Worshipping the Tiger for Its Own Sake

Adrian A. Lopes Dept. of Economics American University of Sharjah [email protected]

Shadi Atallah Dept. of Natural Resource and the Environment University of New Hampshire [email protected]

Selected Paper presented at the 2019 Agricultural & Applied Economics Association Annual Meeting, Atlanta, GA, July 21-23

© Copyright 2019 by Adrian Lopes and Shadi S. Atallah. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

1

Abstract

Several indigenous tribes around the world derive spiritual value from revering fauna and flora species. Species conservation is not a prime objective of such traditions, but rather an unintended consequence. Conventional species management practices ignore this spiritual aspect and tribes are often evicted from protected areas. We use the existence value framework to develop a coupled ecological-economic model of a social portfolio manager who optimizes the net benefits of harvesting a protected resource, which also provides spiritual value. These values are derived from non-consumptive spiritual aspects of the resource. The model is calibrated for the Biligiri Rangaswamy Temple (BRT) Tiger Reserve in India with the resident Soligas tribe who consider tigers as sacred. The model ascertains tiger population dynamics under several management scenarios. Steady-state convergence is observed under secure property rights for the Soligas. Scenarios in which they are evicted from the BRT reserve and lose their property rights yields localized tiger extinction. Our model yields spiritual values that the tribe derives from tigers and estimates the relative magnitude of spiritual to extractive values. We show how the inclusion of spiritual values drives desired conservation outcomes and discuss the implications of explicitly accounting for such values in conservation management practices.

Keywords: tiger; public goods; spiritual value; conservation; bioeconomic model JEL codes: Q20; Q51; Q57; C61

2 1. Introduction

A fourth of animal and plant species are threatened with extinction (IUCN, 2011) by direct threats such as overharvesting and indirect threats such as habitat loss and fragmentation (Ando &

Langpap, 2018). A similar share of carnivores is critically endangered, endangered, or vulnerable

(Hilton-Taylor et al., 2009). Carnivores generate a variety of ecosystems services (ES): some of these are regulation ES whereby carnivores help stabilize ecosystems while others are provisioning

(e.g., pelt) and cultural (e.g., recreation) ES. These ES are derived through use (e.g., trophy hunting) or non-use values (e.g., wildlife viewing). Alexander (2000) demonstrates for African elephants that non-consumptive values are vital to the species’ survival and that some existence value must be explicitly associated with the resource to avoid extinction. Many of these ES, especially those that provide non-use values, are public goods, and consequently, the conservation of the species providing them will be underprovided by private parties engaging in extractive use of the species, destruction of its habitat, or failing to maintain habitat health that is necessary for the survival of the species.

Conservation policies aimed at correcting the market failure in species conservation include habitat conservation programs, policies to encourage habitat ecosystem health maintenance, and management of hunting (Ando & Langpap, 2018). One of the most common habitat conservation policies consists of the establishment of protected areas. When the species of conservation interest coexists with indigenous communities, the enforcement of the protected status of the area often involves the expulsion and exclusion of communities. The practice is controversial on human rights and ethical grounds and its effectiveness has been mixed (Dowie, 2009; Lele et al., 2010). We argue in this paper that, when it involves communities who derive spiritual value from the species, this practice is not supported from a resource economics perspective either.

3 Conservationists have made claims that "tribal peoples are the best conservationists and guardians of the natural world" (Rust, 2016). In some cases, such claims are supported by evidence.

For example, the Soligas tribe in India’s Western Ghats reveres the wild Bengal tiger (Panthera tigris ssp. tigris) according to their customary spiritual beliefs. The NGO Survival International released data showing that the population of tigers in that region doubled between the years 2010 and 2014, and that the population growth rate was higher than the national average in India (Rust,

