The debt-resource hypothesis re-examined with separate markets for unharvested resources
Jason Stevens
Department of Economics, University of Prince Edward Island, Charlottetown, PE, C1A 4P3,
jmstevens@upei.ca
The so-called debt resource hypothesis posits that imperfections in credit markets cause poor owners of
natural resources to over-exploit their endowments in an attempt to increase consumption or reduce
their debt burden. While this hypothesis is intuitively appealing and well established, the supporting
empirical evidence is weak for many resources.
This paper demonstrates that previous studies present an incomplete analysis of the owner’s utility
maximization problem. Specifically, they ignore the possibility for an owner to sell their unharvested
endowment. The analysis presented here demonstrates that incorporating this possibility allows
imperfections in credit markets to potentially have no effect on the rate of extraction, even if an owner
is credit constrained.
1. Introduction
The relationship between credit markets and the valuation of natural resources has been widely studied.
In the most simple terms, equilibrium in Hotelling's (1931) famous model equates the benefit of
delaying extraction (the growth rate of the resource rent) with its opportunity cost; the rate of interest.
The relationship between financial markets and resources has been further generalized1 as some studies
(Gaudet and Khadr (1991), and Slade and Thile (1996)) have extended Hotelling's analysis to include a
larger portfolio of assets.
A key implication of the famous work2 of Hotelling (1931) is that firms extracting a resource, unlike firms
in other sectors, may increase their profit in the present through an increase in production. Based on
this principle, several studies examine the effect of a borrowing limit on the behavior of a resource
owner. With respect to the objectives of this paper, the most notable existing work is that of Strand
(1995), who finds3 that a country will increase its exports of a natural resource to finance spending when
faced with a binding borrowing constraint. Moving in a different direction, Raucher (1989) shows that a
country will increase its exploitation of a renewable resource when its borrowing rate is positively
related to the size of debt. On a similar note, Kahn and McDonald (1995) find a positive relationship
between the rate of deforestation and debt in developing countries. While each of these studies obtains
their main result based on a different approach, all argue that binding deviations from the assumption
of a perfect capital market accelerate the rate at which a natural resource is extracted. These studies all
1
Hotelling's work has inspired an enormous literature examining the optimal extraction of a non-renewable
resource under a wide range of assumptions; while this literature is far too large to be reviewed here,
comprehensive surveys of this literature are found in Krautkraemer (1998) and Gaudet (2007).
2
As Hotelling argued, the cost of extracting the marginal unit of the resource includes a reduction in the firm's
future profit, which implies that profit in the current period may be increased by ignoring this cost. Of course, such
a decision reduces the value of the firm.
3
It should be noted that the majority of Strand's paper goes beyond evaluating the impact of the constraint to
examine various policies designed to alleviate the burden of debt on the country's rate of extraction.
1
conclude that relaxing constraints on the accumulation of debt4 reduces the rate at which the resource
is exploited. While these findings are interesting, it is important to note that the empirical support for
this proposition is far from conclusive. For example, Neumayer (2005) finds no support for this
hypothesis for oil or minerals.
One potential reason for the weak empirical support is the possibility that binding credit constraints do
not affect the owner of a resource endowment in the manner suggested by Raucher (1989) or Strand
(1995). Specifically, these studies ignore the possibility of obtaining revenue through a sale of the
unharvested resource endowment. Under such a scenario, the imperfections in the credit market
affecting the original owner have no bearing on the rate at which the resource is extracted. As it is well
known that many jurisdictions choose to sell the right to extract their resources to large, well-financed
firms, the analysis presented here fills a gap in the existing literature by providing new insight into the
valuation of non-renewable resources.
This paper proceeds as follows: Section 2 presents a simple model of resource extraction when the
owner faces a borrowing constraint, Section 3 analyzes the possibility of selling the owner’s unharvested
endowment, and Section 4 concludes.
2. A simple model
The purpose of this section is to develop a simple model to analyze the utility maximization problem of a
single, price-taking owner of an endowment of a non-renewable resource (S). In order to obtain
analytical solutions, the analysis is restricted to two periods5. The constraint imposed by the nonrenewable nature of the resource is simply:
q0  q1  S
(1)
where qi is the quantity6 of the resource extracted in each period. While the analysis presented here is
focused on the case of a non-renewable, it is clear that the results to follow also apply to a renewable
resource (but the results become much less tractable).
To understand the role of financial markets in the extraction of a non-renewable respource, the owner is
free to accumulate wealth (to save or borrow). The owner obtains income from the sale of some of the
resource in each period at an exogenously determined market price (p), which may be used to purchase
either a composite consumption good (C) or risk-free bonds (with an interest rate of r). If W is defined as
the owner’s level of wealth, the intertemporal budget constraint is written as:
4
Although the studies do not agree on the most effective method to relax the constraint.
