanium average 0.690 -1.386

studies median 0.690 -1.386

#=1 stdev

oldest: 2002 minimum 0.690 -1.386

newest: 2002 maximum 0.690 -1.386

count 1 1

tungsten average -0.150 -0.500 -0.335 1.564 3.513 1.045

studies median -0.150 -0.500 -0.335 1.137 2.784 0.366

#=4 stdev 0.000 0.049 1.362 1.885 1.444

oldest: 1974 minimum -0.150 -0.500 -0.370 0.500 2.176 0.239

newest: 1984 maximum -0.150 -0.500 -0.300 3.482 6.307 3.209

count 2 1 2 4 4 4

uranium average -0.078 -1.393 -0.186 0.494 0.634 0.707 0.421

studies median -0.051 -0.049 -0.083 0.553 0.079 0.608 0.387

#=4 stdev 0.079 1.931 0.273 0.294 0.966 0.550 0.464

oldest: 1994 minimum -0.216 -4.200 -0.780 0.178 0.074 0.176 -0.018

newest: 2011 maximum 0.003 -0.031 0.006 0.840 1.750 1.370 1.180

count 7 5 7 5 3 5 7

vanadium average 0.233 -1.541

studies median 0.233 -1.541

#=2 stdev 0.754

oldest: 1984 minimum -0.300 -1.541

newest: 2002 maximum 0.767 -1.541

count 2 1

zinc average -0.034 -0.124 -0.264 0.669 0.714 0.847 0.113

studies median -0.007 -0.046 -0.067 0.485 0.769 0.664 0.102

#=12 stdev 0.242 0.372 0.850 1.775 0.723 1.988 0.356

oldest: 1975 minimum -1.241 -0.721 -7.337 -7.768 -3.159 -7.317 -0.743

newest: 2020 maximum 0.826 1.572 0.946 8.982 3.560 10.289 0.926

count 100 72 116 109 66 87 62

all average -0.063 -0.198 -0.200 0.803 0.926 1.136 0.255

studies median -0.034 -0.082 -0.110 0.600 0.801 0.897 0.249

#=56 stdev 0.272 0.552 1.183 1.352 1.256 2.612 0.363

oldest: 1970 minimum -1.760 -5.144 -21.810 -7.768 -6.412

-

10.522 -1.141

newest: 2020 maximum 1.257 3.191 11.690 16.198 15.697 33.333 1.180

count 511 567 643 717 344 559 408

Source: Summarized from studies in Dahl Mineral Elasticity of Demand and Supply Database, Appendix

(http://dahl.mines.edu/MEDS.xlsx, worksheet MEDS)

Notes: # under studies shows the number of studies for the material, while oldest and newest indicate the

dates of the oldest and newest studies. Stdev= standard deviation for the elasticities for each material and

each elasticity category. Psr indicates short run price elasticity, Pstat indicates price elasticities from static

models, and Plr indicates long run price elasticities from dynamic models. Ysr, Ystat, and Ylr are similar

elasticities for income or activity elasticities. Qt-1 is the coefficient on a lagged endogenous model for

those models that estimate dynamics in a model using one lagged endogenous model. Count is the

number of elasticity estimates for each material and elasticity category.

Although too soon to make pronouncements on elasticity by material, I make a few observations from the

studies located so far. For materials with more than 2 elasticity estimates, the average tends to be more

elastic than the median. Again, this suggests the estimates are skewed towards more elastic. However, this

pattern is not quite as consistent as it was for supply price elasticities, but the average amounts of

skewness are quite similar. For supply, the short run price tended to be most skewed, while for demand

the long run price was more skewed. Demand income elasticities are less skewed than demand price

elasticities. For demand as for supply, the coefficient on the lagged endogenous variable is the least

skewed. Further study of outliers may help to determine whether they are fantasy or fact.

The relationship between averages and medians is not as well behaved as in the supply estimates. I

expected the long run to be more elastic than the estimate from static models and those from static models

to be more elastic than short run estimates. Although long run averages and medians for each material are

almost always more elastic than the short run for both price and income, the relationship between long-

run and static and the relationship between static and short run is quite mixed, especially for price. The

relationships are more mixed for medians than for averages.

The most studied categories are aluminum, copper, lead, nickel, tin, and zinc. Elasticities from these

metals comprise more than 70% of the collected estimates but no one of them contribute more than 18%.

