Protecting rhinos through legal horn trade
Timothy Fitzgerald∗
Michael ’t Sas-Rolfes†‡
April 21, 2014
Abstract
Rhinoceros populations have suffered in recent decades despite efforts
to ban international trade in rhino horn; despite the threat of severe
consequences if caught, poachers continue to kill animals to the point
that the future viability of populations is in doubt. The possibility of
harvesting horns from live animals to supply a legal market motivates
this study of whether lifting the trade ban can help rhinoceros populations recover. We develop a model of rhino conservation that takes
full account of contemporary conditions (markets, institutions, technology, and relevant biological parameters) and establish conditions
under which an appropriately structured legal trading regime can prevent the extinction of the white rhino in South Africa. We determine
sensitivity to key parameters of the population and market to establish
the likelihood that legalization will protect populations. The results
indicate that intensive management of rhinos, coupled with a legal
outlet for verified horn, could increase rhino numbers while lowering
the effective price for horn. Substantial expenditures for protecting
live rhinos are required, despite which poaching persists—at greatly
reduced levels. The success of such a scheme is not guaranteed, which
underscores the importance of careful attention to design details.
Keywords: endangered species, rhinoceros, poaching, wildlife property
rights, illegal trade
JEL Codes: K42, Q19, Q21, Q27
∗
Montana State University, timothy.fitzgerald@montana.edu
PERC, mtr@perc.org
‡
The authors would like to thank Kurt Schnier, Quinn Weninger, and participants at
the 88th Annual Conference of the Western Economic Association and 14th Occasional
California Workshop for helpful comments. We accept full responsibility for remaining
errors.
†
1
Since 1977, international trade in all rhino products has been banned under
the UN Convention on International Trade in Endangered Species (CITES).
However, poaching has continued to decimate rhino populations, driven by
the lucrative illegal trade in rhino horn. Although official price data are unavailable because of the clandestine nature of the market, undercover surveys
by organizations such as the wildlife trade monitoring network TRAFFIC
reveal that rhino horn prices have risen substantially over the last 36 years.
The per unit retail price of rhino horn in some Asian markets is reputed
to be higher than that of gold or illegal drugs (Graham-Rowe, 2011). High
black market prices have put surviving rhinos at increased risk from poachers. Amid concern for rhinos, the last remaining loopholes for international
trade in rhino horn have been removed. South Africa, which has historically been a safe harbor for rhinos, has experienced geometric increases in
poaching that biological populations cannot sustain.
Economists have proposed regulated legal trade as an alternative solution to the poaching problem for rhinos and other species in a similar
predicament.1 More recently this idea has received broader support from
scientists (Child, 2012; Biggs et al., 2013) and the South African government
has announced its intention to investigate the possibility further. We focus
on the prospects of a legal rhino horn trade relying on the still viable population of white rhinos in South Africa. This notion has not been addressed
in the economics literature so far as we know, yet is the most policy-relevant
setting anywhere in the world.
Circumstantial evidence indicates that effective demand for rhino horn is
price inelastic and that continued efforts at enforcement simply drive up the
black market price (Brown and Layton, 2001). A legal outlet for horn could
increase the quantity reaching market, reduce prices, and therefore remove
the strong incentives that poachers face today. Such a policy would be consistent with the recommendation of Becker, Murphy, and Grossman (2006)
for handling other illegal goods with persistent demand, such as drugs.
Rhino horns are unusual among animal products regulated by CITES
in that they can be harvested from live animals (by “dehorning”) and they
1
’t Sas-Rolfes (1995, 1997); Brown and Layton (2001) are examples in the rhino case.
2
regrow, thus obviating the need to kill the animals to supply the market.
This characteristic strengthens the rationale for legal trade. This differentiates the rhino horn problem from, for example, other widely-publicized
endangered species products such as elephant ivory (Kremer and Morcom,
2000). Poaching mortality is a loss on two counts insofar as not only are
the current horns stolen, but the potential for future horn growth is lost
when the animal is killed. A single rhino might grow the equivalent of eight
complete horns over a lifetime.
The case for a legal trade in horns harvested from white rhinos is more
compelling than the simple “supply-side approach” in the case of black rhinos that has been widely critiqued. White rhinos’ horns are acceptable
substitutes for those of other more endangered species such as Asian species
or black rhinos. The argument can be pressed further, as verified legal horn
may be viewed as a superior alternative to current supplies. We explore how
legal trade of horn from South African white rhinos can offer benefits (or
may create added costs) to other populations.
This article explores in detail the effect of key parameters on the viability
of a legal horn market. Complex dynamics arise in our model, which suggests the possibility of multiple equilibria. Because horn trade is currently
illegal, widespread management of rhino populations for horn production
is largely speculative. Precise calibration of all parameters is not possible.
Therefore we approach the calibration with a goal of establishing approximate necessary ranges for key parameters to ensure the success of a legal
horn outlet. We do have the benefit of detailed information provided by
rhino ranchers in South Africa to help parameterize the supply side. These
parameterizations provide important policy recommendations for the design and implementation of a legal horn outlet. The demand side remains
shadowy.
This article adds to a substantial existing literature on trade in endangered species, and rhino trade in particular. Bulte and Barbier (2005) emphasize that the interplay of economic, ecological, and institutional variables
will determine whether trade is “good” or “bad” in any given situation.
Similarly, Fischer (2010) argues that “it is important to understand the full
3
economic, ecological, and institutional context of the resource, or policies
can indeed backfire.” We agree with these authors and use their conclusions
as motivation for our closer modeling of the situation in South Africa today.