5
It is important to note that numerical solutions obtained for longer horizons are consistent with those
obtained from the simple model. This approach (it will be seen) is able to replicate several prominent
results found in the existing literature while permitting a simple analysis of the effect of a (binding)
borrowing constraint on the behavior of a resource owner.
6
In all that follows, i [0,1] .
2
1
1
C1  C0 
1   0  W
1 r
1 r
(2)
Where profit obtained from the extraction and sale of the resource is formally specified as π = pq – k(q),
k’,k’’>0, and Ci is the owner’s level of consumption. Within the existing literature, these assumptions are
consistent with the work of Dasgupta, Heal, and Eastwood (1978) or Gaudet and Khadr (1991). However,
unlike those studies, the owner here does not accumulate physical capital. It is also important to
recognize that the analysis here is much less general than that presented in these two important
studies.
To complete the model, it is assumed that the amount the owner is able to borrow is bounded from
above by an exogenously determined borrowing limit (φ). Formally, given these assumptions, the
owner’s problem is to maximize:
U (C0 )  U  C1 
(3)
Subject to (1), (2) and:
W   0  C0  
(4)
where U’>0, U’’<0.
As the impact of the borrowing constraint is our main interest here, (1) and (2) may be substituted
directly into (3), allowing the owner’s utility maximization problem to be expressed as a simple
Lagrangean:
L  U (C0 )  U  C1    W   0  C0   
(5)
With the following first order7 conditions:
L
 U '(C0 )  (1  r ) U '(C1 )    0
C0
(6)
L
 U '(C1 )  0 (1  r )  1   0  0
q0
(7)
 W0   0  C0     0
(8)
where λi is the resource rent8. Before proceeding to an analysis of extraction, it is important to note that
the effect of a binding constraint on the dynamics of the owner’s consumption is not analyzed in depth
here. It is easily demonstrated that the effect is consistent with that found in the existing literature
studying consumption behavior; see Deaton (1991) for a very comprehensive treatment.
7
Note that the assumptions made regarding the cost of extraction and standard assumptions regarding utility
functions assure the 2nd order conditions for a maximum are satisfied.
8
Formally,
i 
 i
.
qi
3
With respect to the extraction of the resource, the most important result to come from the analysis is
that extraction depends on the status of the borrowing constraint (binding or not). When the constraint
is non-binding, (7) produces Hotelling’s rule:
0 
1
1
1 r
(9)
This solution corresponds to an owner maximizing the present value of profit obtained from extraction.
Before moving to the case in which the owner is constrained, it is important to note that (9) implies that
the owner’s extraction decision is completely independent of preferences; depending only on the price
of extracted units of the resource (in each period), the marginal cost of extraction, and the rate of
interest; consistent with Dasgupta, Eastwood, and Heal (1978). Furthermore, this implies that any
unconstrained owner will extract the resource at the same rate, regardless of their level of wealth.
However, if the constraint is binding, (5) and (6) imply:
0 
U '(C1 )
U '(C0 )
1
(10)
Which corresponds to the result of Dasgupta and Heal (1974), derived in a closed economy. The
discrepancy between (9) and (10) is due to the differing ability of the owner to smooth his or her
consumption in the binding and non-binding regimes. When the constraint does not bind, the ability to
borrow and lend freely implies it is optimal for the owner to maximize the present value of their
endowment and borrow against the future proceeds to finance current consumption (if necessary). This
corresponds to Fisher’s separation theorem, as well as the results of Raucher (1989) and Strand (1995).
However, when the owner is prevented from borrowing, they are forced to increase extraction in the
initial period. In other words, the presence of the borrowing constraint creates a conflict between the
owner’s desire to smooth consumption and maximizing the value of their resource endowment.
Before closing the discussion, more interesting results can be derived through implicit differentiation of
(10). First, it is easily demonstrated that:
q0
0

It is this result which has received significant attention within the existing literature, as it implies a credit
constrained owner is “forced” to over-exploit their endowment to finance consumption, reducing its
value. Under these assumptions, a reduction in the availability of credit has an unambiguous effect on
the rate at which a constrained owner extracts the resource. However, it is also important to note that
changes in the availability have no effect on extraction if the owner is not constrained.
A similar result can be obtained for the effect of a change in wealth:
q0
0
W
A significant portion of the existing literature examines the ability of several policies to deal with the
over-exploitation of the resource by improving the welfare of the owner. For example, Raucher (1989),
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shows that reducing the debt burden of the owner will slow the rate of extraction. On the other hand,
Strand (1995) finds that several mechanisms which provide relief conditional on a country’s extraction
policy can slow the rate of extraction.
While these results are consistent with the existing literature and have intuitive appeal, the next section
demonstrates that they are derived from an incomplete model.
