Policy, Research, and External Affairs t i - - / -
WORKING PAPERS
Public Economics
Country Economics Department
The World Bank
August 1990
WPS 496
Issues in Evaluating
Tax and Payment
Arrangements
for Publicly Owned
Minerals
Robert Conrad
Zmarak Shalizi
and
Janet Syme
No single revenue instrumilent can be assumed to be superior for
mineral-dependent developing countries. And more than one
instrument may be needed to meet a government's multiple
objectives. <.
The Pohc) Rescarch. and I:xiemal Affair Comp;cx diLnhutcs I'Rl: Workng Papers mindi nsomnatethe indings of workin progress and
to encourage the exchange of idecas amorg Hank saff and all others interested in developmient issues These papers cany the names of
the authors, renect only their views, and should lie used and (tied ac cordingl) The findings. intcrpretauons and conclusions are the
authors ow-l They should not h a:tnhucnd li r lek.-d 3ank. 13,IarJ of I),rc , irs managa-nen.t or an) of iLs.mennbhr countines.
Policy, Research, and External Affairs
Public Economics
WPS 496
This paper -a product of lthe Public Econornics Division, Country Economics Department is part of
a larger effort in PRE to identify mineral payment/tax systems in developing countries that are simple, fair,
and efficient. Copies are availarolc free from the World Bank, 1 818 H Street NW, Washington DC 20433.
Please contact Ann Bhalla, room N I 0-059, extension 37699 (50 pages with Figures and tables, plus 19 pages
of appendices).
Many developing countries depend heavily on instruments affcct risk-sharinig between the
mineral extraction to generate fiscal revenue and govemment and thc producer. Applying critcria
cam foreign exchange. Are thcse countries for ranking revenue instruments to three typical
collecting enough in return for depleting their instruments -royalties, income taxes, and
reserves? Are they carrying too much of the resource rent taxes - they conclude that al-
risk? Conrad, Shalizi, and Symc describe work though profit- and rent-based taxes are gaining in
in progress to develop a practical framework for popularity over production-based taxes, no single
analyzing these questions. instrumcnt can be presumed to be superior for
mineral-dependent developing countries. Each
In the first part of the paper !hey review the country has different endowments and faces
central issues that must be addressed in design- different risks. These factors must be taken into
ing mineral tax and payment schemes. They account when selecting instruments and deter-
note the need to detcrmine both the opportunity mining rates. In somc cases production-based
cost of mineral cxtraction (including externalities payments, suchi as royalties, may be justified and
vis-a-vis other sectors of the economy) and the should not be systematically deemphasized as
costs borne by the country through risk-sharing they arc now.
arrangements.
Using simtlple models of thc type described in
Obscrving that at present there is no practical the paper will enable governments to cngage in
analytical framework to analyze tradeoffs or reasonably sophisticated risk analysis at a
determine the rate structure for differcnt revenue relatively low cost when designing tax and
generating instruments, they introduce a simple payment arrangemetis. Further work is required
cash-flow model in the second part of the paper. to develop a practical framework which models
With this model they illustrate how different additional tradeoffs.
Thc PRE Working Paper Scries disseminalcs thc Findings of work under way in thc Bank's Policy, Rescarch, and External
AffairsComplex. An objective of thescrics is to get these findings outquickly, cven ifprcsentations arc less than fully polishcd.
The findings. intcrprctahions, and conclusions in thcse papers do not necessaril) represent official Bank policy.
Produced hy Lhe I'RE Disseninalion Center
Issues in Evaluating Tax and Payment Arrangements
for Publicly Owned Minerals
by
Robert Conrad
Zmarak Shalizi
and
Janet Syme
Table of Contents
Summary i
Introduction 1
Part I: Evaluating Tax/Payment Instruments in the Mineral
Sector: Selected Issues 3
A. What is Natural Resource Rent? 5
B. Risk Sharing 10
C. Economy Wide Effects 13
D. Tax Policy 15
Part II: An Illustration of Risk Sharing Through Different
Instruments 18
A. Selected Mineral Tax/Payment Arrangements 18
B. Ranking Criteria and Methodology 23
C. Results 30
D. Summary 45
Bibliography 48
Appendices
Summarv
Many developing countries are still heavily dependent on mineral
extraction to generate fiscal revenue and to earn foreign exchange. When
minerals form a significant proportion of the country's asset base it is
particularly important to have a framework to evaluate the adequacy of
compensation schemes. Are these countries collecting enough in return for
depleting their reserves? Are these countries carrying too much of the
risk? This paper describes work in progress in developing such a
framework.
In many mineral dependent countries, the government holds the
mineral rights and enters into compensation agreem,nts with public or
private firms that will extract the resources. In practice, the
distinction between factor payments and taxes is increasingly confused, in
part because governments have a dual role as both mineral owner and tax
collector. This distinction is more than a semantic one since factor
payment policies are judged according to a dIfferent set of economic
criteria than are tax policies. From this perspective, the current
emphasis on modifying mineral tax/payment arrangements to maximize rent-
capture, without adequate evaluation of the opportunity costs associated
with the arrangements, may be misplaced.
Given the high degree of risk and uncertainty associated with
mineral development, determining tax/payment arrangements is further
complicated by the need to develop risk-sharing schemes between the
government (as owner) and the resource extractors, and the need to identify
externalities affecting other sectors in the economy that might justify
additional modification of the tax/p-yment arrangements. The first part of
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the paper reviews these issues briefly and concludes that when objectives
are not perfectly correlated it is preferable to use multiple instruments
and to match each instrument to an objective.
Despite substantial advances in the theoretical literature, there
is at present no practical analytical framework with which to analyze
tradeoffs or to determine the rate structure for the different instruments.
The second part of the paper rarorts or. preliminary results from a simple
cash-flow model designed to illustrate one aspect of the mineral contract:
how different revenue generating instruments affect risk-sharing between
two parties--the resource owner and the resource extractor. In models of
developed economies if the government is owner of the mineral resource it
is assumed to be risk neutral since it is better able than a resource
extracting firm to diversify its portfolio and hedge against risks
associated with resource extraction. However, mineral dependent developing
countries with limited access to international capital markets, may not be
able to hedge adequately against financial risks arising from variations in
commodity prices, exchange rates, interest rates, etc. Even if financial
risks can be accommodated, there are non-financial risks associated with
mineral development, such as reserve or operating risks, which can expose
the public revenue structure o' developing countries to shocks that
necessitate difficult adjustments. Stabilization funds can buffer some
unevenness in revenue flows but are not intended to address risks arising
from project failure.
The purpose of the initial simulations is twofold. First, to
demonstrate that even with a %ery simple model it is possible to illustrate
how different instruments affect risk-sharing between the producer and the
government; and second, to develop a practical evaluation tool that can be
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used in developing countries with limited data. All computations are
feasible on a personal computer using a spreadsheet with a risk simulator.
Government analysts applying this type of model to their country's unique
circumstances will be able to understand better the nature of revenue
variability under different contract regimes.
Three typical instruments found in mineral contracts are used in
the initial analysis: the ad valorem royalty; an income tax of the "free
equity" type; and a resource rent tax (RRT). The ad valorem royalty is a
charge per unit of output measured as a percentage of the nominal price.
The type of income tax used in the analysis is one in which there is less
than perfect accrual accounting. It is similar in effect to a production-
sharing arrangement with allowance for depreciation. That is, the mineral
owner receives a fixed proportion of current book profits for each period
in which profits less accumulated losses carried forward are positive. The
owner receives zero if losses exceed profits. Losses are carried forward
without interest. The RRT scheme carries losses forward with interest when
the net assessable receipts are negative. The RRT scheme provides the
resource owner with positive revenues only in periods where the accumulated
net assessable receipts are positive.
The instruments are analyzed one at a time to illustrate -heir
effect on the risks iacurred by the contracting parties. A highly stylized
mining project cash flow is generated by the model using stochastic prices
and costs with covariance between the two. The model then calculates the
expected value and variance for each instrument's flows to the government
and producer using a risk simulator. To simplify the initial analysis, it
is assumed that the geological composition of the deposit and investment
costs are known with certainty, a-id that the extraction profile is
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determined es Senously (these restrictions vill be relaxed in future
research).
When one party to a contract is risk-averse and tbe' other risk
neutral pareto efficiency requires that the risk be borne by the risk
neutral party. The applied literature has focussed on the ranking of
instruments from the perspective of a risk-averse firm and a risk neutral
government. The simple model used in this paper is able to simulate these
results well. The model can therefore be applied with some confidence to
the ranking of instruments from the perspective of a risk averse resource
owning government. The results show that the ranking of the instruments by
government can be opposite that of the firm's. This is an important issue
which has not been widely addressed in the literature. For example, in
selecting an instrument to address risk and uncertainty it is not
sufficient to look only at the overall variability in a project's cash
flow. It is also important to determine the probability that the net
present value (NPV) of the cash flow is positive. For instance, under a
RRT, the government receives revenues only in cases where the NPV of the
project is positive. Thus, if the probability is 60 percent that the NPV
of the project will be positive, the government stands a 40 percent chance
of never receiving any revenue. The Government will be forced then to
incur adjustment costs even though it depletes the mineral asset. By
contrast, both the royalty and the income tax will lower the risk to the
government (the former more than the latter) since they generate a positive
NPV (revenue flow) to the government in every period that extraction is
positive, whether or not the NPV of the project is positive. This benefit
to the government accrues at a cost to the firm as it lowers the
probability that the NPV of the producer's after-tax cash flow will be
positive. To correctli evaluate the risk element aasociated with each
instrument, however, It is necessary to compare instrumonts holding the
mean NPV shares of tbe contracting parties constant. This requirment
provides a convenient and practical benhomark for determining rates for the
different instruments. That is, if the goverment negotiateo a 40 percent
share of a project's expect-d NPV, then, Siven the paramoters of the model,
it must set the royalty rate at 1 percent or the nT rate at 13 percent
when there is en approximately 40 percent chence that the project will
fail, and at 3 percent or 32 percent respectively if the probability of
failure is much lese at approximately 25 percent. The lower the
probability of failure, the higher the mean WPV and the higher the rate
required to capture 40 percent of it.