All have been included in at least one of some recent fairly comprehensive studies Stuermer (2017),

Fernandez (2018), and Baffes, Kabundi (2020).

The median and average summaries for these most popular to be studied materials suggest the following.

Aluminum price summaries, all less elastic than -0.2 are not so different from the inelastic summaries for

all studies, while the long run income elasticities suggest aluminum might be more income elastic. The

three most recent studies, confirm the low price elasticities but suggest that the income elasticity may

have become less elastic.

The copper elasticity summaries are very near those of all studies with very low price elasticity and

income elasticity near 1. Recent studies do not suggest much change to the elasticities. Lead may be less

price and income elastic than other metals and its income elasticity may have fallen more recently. Nickel

may be more income elastic that average but may have become more income inelastic recently. Tin may

be less income elastic than average with income elasticities near those of lead. There is not strong

evidence that they have changed more recently. Zinc price summary elasticities are fairly near to the

overall medians and averages but may be less income elastic. Zinc income elasticity may have become

less income elastic recently as much tin is used to plate tin cans for food preservation. While canned food

demand is likely to be income inelastic.

Baffes, Kabundi (2020) not only study these six most popular metals, they also aggregate them and

estimate an aggregate metal demand using an Error Correction Model. They report only the long run

elasticities and find the long-run average price elasticity for their various specifications perhaps a tad

more price elastic than for all studies (-0.234 versus -0.20) which is supported more strongly by the

medians. While they also find the average long run income elasticity a bit less elastic than for all studies

(0.91 versus 1.14). However, their median and average income elasticities are almost the same as other

and the overall median.

A few other patterns that are noted for further investigation are as follows. Chromium has exceptionally

elastic price and income response from two studies (-2.622/10.377). I am rather curious about these

results and will go back and see what might be happening. Cobalt, with the most recent study of five

studies found in 1984, has median price elasticities more than twice as elastic as the overall medians.

Median income elasticities are more elastic as well, but not to such a large extend. They exceed the

overall medians by 30 to 70%. There are a couple of interesting outliers that are significantly skewing the

averages. The demand for cobalt as a catalyst in refining and other industrial processes showed U.S. long

run price and static income elasticities of -21.8/15.7 on data for 1967 to 1978. Further study should reveal

whether these extreme values might have come from technical changes that caused a rather swift and

dramatic shift towards cobalt as a catalyst in refining and petrochemical use. As these catalysts lower

energy use in industrial processes, the energy crisis in the 1970s may have contributed to these high

elasticities as well(Cobalt Institute (2020)). In the same study, other non-metallic cobalt uses also had

high though not as extreme elasticities with U.S. long run price and static income elasticities of -5.6/3.2

on data for 1967 to 1975. Since cobalt has numerous applications in green technologies (e.g. in lithium

ion batteries, in magnets for wind turbines and alloys for their blades), its demand along with studies for

its demand are likely to be on the upswing in the coming decade.

There are only a few results for four of the precious metals –gold, palladium, platinum, and silver. Overall

they seem to be more price and income elastic than for the whole sample. Burrows (1974) as quoted in

Fally and Sayre (2018) summarize studies with price elasticities on palladium and platinum. These

summaries suggest that platinum is more price elastic than palladium. However, these estimates predate

catalytic converters, which now consume more than a third of platinum production (Bell (2019)) and

more than ¾ of palladium production (Cowley (2019)). Also no income or activity elasticity is reported in

their summaries. One more recent outlier of note, Evansand Lewis (2002) include estimates for platinum

on data for 1980-1999, which should include the transition toward catalytic converters. Their static price

and income elasticity are high (-3.8/7.6). However, these elasticities were computed by inverting their

estimated price functions, which were functions of quantity of metal and activity. Activity is constrained

to have the same elasticity across a number of the fourteen different metals. Their results on a number of

other metals also tend to be questionable. For example, the extreme results mentioned above on

chromium also resulted from their study. Further adding to my doubt, their very elastic responses for

platinum were not supported by a study almost contemporary to theirs TIAX (2004) that regressed

quantity on price and income from 1975-2000 yielding more conventional looking long-run price and

income elasticities of -1.15 and 0.83. This also puts to question the results on silver, which come from

their study.