Our work differs from some previous treatments in that we do not view
rhinos as an open access resource a priori, but rather as subject to varying
degrees of control by residual claimants. Copeland and Taylor (2009) recognize the endogeneity of property rights regimes to resource management
and identify both enforcement power and underlying bioeconomic parameters as important determinants of the success of resource management. We
focus on bioeconomics and include enforcement decisions through protective
expenditures by rhino owners. We are able to identify critical conservation
thresholds for parameters that in the limit approach open access conditions. Furthermore, we recognize the importance of significant contextual
differences—between species or subspecies, between different range states,
and even between individual populations.
Our approach is novel in two other ways. First, we focus on the possibility of raising white rhinos in a South African wildlife ranching setting to
supply a continuous stream of legal horn to the market. In contrast, many
previous studies have been based on the black rhino, which we view as an
inferior species for these purposes.2 Second, our model recognizes that alternative strategies for rhino conservation have value, and allows for managers
of rhinos to pursue differing strategies.
Rhinos are one example of a broader class of biological resources that
may be susceptible to overexploitation under different trade regimes. American bison (Bison bison) has a unique history of near extinction but modern
recovery under largely private ownership. Taylor (2011) outlines the mechanisms by which international trade in bison products was necessary and
sufficient for the initial massacre of herds of millions of bison. A key difference between the bison case and the market for rhino horn is the underlying
price elasticity of demand. Bison products had a highly elastic demand and
substantial reductions in harvest cost due to new technology. In contrast,
new technology offers to help protect rhinos, and the underlying demand for
2
However, conservation and ranching goals may not perfectly correspond.
4
rhino horn appears to be much less elastic than the market for bison hides.
Private owners eventually were an important element in the protection and
eventual recovery of bison stocks (Lueck, 2002). Whether the private rights
to rhinos already granted in South Africa could be combined with a more
permissive trade regime to help rhinos populations stabilize and recover is
a central theme of this study.
In the following section we present the most important background information on rhino conservation efforts and the horn trade,3 previous treatments of the issue in the literature, and a summary of salient differences in
modern rhino management. In section a model of rhino management and
markets is presented. Section reports simulation results to illustrate effects
of policy changes, along with a number of robustness checks. The policy
implications of this study are discussed at some length before a conclusion
highlights important directions for future work.
Background
From a conservation standpoint, rhinos are imperiled.4 Five of thirteen
species or subspecies are now effectively extinct in the wild, and a further
six remain “critically endangered” (this includes three of five species). Table
1 reports the population levels and trends across the major species of rhinos
over time.
Unfortunately, this situation is not novel. White rhinos were close to
extinct in South Africa by the year 1900, but the population has rebounded
to the point that the country now boasts the majority of the world’s most
numerous species. In comparison to other range states, South Africa has
embraced market institutions as a conservation measure, allowing private
ownership and trade of live animals. South Africa permits commercial trophy hunts and still permitted domestic trade in rhino horn as recently as
2009. Owners of rhinos are allowed to retain and reinvest income from
3
A comprehensive summary of the history of rhino horn trade and its bearing on rhino
conservation efforts is available in ’t Sas-Rolfes and Fitzgerald (2013).
4
The World Conservation Union (IUCN) has two specialist groups working on rhino
conservation issues—one in Africa and another in Asia.
5
live sales as well as ecotourism and related profitable activities. Evidence
suggests that these institutional differences account for South Africa’s relative success with rhino conservation (’t Sas-Rolfes, 1990; Child, 2012). The
most recent (2013) official estimate of South Africa’s white rhino population
placed it at some 18,900 animals, with approximately 5,000 under private
ownership. The balance was owned by the state, by the South African National Parks authority (SANParks) and nine provincial agencies.
The CITES trade ban is intended to protect rhinos by preventing trade
in horn. The imposition of the ban has been incremental over the years
since rhinos were first listed in 1977. Figure 1 illustrates the resurgence of
the rhino horn market as proxied by data on poaching of rhinos in South
Africa. Tighter regulation of the private rhino industry in 2008 (labeled
TOPS in figure 1) was followed by a 2009 moratorium on domestic sales
within the country (so as to thwart illegal exports). An explosive increase
in poaching ensued, reaching over 1,000 animals in 2013. Such increases
cannot be sustained.
Like much of the previous literature, Damania and Bulte (2007) refer to
“wild” rhino populations, implying an open access situation. In reality few
if any surviving rhino populations exist under open access conditions: most
are protected within state parks or on private land under relatively strong
property rights regimes. There is no ambiguity about who owns the rhinos
in national parks. In South Africa, rhino owners and custodians bear the
costs of protection but are also entitled to retain any financial returns that
rhinos may generate. This implies that, to the extent that rhino owners
are able to raise income from their animals (e.g., by selling horn), they
can re-invest the proceeds into protection, thereby effectively raising the
costs of poaching. What is an issue is the extent to which various owners
can exercise control over their rhinos. The cost of keeping track of a rhino
in an open-range environment is likely to be much higher than in a more
controlled setting.5 We capture this reality by allowing for different cost
5
Allen (2002) discusses dehorning of rhinos as intentional obsolesence of (natural) capital. The reason for such an action is to lower costs associated with protecting an animal.
The same idea underlies our conception of different cost functions across manager types.
6
functions across management types.
Damania and Bulte (2007) warn against unqualified acceptance of legalized trade because of the possibility of market power in the horn market.
Legal horn sales could provide cover for the marketing of poached horn. In
the event that legal and illegal suppliers split the market, the form of competition affects viability of rhino stocks.6 The strategic interaction between
legal and illegal horn suppliers is something we consider explicitly below.