2016). However, such claims and descriptive data might include confounding factors leading to this higher-than-average growth rate that might not be related to the co-existence of the species with the tribe. Moreover, there is no formal theoretical or empirical analysis in the conservation economics literature on the effect of deriving spiritual ES from a species on the conservation status of that species by local populations co-existing with it. More generally, the literature on non-consumptive values in conservation tends to be limited to tourism values (Skonhoft 1998). Non-consumptive values are vital to an endangered species’ survival and existence value must be explicitly associated with the resource to avoid extinction (Alexander, 2000) and to avoid socially sub-optimal policy decisions with high social costs (Lele et al., 2010). However, existence values such as tribal spiritual values derived from the Bengal tiger are among the hardest ES values to estimate. This is in part because nonmarket valuation may not be appropriate to estimate the resource values of indigenous peoples who have political structures and decision-making processes inconsistent with the referendum format of valuation surveys (Adamowicz et al., 1998). It is not surprising then that very few studies include the non-consumptive public good value of an endangered species as would be appropriate to do in the case of spiritual values of the Bengal tiger. Zabel et al. (2011) include existence values in their analysis of tiger conservation but recognize the lack of functions that can

4 be used to model such values. In the absence of existence value functions, they focus on deriving a wide range of marginal existence values that guarantee interior solutions.

In this paper, we provide a case study of the Soligas tribe in India’s Western Ghats. This tribe attaches significant spiritual value to the Bengal tiger. We show how taking this spiritual value into account can lead to a higher population of tigers than under exclusionary policies. We develop a bioeconomic model, from the point of view of a social portfolio manager, that includes both extraction (a provisioning ES) and veneration (a spiritual ES) of the Bengal tiger. The model we propose includes a specification of an existence value function, which allows us to estimate spiritual values, as opposed to identifying a wide range of values as in Zabel et al. (2011). We compare conservation policies that consist of either keeping or taking away property rights from the tribe, with and without poaching fines. We find that taking away property rights from the tribe increases poaching, even in the presence of fines, and leads to localized tiger extinction. When the tribe’s property rights are safeguarded, on the other hand, the species population increases. We propose a functional form for the existence values which allows us to numerically estimate the spiritual values the tribe derives from the tiger and the relative magnitude of the spiritual to extractive values. We show how the inclusion of the tribe’s spiritual values drives the desired conservation outcome. We discuss the policy implications of considering the spiritual values in species conservation policies.

We note that the implications of our study are not limited to megafauna. The spiritual significance of flora – as in the case of sacred groves located within forests (Bhagwat et al., 2005;

Reddy & Yosef, 2016; Vipat & Bharucha, 2014) – would also increase their conservation value to society. The policy implications regarding property rights is a salient one because local courts can

5 and have secured rights of indigenous communities to remain or return to their ancestral lands within a tiger reserve through an enforcement of the 2006 Indian Forest Rights Act (Bhullar, 2008).1

The model we use, its results, and policy implications are consistent with the bioeconomic literature on existence value. Clark et al. (2010) consider the case of a social portfolio manager who optimizes the net benefits of harvesting a resource for private gain with the added public benefit of its intrinsic or existence value. Conrad (2010) considers the case of managing a whale population where a proportion of the people consists of whale eaters and the other consists of whale watchers.

While the model we use here is consistent in its findings with those of Clark et al. (2010) and

Conrad (2010), its application to terrestrial megafauna conservation, the explicit modeling of spiritual values, and the treatment of the conservation consequences of the inclusion of both extractive and spiritual values are novel. While the message in not new – conservationists have made claims that "tribal peoples are the best conservationists and guardians of the natural world"

(Rust, 2016) –, the argument, within the context of a bioeconomic model, has not been widely applied to natural resources with spiritual value.

The conservation economics literature investigates different policy approaches available to conserve species. According to Skonhoft (1998), providing locals with benefits from hunting and tourism can reduce incentives for illegal poaching. However, Fischer et al. (2011) find that whether benefit sharing provides conservation incentives depends on the design of the benefit shares, the size of the benefits relative to agricultural losses, and the management of hunting quotas. Bulte &

Rondeau (2007) consider another policy tool, compensation payments, and find that these payments

1 Recent legal developments in the Supreme Court of India have seen a rejection of the land claims of several forest- dwelling tribespeople under the Forest Rights Act (Sengar, 2019). Tribes face eviction because they lack proof that they possessed the land for the last three generations or more. This ruling may create insecurity of land title and potentially lead to situations of de-facto open access where laws are imperfectly enforced. It remains to be seen whether tribespeople like the Soligas would be evicted from their ancestral lands.

6 have ambiguous effects on wildlife stocks and local welfare. While they can reduce hunting effort, they can also provide incentives to convert wildlife habitat into agricultural land. Conservation performance payments are yet another policy tool, which consists of payments for environmental services – either monetary or in-kind payments – made by an agency to individuals or groups and are conditional on specific conservation outcomes (Albers & Ferraro, 2006; Engel et al., 2008).