Evansand Lewis (2002) have the only estimate on titanium but their price elasticities are positive and their

income elasticities are negative. They also find this pattern on vanadium, while the other vanadium study

finds a negative price elasticity more in line with other metals. Their estimate for niobium also has a very

high price and income elasticity, while the other estimate for niobium price elasticity is from a summary

of studies by a well know expert in mineral economics Radetzki (1984), who again puts the price

elasticity much more in line with other metals. Burrows (1974) as quoted in Fallyand Sayre (2018) also

summarizes studies with price elasticities for mercury (unitary elastic in the long run) and tungsten (less

elastic then -0.4).

Nothing out of the ordinary for magnesium and manganese with one or two studies that suggest price

elasticities less than -0.4. No activity elasticities are reported. The four studies on uranium spanning 1994

to 2011 have some interesting anomalies. The average static price elasticity is a little more elastic than -1,

while its median is only -0.152. This results from a very elastic response in the small spot market demand

and in the demand for Australian uranium while holding other uranium prices constant. Omitting these

highly elastic values makes the average and median static price elasticity line up quite nicely near a more

expected -0.045. Activity elasticities are a bit erratic as well, which is largely explained by the activity

chosen. When activity is GDP on data through 1989, averages and means for all income elasticity

categories are less 0.2. When activity is nuclear power production the mean and average short run activity

elasticity is about 0.7 with long elasticities greater than 1.

The two rare earth studies with numerical elasticities found (both published since 2014) are Pothen (2014)

and Nguyenand Imholte (2016). They seem to arrive at static price elasticities for rare earths by expert

judgement. Their elasticities span -0.4 with light rare earths thought to have an elasticity of -0.5 and

heavy rare earths an elasticity of -0.3. Desormeaux (2013) estimates a static demand price elasticity for

lithium near that for light rare earth's of -0.54. While Rosendahland Rubiano (2018) assume a price

elasticity of -0.5 in their dynamic world lithium model. None of these studies with estimated elasticities

report activity elasticities.

Polli (2016) estimates demand for indium and tellurium. He only estimates a static model with average

price elasticity of 0.151, but a quite high income elasticity greater than 2. Tellurium estimated with both

static and dynamic models is likely more price elastic with a long run elasticity of -0.5 than indium but

less income elastic. For both metals, using an instrumental variable for price noticeably increased the

elasticities for price and income.

I conclude this discussion by material with the large iron and steel market. For iron, median and average

elasticities for all categories are reasonably well behaved with all summary price elasticities less elastic

than -0.247 and static and long run activity summary elasticities near 1. The activity vector is steel

production. Most of the estimates are for iron ore, with a couple for scrap. Demand for scrap both old and

new may be slightly less elastic than demand for iron ore, while activity elasticity for new scrap many be

more elastic than for iron ore.

Steel has similar price elasticities to the overall averages and medians in the short run and from static

models. Its long run price elasticity from Considine (1990) at -0.805 is rather more elastic than other

studies. It comes from a dynamic logit model that includes prices for copper, aluminum, and plastic.

Plastic is even more price elastic in the long run (-2.083) in his study. Whether a more elastic response is

the result of including other prices is an interesting question that might be further pursued. My impression

from my work in energy markets is that models with cross prices often have more elastic own price

response than models without. For example, in my Dahl energy demand database (DEDD), there are 77

studies on aggregate energy demand in industries that span the years 1975 to 2010 with 672 sets of

elasticities that include cross prices (most typically for capital, labor, and materials). There are 54 studies

that span the years 1968 to 2011 with 452 sets of elasticities that do not include cross price. The summary

statistics for each of these categories are shown in Table 4. Averages and medians suggest that estimates

of energy demand may tend to be more price elastic in studies which include cross prices than from those

that do not, while income elasticities are more similar.

Table 4 Summary of energy price elasticities in models with and without cross prices (typically capital,

labor, and materials (intermediate goods)).