Another important issue is the substitutability of farmed horn for poached
wild horn. Under a prospective legal horn trading regime, all legal horn
passes through a certification system that involves DNA testing and microchipping of legal horns. Poached horn would not be certified in this way
and therefore would not enjoy a guarantee of authenticity.7 Other endangered species products, notably tiger bone and bear bile, are more susceptible to the argument that the farmed product is inferior. Evidence of this
effect is limited in the case of rhino horn. Counterfeit or impure rhino horn
is a concern for illegal purchasers, and a source of verified and traceable
horn is likely to be viewed as comparable or even superior to an unverified
horn.8
The conservation history of other species offers some insight as well.
As one example, Lueck (2002) examines the role of property rights in the
history of the exploitation and conservation of the American bison. During
the 19th century, bison evolved from a common property resource into an
open access resource. Bison were valued largely for their hides or robes,
much like rhinos are valued primarily for their horns. The stock of bison
was dramatically reduced under open access conditions, compounded by
6
General agreement that the illegal horn market is not perfectly competitive is not
based on definitive positive evidence. Damania and Bulte (2007) model a duopoly between
legal and illegal players
7
Like any other legal barrier, this verification is subject to corruption and counterfeit.
8
Anecdotal evidence from the horn market suggests that one reason illegal horns are
smuggled whole (which increases probability of detection) is so that final consumers can
see the whole horn and watch the horn being shaved. This tactic reduces verification costs
at the retail level in exchange for increasing costs at the distribution level. Because we use
farm gate prices in our simulation study, and therefore remain agnostic on the markup in
legal versus illegal markets, we address this point only crudely by adjusting elasticities of
substitution.
7
technological improvements that lowered harvest costs. As stocks dwindled,
private individuals recognized the value in keeping the species and began to
create private herds. These private herds, along with a handful of surviving
public herds, were crucial to helping engineer the restoration of bison herds
to levels that ensure safety from extinction.
Expanding analysis to additional species, whether formally endangered
(like elephants) or not (like bison), runs a risk of muddling the defining
biological characteristics of individual species. Figure 2 clarifies why rhinos
are a good candidate for a legalized trade regime. The columns index the
effect collection of products has on an individual animal. Rhino horns can
be collected quite easily and regularly, without harming, let alone killing,
the animal. In contrast, tiger bone is collected after the animal is killed.
Elephant ivory can theoretically be collected in limited quantities without
killing the animal, though it typically is not. Elephant tusks grow back very
slowly after harvest, and therefore represent a stock harvest decision. The
rows in the figure delineate how the product is used. Medicinal products, like
tiger bone and rhino horn, are consumed in use. In contrast, ivory products
are generally durable, so additional harvests add to the extant stock.9
A Model of Rhino Ranching and Horn Trade
We observe the emergence of two different rhino management strategies,
which we refer to as extensive and intensive. The more traditional form
of extensive management retains natural habitat conditions without supplementary feeding or genetic selection. Many national and regional parks
pursue this strategy. Extensive managers earn income from some combination of tourism viewing, live sales, trophy hunts, collections of horn from
deceased animals, and potentially by capturing indirect values through donations or subsidies. Because many extensive managers are national or
provincial parks, this last pathway is particularly important. Few extensive
9
Rhino horn also has durable uses, such as for dagger handles. However, the primary
use is medicinal. Rhinos that are dehorned regularly provide a product ideal for medicinal
as opposed to durable use.
8
managers allow trophy hunting on their properties, but some sell live animals to private landowners. Those live animals may then enter the trophy
market, or may augment existing intensive herds. If horns are collected from
naturally deceased animals, under the current policy regime that product
must be stockpiled because it may not legally be sold.
In general, extensive managers simply husband rhinos in a largely native state. The extent of management is typically to collect revenue where
possible and to try to protect rhinos from poachers. As a last resort, extensive managers may temporarily employ dehorning as a security measure,
but typically would avoid this as it may negatively impact tourism, trophy
hunting, and other potentially valuable aspects of rhinos. Because horn cannot be legally exported or even sold within South Africa, the only benefit
to this strategy is the prophylactic benefit of reducing poaching risk.
The emerging form of intensive management is characterized by routine dehorning and higher stocking rates. The rhinos are still free-ranging,
but some breeding manipulation may take place. In this sense intensivelymanaged rhinos are not different from other range livestock or game ranching
operations. Intensive managers may still derive income from tourism, but
this is likely to be at a reduced rate. Similar discounts are likely for other
indirect values that an owner may be able to capture. Live sales are still
a possibility, perhaps at a price depending on the extent to which horns
have been trimmed. As additional rhino farmers wish to enter the business,
live animals from intensive managers are likely to be an important source of
seedstock.
The distinction between extensive and intensive management is significant in that conservation bodies such as the IUCN would not consider the
latter practice to satisfy its conservation criteria. Accordingly, a principal
conservation policy objective is to maintain a minimal viable population of
extensively-managed rhinos (Eiswerth and van Kooten, 2009). The most
pressing policy question is whether or not a legal horn regime can relieve
poaching pressure on extensive rhinos sufficiently so that a conservation
population survives.
A key distinction of our model is the interaction between both types of
9
management and poachers. We assume that managers of both kinds are
able to invest in protection, and that such protection is able to deter poachers by increasing the costs of poaching. We allow for these relationships
to differ by management regime. Although poaching of an individual rhino
may be probabilistic, in aggregate, we view poaching pressure as determined
by horn prices and protective expenditures. The extent to which additional
expenditures are able to prevent poaching is fundamentally an empirical
question. While fences and armed guards come to mind immediately, less
salient expenditures such as establishment location may also be important
determinants of poaching prevention. Expenditures on political efforts to
increase sanctions for apprehended poachers could also yield valuable returns. Without the ability to increase protection for rhinos, it is not clear
how the species will survive given the two management types, regardless of
the legality of horn trade.