Focusing on the case of co-existence of tiger and livestock, Zabel et al. (2011) find that conservation performance payments can generate enough incentives for livestock herders to refrain from hunting so that the carnivore population reaches its socially optimal level.

We contribute to the conservation economics literature by analyzing the explicit inclusion of non-use values such as spiritual values in conservation policies, as opposed to analyzing traditional policies focusing on monetary or physical incentives and disincentives in the presence of wildlife-livestock or agriculture conflict. We show that accounting for such spiritual values outperforms conservation policies that exclude tribes that venerate a species or natural environment.

The paper is structured as follows: Section 2 introduces the theoretical model of spiritual values developed to compare the alternative policy schemes and provide the economic rationale for its steady-state equilibrium conditions. In Section 3, we apply the model to study the spiritual aspect of tigers for the Soligas tribe residing in and around the Biligiri Rangaswamy Temple (BRT) Tiger

Reserve in southwestern India. We examine several policy scenarios to ascertain potential resource dynamics that might result in either the sustainability or localized extinction of tigers within the

BRT. We compare four policies that vary in whether they secure property rights of the tribe or evict it and whether a poaching penalty is imposed. In Section 4, we discuss the policy scenario simulations resulting from the application of the bioeconomic model and conclude with pertinent conservation policy observations.

7 2 The model of existence value

Clark et al. (2010) consider the case of a social portfolio manager who optimizes the net benefits of harvesting a resource for private gain with the additive public benefit of its intrinsic or existence value. We set up the discrete-time version of the Clark et al. optimization framework as follows.

∞ 푡[ ( ) ( )] maximize∞ 푊 = ∑ 휌 휋 푌푡, 푋푡 + 푉 푋푡 {푌푡}0 푡=0

푡 subject to 푋푡+1 = 푋푡 + 퐹(푋푡) − 푌푡, 푋0 > 0, and lim 휌 휆푡푋푡 = 0 푡→∞

휋푌 > 0, 휋푋 > 0, 휋푌푌 < 0, 휋푋푋 ≤ 0, and lim 푉′(푋) = ∞. 푋→0

The function 휋(푌푡, 푋푡) is the private benefit minus cost to the harvester, where 푌푡 is the extraction and 푋푡 is the resource stock. This net benefit function indicates the possibility of extraction from the resource for private gain. Harvest cost increases with 푌푡 and reduces with 푋푡 – signifying that as the resource becomes scarce it becomes more costly to source and harvest it

(Clark et al., 2010; Conrad, 2010). The function 푉(푋푡) respresents the additive existence value derived from the public goods charcteristic. As in (Clark et al., 2010) we assume for the existence value function that its marginal value approaches infinity as the stock is depleted, i.e., lim 푉′(푋) = ∞. The discount factor, 휌, is equal to 1⁄(1 + 훿), where 훿 is the capital interest 푋→0 rate in the market. The iterative map 푋푡+1 = 푋푡 + 퐹(푋푡) − 푌푡 captures the evolution of the resource stock, where 퐹(푋푡) represents the stock’s growth during period 푡, 푋0 > 0 is the initial

푡 level of the resource stock, and lim 휌 휆푡푋푡 = 0 is the transversality condition that as 푡 → ∞ the 푡→∞ discounted value of the resource stock becomes zero so as to ensure a maximum (Conrad, 2010).

The Lagrange expression for this infinite horizon, discrete-time problem assumes the following form.

8 ∞ 푡 퐿 = ∑ 휌 {휋(푌푡, 푋푡) + 푉(푋푡) + 휌휆푡+1[푋푡 + 퐹(푋푡) − 푌푡 − 푋푡+1]} 푡=0

The first-order necessary conditions are accordingly derived for the control variable (푌푡), state variable (푋푡), and co-state variable (휌휆푡+1).