When the probability of a positiv NPV for the project is leos
than 100 percent, the probability distributions are also no longer
symnetric about the mean. As a result the varince Is not an adequate
measure of risk. In such situations, particu *1.y if the parties are risk-
averse and the various instrumnts treat positive and negative projcąt
outcomes differently, it is better to use second-order stochastic dominance
as a general measure to rank risk-sharing features of revenue Instruments
in lieu of mean-variance analysis.
Applying these techniques to the simple model enables one to
demonstrate numerically a famillar result from the risk-sharing literature;
namely, if both parties are risk averse, they will not necessarily have the
same ranking of schemes, holding the mean returns covetant. Therefore, in
general, it will be necessary for contracting partzes to trade mean
expected values for risk. This Implies that no single Instrument (or set
of contract terms) can be, * Sz , a4wdvocated as superior for *mneral
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dependent developing countries. Each country has diffcarent endowments
(portfolio of initial assets) and faces different risks. These factors
must be taken into account when selecting instruments and determining
rates. In some cases royalties may be justified and should not be
systematically deemphasized as they are iow. The current tendency to focus
on mean values in mineral project evaluation could also be misleading since
the probability is zero that the mean value will o-cur.
The advantage of the practical framework being developed i thIat
it will eventually enable governments to engage in this type of risk
analysis at a relatively low cost when designing tax/payment arrangements.
The results reported in this paper are illustrative and preliminary, bott
they point in the direction where future work is necessary such as
developing additional tradeoffs, empirically estimating parameters, and
testing the simple framework in applied situations.
INTRODUCTION
1. Many developing countries are still heavily dependent on mineral
extraction to generate fiscal revenue and to earn foreign exchange. In
over thirty developing countries, mineral exports account for 25 to 75
percent o. total exports. Unlike other export oriented sectors, however,
mineral sectors tend to be enclaves with few inter-industry linkages.
Therefore, for mineral wealth to become a major endowment for financing
development (in other words, to facilitate growth and diversification of a
country's asset base), it is necessary not only to extract itl but also to
ensure a positive net fiscal impact over and above that required to replace
the asset.
2. An important feature of mineral sectors is the presence of "rent",
in fact a variety of rents -- natural resource rents, Ricardian relLts,
monopoly rents, windfall rents, and so on.2 This opens up options for
tax/payment arrangements not often available to non-mining economies. It
is not surprising, therefore, that, on average, mining economies have
public revenue3 to GDP ratios approximately twenty five percent higher than
non-mining economies.4 Or. tne other hand, there are also constraints on
I/ Mineral wealth, unlike many other types of economic assets, can generate in.ome
(liquidity) only if extracted. Since extraction is irreversible (depletion), it is
equivalent to selling the asset.
2/ Definitions of these terms and a selected set of others used in the paper are provided
in Appendix 4.
3/ Public revenue consists of tax revenue and non-tax revenue (such as fees, royalties and
other payments).
4/ A considerable number of these mineral exporting countries collect a third to two thirds
of their revenue from the mineral sector.
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how much revenue they can extract from the mining sector. If a country's
mining taxes are too high relative to competing countries, investment may
choose to shift to the relatively lower tax countries. In practice there
is a substantial variation in the ratio of mineral revenue to mineral value
added between countries (for example, 75 percent in Botswana versus 25
percent in Papua New Guinea). These differences are significa-t. They
might be explained by differences in the composition of the mineral base,5
by phases in the life cycle of mineral extraction,6 or by risk sharing
arrangements, among other possibilities. However, no framework based on
practical criteria has yet been developed that can determine whether the
revenue instruments are collecting too much or too little from the mineral
sector or whether the revenue instruments in use generate signals that are
consistent with the overall development of the sector, as well as, the rest
of the economy.
3. When minerals form a significant proportion of a developing
country's asset base, it is particularly important to have a framework to
evaluate the adequacy of compensation schemes. Are these countries
collecting enough in return for the depletion of their reserves? Are these
countries carrying too much of the risk? This paper describes the work in
progress in developing such a framework.
4. The first part of the paper briefly reviews the issues that need
to be included in an analyt. 1 framework before it can be used to evaluate
different tax/payment instruments. The second part of the paper reports on
5/ Sane inerals have a higher rent content then others (for example, diamond va copper).
j/ At earlier pbasee of developcnt, net revenue is often low as the initial outlay _.n
capital lntensive Investments Is recouped through "expensaing or accelerated
depreciation.
the developmant of a module to examine the risk sharing features of
selected revenue instruments.7 The paper concludes with a summary and a
set of appendices.
PART I
EVALUATING TAX/PAYMENT INSTRUMENTS IN THE MINERAL SECTOR: SELECTED ISSUES 8
5. The literature on mineral economics is vast and a number of
approaches have been developed to address different problems. Each problem
is defined narrowly in order to make it tractable. However, tax/payment
instruments are ranked differently depending on the problem addressed. For
example, cash flow taxes emerge as eminently suitable for collecting
economic rent and for sharing risk when the contracting parties are risk
neutral but not if they are risk averse. Production or profit sharing
contracts are good for generating revenue but not for economizin- on costs.
Each result depends on assuming away some of the other issues which,
however, cannot be igrored in practice.
6. In many mineral dependent countries, the government holds the
mineral rights and enters into compensation agreements with public or
private firms that will extract the resources. As a result, in practice,
the distinction between factor payments and taxes is increasingly confused,
in part because a government has a dual role as both the seller of
7/ This does not imply that risk sharing can necessarily be separated from the other
elements of a contract. Often, all contract terms are not strongly separable. For
instance, the level of risk borne by all parties might be a function of the total
quantity extracted and the time period in which the particular quantities are extracted.
However, an examination of risk sharing in Isolation enables a comparison of particular
contract terms relative to an exogenous distribution of risks and returns.
I/ This section Is based on Part II of a research proposal to develop a framework to
evaluate mineral :;yments/taxation scheme (Shalizi and Conrad, 1989).
- 4 -
resour-ms and the collector of taxes. This distinction is more than a
semantic one as factor payment policies are judged according to a different
set of economic criteria than are tax policies. From this perspective, the
current emphasis on modifying wineral tax/payment arrangements to maximize
rent capture, without adequate evaluation of the opportunity costs
associated with the arrangements, may be misplaced. Given the high degree
of risk and uncertainty associated with mineral development, determining
tax/payment arrangements is further complicated by the need to develop risk
sharing schemes between the government (as owner) and the resource
extractors, and the need to identify externalities affecting other sectors
in the economy that might justify additional modification of the
tax/payment arrangements.
7. As mineral stocks represent part of an economy's capital endowment
at any point in time, it is important that the government compute the
public sector selling price of its reserves and evaluate the variability of
its returns through t'me. This price will be based on the opportunity cost
of extraction and can include up to three interrelated elements (Conrad
1989): (i) the scarcity value of the finite reserves; (ii) pure risk
sharing; and (iii) the general equilibrium opportunity cost of extraction.
The government, acting as tax collector, can then assess taxes.
8. Thus, of the many issues addressed in the literature, four have
been identified as being particularly important in designing a practical
framework to evaluate tax/payment instruments: (1) how to design natural
resource rent collection schemes; (2) how to design risk sharing
arrangements; (3) how to incorporate general equilibrium effects/adjustment
costs of the transition to and from mineral dependency; and (4) how to
design tax policy in the mineral sector. These issues are distinct, and
lack of attention to the distinctions can lead to inappropriate policies in
developing economies, such as overstating the supposed inefficiency of
extraction-related payments. We now discuss each issue and place them in a
broader framework.
A. What is Natural Resource Rent?
9. A central feature of the literature on mineral economics has been
the development of methods for the determination of an efficient
intertemporal extraction profile. The time path of extraction is treated
as an endogenous variable.9 The general result of this literature is that
extraction should proceed in each time period until the discounted
opportunity cost of extractior is equal between any two time periods. This
result defines an allocative suPPlY price based on the rent accruing to a
finite. depleting stock. In Hotelling's (1931) original formulation, this
implied that the time path of the supply price of the resource (opportunity
cost of extracting the resource) should rise at the rate of interest.
10. Hotelling's model presumed physical exhaustion of the resource (a
rare occurrence in reality as increasing marginal costs of extraction
usually preclude physical exhaustion) and constant returns to scale (zero
extraction costs are a special case of constant returns to scale). With
the subsequent incorporation of stock effectsl0 and increasing marginal
costs of extraction, physical resource exhaustion is no longer required to
generate positive natural resource rents in theoretical models. Economic
9/ This differs from some practical approaches where, in order to facilitate and simplify
determination of user costs/prices for natural resources, it is assumed that the
extraction profile is exogenous (see Schramm 1986).
IO/ Such as changes in the cumulative stock of resources due to exploration efforts or
depreciation.
-6-
depletion thus preempts physical depletion. As a result, the Hotelling
rule has evolved into a more general rule that states that the resource
payment (in other words, user cost or natural resource rent) should equal
the opportunity cost of capital. While the shadow price of the resource
(the "royalty" as defined by Hotelling) is constant in real terms, there is
no longer a requirement that its time path should rise at the rate of
interest.11
11. "Natural resource rent" (or the price of the unprocessed mineral
below ground) is the difference between the market price of the unprocessed
mineral above ground and the marginal cost of extracting it. However, the
more general formulation that the opportunity cost of mineral resources is
the same as the opportunity cost of capital has led some authors in the
1970s to equate "natural resource rent" with "pure economic rent". Such
treatment de facto implies that "natural resource rent" serves no
allocative function (as it did in the Hotelling formulation). As a result,
this rent can be captured by charges that are not related to extraction
with no efficiency cost. This interpretation has led to proposals to
maximize rent collection, favoring income related charges over royalties,
culminating in instruments such as the Garnaut and Clunies-Ross Resource
Rent Tax (RRT).12
12. It is inappropriate to equate "natural resource rent" with pure
economic rent. Natural resource rent is a price and serves as an important
11/ See Fisher (1979).