With no cross prices included energy demand may tend to be less price elastic

Psr Pstat Plr Ysr Ystat Ylr

Average -0.15 -0.53 -0.57 0.44 0.77 0.95

Median -0.12 -0.45 -0.33 0.50 0.78 1.00

Stdev 0.17 0.49 1.73 0.50 1.12 0.65

Minimum -0.94 -2.54 -26.00 -1.40 -11.47 -2.31

Maximum 0 0.53 1.32 1.77 4.70 3.94

Count 94 141 259 82 147 216

With cross prices included energy demand may tend to be more elastic

Psr Pstat Plr Ysr Ystat Ylr

Average -0.50 -0.56 -0.77 0.50 0.76 0.79

Median -0.43 -0.51 -0.56 0.48 0.76 1.00

Stdev 0.66 0.99 0.85 0.49 0.45 3.06

Minimum -5.00 -4.69 -5.05 -1.68 0.11 -22.87

Maximum 2 14.52 0.79 1.63 1.71 7.93

Count 154 481 162 64 23 73

Source: Studies in Dahl energy demand database (DEDD)

The histograms of elasticities by category, shown in figure 7 also tend to support the observation that

studies with cross prices tend to find more elastic price responses.

Figure 7 Histograms that summarize the range of energy demand price elasticities computed from studies

with and without cross prices in Dahl Energy Demand Database

More than 85% of the energy studies with capital, labor, energy, and materials (with these four inputs

often referred to as KLEM) studies use a translog model. For more on the translog model, I turn back to

the MEDD database. One study Pei (1996) uses a translog model on aluminum, copper, lead, nickel, tin,

and zinc, but also does a separate lagged endogenous model on each metal on data for 1963-1992. She has

separate sets of estimates using these two model types for 29 countries or groups (Argentina, Australia,

Austria, Bangladesh, Brazil, Canada, France, Germany, FR, Greece, India, Indonesia, Italy, Japan, Korea,

Mexico, Netherlands, Nigeria, Pakistan, S. Africa, Scandinavia, Spain, Switzerland, United Kingdom,

United States, Zambia, Zimbabwe) as well as some groupings by region and by income. Summary

statistics for all her models are shown at the top of Table 5. Concentrating first on the own price

elasticities, these summary statistics show little short and long run price elasticities but considerably more

elastic response from static models. Dividing elasticities across model types, we see all the short and long

run price elasticities are from her lagged endogenous models and all the static elasticities are from the

translog model. Although we can't make strict comparisons by elasticity category, we can still see some

patterns. For the lagged endogenous models, only about 10% of the short run price elasticities are

significantly negative at the 10% level or better for a two tailed tests. For the translog model, the median

No Cross Price Included Cross Prices Included

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Histogram of Energy Demand Price

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Histogram of Energy Demand Price

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static elasticity is a much more elastic -0.71 with more than 85% of the estimates significant at the 10%

level or better with no positive elasticities.

Table 5: Some Model Comparisons from Pei (1996)

Metals= aluminum, copper, lead, nickel, tin, zinc. Data=1962-1993

All Psr Pstat Plr Ysr Ystat Ylr Qt-1

average -0.004 -0.754 -0.003 1.032 0.798 1.287 0.254

median 0.002 -0.713 0.004 0.712 0.797 1.086 0.226

stdev 0.251 0.186 0.769 1.832 0.056 2.794 0.353

min -1.410 -1.715 -2.439 -7.768 0.582 -10.522 -0.743

max 1.257 -0.323 11.690 16.198 1.004 31.241 1.026

count 344 72 344 344 72 344 344

All estimates from lagged endogenous models

average -0.004 – -0.003 1.032 – 1.287 0.254

median 0.002 – 0.004 0.712 – 1.086 0.226

stdev 0.251 – 0.769 1.832 – 2.794 0.353

min -1.410 – -2.439 -7.768 – -10.522 -0.743

max 1.257 – 11.690 16.198 – 31.241 1.026

count 344 – 344 344 – 344 344

All estimates from lagged endogenous models with time trend

average -0.002 – 0.028 1.400 – 1.729 0.155

median -0.006 – -0.005 1.338 – 1.652 0.126

stdev 0.267 – 0.951 2.222 – 3.473 0.331

min -1.200 – -1.467 -7.768 – -10.522 -0.743

max 1.257 – 11.690 16.198 – 31.241 0.971

count 172 – 172 172 – 172 172

All estimates from lagged endogenous models without time trend

average -0.006 – -0.034 0.666 – 0.848 0.352

median 0.007 – 0.018 0.451 – 0.791 0.394

stdev 0.233 – 0.531 1.237 – 1.797 0.349

min -1.410 – -2.439 -1.337 – -5.956 -0.613

max 0.802 – 3.154 7.681 – 13.232 1.026

count 172 – 172 172 – 172 172

All estimates from translog model (Al, Cu, Ni, Pb, Sn, Zn)

average – -0.754 – – 0.798 – –

median – -0.713 – – 0.797 – –

stdev – 0.186 – – 0.056 – –

min – -1.715 – – 0.582 – –

max – -0.323 – – 1.004 – –

count – 72 – – 72 – –

Source: Summarized from studies in the Appendix (http://dahl.mines.edu/MEDS.xlsx, worksheet MEDS)