( ) 휕퐿 푡 휕휋 ∙ = 휌 { − 휌휆푡+1} = 0 휕푌푡 휕푌푡

( ) ( ) ( ) 휕퐿 푡 휕휋 ∙ 휕푉 ∙ 휕퐹 ∙ = 휌 { + + 휌휆푡+1 [1 + ] − 휆푡} = 0 휕푋푡 휕푋푡 휕푋푡 휕푋푡

휕퐿 푡 = 휌 {푋푡 + 퐹(푋푡) − 푌푡 − 푋푡+1} = 0 휕휌휆푡+1

The three first-order conditions can be solved for the steady-state equilibrium in which the three variables are unchanging with time. We carry this out by dropping the time (푡) subscripts from the variables, i.e. 푌푡+1 = 푌푡 = 푌, 푋푡+1 = 푋푡 = 푋, 휆푡+1 = 휆푡 = 휆.

휋푌 − 휌휆 = 0 (1)

휋푋 + 푉푋 + 휌휆[1 + 퐹푋] − 휆 = 0 (2)

푌 − 퐹(푋) = 0 (3)

In steady-state, Equation (1) implies that the harvester would extract until the marginal benefit of harvest equals the discounted shadow price of the resource in the next time period; essentially it is the user cost of the resource. 휆 is the value of an additional unit of the resource in period 푡. Equation (2) implies that if this resource is to be optimally managed, then the marginal value of the resource must equal its marginal net benefit (휋푋(∙) + 푉푋(∙)) plus the discounted marginal benefit of an unharvested unit of the resource that accrues in the following period

9 (휌휆[1 + 퐹푋(∙)]). This total marginal benefit must reflect the value of an additional unit of the resource, 휆. Equation (3) implies that in steady-state, the resource is neither growing nor diminishing over time or that harvest equals the growth in each 푡. Using the fact that

휌 = 1⁄(1 + 훿) and rearranging equations (1), (2), and (3) we can derive the following expression.

휋푋(∙) + 푉푋(∙) (4) + 퐹푋(∙) = 훿 휋푌(∙)

Equation (4) is the well-known fundamental equation of renewable resources with the addition of the marginal benefit of existence value (Clark et al., 2010). The first term on the left- hand side of (4) is the ratio of marginal value of 푋 relative to the marginal value of 푌. This is also referred to as the marginal stock effect (Conrad, 2010). The second term is the marginal net growth rate of 푋. Their sum must equal the rate of interest in the capital market for optimal resource management by the social planner. On substituting 푌 = 퐹(푋) from (3) into (4) we can solve for the pair of steady-state values (푋∗, 푌∗). Equation (4) would yield a curve in the (푋 − 푌) space in implicit form 휙(푋, 푌; 훿) = 0. Three representative curves are shown in Figure 1. 휙1(푋, 푌; 훿)

∗ implies that extinction might be optimal (i.e. 푋1 = 0) when either 푋 grows too slowly, 훿 is very high, or the market price is much higher than the harvest cost of the last resource unit (Conrad,

∗ ′ 2010). For the steady-state value 푋2 the marginal stock effect is less than 훿 since 퐹 (푋) > 0. For

∗ the steady-state value 푋3, the marginal stock effect is greater than 훿, and thereby it might be optimal to have a higher steady-state value of 푋; this is shown below to be greater than the stock level at the maximum sustainable yield or the highest growth rate of the resource (i.e. 푋푚푠푦).

We can numerically solve for pairs of steady-state values (푋∗, 푌∗) by specifying functional forms for 휋(∙), 푉(∙), and 퐹(∙), and assuming a set of parameter values in this model. Once we have our (푋∗, 푌∗) values we can then simulate the evolution of 푋(푡) and 푌(푡) over time and examine if

10 their approach paths converge to the analytical steady-states when the initial values of resource

∗ ∗ stock and harvest are different from them, i.e. if 푋0 ≠ 푋 and 푌0 ≠ 푌 . In Section 3.1, we assume functional forms for 휋(∙), 푉(∙), and 퐹(∙), and calibrate the model for the tiger population in the

BRT tiger reserve in southwestern India with the resident Soligas tribe. We will simulate approach paths under several conservation management scenarios.

Figure 1: Representing the fundamental equation of renewable resources in (푋 − 푌) space.