12/ An RRT is essentially a cash flow tax except that, in the case of losses, an RRT does
not result in a rebate to the firm, as would happen in a cash flow tax, but allows
losses to be carried forward at the rate of interest. As noted in Lund (1985), the RRT
was origiually proposed as a complete mineral payment/tax system. In practice, it has
also been used in conjunction with other instruments.
-7-
market signal to ownerlproducers indicating how to allocate the resource
intertemporally so that they can be indifferent about whether to extract
now or later. As a first approximatlion, the price represents the "scarcity
rent" arising from supply restrictions on a finite resource of uniform
quality and has nothing to do with Ricardian differential rents13 or other
forms of economic rent based on monopoly, windfalls or other factors. As a
price of an input, it is an element of the cost of production and not an
intramarginal rent. Without knowing the shadow price of extraction, no
party, owner or producer can determine an efficient extraction profile. It
might be possible to reduce this stream of payments to a lump-sum
contemporaneous payment, like the valuation of corporate stock. However,
it must be emphasized that the source of this equality stems from the
computation of the shadow price of reserves on a Rer unit basis. That is,
only after determining the natural resource rent or price can one determine
the present value of any deposit.
13. A related strand of this literature has focused on auctions as the
best means for the owner of the resource to capture the present value of
the resource due to him as the holder of the property rights. This
approach is applicable in principle both to private and public owners of
the resource. (It is used, for example, by the U.S. in leasing offshore
tracts). Note that in practice, however, if there is inadequate
competition in the auction bidding process, the government has to determine
a reservation price for the resource.14 This can be done using a portfolio
13/ Op cit.
14/ Recently bonus bids or auctions have also been contested on theoretical grounds vhen
sovereign risk and moral hazard problems are incorporated into the analysis (Nellor and
Robinson, 1984)--problems more prevalent in developing countries. If subsequent
goverrments are aot bound by auction results, then a stream of payments (in the form of
royalties) may be superior to collecting the net present value at one tlme in an
auction.
- 8 -
or factor of production approach to analyze the efficient use of the
natural resource.
14. In a portfolio approach, natural resources are one component of an
economy's capital stock. Without a competitive return, no party, including
the government, would be willing to own and husband this stock. Thus, in a
portfolio type model, "natural resource rent" serves as the return from
investing in ownership of stocks in the ground relative to the return from
investing in other types of capital. In effect, this is what is implied by
the original Hotelling Rule. Minerals in the ground must be extracted to
generate cash through time. This time path of cash withdrawals is
calibrated so that the owner of the stock captures a return just sufficient
to hold reserves for future use. Again, "natural resource rent" serves an
important allocative function. This allocative function is implicit in the
demonstration by Feldstein (1977) in which he changed the allocation of
capital within and among sectors to prove that attempts to "tax" this rent
can be inefficient.
15. In a factor of production approach, "natural resource rent" is the
return to the owner from a factor of production and thus constitutes an
efficiency based payment (Conrad 1989). That is, the owner of mineral
rights is the owner of a productive input, not output. To produce mineral
outputs, labor, capital and mineral inputs are required. The cost of
reproducible capital and labor are included in the expenses that are
incurred in the production of mineral outputs. The cost of mineral inputs
should also be included. This point has been a source of some confusion as
many theoretical models used in the economic analysis of mineral
development do not make a distinction between the resource owner and the
producer. This distinction is conceptually important because "natural
-9-
resource rent" is the payment made by the producer to the rwner for the
purchase of the resource input (even if they are legally the same entity in
practice). Furthermore, this efficiency payment is defined on a per unit
basis, just like the wage rate for labor or the rental value of capital.
Thus, like the supplier of any factor, the resource owner must determine
how to sell his inventory intertemporally and what opportunity costs exist
to establish the relevant reservation wage for this factor of production.
16. In summary, what these different approaches to shadow pricing the
resource have in common is that in all cases the extractioLi related
payments serve an important allocative function both for the resource owner
and the economy as a whole. Such payments (suitably calibrated) are
efficient and do not distort extraction decisions. The payment for the
sale of a ton of minerals in the ground should not be conceptually any
different from the payment for the sale of any other input.
17. Because of this, recent attempts to equate natural resource rent
with pure economic rent have been problematic, leading to poor policy
analysis. In particular, the current emphasis on income related charges
has concentrated the debate on the maximum amount a country can receive for
its minerals, with little regard to intertemporal and intersectoral
opportunity costs or to the risks to the country associated with mineral
extraction. A return to a more appropriate factor payment policy might
force decisionmakers to examine the costs as well as the benefits of
mineral developments. More importantly, regardless of the ultimate method
employed by a government to collect the value of its mineral wealth,
renewed emphasis on the supply price of the resource will serve as a
benchmark for evaluating alternative policies.
- 10 -
B. Risk Sharing
18. Given the inherent uncertainty regarding the size of mineral
stocks before exploration and of the revenue and cost streams associated
with mineral development after exploration, risk sharing arrangements are
important in the rational development of mineral tax payments/sch-mes.
This is particularly important where markets for contingent claims across
different states of nature are neither complete nor perfect. One of the
major innovations in recent mineral contracts, in the petroleum sector in
particular, is the development of risk sharing contracts or contracts with
significant risk sharing aspects. In general, these innovations require
the mineral producing firm to surrender part of the "net profits" from the
positive cash flows that are generated after exploration and development
costs are recouped. Theoretical support for such schemes was first
established in an important paper by Leland (1978). Leland demonstrated
that an extraction related charge (for example, a royalty) is an
inefficient method for risk sharing.
19. Subsequent analysis of risk sharing between two risk neutral
parties has shown that in the case of mean preserving spreads (in other
words, for equal expected levies), profit sharing is a more effective
method for spreading risk, followed by royalties and then fixed fees (such
as bonus bids). However, in the case of a small, risk averse firm and a
large, risk neutral (diversified) government (such as the U.S. or Canada),
royalties could be superior to profit sharing when there is positive
covariance between uncertain revenues and costs (Sebenius and Stan 1982).
In the case of developing countries, the issues are slightly different as
the contract is likely to be between a large multinational firm and a
small, poorly diversified developing country (Garnaut and Clunies Ross
- 11 -
1975). The ranking of instruments, however, is likely to depend again on
the covariance between uncertain revenues ar.d costs.
20. Mineral reserves have uncertain present values, as does labor in a
dynamic labor market. This implies that the Hotelling formulation, while
instructive, may not be appropriate in all situations where physical
capital, labor and reserves are owned by different parties and where there
are risks that must be borne by some (or all) parties. In such cases, two
prices might be computed, one for the real wage for minerals and one for
the price of risk bearing. Mineral owners and contractors, have developed
numerous methods whereby both risk and return can be combined into a single
payment, again as in contracts between employers and employees.
21. The fixed wage rate is itself one type of risk sharing device with
the particular property that the firm will continue to employ that factor
as long as it is profitable to do so. Thus, the input seller bears the
risk that his fixed price is too high relative to the value of his marginal
product as dictated by either current (or future) market conditions. In
minerals, such unemployrent of factors is sometimes called "high grading".
However, the use of a fixed wage rate is not irrational for the mineral
owner as long as the opportunity cost of selling additional inputs is not
zero. Rationality in this context includes weighing the potential gains
against the risk of unemployment and will depend on the risk preferences of
the input seller.
22. In general, not only must risk sharing be evaluated in the proper
context, but specific instruments might have to be used to accommodate risk
relative to other costs associated with mineral ownership and development.
That is, it may not always be efficient to design a single payment
structure (for example, a profit sharing contract or a resource rent tax
- 12 -
[RRT]) both to capture the natural resource rent and to provide for risk
sharing.15 The ability of a particular economy to bear the significant
risks associated with such schemes as profit sharing or the RRT will depend
on the particular attributes of the economy, for example, the degree of
existing diversification, the relative size of the mineral sector and the
overall level of wealth. It is necessary, therefore, to price the risk.
To our knowledge, there is no theoretical demonstration that in general it
is efficient for small, poorly diversified developing economies to bear a
disproportionate amount of risk relative to large diversified multinational
firms.
23. Thus, the high amount of risk bearing currently undertaken by some
countries (for example, Gambia and Nigeria) may be the inadvertent
consequence of failing to differentiate between risk bearing and the
collection of natural resource rent, both at the margin and in total.
Willingness to bear risk is a form of insurance provided by the country to
the firm, while natural resource rent is the factor payment to which the
country is entitled by right of property ownership. The payments are
conceptually different, and practical policy advice should be directed
towards clearly distinguishing these concepts and to developing alternative
instruments where necessary. These differences are important as a country
that adopts an RRT, profit sharing or income related scheme exclusively
could have all its natural resource endowment extracted, incur significant
15/ For instance, the RRT propob.)d by Garnaut and Clunies-Ross (1983) is designed to capture
rent (regardless of the nature of these rents). It handles risk to the firm by
excluding from the tax base a high rate of return on investment (no distinctions are
made between discount rates before and after exploration or between returns on total
investment versus equit- investments). However, neither the RRT nor other means of
capturing supposed natural resource rent directly address the issue of risk bearing by
the country or the price of this risk.
- 13 -
transition costs and never collect a positive payment for its ownership of
tbe resource endowment.