“Ownership” and Control of Rhinos
Although we consider all rhinos as valuable in avoiding extinction, to answer some policy questions it may be useful to consider the population in
each regime. The aggregate stock of rhinos is the sum of the intensive and
extensive owner stocks.
s = sI + sE
The possibility of poaching from either type of owner further motivates the
consideration of separate populations. Designating legal harvest (live sales)
as h and poached animals as z, we can summarize the total harvest of rhinos.
h = hI + hE + z I + z E
We consider an average horn yield function that varies by management
regime, designated y(·).10 The total amount of horn available to the market
10
Consider that the yield of horn from a poached rhino is likely to differ from the stream
of horn an intensive manager can realize from a given stock. In fact, poached rhinos may
yield different amounts of horn depending on whether or not they have been previously
dehorned (and how recently). These details are important in an empirical sense but
10
is given by:
y = y I (sI + z I ) + y E (z E )
This implies a legal stream of horn provided by intensive managers and
illegal horn derived from poached animals. Both potentially satisfy the
market demand, though we explicitly consider the interaction between the
stocks below.
Biological Representation and Dynamic Optimization
Represent the stock of white rhinos at time t as st . Rhinos are a biological
resource that grows at a rate depending on the stock level, which can be
represented with a concave growth function f (st ). The parameters of this
growth function can be deterministic or stochastic, and can vary between
types of stocks.
Combining the biological growth, harvest, and poaching, we have a population transition equation for each management regime that describes the
change in rhino stocks over time.
st+1 = f (st ) − ht − zt
Owners maximize the net present value of expected payoffs subject to the
biological transition. Because we assume that intensive owners dehorn all
rhinos, there are only two decision variables for the intensive owner: live
harvest and protective expenditure. The value function for the intensive
owner is:11
V I = max
hIt ,ρIt
∞
X
β t RI (pt , sIt , ytI (sIt ), hIt ) − cI (sIt , ρt , hIt )
(1)
t=0
The optimization is subject to the state transition equation and an initial
subsumed into potentially different concave horn production functions. From the point
of view of the poacher’s problem, we can treat the revenue function as separable in dead
rhinos from different sources.
11
The specific functional forms for the components of the value function that are employed in the value function iteration are discussed in appendix B.
11
condition:
sIt+1 = f (sIt ) − hIt − ztI (ρt )
sI0 = S̄ I
The parameters in the value function include the farm gate price (pt ), the
stock of rhinos, the amount of horn produced each period, and the live
harvest of rhinos each period. The level or protective expenditures ρt is also
included.
The value function for extensive owners is similar, with the same choice
variables but a different reward function, because there are no horns harvested:
V
E
= max
E
hE
t ,ρt
∞
X
E
E E
E
β t RE (pt , sE
t , ht ) − c (st , ρt , ht )
(2)
t=0
again subject to the state transition equation and an initial condition:
E
E
E
sE
t+1 = f (st ) − ht − zt (ρt )
E
sE
0 = S̄
In this case the horn price is driving the non-horn value of rhinos as well.
Poaching
The imminent threat to rhinos is poaching, primarily motivated by the valuable horn. Instead of harvesting horn as intensive managers do, poachers kill
the rhino and harvest the horn from the dead animal. Poachers are stealing
owners’ rhinos with their clandestine kills; we assume that all poaching of
horn is fatal to the rhino.12 It is possible that they might steal from either type of owner, depending on the amount of horn that a stock of rhinos
12
It is possible that poachers could employ the same dehorning tactics as intensive
owners, and there have been poaching episodes in which rhinos have not been killed.
However, the norm is that the rhino is killed, allowing the poacher to extract the root
of the horn from the carcass. One reason for this is that the cost of killing an animal is
typically lower than the cost of sedating it.
12
has and the protective expenditures made on behalf of those rhinos.13 The
poacher simply weighs the benefits and costs of poaching. The model here
presents the poacher’s objective as a static problem without foresight. That
is, in all time periods t the poacher chooses from which type of owner to
steal rhinos (z):
max R(z I , z E ) − C(sI , ρI , z I , sE , ρE , z E )
z I ,z E
Poachers equate the marginal return to poaching (farm gate price in the
black market) with the marginal poaching costs (including expected probability of detection and preventive expenditures) across the intensive and
extensive populations. Standard assumptions apply to the poaching cost
function: more enforcement makes poaching more costly at a decreasing rate
(Cρ > 0, Cρρ < 0); marginal costs are positive and increasing (Ch , Chh > 0);
and a larger stock of animals reduces the cost of poaching (Cs , Chs < 0).14
This simple model yields reasonable predictions: an increased price will
increase poaching from both types of owners. Higher protective expenditures
decrease poaching, and higher stocks increase the potential for poaching.
Consumer Demand
We explicitly consider three streams of value from rhinos. Some value is
derived from the presence of the stock—for example, wildlife viewing or
pure existence values. These values depend on the stock of rhinos, st , as
defined above. Value is also derived from removing an animal from the
population, such as by trophy hunting. These harvests are included in ht
defined above. Finally, a strong demand for rhino horn persists despite the
international trade ban. In our model all intensive managers dehorn every
13
Bulte (2003) identified a similar type of switching by poachers (between rhinos and
elephants) as they pursue the higher-value population.
14
The poaching problem can be separable by type of rhino, and we think of the poaching
decision in this way. The process of smuggling horn poached from different sources to a
retail market is likely to be less discriminating. However, we do not explicitly consider the
intermediate markets here. For an explicit model of how protective expenditures affect
poaching, see appendix A.
13
animal in every period.
We begin by considering a stationary demand with competitive suppliers,
and move on to varying degrees of market power below. A key distinction
of this model from others is in how consumers view the legal and illegal
products. Previous work has assumed that the poached product is superior
(Damania and Bulte, 2007). Advances in DNA technology and the stockpile
registration system provide decisive steps toward a certification and verification system. This system could provide a competitive advantage to legal
horn sellers as there is apparently a high level of counterfeit horn in the
illegal marketplace (Nowell, 2012). We therefore take a conservative view
that the two sources are perfect substitutes for one another and specify the
horn demand as a function of aggregate supply. This is despite the reasons
mentioned above that a legal supply might in fact be superior to illicit horn.