Next, let's consider the cross price elasticities. She includes some cross prices in her lagged endogenous

model for all the metals but lead. The price of copper is included in the demand for aluminum, nickel, tin,

and zinc, while the price of aluminum is included in the demand for copper equation. In the translog

model, all the cross prices are included. Thus, we can't make a strict comparison for including or not

including cross prices but will still take a quick look to see if any interesting patterns emerge across the

two models for further investigation.

In the lagged endogenous models, the estimates for the cross price elasticities are more often found to be

positive (159 out of 286) suggesting substitutes, as expected, but fewer than a third of these positive

values are significant at the 10% level for a two tailed test. Less than 10% of the negative cross price

elasticities are significant at the 10% level for a two tailed test. Figure 8 shows that the short run estimates

for all countries and metals hover between -0.2 and +0.2 with an average near zero. Long-run cross price

elasticities are roughly 1.4 times more elastic.

Figure 8: Histogram of Short Run Energy Demand Cross Price Elasticities (Pei 1996).

Source: Summarized from studies in Appendix (http://dahl.mines.edu/MEDS.xlsx, worksheet MEDS)

The lack of significance of cross prices of related goods is common and often the result of collinearity in

the prices. Introducing flexible functional forms such as the translog, which are estimated with cross

equation constraints, is one remedy that has been tried. In her translog model, when the prices of all six

metals are included data restricts estimates to a smaller sample of twelve countries or regions: Germany,

Scandinavia, France, United Kingdom, Italy, Netherlands, Spain, Austria, Switzerland, Japan, Canada,

United States. The over-all summary statistics for all price and cross price elasticities for the translog

models are shown at the top of table 6.

Evidence from medians is strongest that aluminum and copper prices affect other metals as substitutes.

The median cross price elasticities for the various metals with respect to the prices of aluminum and

copper are similar at 0.19. At least 57 out of the 60 estimates are positive for each of these metal prices

and more than 80% of them are significant at the 10% level. Lead and zinc price effects on other metals

come next with the medians both near 0.15, 59 out of 60 are positive, and more than ¾ of each are

significantly positive at the 10% level. Nickel and tin prices show a lesser cross price effect on other

metals with cross price medians of 0.12, and 0.09. However, less of these cross prices are positive and a

quarter or less of them are significantly positive.

The second block of elasticities is the breakdown of the translog static elasticities into medians across

countries by each metal and the third block is the short run and long run comparable estimates from the

lagged endogenous models. What is striking and a takeaway for further investigation is how much more

elastic the responses are with the translog than with the lagged endogenous model.

The last comparison across these estimates from Pei (1996) is a quick look at the income elasticities and

time trends. For the lagged endogenous model, she runs the model for each country or grouping and each

metal with and without a time trend. Adding a time trend is always problematic. It is an expression of

ignorance, since we do not know what it is capturing. Presumably it is mopping up any effects correlated

with time that are not otherwise included. Most often authors claim it captures technical change. My

experience with energy models is that the coefficient on trend is often positive and its inclusion lowers the

income elasticity. I suspect it may just be picking up part of the income effect because its change is

0

5

10

15

20

25

Fre

qu

en

cy

Histogram of Energy Demand Cross

Price Elasticities: Short Run

smoother than income and may act more like lifecycle or expected income. In Pei's model the opposite

occurs. The coefficient on the time trend is usually negative and the median income elasticity both short-

and long-run more than double. While time trends are more likely to be higher for lower income countries

as are income elasticities.