C. Economy Wide Effects
24. Much of the development literature has emphasized the enc'sve
nature of mineral developments and that the primary linkage between natural
resource production and the remainder of the economy is fiscal (Nankani
1979). This is true to a certain extent, but as another strand of the
literature has noted, important indirect production linkages can arise
through factor markets and through changes in key macro prices such as
exchange rates, interest rates and wage rates (Corden 1984). This occurs
most noticeably when significant mineral deposits are disaovered16 that
increase an economy's capital stock in a sector specific way. In this
case, there will be a change in the economy's comparative advantage even if
there are no other direct linkages with the rest of the economy. For
instance, signi icant mineral discoveries can change the nature of
comparative advantage from traditional exports (such as agriculture) to
mineral exports. If the country is a price taker, one can expect that, as
mineral development proceeds, mineral exports will rise and traditional
exports will fall (holding world prices constant). This process also
operates in reverse. That is, as minerals are depleted and production
costs rise, the economy's comparative advantage might return to traditional
exports (or to output from other sectors into which the economy has
16! The significant scale of the discovery relative to the size of the economy is important
in determining vhetber or not to incorporate general equilibrium effects. For genuinely
marginal finds, partial equilibrium analysis is sufficient to determine the endogenous
extraction profile.
- 14 -
diversified). Such incremental changes in comparative advantage due to
mineral developments are one component of "Dutch Disease". This
substitution effect is generally complemented by an income effect since a
mineral discovery increases the economy's wealth. It is even possible for
changes in the nature of demand (for example, a rise in demand for non-
tradables) to occur when there is no change in the economy's production
possibilities.
25. To the extent that such changes in comparative advantage result
from well functioning markets, "Dutch Disease" is not a disease; that is,
it is not an inefficient outcome. However, markets do contain friction and
adjustment costs from one type of comparative advantage to another as
capital and labor previously employed in one export sector (say, from
traditional exports initially to mineral exports subsequently) flows to
another sector. This can become a problem for the economy if the period of
mineral dependency is relatively short. It must, therefore, be
incorporated in any framework determining the rate of extraction and
compensation arrangements. In such cases, governments must be concerned
about developing mineral extraction profiles consistent with the more
general benefits of joint outputs (minerals plus other outputs) rather than
simply maximizing mineral values. As mineral exhaustion causes a
continuous change in the nature of comparative advantage (in other words,
in the marginal rate of transformation) through time, the optimal
extraction profile for the resource owner will be affected.
26. It is thus misleading to think of mineral development as truly
enclave in nature. Even in cases where the major source of project finance
and skilled labor is external, mineral developments may generate
significant costs to the economy at the margin. This should not be a
- 15 -
surprise. Rather, it is simply a restatement of the fact "that there is no
free lunch". An economy must adjust to changes in its comparative
advantage in minerals. This implies that from a general equilibrium
perspective, the government must -ompute the cost of increased current
mineral output as the value of output foregone in other sectors. Thus, a
supply curve for resource sales (a scarcity value) can be generated even in
cases where the mineral is not physically exhausted. That is, the value
added of increased sales from mineral inventories shouid be equal to the
marginal value of output foregone in other sectors before the country
decides to increase extraction. Thus, the supply curve of resource sales
is not perfectly inelastic either within or bet-'een time periods.
27. In the presence of significant adjustment costs in the transitions
to and from mineral dependence, countries with major mineral endowments
might need to attribute the proceeds from sales between two cateories of
compensation--one for the finite nature of the mineral and the other for
the cost of foregone output in other sectors. Proper attribution of these
costs at the margin is important so that the country is compensated for
them and so that the asset sales profile is adjusted until exogenous
marginal gains equal endogenous marginal costs. If such costs are not
recovered, then the benefits from mineral ownership and development may be
lost.
D. Tax Policy
28. One means of capturing rents of any form is to use national
taxation. However, in an economy where mineral rights are held by the
state, "taxing the natural resource rents" will merely amount to the
government taxing itself if the natural resource pricing policy is properly
- 16 -
designed. In reality, government must wear two hats--tax collector and
natural resource owner. Thus, there must be a clear delineation of the
role of taxes and efficiency prices to ensure consistent policy.
29. The large literature on natural resource taxation (Dasgupta, Heal,
Stiglitz 1980; Conrad and Hool 1981; Slade 1982; Nellor 1984; Heaps and
Helliwell 1985) has demonstrated that output related charges (such as
royalties and export taxes) employed as taxes may generate significant
efficiency costs. Such instruments can result in "high grading" or in the
premature closure of marginal mines. However, as already noted, a charge
by the owner for the sale of minerals is no more a tax than the wage
charged by a worker for his labor. The allocative incentives created by
different types of payments must be evaluated relative to the intention of
the policy. There is no necessitY to aRRlv the 'neutrality" norm of tax
analysis to those extraction related charges designed to compensate
government for its ownership of mineral riRhts.17
30. Many developing country governments have begun to rely more
heavily on income related charges in the mineral sector. As a result,
general income tax rules are superseded and modified for the mineral
sector. This creates difficulties in comparing effective rates of taxation
(both average and marginal) across sectors. For instance, it is difficult
to measure the marginal effective tax rate unless the resource is correctly
costed and deducted from the corporate tax base with adjustments for risk
sharing provisions. If the opportunity costs of mineral sales are
understated (through, for example, inadequate deductions for the legitimate
171 The use of terms such as the Resource Rent Tax further confuses the issue. A scheme to
capture 100 percent of the "natural resource rent" for the owner Łs not a tax at all as
established by Hotelling. It is important for governments to set a price for mineral
extraction before different taxes or other instruments are employed.
- 17 -
cost of mineral inputs), the true burden of taxes will be overstated. On
the other hand, if provisions in the tax code to compensate for risk are
treated as deductions, the tax burden will be understated. Some recent
studies of developed economies (Kemp 1987; Boadway, Bruce, McKenzie, Mintz
1987) have found that current tax/payment schemes are not even efficient at
collecting rent as the mineral sector is subsidized at the margin (negative
marginal effective tax rates). These findings are disturbing as they
suggest that, despite the high rents in the sector, the incentives in the
fiscal system are biased in favor of heavier investment in minerals
relative to other sectors. Little empirical work has yet been done for
developing economies along these lines.
31. Mineral tax policy should definitely be separated conceptually,
and possibly in practice, from natural resource pricing policy (user costs)
and risk sharing arrangements. To increase intersectoral neutrality,
mineral developments should be taxed in a manner similar to other sectors.
Sector specific mineral features should be addressed through otter
instruments. Thus, general taxation instruments that cut across sectors
should not be modified to become a means of collecting payment for the
resource as a factor input, of sharing risks or of compensating for general
equilibrium effects, thus having to do double duty. Therefore, when
objectives are not perfectly correlated, it may be preferable to use
multiple instruments and to match each instrument to an objective.
- 18 -
PART II
AN ILLUSTRATION OF RISK SHARING THROUGH DIFFERENT INSTRUMENTS
32. The second part of this paper describes preliminary results from a
simple cash flow module18 designed to illustrate one aspect of the mineral
contract: how different revenue generating instruments affect risk-sharing
between two parties--the resource owner and the resource extractor. One
purpose of these simulations is to demonstrate the utility of simple models
as practical evaluation tools. All computations are feasible on a personal
computer using a spreadsheet with a risk simulator. The presentation of
this part is in three sections: in Sr-^tion A the instruments selected for
simulation are described; in Section B, the ranking criteria and
methodology; and in Section C, the results.
A. Selected Mineral Tax/Payment Arrangements
33. Three typical instruments found in mineral contracts are used in
the initial analycis--the ad valorem royalty, an income tax of the "free
equity" type and a resource rent tax (RRT).
18/ Despite substantial advances in the theoretical literature, there is at present no
practical analytical framework with which to analyze tradeoffs or to determine the rate
structure for the different instruments used to collect public revenue from the mineral
sector. Work is in progress to develop such a framework. The framework will consist of
a number of modules. The first module will be used to compute a price for the resource
that is unadjusted for risk. This will generate an endogenous extraction profile for
the resource. In the next module, the risk sharing features of the revenue instruments
will be evaluated, taking the extraction profile as exogenously determined. The
preliminary form of this module is described in the section above. Other modules will
address general equilibrium effects and intersectoral taxation, for example. To be
practical, it should be possible to operate the modules separately. To be useful,
however, they will have to be mutually consistent.
- 19 -
(a) Ad Valorem Royalties
34. An ad valorem royalty is a charge per unit of output measured as a
percentage of price. Unlike a per unit or "specific" rate charge, the
resource owner now participates in price risk.19 The extensive (and
exclusive) use of royalties to capture the return from mineral extraction
and to share risk has declined during the past 20 years in developing
countries.20 Economists have contributed to this decline by showing
separately that, as a tax, ad valorem royalties can distort production
decisions to result in inefficient resource use (Conrad and Hool 1981) and
that fixed rate royalties may not be optimal as a first best method of risk
sharing (Leland 1978). First best risk sharing is essentially the
provision of optimal (mutual) insurance. The fact that a fixed percentage
royalty is not optimal results from the simple fact that the insurance
agent (the government in this case) does not compensate the insured in bad
states of the world (negative present values).21 Both criticisms are
justified subject to a couple of caveats. First, if royalties are designed
to collect the value of the resource they can function as a user cost
rather than as a tax. As a reflection of the opportunity cost of mineral
extraction from the resource owner's point of view, the royalty would be a
charge leading to the efficient allocation of resources rather than a tax
leading to the inefficient allocation of resources. Second, given
monitoring costs (on both sides of the contract), administrative costs,
19/ The value of this payment to the resource owner varies both with the volume and the
price of the output. This variation is perfect in the case of a fixed percentage
royalty but not in the case of a progressive rate royalty.