We parameterize demand both linearly and with an isoelastic specification.
Market Simulation
Calibrating Data
Parameterization of the simulation model, especially for our prospective
intensive owners, is critical to accurate inference. We have data from entrepreneurs in South Africa who are currently dehorning rhinos and stockpiling horn in anticipation of a legal outlet for horn such as we consider
here. The information provided by these operations is the source of calibrating values for the simulation study.15 One contribution of this article is
to bring calibrating data from current intensive entrepreneurs to the debate
over horn legalization. We then robustness check the parameters derived
from the data.
The science of rhino husbandry is still nascent. According to Rachlow
and Berger (1997), free-ranging white rhino population annual growth rates
vary between 6–11 percent. Growth rates may be affected by stocking rates,
15
Because of the coarseness of the biological model, we estimate cost parameters based
on aggregate population size. For details, see appendix B.
14
quality of habitat, and management considerations. Higher rates may be
achieved with intensive and selective management of sex ratios. We take a
naive, and in our view conservative, approach by using extant estimates in
conjunction with a growth function drawn from the logistic family.
The rate of horn growth is crucial. This presents an interesting problem
of a renewable resource (horn) within another renewable resource (rhinos).
Reports from current dehorning operations suggest that there is substantial
natural variation in the rate of horn growth across individuals. Because
we lack sufficient information about the range of possibilities, we opt for a
simpler average horn growth function.
We include a periodic stochastic shock in the state transition. This
shock could be interpreted as a drought, disease, or other idiosyncratic factor
that affects recruitment in each year. The shocks are drawn from a normal
distribution. Because individual shocks affect the time path of choice and
state variables, we repeat the experiment with different draws and report
mean outcomes (with confidence bounds as appropriate) in the results.
Numerical Approximation by Value Function Iteration
The relationship between two populations of rhinos, their owners, poachers,
and consumers in a worldwide market presents a complex dynamic system.
In such situations, multiple equilibria can be expected. Because we cannot
solve for these equilibira in closed form, nor can we observe a legal horn trade
regime, we investigate the system via simulation. The simulation model relies on iteration of the value functions described above. The models were
calibrated using data on rhino population and horn growth from contemporary intensive and extensive rhino managers in South Africa described
above.
In order to gain additional insight into this problem, we use value function iteration to numerically compare alternative policy regimes. The functional forms of the value functions are explained in detail in appendix B.
This allows rhino owners and poachers to individually optimize and generate
market-clearing prices as an outcome of the model. As a first step we iden-
15
tify the value functions for farmers, non-farmers, and poachers. The state
variables are the stock of rhinos and prices of both live rhinos and horn.
The control variables are the number of rhinos harvested by poachers (from
each type) and both intensive and extensive owners. Harvest includes both
owner and poached harvest.
We conduct the value function iteration following in the tradition of Rust
(1987), partitioning the state and action space into discrete blocks. We used
a 100 by 100 grid, though only the upper triangular portion of the matrix
is non-zero because it is not possible to harvest rhinos that do not exist.
We interpret the discrete partition as representing percentiles of carrying
capacity. The relatively dense grid increases the computational cost of the
algorithm, but we accept this cost to aid the interpretation of the results.
In cases where the optimal action interpolates between our discrete points,
we force the action and state to maintain our discrete network. This may
introduce a bias towards extinction at low population levels, which we feel
is conservative given our other results.
Baseline Results
The results of the value function iteration are presented graphically. Figure 3 shows the stark contrast in the total population of rhinos when trade is
allowed as compared to continuation of the current ban. In a strictly deterministic simulation rhinos are not poached into extinction. The extinction
depicted in the left panel of table 3 is attributable to the stochastic shock
that eventually damages the population irreparably. In contrast, the right
panel reports a projected increase in the number of rhinos if a legal outlet
for horn is created. Under either regime poaching persists so long as there
is a population to poach—it is never completely prevented. The key difference is that intensive owners are able to generate enough revenue through
horn sales to afford sufficient protective expenditures to keep poaching to
manageable levels for both their own herds and for the extensive herds as
well.
A slightly different depiction of rhino stocks is in figure 4. Because
16
conservation objectives may be sensitive to the management regime, decomposing the population into intensive and extensive stocks is instructive. The overall growth in rhino stocks is through intensively-managed
herds. Extensively-managed populations are effectively constant over time.
The simulations indicate that intensive rhinos are likely to exceed extensive
stocks, but it will take 25 or more years for the private herds to be built up
to that level. The transition could happen faster if current extensive herds
switch over to an intensive regime.
Growth in intensive herds is driven by the profitability of the farming
rhino horn. Introducing a legal outlet for horn is obviously a central issue.
Figure 5 offers a stark testament to the value of horn and the comparison
across a legal trading regime and continuation of the status quo. The figure
focuses on long-term price dynamics. Continuation of the current trade ban
leads to a monotonic increase in horn prices, with falling quantity reaching
market. Poaching accounts for all of this horn, and all poaching is fatal to
the rhino in our model.16 In contrast, under the legal regime, prices gradually fall as a greater quantity reaches the market. This is also a long-term
prediction, not accounting for the possibility of selling existing stockpiles—
the South African government currently holds a stockpile purported to be
worth approximately $1 billion at current black market prices.
While population and poaching data are important measures of conservation goals, and the operation of a prospective legal horn market is clearly
of paramount interest, the value function iteration allows for direct comparison of economic value under alternative regimes. In figure 6, the comparison
across regimes is depicted. Without trade, all rhinos are de facto extensive.