Table 6 Comparing price elasticities from translog and lagged endogenous models in Pei (1996)

Translog

Own

Price Cross price elasticities

All metals P_Al P_Cu P_Pb P_Ni P_Tn P_Zn

average -0.754 0.206 0.109 0.241 0.113 0.046 0.190

median -0.713 0.190 0.188 0.142 0.120 0.087 0.152

stdev 0.186 0.143 0.506 0.422 0.097 0.153 0.432

min -1.715 -0.274 -3.550 -0.026 -0.116 -0.959 -1.123

max -0.323 0.904 0.386 2.587 0.660 0.187 3.204

count 72 60 60 60 60 60 60

Translog: Median own and cross price elasticities for the ten countries by metal from translog

model

Demand P_Al P_Cu P_Pb P_Ni P_Tn P_Zn Aluminum -0.670 0.186 0.134 0.103 0.081 0.166 Copper 0.198 -0.668 0.135 0.099 0.075 0.162 Lead 0.177 0.169 -0.684 0.135 0.071 0.134 Nickel 0.229 -0.116 0.544 -0.904 -0.066 0.312 Tin 0.211 0.117 0.267 0.129 -0.901 0.174 Zinc 0.216 0.192 0.127 0.097 0.067 -0.697

Lagged endogenous: Median short-run and long-run (sr,lr) own and price elasticities

across countries by metal from LE model Demand P_Al P_CU P_Pb P_Ni P_Tn P_Zn Income

Aluminum -0.1,-0.12 +0.08,0.11 – – – – 0.840

Copper

-0.02,-

0.03 -0.13,-0.14 – – – – 0.755

Lead – – -0.07,-0.22 – – – 0.773

Nickel – +0.06,0.08 – -0.14,-0.12 – – 0.841

Tin – +0.04,0.07 – – -0.1,-0.21 – 0.789

Zinc – +0.02,0.03 – – – +0.03,0.04 0.789

Source: Summarized from studies in the Appendix (http://dahl.mines.edu/MEDS.xlsx, worksheet MEDS)

In the lagged endogenous model, the activity variable is GDP. In the translog model, it is assumed that the

six metals are separable from the rest of the economy and shares equations are estimated. In the share

equations the activity variable is metal consumption. The activity elasticity from the share equation shows

how one metal's share changes as metals change. To get the total change in a metals demand, we need to

adjust the share elasticity by how income changes total metal demand. Pei does not estimate a total metals

demand and makes this adjustment by assuming three cases for returns to scale. With increasing returns to

scale she assumes that the elasticity of metal demand with respect to income (∂lnM/∂lnY=0.833), with

constant returns to scale ∂lnM/∂lnY=1, and with decreasing returns to scale ∂lnM/∂lnY=1.2. The

estimates reported in Table 5 are for the increasing returns to scale case as they seem most comparable to

the lagged endogenous estimates with no time trend.

I consider one last class of models in this review. As mentioned above, a number of studies have taken a

top down look and estimated models in a system with demand for capital, labor, energy and materials

(KLEM models) in industry. In some of the estimate in Berndt, Fuss, and Waverman (1980) energy is

divided into fossil fuels and primary electricity. Resource for the Future (1984) capital is divided into

equipment and structures. Sometimes the estimates are by separate industry, sometimes total

manufacturing, or total industry. The materials portion in these demand systems includes metals and other

materials but usually includes other nonmaterial intermediate goods and services, which can bias the

estimates. However, in some industries materials strongly dominate this category suggesting that the

materials elasticity may impart some information about materials elasticity. For example, in U.S.

manufacturing and in primary metal production in 2017 more than 80% of the purchases of intermediate

products is materials while more than 90% is materials in motor vehicle manufacture (U.S. Bureau of

Economic Analysis (2020)).

I have located 34 such studies that span the years from 1975 to 2019 with 313 sets of elasticities.

Summary statistics from all the models are shown at the top of table 7.