20/ It is still extensively used by private mineral owners in the United States.
21/ This is equivalent to purchasing fire insurance where the insured pays a nonnegative
premium for fire insurance but receives no payment even when the house burns down.
- 20 -
asymmetric information and other market friction, it is possible that a
royalty used as a factor payment is still in contention as a second best
policy for risk sharing.22
(b) An Income Tax of the "Free Equity" Type
35. A second type of compensation scheme for mineral owners has been
labeled "free equity." In this scheme, the owner receives a proportion of
the stock issued from formulating the project. In other words, the mineral
owner receives a fixed proportion of current book profits for each period
in which profits less accumulated losses exceed profits. Exploration and
development costs are immediately expensed (written off) and losses are
carried forward without interest.
36. Free equity is actually a misnomer. Mineral production requires
two types of capital--non-renewable minerals in the ground and reproducible
physical capital. The asset base is, therefore, the summation of the value
of minerals in the ground plus the value of the other types of capital. A
free equity share of, say, 40 percent is thus effectively a statement about
the proportion of the value of mineral assets to total capital (minerals
plus physical capital). From this perspective, free equity is no more
"free" than an entrepreneur with an idea for a new product who forms a
corporation with owners of physical capital and receives in return a
proportion of the common stock.23
22/ Unlike windfall profits, a royalty is paid for each and every ton of ore extracted.
Thus, there is a tangible relationship between extraction and payment. A resource firm
might prefer such a payment system to a windfall profit scheme, for example, if the
likelihood increases with the latter scheme that the resource owner might stop selling
the resource, nationalize production or seek new contract terms because the resource
owner observes extraction for several years with no compensation and with only a promise
of future compensation.
23/ The value of the reserves in the ground (as well as the value of the idea) may not be
known with certainty. However, this does not preclude the contracting parties from
agreeing on an initial ex-ante division of the total returns to capital.
- 21 -
37. In such an agreement, both parties expect to receive the risk
adjusted return to their capital bases. If perfect income accounting were
possible, one method to do this would be to repay invested capital via
depreciation and depletion deductions, and to charge the respective capital
balances the appropriate interest charge. In actual situations, the return
to equity (both minerals and physical capital) is based on cash flow after
book depreciation (and perhaps book depletion) and the opportunity cost of
funds is not a charge against income. Thus, in practice, the 40 percent
ownership interest in the present value does not necessarily correspond to
40 percent of the cash flow due to timing and other book accounting
differences. Like the purchaser of any common stock, the mineral owner has
limited downside risk with free equity. If the present value of the
project is -egative, the resource owner's liability is limited to the
initial invested capital. This can affect the risk-sharing structure
relative to contracts where equity's liability is not limited as in a
general partnership.24
38. Common production sharing agreements are akin to free equity in
terms of their risk sharing properties. Production sharing agreements
generally allow an investor to recover the capital investment (in
undiscounted terms) using immediate expensing, and allow losses to be
carried forward without limit before the resource owner receives any share
24/ It is well known that pure unlimited liability shares are efficient risk sharing
devices. However, whether such an arrangement is optimal in a particular situation
depends on the distribution of possible outcomes and the preferences of the partners.
Few arrangements in pure form are found in practice and with good reason. Part of the
contract structure must include the opportunity cost of the resource owner and some
positive payment may also be required to compensate the resource owner for risk.
- 22 -
of the gross (or net) proceeds. Once the capital is recovered, the
resource owner gets a specific share of the net cash flow (either in cash
or in kind).
(c) Resource Rent Tax or Excess Profit Charges
39. Some countries have contract terms that specify that the return to
mineral ownership should be an increasing function of some measure of ex-
post profitability. The most famous type of charge is the Resource Rent
Tax (RRT) advocated by Garnaut and Clunies-Ross (1975; 1979; 1983).25 Tiis
charge is zero if the net present value of the project is less than or
equal to zero, and is positive (at proportional or progressive rates) if
the net present value is positive.26 To a developing country that is
relatively poor but rich in resources and that anticipates using mineral
resources to finance development and diversification, this charge can have
significant risk as it is possible for the mineral asset base to be
exhausted without ever generating a single payment to the resource owner.
40. A larger array of contract arrangements are described in Appendix
1 with their risk sharing properties and structure. The use of any
particular instrument (or combination of instruments) will depend upon the
nature of the mineral deposit, the general structure of risk in the project
and the extent of risk aversion of the parties.27 To make better
decisions, it is important for decisionmakers to be aware of the risk
25! Windfall charges and excess profit charges are used in Indonesia, Papua New Guinea, and
some provinces in Canada.
26/ The discount rate used for the purpose of computing the present value is generally a
contract term.
27/ If both parties are risk neutral, then the issue of risk sharing would be irrelevant as
all decisions would be based on the expected values with no regard for the expected
variation.
- 23 -
sharing properties of each instrument and how the instruments rank relative
to some criterion of risk bearing. The next section describes a
metholology that can facilitate such an analysis. It illustrates how
rankings can be developed for each party.
B. Ranking Criteria and Methodology
41. Ranking Criteria: If both parties to a contract were risk neutral
or if markets for contingent claims were complete and perfect, the-e would
be no need to examine and rank the risk sharing properties of instruments.
Because markets for such claims do not always exist and one or both parties
to a contract may be risk-averse, it is necessary to evaluate the risk
sharing properties of tax/payment instruments.
42. When one party to a contract is risk neutral and the other risk-
averse, pareto efficiency requires that the risk be borne by the risk
neutral party (that is, the one who is better able to carry the risk). In
the analytic literature used to rank pure forms of tax and contract
instruments that spread risk (Sebenius and Stan, 1982) it is assumed that
the agent--the resource extracting firm--is risk-averse and the
principal--the government--is risk neutral. This assumption is generally
borne out in analysis of developed economies as the government is better
able than a resource extracting firm to diversify its portfolio and hedge
against the risks associated with resource extraction. In such cases, it
is sufficient for the government to rank projects based on their expected
value, that is the mean net present value. (This is relatively straight-
forward and is common practice in project analysis).28 The results of the
28/ Note that the most likely value (the mode) will be the same as the expected value (the
mean) when the probability of different outcomes is normally distributed. However, when
the two measures of central tendency deviate, it is the mean that is the more
appropriate statistic for risk analysis.
- 24 -
analytic literature show charges on income (such as an income tax) to be
superior to charges on output (such as a royalty) which are in turn
superior to fixed charges (bonus bids). A sufficient condition to obtain
these risk sharing rankings is to have statistical independence between
prices and costs as noted by Thon and Thorlund-Petersen (1987). If prices
and costs are statistically dependent, however, the ranking may or may not
hold. Thus when there is covariance between prices and costs, simulation
techniques are necessary to rank instruments.
43. When there is uncertainty and returns are normally distributed, a
conventional way of describing the risk associated with an investment is to
specify the variance of the distribution of returns in addition to
specifying the mean. Using this mean variance analysis, instruments can be
ranked by a pair of values--mean and variance. The instrument with the
highest mean and lowest variance is to be preferred. When an instrument
does not dominate both statistics, it is still possible to rank those with
one statistic in common. That is, for a given risk (holding the variance
constant) one can select the instrument with the highest return (highest
mean value), or for a given return (holding the mean value constant) one
can select the instrument with the lowest risk (lowest variance). The
ranking can be made independent of the unit of measurement by using a
standardized measure of the project's variability known as the coefficient
of variation (standard deviation divided by the mean). Ranking by a pair
of values (mean and variance) becomes problematic when one instrument has
both a higher mean (desirable) and a higher variance (undesirable) than
another instrument. In such cases, the criterion of first order stochastic
dominance can be used to rank instruments.29 With this criterion, an
instrument X is ranked superior to an instrument Y if X's cumulative
29/ Actually it is not the instrument itself but the value of the asset associated with the
use of the instrument that is ranked.
- 25 -
probability distribution always lies to the right of Y's. This is
equivalent to saying that for any arbitarily chosen threshold w*, there is
a greater probability that the return Wi is smaller than w* for instrument
Y than for instrument X.
44. These criteria cannot be used, however, if the contracting parties
are risk averse or the probability distribution of their returns is not
normal. Mineral dependent developing countries, with limited access to
international capital markets, may not be able to hedge adequately against
financial risks arising from variations in such factors as commodity
prices, exchange rates and interest rates. Even if financial risks can be
accommodated, there are non-financial risks associated with mineral
development, such as reserve or operating risks, that can expose the public
revenue structure of developing countries to shocks that necessitate
difficult adjustments. Stabilization funds can buffer some unevenness in
revenue flows but are not intended to address risks arising from project
failure. It is, therefore, more appropriate to treat mineral dependent
developing countries as risk averse. This can have a bearing on the choice
of instrument and the setting of rates.
45. It is important to note that in evaluating the risk sharing
characteristics of an instrument, it is not sufficient to look only at the
overall variability in a project's cash flow. It is also necessary to
determine the probability that the net present value (NPV) of the cash flow
is positive. For instance, under an RRT, the goveranent receives revenues
only in cases where the NPV of the project is positive. Thus, if the
probability is 60 percent that the NPV of the project will be positive, the
government stands a 40 percent chance of never receiving any revenue. The
government will then be forced to incur adjustment costs even though it
depletes the mineral asset. By contrast, both the royalty and the income
- 26 -
tax will lower the risk to the government (the former more than the latter)
because they generate a positive NPV (revenue flow) to the government in
every period in which extraction is positive, whether or not the NPV of the
project is positive. This benefit to the government accrues at a cost to
the firm as it lowers the probability that the NPV of the producer's after
tax cash flow will be positive. When the probability of a positive NPV for
the project is less than 100 percent and prices and costs are not normally
distributed, the probability distributions are no longer symmetric about
the mean. As a result, the variance is not an adequate measure of risk.