Unfortunately, our results indicate that the value of these herds is likely to
be eroded by ever-greater but sadly ineffective protective expenditures.17
Eventually, as stochastic shocks press rhinos to the limit of extinction, the
16
Note that we do not explicitly account for storage and temporal arbitrage of horn in
this model. See Mason, Bulte, and Horan (2012) for an explicit treatment. In our view,
such a model needs to explicitly consider the share of horn for medicinal and ornamental
uses, because medicinal usage is consumptive and ornamental usage is not.
17
These estimates make no attempt to consider all non-use values, only the share that
owners are able to capture. We model that share as a function of the number of rhinos.
17
value of the non-existent herds falls to zero. Under a legal trade regime, we
show different value functions for intensive and extensive stocks (these values are aggregated on assumption of stocks in figure 4). Extensive stocks are
able to hold constant and maintain a constant value. Due to the profitable
horn trade, the growing herds of intensive rhinos are projected to increase
in value over time. The comparison in aggregate value between the current
trade ban and a prospective legal trade regime is dramatic.
Robustness Checks
Sensitivity to parameters is a central concern in a study of this kind, so a
variety of robustness checks were performed. The results of some of those
tests are discussed here. We focus the narrative on three counterfactual
worlds that we consider particularly pertinent: one in which poaching costs
are far lower because protective expenditures have a lower deterrent effect;
a second in which stochastic shocks to rhinos populations are drawn from a
distribution with greater variance; and a third in which legalization significantly changes demand. If poaching is more costly to prevent, we expect
the population level will be driven lower. If stochastic shocks are larger, the
minimum viable population is larger. If demand shifts dramatically when
legal trade is permitted, the increase threatens to swamp the ability of legal
suppliers to provide horn, with the balance made up by additional poaching
with attendant laundering of illegal horn.
Suppose that protective expenditures cannot deter poaching. In that
case, whether there is legal trade or not, rhinos are in a dire predicament.
Non-price barriers such as verification offer some prospects for helping protect populations, but those types of policies are not easily incorporated into
our model. Lower costs of poaching lead to fewer extensive rhinos, which
bear the brunt of poaching pressure. In all models poachers are attracted
to extensive rhinos and their large, intact horns. The left panel of figure 10
shows the reduction in value for all owners, especially for extensive owners
regardless of trade policy. As one might expect, lower costs of poaching
leads to more of it and a faster approach to effective extinction.
18
Larger shocks to rhino populations could be motivated by climate change
or outbreaks of a generalized infectious disease. The right panel of figure 8
shows the larger confidence intervals around mean population projections.
One effect of the stochastic process we have used is that positive population
shocks are as likely as negative shocks. The effect on the horn market of this
additional uncertainty is minimal (figure 9), but the value of rhino stocks is
reduced for all owners even though they are risk-neutral.
A third important class of concerns are those raised by Fischer (2004)
about possible demand expansion because of legalization—so-called “stigma
effects.” When we allow demand to expand dramatically, we observe a higher
price but similar price dynamics over the long run. The dynamics of the demand expansion are important; we have assumed demand immediately and
irrevocably expands, but suspect that such transitions might be slower and
allow for growth of legal supply in the interim. This higher price attracts
more poachers and reduces the value for legal owners, especially extensive
ones. The protective expenditures required to maintain herds consumes
much of the value that would otherwise be generated. When shifting demand outwards, we do not account for the potential to discriminate between
legal and poached horn. We remain optimistic that a legal market can use
verification to signal quality and authenticity to potential consumers.
Policy Implementation
Rhino populations will remain seriously threatened if poaching continues
along the current trajectory. Without significant and increasing external
sources of funding, rhino managers and custodians seem unable to afford the
substantial and increasing costs of field protection. The horns are simply
too valuable in relation to all the other sources of revenue from rhinos. If
the market can only acquire horns by illegally killing rhinos, it seems that
wild populations are mostly doomed. However, the results above suggest
that there is hope for rhinos by establishing a legal outlet for horn. Here
we consider the details of transitioning to such a legal trade regime. We
focus on the possibility of side payments to cover protective expenditures
19
and market structure concerns in a legal regime.
Legal trade would yield the most positive direct results for intensively
managed white rhino populations in South Africa. Extensively managed
populations of white rhinos could benefit to the extent that horn stockpiles
from natural mortalities are sold, sale prices of live animals increase and
incentives for poaching are reduced. Black rhino populations would also
benefit to the extent that they share habitat with white rhinos as well as
indirectly if illegal horn prices decline. Rhino populations in other African
countries would also benefit somewhat less and indirectly and perhaps the
least benefit would be to populations of the Asian rhino species. The only
benefit to the latter would be by way of reduced horn prices. However,
the protection of these other populations is necessary to preserve a captive
market for legally-provided horn.
In figure 6 we highlighted the divergence in value of extensive and intensive rhino stocks. Intensively managed rhinos recognize the full opportunity
cost of horn and the poaching risk it entails. Therefore we expect poachers to target extensive rhinos, which then require greater expenditures to
protect. However, the extensive manager does not benefit directly from the
legal trading regime—the intensive owner does.18 This raises the possibility
of side payments from intensive to extensive owners. Those payments could
be used to afford the protective expenditures required to deter poachers.
The transfer payments could be collected before sale through the licensed
outlet.
An interesting complementary result is that extensive owners alone are
better off under the trade regime than the non-trade regime, as measured
by their value functions. We attribute this to a new source of demand for
live rhinos and a reduction in poaching pressure thanks to a legal outlet for
horn. The reported value functions do not include transfer payments.