Table 7: Summary of Industrial Demand Elasticities from KLEM models

Own demand elasticities for materials from all KLEM models

All Psr Pstat Plr Ysr Ystat Ylr

Avg -0.239 -0.488 -0.394 1.080 0.986 0.857

Median -0.110 -0.340 -0.300 1.057 1.000 0.985

Std 0.317 0.547 0.470 0.210 0.162 0.808

Min -1.750 -2.780 -2.000 0.650 0.110 -4.458

Max 0.100 1.130 2.170 1.617 1.280 2.350

Count 103 201 107 27 72 62

Own demand elasticities for all metals and materials from MEDS in Table 3 above

Avg -0.063 -0.198 -0.200 0.803 0.926 1.136

Median -0.034 -0.082 -0.110 0.600 0.801 0.897

Std 0.272 0.552 1.183 1.352 1.256 2.612

Min -1.760 -5.144 -21.810 -7.768 -6.412 -10.522

Max 1.257 3.191 11.690 16.198 15.697 33.333

Count 511 567 643 717 344 559

Own demand elasticities for materials from all KLEM translog models

Avg -0.147 -0.508 -0.272 1.080 0.986 0.574

Median -0.070 -0.360 -0.220 1.057 1.000 0.822

Std 0.195 0.556 0.433 0.210 0.161 1.065

Min -1.028 -2.780 -1.620 0.650 0.110 -4.458

Max 0.090 1.130 2.170 1.617 1.280 1.054

Count 67 184 70 27 65 27

Own demand elasticities for materials from all KLEM non-translog models

Avg -0.409 -0.269 -0.625 – 0.984 1.075

Median -0.250 -0.216 -0.600 – 1.000 1.100

Std 0.420 0.387 0.456 – 0.193 0.437

Min -1.750 -1.703 -2.000 – 0.644 -0.050

Max 0.100 0.023 -0.050 – 1.248 2.350

Count 36 17 37 – 7 35

Source: Summarized from studies MEDS. (http:\\dahl.mines.edu\MEDS.xlsx, Worksheet KLEM.

Summary statistics show the price elasticities to be a little larger for these intermediate goods than those

from studies for separate metals and materials (repeated in the 2nd bank of elasticities in Table 7) but are

all less elastic than -0.50. This suggests that non-material intermediate good are likely more elastic than

metals and materials. The demand for materials in material intensive industries–iron and steel, all primary

metals, and motor vehicles–all have price elasticities near those for all the studies in MEDS. Static price

elasticity summary statistics are not as well behaved and are larger than those designated as long-run.

There are not as many estimates available for activity elasticities as for price and summary statistics for

activity are all near 1.

The most popular model is the translog model with 29 of the 34 studies using it. It is often referred to as a

flexible functional form, and the estimating equations are typically derived from a translog cost function.

The third block of estimates in table 7, show summary statistics from this model. As they dominate the

static estimates, little changes with their summary statistics. Their summary statistics do, however, show a

little less short and long run price elasticity and long run activity elasticity.

Only nine studies estimate on functional forms other than the translog, which are usually flexible

functional forms as well. They also typically start with a cost function to derive demand or share

equations. They include the generalized Leontief, the linear logit, the generalized Box Cox, the quadratic,

the square root quadratic, and the symmetric generalized McFadden. Their summary elasticity statistics

are shown in the last bank of summary elasticities in Table 10. Given the heterogeneity of modeling

techniques in the non-translog estimates, it is not so surprising the results across the two categories are

mixed. Summary statistics suggest the translog model gets less elastic short and long run price elasticities,

but more elastic price static elasticities. Four studies (Berndt, Fuss (1980), Considine (1989), Dargayand

Gately (2010), and Friesen (1992)), make a fairer comparison of the translog to another model on

consistent data but I did not see any interesting anomalies in their results.

None of the dynamic models, which get short and long run elasticities, are estimated using a lagged

endogenous model. Rather the dynamics tends to take on two forms. Berndt, Fuss (1980) denote the static

translog model as first generation and suggest two dynamic equations. Their second generation models

includes the capital stock as fixed in the short run in the demand or share equations rather than including

its price giving short run elasticities. Long-run elasticities are derived from an estimated cost function and

long-run optimizing conditions for capital stock. Their third generation dynamic model includes both the

capital stock and the change in capital stock in the short run share or demand equations. Long run

elasticities and the adjustment path are derived from and estimated cost function and dynamic conditions

for cost minimization.

Data Sources: As data is always a challenge in econometric work, I will also start compiling data sources

in the database. In this paper, I will only mention a few of the more obvious price sources, with

continuing work to uncover more that will be included in the database. Futures exchanges offer relatively

transparent prices and often the one-month future is used as a spot price. For example, London Metal

Exchange (LME) has contracts for aluminum, aluminum alloy, North American special aluminum alloy,

cobalt, copper, lead, molybdenum, nickel, steel billet, steel rebar, steel scrap, tin, and zinc. Comex, the

metal trading branch of CME group (formerly the Chicago Mercantile Exchange), trades gold, silver,

copper, aluminum, palladium, platinum, and steel. The Shanghai Metal Exchange trades refined copper,

aluminum ingot, lead, zinc, tin ingot, nickel, domestic lead concentrate, imported lead concentrate, and

refined cobalt.