Thus, mean variance analysis does not correctly rank risk sharing
instruments when the agents have concave utility functions (in other words,
are risk averse) or when the frequency distribution of outcomes for each
party is not symmetric (or both).
46. Therefore, to evaluate the risk element associated with each
instrument correctly, it is necessary to compare instruments holding the
mean NPV shares of the contracting parties constant (mean preserving
spread). This implies that the risk sharing issue becomes one in which the
parties select among alternative distributions of outcomes with a constant
mean return. Thus, in situations where the contracting parties are risk
averse and the various instruments treat positive and negative project
outcomes differently, it is better to use second order stochastic dominance
as a more general measure30 to rank risk sharing features of revenue
instrulments.
47. One distribution, f(x), of uncertain outcomes is said to dominate
another distribution, g(y), if:
30/ In which it is not necessary to specify the utility function of the agents.
- 27 -
rwi
(1) | CGy (W) - Fx (W)] dW - 0 for all W
J -~
and
Gy (Wi) F Fx (Wi) for some Wi
where: Gy = cumulative density for Y
Fx = cumulative density for X
Wi - wealth in state i.
Equation (1) says that, in order for instrument X to be preferable to
instrument Y, the accumulated area under the cumulative probability
distribution of Y must be greater than the accumulated area for X, below
any given level of wealth (wi). In other words, instrument X has a lower
variability than instrument Y if the cumulative difference between Gy and
Fx is non-negative for any level of wealth wi.31
48. The importance of second order stochastic dominance is that all
risk-averse investors32 would consistently prefer one distribution of
outcomes over another if the criteria in equation (1) are satisfied. It
should be noted that this criterion is not an efficiency rule but a ranking
rule for alternative distributions of uncertain outcomes. It is not the
purpose of this paper to explore optimality issues at this stage. Rather,
the intention is to illustrate that governments (and firms) must evaluate
the entire distribution of outcomes and not simply the mean.
49. Methodology: Even though rankings have been determined
analytically in the literature in an expected utility or mean variance
31/ See Copeland and Weston (1980) for a non-technical introduction of this concept.
32/ Investors with concave utility functions in wealth.
- 28 -
framework as noted earlier, they have been unable to provide policymakers
with the practical tools needed to form tax policy. When models are too
complex to give analytic solutions, simulation provides a practical
alternative.33 By describing individual events in the system rather than
its overall behavior, the simulation model shows how risks are shared under
alternative contract terms. The cash flow model used can include standard
investment items such as exploration and development costs as well as
quancities extracted, price and operating costs. Changes in the time path
of real prices as well as in inflation should be incorporated as parameters
that can be changed at the user's discretion. To simplify the initial
analysis, it is assumed that the geological composition of the deposit and
investment costs are known with certainty,34 that real relative prices are
constant,35 that price and cost uncertainty do not increase with time, and
that there is no inflation. For purposes of clarity, the instruments are
analyzed one at a time to avoid any interaction between instruments that
can complicate the analysis. In the reported simulations, an instrument
that is preferred by one of the parties for a given set of project
33/ Deacon (1990) uses a simulation model to examine the welfare loss of different taxes in
the petroleum industry in the U.S.
34/ Allowing for uncertainty in development costs flattens the distribution of returns
(NPV).
35/ When the price follows a Brownian motion (increasing uncertainty over time), the
variability of returns (NPV) to both parties increases, but the rankings remain
unchanged. It is important to differentiate between the time path of nominal and real
cost. It is assumed in many projects that real relative prices have no time trend (for
example, the real price of copper over the past 120 years [Gordon et al. 1987]) and thus
only nominal adjustments are made. This assumption is neither general nor satisfactory
for many inputs and outputs, labor in particular. A constant real wage is tantamount to
assuming that real GDP increases only at the rate of population growth. While a
convenient assumption for eteady state theoretical analysis, a constant real wage is not
consistent with the historical development of most economies.
- 29 -
assumptions is also preferred under alternative project assumptions. This
is not a general result, but may nevertheless seem somewhat surprising. It
is partly explained by the fact that the parties are assumed to prefer
lower variance in expected net present value rather than lower variance in
the profile of a project's cash flow over the years.36
50. As noted earlier, the extraction profile is determined
exogenoLasly. The reason for this is that, in order to analyze risk
sharing, it is necessary to hold constant the total risk to be shared.
This in turn requires total extraction to be held constant as changes in
the total volume of output can change both the marginal and total risk of
the project.37
51. A stylized mining project cash flow is generated by the model.
Large capital costs are assumed to have been incurred and known at the time
of analysis. Operating costs, however, are uncertain. Probability
distributions are, therefore, specified for both prices and costs. For
purposes of the current illustration, a joint normal distribution is
selected with no autocorrelation through time but with positive covariance.38
The latter assumption is consistent with basic microeconomic theory (an
36/ It is with respect to variance of cash flow for a given project that the instruments
differ most in terms of risk sharing capability. In a model where the variance of cash
flow appears, it is more likely that a chFnge in raking between instruments would occur
when project assumptions change. This obviously warrants some theoretical clarification
between further simulations are performed.
37/ It is easy to demonstrate that the total variance of a project increases with total
extraction if production exhibits decreasing returns to scale.
38/ In the general model, autocorrelation (in real terms) and covariance (either positive or
negative) can be introduced.
- 30 -
increase in the price of oil will generally be expected to lead to an
increase in the price of oil drilling equipmein j.39
52. The total cash flow is then divided between the two parties to the
contract using a risk simulator. In this study, it is assumed that the
government seeks to obtain 40 percent of the expected net present value of
the project. This value may be interpreted as the amount in present value
terms that a risk neutral resource owner might be paid today for the
mineral rights. Thus, 40 percent of the present value is essentially the
minimum opportunity cost of a risk neutral resource owner.
53. The rate of each instrument is then calibrated so that the
government receives the specified share of the expected value. The royalty
rate is determined by dividing the present value of the government's share
by the expected present value of total receipts. The rates for the RRT
must be determined iteratively in the context of the simulations. These
contract terms create autocorrelation in the distribution of cash flows
that arises from the provisions that losses can be carried forward and that
no payments are made in situations where the present value is zero. For
these reasons, it is necessary to make an initial estimate of the rate and
to revise the rate through iterations until the contracting parties receive
their respective shares.40
C. Results
54. Two simulations are presented to provide a preliminary
illustration of the methodology and ranking system. The only difference
39/ The covariance is assumed to be contemporaneous for present purposes even though it may
occur with a lag in actual situations. When zero covariance is assumed, the total
variability to the project decreases, but in this case the relative rankings between
agents remains the same.
40/ A brief description of the model and simulation procedure is contained in Appendices 2
and 3.
- 31 -
between the simulations is the probability of negative present values. The
probability of a negative net present value is 26 percent for Case #1 and
42 percent for Case #2 (see Figure 1).41 The contract rates are reported
in Table 1 for each case, along with summary statistics in Tables 2 and 3.
55. The use of a constant mean provides a convenient and practical
benchmark for determining rates for the different instruments in light of
their respective risk sharing features. That is, given the parameters of
the model, if the government wants 40 percent of a project's expected NPV,
then it must set the royalty rate at three percent or the RRT rate at 32
percent when there is a 26 percent chance that the project will fail, and
at one percent or 13 percent respectively if the probability of failure
increases to 42 percent. The higher the probability of failure (negative
NPVs), the lower will be the mean NPV and the lower will be the rate
required to capture 40 percent of it. The rate changes are non-linear with
respect to the probability of failure.
56. It is interesting to note the relatively low rates necessary for
the government to accrue 40 percent of the net present value for all three
contract terms. The royalty consistently has the lowest rate as it is
computed from the largest base (sales). The free equity type of income tax
rate is also low (nine percent in Case #1) relative to expectations. There
are a number of reasons why such a low rate can generate sufficient revenue
to accrue 40 percent of the net present value. First, revenues accrue only
when the base is greater than zero. The government has no losses of its
own to recoup and so this lowers the rate. Second, the opportunity cost of
41/ In the simulations reported, the higher probability of failure arises from higher
initial costs. It is possible with the model, however, to have the higher probability
of failure arise from other causes, such as greater uncertainty over time with respect
to prices and operating costs, for example.
- 32 -
Figure 1: Expected Value of Project Returns (NPV) Given Different Probabilities of Failure
a) Case 1
26 Percent Probability that NPV < 0
Expected Value = $400
10% o .......... ...... --------- I---------
Frequency of
Occurence l
A%. .........................
4%) -------------------- .. .............
2%.1
0%0
-g500 -1875 -1250 -625 0 625 1250 1875 2500
NPV($)
b) Case 2
42 Percent Probability that NPV < 0
Expected Value = $100
1 - - -- - - - - -- - - ..... ........... ...... ........... ...... ......... ..... ............ ..... ............ .........
Frequency of
Occurence l
8% ~~~~~~.... .. ...... .. ----------------------------------.... .... .. ....
6% -- - -- - -- - -- - -- - -- - - .4 .... ...... ....... ... ....... .... ...... ....
470 --- --------------------...............
2% - ... ................. . ....................
-2500 -1875 -1250 -625 0 625 1250 1875 2500
N;PV(S
- 33 -
Table 1: Comparison of Rates When Government Receives
402 of Proiect Cash Flow
Case 1 Case 2
Project NPV $400 $100
Prob. NPV < 0 262 422
Output Royalty 32 12
Income Tax 92 21
Resource 321 131
Rent Tax
- 34 -
Table 2: Summary Table
Case I
Expected NPV Prob. NPV s 0
Mining Project $400 26Z
Share of NPV received by:
Royalty Government $160 0%
Firm $240 33%
Income Tax Government $160 0%
Firm $240 33%
Resource Government $160 26%
Rent Tax Firm $240 26%
Notes:
-exclusive use of one tax/payment instrument.