Previous authors have suggested establishing some type of cartel for the
purposes of re-establishing a legal trade (’t Sas-Rolfes, 1995; Abbott and van
Kooten, 2011; Biggs et al., 2013). The benefits of centrally-administered auc18
Extensive owners could benefit directly by selling horn stockpiles or horn from natural
mortalities.
20
tions of legally-available horn are potentially similar to a cartel. Duopoly
interaction between a legal and illegal provider of horn have been explored
by Damania and Bulte (2007). Registration of approved suppliers and certification is necessary. This would also allow extensive owners an outlet
for horn from natural mortality. Such a system could be linked to CITES
in such a way as to ensure that only sealed batches of approved horns are
shipped from range states to consumer countries at regular intervals (e.g.,
quarterly).
The system could also be designed to restrict the quantity of legal horn
exported to ensure that supply levels are sustainable. Such a program is
an exception to CITES rather than a program requiring broader repeal or
lifting of protections. Auctioning batches of horn with a blind reserve price
to registered bidders offers good prospects for aligning a legal trade with
conservation objectives. Existing stockpiles of horn could be used to help
smooth short-term supply interruptions.
To overcome the current risk of purchasing fake horns, retail buyers demand to see the whole horn because they are readily verifiable. This forces
smugglers to handle whole horns. Because of the distinctive shape and size,
whole horns are costly to conceal and transport. Legal and certified horns
offer a low-risk alternative and would likely be preferred some consumers.
Regular batches of legal supply rather than one-off sales would provide supply certainty in the market to reduce incentives for speculation. We expect
that legal suppliers will strongly support existing deterrents for all forms of
illegal activity.
Conclusions
Poaching of rhinos in South Africa has expanded dramatically in the past
several years. As various pathways for rhino horn from controlled or nonfatal sources to enter the lucrative Asian markets have been shut off, both
prices and poaching have soared. Without effective policy intervention,
white rhinos may once again face extinction in South Africa. This paper
suggests a radical policy shift. This would entail the regulated legalization
21
of trade in verified rhino horn, which would require amendment to the current ban established by CITES. We simultaneously propose allowing rhino
owners who regularly dehorn their animals to sell the harvested horns in the
verified horn market. This creates a strong financial incentive for intensive
managers to protect their lucrative rhino stock. Poachers harvest one horn
from an animal, but an intensively-managed rhino can produce as much as
eight times the volume of horn over its lifetime.
Unlike many other banned products from endangered species, rhino horn
can potentially be supplied without endangering the population. There
are substantial (and increasing) existing accumulated (legal) stockpiles from
natural mortality and dehorning of live animals. In light of this important
distinction, a revision of the prohibitionist policy seems appropriate.
Our simulation study suggests that a legal rhino horn trading regime
would increase both horn and rhino stocks while lowering horn prices. The
creation of such a regime would likely require large immediate investments
in rhino protection. However, we expect such expenditures to decline (in
real terms) over time. The rents from a legal horn trade could provide
funding for these needed protections. Without a policy change, the remaining population requires substantial additional protective expenditures that
have no apparent source, and leaves the remaining rhino stocks susceptible
to possible environmental or market shocks.
A number of possible extensions to this work deserve additional study.
First, sellers in the new verified rhino horn market may attempt to act as
a cartel. The goal of higher revenues may have an unintended consequence
of increasing poaching pressure, especially on rhino populations outside the
cartel. Second, the animal science of a nascent intensive rhino farming sector
offers considerable room for improvement. Third, because the only current
outlets for horn are illegal, the dynamics of transition to a verified market
deserve further study. Some inference may be drawn from the legalization
of other illegal goods, such as some recreational drugs. Establishing the
optimal timing of legal sales deserves further consideration, especially given
the large protective expenditures that we anticipate will be necessary while
the market develops. A legal market would provide valuable information
22
about underlying fundamentals. Finally, because rhino horn can be stored,
strategic release of existing stockpiles creates the possibility of price effects
that we do not explore here. Experience in other commodity markets suggests that a full array of future and option contracts will smooth the price
path; existing stockpiles can augment the flow of legal horn from intensivelymanaged rhinos. These topics are important to current policy debates over
the poaching epidemic.