Conclusions

This ends the summary of the status of my Mineral Energy Demand and Supply Database at the date of

this version of the working paper. Most of my effort so far has gone into collecting studies, collating

elasticities, and checking data. This first pass through the database has been visual observation,

considering summary statistics and watching for patterns and hypothesis for further testing with little

statistical effort or more comprehensive consideration of methodology by study.

As studies, results, and outliers have not yet been thoroughly checked and vetted, any conclusions at this

point are tenuous at best. Nevertheless, as interest in mineral demand and supply seem to be on the

upswing, I offer up this labor intensive database to other researchers as a leg up in their literature review

with the caution that nothing is definitive at this point and statistics should be rechecked before use.

Although I will continue to collect studies, I will now also be shifting my attention towards more detailed

and critical analysis.

From this broad top down look, I offer the following observations. Outliers in many of the categories can

be quite extreme. In some cases, I have looked at a cause for the outliers in this paper. For example,

models with very low and or negative coefficients on a lagged endogenous variable, often give

unbelievable elasticities. Until all these outliers are vetted and are either rejected or explained, I keep

them in the database but am inclined to put more emphasis on group median elasticities than averages.

Despite supply and demand varying by time, place, metal, geological conditions, costs, stage of economic

development and model chosen for estimation, all of which very considerably across studies, the

clustering of elasticities for all the elasticity categories gives us some confidence that medians might be

capturing some useful similarities.

For supply models, shorter-term elasticities are likely to be less than 0.4 while the longer-term elasticities

tend to be less than one. One reservation I have in using econometric work for long-term supply equations

is that mine development may be responding to many years of data, new supply may take many years to

be developed and that development may be highly variable and location specific. Capturing these

dynamics econometrically is then difficult and may help explain why there are far fewer econometric

estimates for supply than for demand. It also leads me to suspect that long run supply elasticities may be

larger than those estimated. In addition, if the industry is not competitive, a supply curve does not exist.

Econometric work to date suggests that material demand is quite inelastic with the bulk of short-run,

static, and long-run elasticities being less elastic than -0.5. A disconcerting number are not significant or

are positive. More work will be done to investigate the rather suspicious cases that lack any price

response. As metals and materials are often sold under long-term contracts with proprietary information,

LME and other more transparent prices are often used. It is unclear how good these other prices proxy the

actual prices. Second, given how capital-intensive manufacturing is, lags in response to price may not be

well reflected in the lagged endogenous model that puts the largest response in the current period. Support

for this theory comes from models that use distributed lags on price. In such models, the long run

elasticities are more elastic than -0.6, and the current time period does not show the largest response. A

further anomalous result for the lagged endogenous model is how short the adjustment period is in the

capital-intensive industries that use metals and materials. Last flexible functional forms with cross price

elasticities estimated tend to get a more elastic own price response as well. How the functional form as

well as including cross prices influences the own price elasticity estimate will be further scrutinized.

Clusters for demand activity elasticities tend to be much wider than those for price. For example, mineral

demand elasticities in the short run cluster between 0 and 1.2, from static models from 0.5 to 1.5, and

long-run models from 0 to 2. Some of this deviation is likely the result of the choice of activity. If the

choice of activity is the product directly made from the metal with the metal being incorporated in the

product, we would expect this elasticity even in the short run to be near to 1. It should only change in

response to the substitution across material inputs in response to changes in price and technology. If the

activity variable is GDP, activity elasticity reflects increases in the final product from increases in GDP as

well as changes in GDP towards more or less material intensive products.

For the latest database with elasticity estimates by equations for a metal product including region and

years for the estimate, included variables, and measure of statistical fit see

http://dahl.mines.edu/MEDS.xlsx, worksheet update. The bibliography of studies included in the most

recent update can be found at http://dahl.mines.edu/MEDSBib.pdf. Enjoy and send along your comments,

corrections and suggested additions (cadahl@mines.edu).

Reference

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column F under references. It is usually three letters and the last two digits of the year. It is followed by a

small letter if it is not unique (e.g. Dah20a, Dah20b) If the code is followed q and another code the

elasticities have been quoted from a second source.

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