3. Applying the Model to a Tiger Population and a Resident Tribe

2 Let us assume that 휋(푋푡, 푌푡) = 푝푌푡 − (푐⁄2) 푌푡 ⁄푋푡 where 푝 is the per unit price of the harvested resource and 푐 is a harvest cost parameter. For the existence value, which is a spiritual value in our

11 case, we assume that 푉(푋푡) = 훽 ln(푋푡) where 훽 is a spirituality weight, interpreted as the relative magnitude of the spiritual to extractive values. These functions satisfy the necessary assumptions for an interior solution: 휋푌 > 0, 휋푋 > 0, 휋푌푌 < 0, 휋푋푋 ≤ 0, and lim 푉′(푋) = ∞ (Clark et al., 푋→0

2010). The tiger population grows as per a standard logistic growth function 퐹(푋푡) =

푟푋푡(1 − 푋푡⁄퐾), where 푟 is the intrinsic growth rate and 퐾 is the environment’s carrying capacity.

The optimization problem for the social planner is set up as:

∞ 푡[ ( ⁄ ) 2⁄ ( )] maximize∞ 푊 = ∑ 휌 푝푌푡 − 푐 2 푌푡 푋푡 + 훽 ln 푋푡 {푌푡}0 푡=0

푡 subject to 푋푡+1 = 푋푡 + 푟푋푡(1 − 푋푡⁄퐾) − 푌푡, 푋0 > 0, and lim 휌 휆푡푋푡 = 0 푡→∞

We accordingly set up the Lagrangean (퐿) for this infinite time horizon optimization problem, derive the first-order necessary conditions in steady-state, and substitute 푌 = 퐹(푋) =

푟푋(1 − 푋⁄퐾) to get the fundamental equation of renewable resources, 휙(푋, 퐹(푋); 훿) ≡ 0 in

Equation (5). Equation (5.1) represents the fundamental equation of renewable resources without the addition of existence or spiritual value in the social planner’s framework.

∞ 푡 2 퐿 = ∑ 휌 {푝푌푡 − (푐⁄2) 푌푡 ⁄푋푡 + 훽 ln(푋푡) + 휌휆푡+1[푋푡 + 푟푋푡(1 − 푋푡⁄퐾) − 푌푡 − 푋푡+1]} 푡=0

푐 푋 2 훽 푋 2푋 (5) 휙(∙) ≡ 푟2 (1 − ) + + [푝 − 푐푟 (1 − )] [푟 (1 − ) − 훿] = 0 2 퐾 푋 퐾 퐾

12 푐 푋 2 푋 2푋 (5.1) 휙(∙) ≡ 푟2 (1 − ) + [푝 − 푐푟 (1 − )] [푟 (1 − ) − 훿] = 0 2 퐾 퐾 퐾

Furthermore, we consider a policy scenario where harvesting the tiger resource attracts a poaching penalty. With this penalty in place there is a chance that the harvester would be caught poaching by conservation authorities. We presume that a greater amount of illegal activity increases the chance of being caught (Copeland & Taylor, 2009). We consider an exponential probability density function (Pishro-Nik, 2014) of the following form: 휔(푌푡, 푋푡) =

(휃(1−푌푡⁄푋푡)) (푌푡⁄푋푡)푒 . In this probability density function we have 휃 ≤ 0 and 푋푡 ≥ 푌푡 ≥ 0, and it indicates that as illegal harvest increases so does the chance of being caught by conservation authorities. If the harvester is caught then a penalty of $퐵 is imposed on her, and this enters as an expected payment that is deducted from her private net benefit. The social planner would accordingly maximize the expression 피[푊퐵] below. For the discrete-time infinite horizon problem one can set up the Lagrangean (퐿퐵) and derive the corresponding fundamental equation of renewable resources (휙(푋, 퐹(푋); 훿, 퐵) ≡ 0) as listed in Equation (6) below. Equation (6.1) represents the fundamental equation of renewable resources in the presence of a poaching penalty but without the addition of existence or spiritual value in the social planner’s framework.

∞ [ 퐵] 푡 ( ⁄ ) 2⁄ ( ⁄ ) (휃(1−푌푡⁄푋푡)) ( ) maximize∞ 피 푊 = ∑ 휌 [푝푌푡 − 푐 2 푌푡 푋푡 − 푌푡 푋푡 푒 . 퐵 + 훽 ln 푋푡 ] {푌푡}0 푡=0

푡 subject to 푋푡+1 = 푋푡 + 푟푋푡(1 − 푋푡⁄퐾) − 푌푡, 푋0 > 0 given, 휃 ≤ 0, and lim 휌 휆푡푋푡 = 0 푡→∞