3. Implications of conditional valuation of the endowment
As a first step, note that the solution to the model presented in the previous section yields an indirect
utility function:
U *  U ( S ,W ,  )
(11)
Which is strictly increasing in all three arguments9. The existing literature does not allow a full account
of the choice set of a credit constrained owner; assuming the only option is to increase the rate of
extraction. One of the most important aspects of (11) is that the valuation of a resource endowment is
determined by the characteristics of its owner; such as wealth and discount factor. If we consider the
possibility of an economy with heterogenous agents, the results presented in Section 2 imply these
agents form differing valuations of the same resource endowment, introducing new possibilities into the
analysis. Simply stated, a difference in valuation creates the basis for a mutually beneficial exchange
between a constrained owner, and a non-constrained potential buyer.
Having identified a difference in valuation, the problem of negotiating a transfer is simple to analyze as
an application of Nash bargaining (Nash (1950)), with the no-agreement levels of utility produced by
(11). To maintain the simplicity of the analysis, the credit constrained (current) owner of the resource
endowment is referred to as the seller, and the non-credit constrained perspective future owner is
referred to as the buyer. Define Z as the negotiated transfer fee, which may be paid over multiple
periods.
For this potential bargain, the Nash product is simply:
N  U S  Z   U S* U B (Z )  U B* 
(12)
Where U(Z) denotes the individual’s indirect utility function after a payment of Z has been exchanged for
the unharvested endowment of the resource. As by definition, the seller obtains the same utility if Z is
equated to the proceeds obtained from extraction in the analysis of Section 2, there exists a non-empty
set for which N>0, guaranteeing the possibility of a bargain. The existence of a bargain implies that the
resource will be transferred from its credit constrained owner to an unconstrained owner; suggesting
that the constraints facing the original owner may have no bearing on the extraction of the resource.
This is consistent with the empirical findings of Neumayer (2005), who finds no support for this
hypothesis in the case of minerals and energy.
9
Of course, this also depends on the price of the resource in each period and the interest rate, but these play no
role in the analysis to follow.
5
With respect to the original Hotelling model, a trivial implication of the results presented in Section 2 is
that owners place the same valuation on the resource in the absence of borrowing constraints, transfers
do not occur. In other words, mines will never be sold under the original assumptions.
4. Conclusion
Having established that a transfer will occur, it is straightforward to evaluate the implications for the
distribution of profits produced by the resource. Note that, since it has been established that a transfer
will occur, the present value of the proceeds obtained from the resource is maximized; implying
negotiations simply cover the distribution of proceeds derived from the resource.
Given that the final outcome is the result of a bargaining process, the fact that the share of the proceeds
obtained by the original owner is increasing in the strength of his or her default position yields two
interesting conclusions.
First, a contraction of the borrowing limit will reduce share of the proceeds obtained by the credit
constrained owner. Assuming that the owner of the resource wishes to borrow funds, further restricting
their ability to do so decreases their welfare in the default position; weakening their bargaining power
and reducing the sale price of the endowment. This result has a very different implication than
expressed elsewhere in the literature.
Second, aid policies such as those described by Raucher (1989) and Strand (1995) will increase the share
of the proceeds obtained by the owner. This finding has important policy implications, particularly for
those considering providing aid to credit constrained owners of natural resources. The results presented
in the existing literature suggest that aid policies both increase the welfare of the recipient and decrease
the rate of resource extraction. However, the results presented here suggest that these policies may
only impact the welfare of the recipient by increasing their negotiating position as they consider the sale
of their resource endowment.
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References
Dasgupta, P., Eastwood, R., & Heal, G. (1978). Resource management in a trading economy. The Quarterly Journal
of Economics, 297-306.
Dasgupta, P., & Heal, G. (1974). The optimal depletion of exhaustible resources. The review of economic studies, 328.
Deaton, A. (1991). Saving and liquidity constraints. Econometrica, 59, 1221-1248.
Gaudet, G. (2007). Natural resource economics under the rule of Hotelling, Canadian Journal of
Economics 40, 1033-1059.
Gaudet, G., & Khadr, A. (1991). The evolution of natural resource prices under stochastic investment
opportunities: an intertemporal asset-pricing approach. International Economic Review, 441-455.
Hotelling, H (1931). The economics of exhaustible resources, Journal of Political Economy, 39, 137-175.
Kahn, J., & McDonald, J. (1995). Third world debt and tropical deforestation, Ecological Economics, 12,
107-123.
Krautkraemer, J (1998). Nonrenewable Resource Scarcity. Journal of Economic Literature 36, 2065-2107.
Nash, J. (1950). The bargaining problem. Econometrica, 155-162.
Neumayer, E (2005). Does high indebtedness increase natural resource exploitation? Environment and
Development Economics, 10, 127-141.
Raucher, M (1989). Foreign debt and renewable resources, Metroeconomica, 40, 57-66.
Slade, M., & Thille, H. (1997). Hotelling confronts CAPM: a test of the theory of exhaustible resources,
Canadian Journal of Economics, 30, 685-708.
Strand, J (1995). Lending terms, debt concessions and developing countries' resource extraction.
Resource and Energy Economics, 17, 99-117.
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