-the government and firm share the NPV of the project 40/60.
- 35 -
Table 3: Summary Table
Case 2
(higher exploration costs)
Expected NPV Prob. NPV s 0
Mining Project $100 42S
Share of NPV received by:
Royalty Government $40 0%
Firm $60 44%
Income Tax Government $40 0t
Firm $60 44%
Resource Government $40 42%
Rent Tax Firm $60 42%
Notes:
-exclusive use of one tax/payment instrument.
-the government and firm share the NPV of the project 40/60.
- 36 -
capital is not incorporated. This further increases the effective base.
The RRT has the highest rate of the three instruments but it is
significantly lower than the 40 percent NPV share (32 percent in Case #1).
Unlike the income tax base, the base for the RRT incorporates the
opportunity cost of capital, which defers the accrual of positive cash flow
for the government. However, like the income tax, the government only
receives positive cash flow if the base is greater than zero. This will
reduce the rate below 40 percent as the rate is based only on expected
positive outcomes.
57. In Case 12, the initial costs are higher. Thus, there is a shift
in the expected value of the overall distribution of outcomes with no
change in the overall variability of project revenue. The royalty rate is
lower in Case #2 as would be expected given that a lower present value
needs to be collected. Both the income tax and the RRT rates decrease
dramatically. Higher investment costs imply higher loss offsets that
increase the period of zero government revenues. However, the effective
base falls by less than the present value of expected revenue for
government. This decreases the rate.
58. The time profiles of revenue to the government under the three
instruments are dramatically different though their mean NPV is identical.
Positive cash flow accrues to the government under both the royalty and the
income tax in every state of the world simulated (see Figures 2b and 2c).
A royalty is paid on extraction regardless of whether the net present value
is positive or not. Thus, this result is to be expected. It is also to be
expected that there will be a positive cash flow to the government under
the income tax in all cases. Book accounting and the non-incorporation of
the opportunity cost of capital combine to increase the base of the charge.
- 37 -
Figure 2: Time Profile of Returne Under Uncertaint,
a) >w1^t R Lerend
.. ........ .. .. .. . . ...... .. ... . ........ .. .
Notel Center Line: Trend in
In this example, ..... .............. expected value.
investment costs are Sbaded Areas One
known vith certainty o_>r. _ 5 .. ......oveandarddovito
$ 0 ~~~~~~~~~~above and below
.. ...x . . . _ _ . .pected value.
v \ 1 okc~~~~~ppr Bound: 9Sth
... .. . .percentile.
Lover Bound: 5th
-2x00 _ , , ,_ percentile.
10 20 Yt
b:F) Royalty: 1ecute to f Ltt b :Gft t urns R m tto 04n"tm
.. .......... ... .... .. ...................... ........ . _....._...._.,... . ..... ....
...2.0........1
. 1 n \~~~~~~~~~~~~~~~~~~~~~6 ..................... .................. ............... .. .hot:\:
-1X -, ? f. _ 102
c G) tncawefO?u rex-i to orsfYmwnt
-30 2X 4 . __. _*40.......... ......... ...... . ................ . . _.......I.... ..
1500~~~~~~....... . ............... ......... .. . _ < . e ........................... . ......... . .........
.1500 2~~~~~~~~~~~~~~~~40.- . -.-
-5CO ' A_^; s 140~~~~~~~~~~~~~~~~~~~~~~. ................... .......I. ............. .... . ......
-oo... ............ ... ...... ..... __.._ . _.,.......,-_
$0~~~~~~~~~~~~~~~-0
-2X10 _ 10 20.a 10 20 year
d:F) o"e Rent 'fox-tx T R nx to rmn d:G) t.at" e nt te l" ('A
* 2500 -.2*ll 40.-.l~
_90 , ...... ... . .............. .. . ... ...TS -el .......................-''-''-'-'''---'-'-'--
No -''l' ------------ '''' '''-''''''' ---.......'''' - .
-250 ff [- ' - 10 2|@ 20 -O'
- 38 -
The effective base of the income tax is cash flow adjusted for
depreciation. The summation of cash flow can be positive even when the
present value of the project is negative. This benefit to the government
accrues at a cost to the firm as it increases the probability that the firm
will have negative present values. For instance, in Case #1 (Table 2), the
probability of a negative present value for the firm increases to 33
percent under the royalty and the income tax, compared to 26 percent under
the RRT. Under the RRT, the government and firm each have the same risk as
the overall project. Unlike the royalty and income tax, which have no
downside risk for the government, under the RRT the government collects no
cash 26 percent of the time in Case #1 and 42 percent of the time in Case
#2 (Table 3). In other words, the downside risks to the government
increase dramatically under the RRT relative to the other two instruments
(solid line with zero revenue in Figure 2d), whereas the risks to the firm
do not increase as dramatically under the royalty and income tax compared
to the RRT.
59. An examination of the distribution of outcomes under each scheme
reveals that the income tax of the free equity type and the royalty are
remarkably similar (see Figure 3). Two factors combine to yield this
similarity. First, the covariance between revenues and the present value is
high. Second, the positive covariance between prices and costs increases
the pos..tiva relationship between revenues and present values. The
covariance effect can be illustrated by the simple case of one period where
costs are a linear function of prices with no supply shocks. If the
probability of negative present values is zero, then the distribution of
the income tax and the royalty will be identical. This is true because
profit is merely a linear function of price shocks, which implies that for
Figure 3: Variations in the Returns to Government and Firm with the
Same Expected Value Across Instruments
3E ~~~~~~~~~~~~~~~~....... .._. _. . .. ._... _... 3 .. ... -- - -- - --- ...... .. ._ .... ... .
ProbM" Pwb.bAS *' Pfobabit y
.. * . ..._ 2. _ .................
., ., .
1I ------ ....13 . .... ....... 13 W
' ---------a---- - --- . g. .... .... i
* _ a U I
-M -N5 -1250 - 0 65 130 W5 20 - -115 -M - 0 62i 1N 1V5 29 -2W-5BT-1 - 0 6i 16 N IV a
NPV(S NPV( NPV CS)
a) Royalty on Output b) Income Tax of the c) Resource Rent Tax
"Free Equity" Type
Legend
White Area: Uncertainty in Firm's Returns
Black Area: Uncertainty in Government's Returns
Note: Case in which there is 26 percent probability that project NPV < 0.
- 40 -
the same revenue the income tax and the royalty would be perfectly
correlated yielding identical distributions.
60. Figure 3c illustrates more clearly that under the RRT, downside
risks to the government are much higher relative to the other contract
terms as the probability of a zero NPV is much higher. By contrast, for
the firm, the RRT has both lower downside and lower upside potential
compared to the other instruments, which implies that the mass of the
frequency distribution is more concentrated.
61. Since distributions for the various instruments are very
dissimilar, it is necessary to compute the differences in the cumulative
distributions both for the government and the firm to determine if one
instrument can consistently be prefe-red over another. The results are
depicted graphically in Figures 4a through 5b. The graphs show that the
government will rank the royalty higher than either the income tax or the
RRT, and rank the income tax higher than the RRT. However, the exact
opposite ranking is found for the firm.42 That is, the firm would prefer
the RRT to the income tax and the income tax to the royalty. Furthermore,
these rankings are the same across cases. These results are consistent
with theory43 and with logic. Given a specific total risk to be shared, an
instrument that creates lower variability for one Rarty will of necessity
shift more variability onto the other Rarty. Thus there is a natural
conflict of interest between the parties with respect to risk, holding
their respective mear constant.
42/ Recall the definition of second order dominance found in equation #1 as a measure of the
cumulative differences. The graphs should be read with this in mind and with respect to
the legends presented on the graphs.
43/ See Conrad (1988) and the references therein.
- 41 -
Figure 4a: Difference in Cumulative Probability Distributions for Government.
600 -
500 X
400 -
300
200 -
Sum of Difference 100 0
in Cumulative
Distributions 0 I I I I
-100-
-200 -
-300-
-400 -
-500 -
0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570
NPV ($)
0 tRT-ROYALTY + INOOME TAX4YALTY 0 NCOME TAX-FRT
Note: Case in which there is 26 percent probability that project NPV 0. The gross cash flow minus the
payments to the government in each period yield the after tax flows to the firm.
(13) Observed Government revenue in period t - r (NCFt - Lt) when (NCF, - Lt)>O,
G 0 when (NCFt - Lt)-O
(14) Observed Firm cash flow in period t - CFt - Government share in period t
iii. Resource Rent Tax (RRT)
The base for the resource rent tax is cash flow (equation (4)) with a loss
carry forward provision. All capital costs (such as exploration investment)
are expensed, and losses are carried forward at the rate of interest. Hence,
the taxable base is determined according to the following rule:
Lost crry Forward Rule:
(15) For all CFt - L, L 0 : No loss carry forward
(15a)For all CFt Lt < 0 : Carry forward Lt., into next period,
whereLt+1-ICFt - L,1(1+i)
CFt-gross cash flow in period t
Lt- stock of loss carry forward in period t
i - Interest rate
The resource rent tax rate, X, is applied in each period that CFt - Lt >
0. The after tax flows to the firm in each period are equal to the total cash
flow minus the payments to the government in that period.
(16) Observed Government revenue in period t - +(CF, - Lt) when (CF, - Lt)>O-
- 0 when (CFt - Lt)SO
(17) Observed Firm * > i flow in period t - CF, - Government revenue in period t
11
The rate for the RRT must be determined iteratively in the context of the
simulation, due to the combined effect of the loss carry forward property and
the fact that the government receives no revenue when the base is zero (this can
be a significant time period when losses are large in the initial stages of the
project). The RRT rate is determined by the following:
(18)X - G
NPVCF'
where NPVCF' - NPV of years when CFt - L, > 0
As the probability of negative project NPV increases, the RRT rate will
decrease. At first glance this may seem counterintuitive, but it makes sense
as losses reduce the expected NPV of project cash flow. The lower the
probability of failure, the higher will be the expected NPV of project cash flow
and the higher will be the rate required to capture G.