23
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26
Figures and Tables
Figure 1: Recent poaching levels in South Africa and possible influences
27
Non-Fatal
Consumptive
Usage
Fatal
tiger bone
rhino horn
Durable
Figure 2: Classifying products from endangered species
Collection
elephant ivory
Figure 3: Baseline Simulation Results: Rhino Population and Poaching
No Trade
Trade
28
Figure 4: Baseline Simulation Results: Rhino Populations by Type
Blue: all Green: extensive Red: intensive
Figure 5: Baseline Simulation Results: Horn Price and Quantity
Price
Quantity
29
Figure 6: Baseline Simulation Results: Comparison of Value Functions
Figure 7: Simulation Sensitivity Tests: Rhino Population and Poaching
Low Cost
High Uncertainty
30
Figure 8: Simulation Sensitivity Tests: Rhino Populations by Type
Low Cost
High Uncertainty
Blue: all Green: extensive Red: intensive
Figure 9: Simulation Sensitivity Tests: Horn Price and Quantity
Horn Price
Horn Quantity
31
Figure 10: Simulation Sensitivity Tests: Comparison of Value Functions
Low Cost
High Uncertainty
32
33
Scientific Name
Dicerorhinus sumatrensi
Rhinoceros sondaicus
Rhinoceros unicornus
Diceros bicornis
Ceratotherium simum cottoni
Ceratotherium simum simum
Source: IUCN
Sumatran
Javan
Indian
Black
White
Species
<50
<100
<1,000,000
1900
700
65,000
2,000
1,552
<600
50
1,500
12,753
<20
<3,561
<540
<100
<2,025
2,550
<30
6,784
Population Estimate
1970
1981
1993
<100
50
2,600
5,055
0
20,405
2013
critically endangered, decreasing
critically endangered, unknown
vulnerable, increasing
critically endangered, increasing
effectively extinct
near threatened, increasing
Current
IUCN Status
Table 1: Selected past population estimates and current status of rhino species
34
Rhinoceros sondaicus sondaicus
Rhinoceros sondaicus annamiticus
Javan
White
Black
Ceratotherium simum simum
Ceratotherium simum cottoni
Diceros bicornis bicornis
Diceros bicornis longipes
Diceros bicornis minor
Diceros bicornis michaeli
Rhinoceros unicornus
Rhinoceros sondaicus inermis
Dicerorhinus sumatrensis sumatrensis
Dicerorhinus sumatrensis harrissoni
Dicerorhinus sumatrensis lasiotis
Sumatran
Indian
Scientific Name
Species
Swaziland, Mozambique, Zimbabwe
Uganda, Chad, Sudan, Cent. Afr. Rep.,
Dem. Rep. Congo
Botswana, Namibia, South Africa,
Sudan, Ethiopia, Somalia, Kenya, Tanzania, Rwanda
Cameroon, Chad
Tanzania, Zambia, Zimbabwe, Mozambique, South Africa,
Dem. Rep. Congo, Angola, Botswana,
Malawi, Swaziland
Namibia, Angola, Botswana, South
Africa
India, Nepal, Pakistan, Bangladesh,
Bhutan, Myanmar, China
Indonesia
Vietnam, Cambodia, Laos, Thailand,
Malaysia
India, Bangladesh, Myanmar
Thailand, Malaysia, Indonesia
Indonesia, Malaysia
India, Bhutan, Bangladesh, Myanmar
Historic Distribution
South Africa, Namibia, Botswana, Zimbabwe,
Swaziland, Zambia∗ , Kenya∗ , Uganda∗
Note: ∗ indicates non-native (introduced) population.
EXTINCT
EXTINCT
South Africa, Zimbabwe, Tanzania,
Botswana,
Malawi, Swaziland, Zambia, Mozambique
Namibia, South Africa
Kenya, Tanzania
India, Nepal
EXTINCT
Indonesia
EXTINCT
Indonesia, Malaysia?
Malaysia, Indonesia?
Myanmar?
Current Distribution
Table 2: Past and present distribution of all rhino subspecies
A
Preventing Poaching
Becker (1968) presents a canonical model of crime and punishment for illegal
activity. Building on this framework, we foresee expenditures to reduce
poaching potentially operate through three channels:
1. increased probability of detection and apprehension
2. increased penalty in event of detection or apprehension
3. higher cost to hold probability of detection and penalty equal
An example of the first channel is to simply pay more people (or perhaps
pay the same number of people more to watch more closely) to watch rhinos
and protect them from poachers. However, more technology such as nightvision goggles or infrared sensing could be used to increase the probability
of detection.
We anticipate expenditures leading to higher penalties through two avenues. One is that rhino owners can make being detected and apprehended
more costly to poachers. In a dramatic example, this could be through a
“shoot first, defend in court later” policy. However, collecting additional
photographic and video evidence is one way that owners could help increase
penalties. Another related channel might be through lobbying to increase
poaching penalties. In a spirit similar to Mason, Bulte, and Horan (2012),
who predicted a need for trade bans on extinct species, we foresee the need
for poaching penalties even after populations have recovered from the brink
of extinction.
In order to hold the probability of detection and penalties constant,
we anticipate poachers can use technology or bribery to avoid detection or
apprehension. There is evidence that this is occurring today in South Africa.
The cost function for poaching depends on at least three terms: the
marginal harvest cost, effect of stock, and the expected penalty. The expected penalty is the probability of detection or apprehension times the
expected sanction F . One possible cost function is:
C = c(z, ρ) + c(s) − P r(ρ) · F (ρ)
(A.1)
If the cost function took this separable form, we would expect the following
relationships to hold.
∂2C
>0
∂z 2
∂C
>0
∂z
35
∂C
>0
∂ρ
∂2C
>0
∂ρ2
∂2c
>0
∂z∂ρ2
∂C
∂2C
>0
<0
∂s
∂s2
Regardless of how expenditures are made, we require that:
∂C
>0
∂ρ
This implies that additional protective expenditures can raise costs for poachers. Examples of protective expenditures are fencing, GPS location, helicopter patrols, and employee bonuses when no poaching occurs. Currently
we observe use of night vision equipment and drones as low-cost alternatives
to helicopters, but they are examples of protective expenditures. While we
expect diminishing returns to additional expenditures, our framework only
requires that additional expenditures always add to the costs of poaching.
B
B.1
Functional Forms
Cost Functions
The main cost functions used are quadratic to ensure unique solutions to
the system. The calibration is derived from intensive manager cost data
supplied to the authors. Those data are used to estimate monthly costs in
a linear regression for the winter months (March – September):
2
EXP EN SEm = β1 SIZEm + β2 SIZEm
+ εm
(B.1)
The estimates for β1 and β2 are 6616 and -2.03, respectively. The units
of expenses are South African rand. We use the point estimate to take
the average across the winter months, and add the average monthly nonfeed (overhead and labor) costs to derive an annual cost estimate that is a
baseline for the simulation study.
B.2
Value Functions
ΠIt = pht y(s) + p`t ∗ ht + α ∗ st − 0.05 ∗ s2t ;
(B.2)
`
2
ΠE
t = pt ∗ ht + α ∗ st − 0.05 ∗ at ;
(B.3)
E E
I I
I I
ΠP = (pht ∗(1/y I ztE +ztI )+β∗(ztE +ztI )+ztE ρE
t +zt /st +zt ρt +zt /st ); (B.4)
36