13 퐵 ∞ 푡 2 (휃(1−푌푡⁄푋푡)) 퐿 = ∑푡=0 휌 {푝푌푡 − (푐⁄2) 푌푡 ⁄푋푡 − (푌푡⁄푋푡)푒 . 퐵 + 훽 ln(푋푡) + 휌휆푡+1[푋푡 + 푟푋푡(1 −

푋푡⁄퐾) − 푌푡 − 푋푡+1]}

푐 푋 2 푋 훽 휙(∙) ≡ 푟2 (1 − ) + 퐵. 푟 (1 − ) 푒(휃(1−푟(1−푋⁄퐾)))[1 − 휃푟(1 − 푋⁄퐾)] + + [푝 − 2 퐾 퐾 푋 (6)

푋 퐵 2푋 푐푟 (1 − ) − 푒(휃(1−푟(1−푋⁄퐾)))[1 − 휃푟푋(1 − 푋⁄퐾)]] [푟 (1 − ) − 훿] = 0 퐾 푋 퐾

푐 푋 2 푋 휙(∙) ≡ 푟2 (1 − ) + 퐵. 푟 (1 − ) 푒(휃(1−푟(1−푋⁄퐾)))[1 − 휃푟(1 − 푋⁄퐾)] + [푝 − 2 퐾 퐾 (6.1)

푋 퐵 2푋 푐푟 (1 − ) − 푒(휃(1−푟(1−푋⁄퐾)))[1 − 휃푟푋(1 − 푋⁄퐾)]] [푟 (1 − ) − 훿] = 0 퐾 푋 퐾

We can now calibrate our model for the BRT tiger reserve and numerically solve the fundamental equations of renewable resources to derive the steady-state values (푋∗, 푌∗) under different policy scenarios. Table 1 lists the model’s parameters as applied for the BRT tiger reserve and its resident Soligas tribe.

Table 1: Empirical parameters for model simulation

Parameter Value Source

Tiger growth rate 푟 = 0.05 Smirnov & Dale (1999); WWF (2016)

Carrying capacity 퐾 = 86 tigers Damodaran (2007); KFD (2017)

Initial stock 푋0 = 35 tigers Varma (2015)

14 Harvest cost 푐 = $216 GOI (2018); WPSI (2010)

Poaching price 푝 = $36/tiger Damania et al., (2003)

Discount rate 훿 = 0.08 Zabel et al. (2009)

Spirituality weight 훽 = 150 – 900 Initial value range

Penalty 퐵 = $769 MOEF (2013)

Probability parameter 휃 = -5 Authors’ calculation

Smirnov & Dale (1999) estimate the tigers grow at an annual rate of 푟 = 0.06. However, this value of 푟 might be overestimating the growth rate of tigers in the wild. According to tiger census reports global tiger population increased from 3,200 in the year 2010 to 3,890 by the year

2016 (WWF, 2016); these figures yield an annual growth rate of approximately 0.04. We consider an average rate of 푟 = 0.05 to account for overestimation or underestimation. Damodaran (2007) reports wild habitat carrying capacity as 6.25 tigers per square kilometer. The BRT Tiger Reserve

540 is 540 km2 (KFD, 2017), which implies a carrying capacity of 퐾 = = 86 tigers. The BRT 6.25

Tiger Reserve had approximately 35 tigers in 2010 (Varma, 2015).

A considerable amount of planning and time goes into killing a tiger. According to investigations and reported poachers’ confessions poaching takes between three to four weeks for a kill from planning to execution (WPSI, 2010). Poachers sometimes use rudimentary traps to snare tigers and kill them. These traps are low-cost (approximately $3.50 per trap). One could use the daily wage rate in India to estimate the opportunity cost of poaching. The daily labor wage rate is INR272 (US$4.18) per day in India (GOI, 2018). We use this information to arrive at a value for our harvest cost parameter, 푐 = (272 × 25 + 3.5 × 65⁄65) × 2 = $216 by assuming twenty-

15 five days are devoted for a tiger poaching expedition.2 The poacher carries the tiger skin and body parts back to the village where he/she eventually sells it to middlemen. Poachers might receive only as little as INR1,000 per tiger (Damania et al., 2003). Accounting for inflation (WB, 2017), and converting to US$, we derive a poaching price value of (1000 × 141⁄61)⁄65 = $36 per tiger.3

We assume a rate of time preference 훿 = 0.08 in developing countries as used by (A. Zabel et al., 2009).4 An existence value parameter for the spirituality of tigers can be numerically estimated in our model. We assume a wide range of initial spirituality weights (훽) between 150 and 900. In the model simulations, we will numerically estimate these spirituality weights for the steady-state equilibria derived under different policy scenarios. In one such scenario, we will consider tiger population dynamics under the policy of penalty imposition for poaching. The poaching penalty in India is INR50,000 (i.e. 퐵 = $769) as per the Indian Wildlife Protection Act

(MOEF, 2013).