12
Appendix 3
Model Parameter Values
Parameters for Case 1 V:s
Project life - 25 years
Interest rate - ' 6 percent
Total Production - 700 barrels
Expected Oil Price - $16.50/barrel
Operating Costs - $1.50/barrel
Exploration Costs - $3.50/barrel
Development Costs - $4.00/barrel
Depreciable Capital - $0.50/barrel
Costs
Government share of NPVCF - 40 percent
Time Profiles:
Tear. 1-3: Exploration costs are incurred.
Years 4-6t Development and depreciable capital costs are incurred.
Year 6: Extraction begins and is spread over a 15 year period (with
production at its maximum rate during the second and third
years (8.79 percent) and deeliinig for each successive year).
Simulation Procedure
A Lotus 1-2-3 add-in program called "BRISK" is used. Using @RISK, the
price and operating cost parameters are represented by probability distributions
which are used during the simulation.'V
The expected price of oil, E(P,) is $16.50 per barrel and is constant for
It In case 2, exploration costs are increased to $4.00/barrel.
it The nominal and real interest rates are equivalent since there is no lnflation In the model.
7/ The Latin Hypercube method of sampling vas used, bowever, the Monte Carlo method can also
be used.
13
the life of the project. The simulated price in year t follows equation (1) in
Appendix 2.1' The price shock, a,, is normally distributed (0, 6.8)!1, consistent
with the historical oil price trend. P, is multiplied by the quantity extracted
in each year to get project revenue, R,.
Expected operating costs, E(C,), are $1.50 per barrel for the life of the
project. Actual operating costs are calculated according to equation (2) in
Appendix 2. The regression coefficient, 0, is set to 0.5. This is motivated
by the assumption that operating costs, as woll as the other variables in the
model, are damand determined. The independent shock, v,, is normally distributed
(0, 0.5). After being subjected to the independent shock, the cost is then
multiplied by the covariance effect as shown in equation (2).
Once NPVCF has been determined according to equations (4) and (5), it is
multiplied by 6, the fixed percentage of the expected NPVCF the government
receives. The tax rates are calculated and applied to each base as shown below.
In an alternative scenario, price follovw a uniform distribution. This year's price falls
vithin a range of x percent higher or lower than last year's price.
9/ The second number in the parentheses refers to the standard deviation.
14
Base Loss Carry Forward Provision
Instruments
Royalty R. None
Income Tax R, -C - V, - D, + L.+1 Without interest
Resource
Rent Tax CF, + L,., With interest
P - project revenue in year t
CFt - cash flow in year t
C5 - operating costs in year t
Kt- capital costs in year t that are fully expensed
Dt- total depreciable capital written off in year t,
according to depreciation method. For straight line
depreciation:
Dt - EZ ddtj
s-0
where ddtJ - Vt/n if t S J+n
or - 0 if t > j+n
j - year in which asset K"t is written off
-, depreciable capital incurred in year t
n - tax life of the asset
L,.u- loss carry forward, when applicable
15
Tex/Pameut Rates for Case 1 and Case 2
Case 1 Case 2
Output Royalty 32 1S
Income Tax 91 21
Resource 321 131
Rent Tax
16
Apiendis 4
Glossary of TermsW°
Cumuletive Freauency Distribution
A cumulation of the frequency (progressively adding bar heights) across
the range of a frequency distribution. A cumulative distribution can be an
"upwardly sloping" curve, where the distribution describes the probability of
a value less than or equal to any variable value. Alternatively, the cumulative
curve may be "downwardly sloping", where the distribution describes the
probability of a value greater than or equal to any variable value.
Economic Rent
The return to a factor over and above that needed to induce the allocation
of the factor to a given activity. Thus, changes in economic rent (for example
through taxation) will not affect the allocation of resources at the margin.
Expected Value (Mean)
The sum of all values in the set, divided by the total number of values
in the set.
Frequencv Distribution
Constructed from data by arranging values into classes and representing
the frequency of occurrence in any class by the height of the bar. The
frequency of occurrence of a class relative to total occuarrences represents the
probability of occurrence (hence it is also called probability distribution).
Iteration
A recalculation of the model during a simulation. During each iteration,
all uncertain variables are sampled once according to their probability
distributions, and the model is recalculated using these sampled values. The
number of iterations desired is specified when using the @RISK program.
Latin Hvpercube Sampling Technicue
A relatively new stratified sampling technique used in simulation modeling.
Stratified sampling techniques tend to force convergence of a sampled
distribution in fewer samples than in a Monte Carlo sampling technique.
Stratification divides the cumulative curve into equal intervals on the
cumulative probability scale (0 to 1). A sample is then randomly selected from
each interval of the input distribution, thus recreating the input distribution.
L°l Some definitions taken from 6RISK User's Guide (1989).
17
Mean Variance Analysis
Mean variance analysis has been extensively employed in risk analysis.
It describes attitudes to risk in terms of the mean and variance of income. Its
use is appropriate when the distribution of income is normal, or when all assets
together have normally distributed returns. This type of analysis is not
appropriate when distributions are not normal or when the actor's choice changes
the form of the distribution of returns (trying to reduce the weight in the tail
of the distribution).
Monopolv Rent
Monopoly rent can arise for any number of reasons: barriers to entry,
technological innovation, etc. For example, the structure of the market can
generate monopoly rents in two ways. First, the oligopolistic nature of the
intermediate demanders (the multinationals--MNCs) can give rise to the existence
of excess profits for the sole (monopsonistic) supplier. Second, it is possible,
as OPEC price increases have demonstrated, to increase monopoly rents, even for
an oligopolistic supply structure, by in effect "taxing' competitive final
demanders. The extent to which the intermediate demanders (MNCs) are able to
shift the tax onto the final demanders depends on the degree of competitiveness
of the final demand market and on the existence of substitutes. Where
substitutes are few and markets at the final demand stage are competit4ve, the
tax will be more easily shifted to the final consumer. Thus, the two kinds of
monopoly rent differ in who eventually bears the burden of the tax.
Natural Resource Rent
Natural Resource Rent arises due to the exhausLuble nature of m,nerals.
The rent increases as total stocks (reserves) diminish. This type of rent arises
even when the resource is of uniform aualitv and distrioution. In audition,
changes in the size of this rent affects behavior at the margin. Thus, it is
a price not an economic rent.
Opportunity Cost
The amoant of a good that must be given up in order to produce another
good, or the value of the next boet alternative. Intertemporally it represents
the value of goods today (current) in terms of goods foregone tomorrow (in the
future). Intersectorally it represents the value of goods in one sector in terms
of goods foregone in other sectors.
Probability Distribution
A probability distribution or probability density function is the
statistical term for a frequency distribution constructed from an infinitely
large set of values where the class size is infinitesimally small. See frequency
distribution.
Quasi-Rent
Since the mining industry is highly capital-intensive and its capital is
18
immobile in the short-run, capital in the sector enjoys a sizeable quasi-rent.
As a result, in the short run, taxation of capital is not likely to discourage
the use of capital as much as taxing labor is likely to discourage the use of
labor (which is often more mobile). However, in the long run taxing capital can
discourage investment. In addition, other relatively scarce factors in mining
such as managerial and technical know-how also enjoy quasi-rents.
Ricardian Rent
Ricardian rent arises from quality differences. It is normally associated
in agriculture with differential fertilities or location of land--the marginal
land generating zero rent even though it has a positive price associated with
its scarcity value. In the mineral sector it arises due to differences in
quality of ores, pressure of oils and gases, location, or ease of mining.
Risk
Risk measures the probability and severity of loss. The notion of risk
epresupposes a lack of predictability, but it acutally arises from a well
understood probabilistic process. For example, the risk associated with a bet
on a fair coin toss is known with certainty; the risk has no uncertainty,
although the outcome of the toss is uncertain.
Shadow Price
The social opportunity cost of goods and services estimated for the economy
as a whole.
Skewness
Skewness is a measure of the shape of a distribution. It indicates the
degree of asymmetry in a distribution. Skewed distributions have more values
to the one side of the most likely value, that is, one tail is longer than the
other. The higher the skewness value, the more skewed will be the distribution.
Standard Deviation
Tne standar' deviation is the square root of the variance.
Stochastic
Stochastic is a synonym for uncertain.
Stochastic Dominance
First Order Stochastic Dominance: An asset is said to be stochastically
dominant over another if an individual receives greater wealth from it in every
(ordered) state of nature. This is known as first order stochastic dominance
and applies to all increasing utility functions including linear functions.
Second Order Stochastic Dominance: Second order stochastic dominance not
only assumes utility functions where me.rginal utility of wealth is positive,
19
but also that total utility must increase at a decreasing rate, that is, the
utility function is concave. Hence, under second order stochastic dominance,
individuals are assumed to be risk averse.'
User Cost
The payment which is collected by the owner of an endowment based on its
scarcity value.
Uncertainty
Uncertainty refers to lack of definite knowledge or a lack of sureness.
Here, the lack of predictability arises from insufficient knowledge.
Variance
The variance measures how widely dispersed values are in a distribution,
and is a measure of risk in symmetric distributions. It is calculated as the
average of the squared deviations about the mean. The variance is the square
of the standard deviation.
Windfall Rent
Windfall rents (gain) are largely due to sudden increases in demand in the
presence of low short-run supply elasticities. Taxing these rents is neutral
intertemporally only if windfall losses are subsidized.
l~ See Copeland and Weston (1980).
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