3.1 Tiger dynamics under different policy scenarios

3.1.1. Exclusion conservation policy

In the first policy scenario, the property rights to the sacred tiger forest are taken away by conservation authorities and the native Soligas tribe’s spiritual values are ignored in resource

2 The expression is multiplied by 2 because in the cost function in 휋(푋푡, 푌푡) we have 푐/2. This value of 푐 = $216 is slightly higher that the cost estimate of 푐 = $180 for poaching expeditions reported in Bulte & van Kooten (1999) and Milner-Gulland & Leader-Williams (1992). 3 The price received by poachers is not to be confused with buyer black market prices, which can reach $15,000- $20,000 (Damania et al., 2003). 4 Individuals or a society with higher rates of mortality, and thus shorter life expectancy, are likely to exhibit higher rates of time preference. The value of 훿 = 0.08 is in the range estimated for developing countries.

16 management. In this case, the myopic manager solves a conservation problem where the tiger stock

푋t is simply treated as a parameter in each 푡. Thereby, the harvester would maximize net benefits myopically in each 푡 without concern for how the current period’s harvest affects the resource in the following period, i.e. 푋t+1. In the optimization framework this would imply that 휌휆푡+1 = 0 in the Lagrangean used for Equation (5) and the harvester simply chooses 푌푡 to maximize net benefits,

푊푛푝, in each 푡 as follows.

푛푝 2 maximize 푊 = {푝푌푡 − (푐⁄2) 푌푡 ⁄푋푡 + 훽 ln(푋푡)} 푌푡

The first-order necessary condition yields optimal harvest as 푌푡 = (푝⁄푐)푋푡 in each 푡. One may note that the spiritual value 훽 ln(푋푡) does not feature in this myopic manager’s decision- making framework. We use the parameters from Table 1 to derive the approach path of 푋(푡) in this policy scenario, i.e. without secure property rights to sacred tiger resource. This approach path is shown in Figure 2 with a starting value of 푋0 = 35 tigers. We observe that the resource stock

푋푡 → 0 and localized tiger extinction in the BRT occurs as 푡 → 38 years. This occurs in consonance with the implicit equation, 휙1(푋, 푌; 훿) = 0, that yielded localized tiger extinction in the phase diagram of Figure 1. This implies that extinction is optimal when poaching is driven up by the manager’s myopic behavior with a high discount rate 훿 that results in 푋 growing slower than the offtake.

< Figure 2 >

17 40 35 30 25 20 15

10 Tiger Populatoin (Xt) Populatoin Tiger 5 0 0 5 10 15 20 25 30 35 40 45 Time (t)

Figure 2: Approach path of 푋(푡) without secure property rights to sacred tigers.

3.1.2. Exclusion conservation policy with a poaching penalty

Next, we will consider a policy scenario where harvesting of the tiger resource attracts a poaching penalty, still under an exclusionary policy. The myopic manager would again treat 푋푡 as a parameter in each period without concern for the effect of current harvesting on the next period’s resource stock (i.e. 휌휆푡+1 = 0 in the Lagrangean used for Equation (6)). The optimization problem

휕피[푊퐵] is written as 피[푊퐵] below and the first-order necessary condition, , can be numerically 휕푌푡 solved to yield 푌푡 in each 푡 by using the parameters from Table 1.

퐵 2 (휃(1−푌푡⁄푋푡)) maximize 피[푊 ] = {푝푌푡 − (푐⁄2) 푌푡 ⁄푋푡 − (푌푡⁄푋푡)푒 . 퐵 + 훽 ln(푋푡)} 푌푡

퐵 (휃(1−푌푡⁄푋푡)) 휕피[푊 ] 푐푌푡 푒 = 푝 − − 퐵. (1 − 휃 푌푡⁄푋푡) ≡ 0 휕푌푡 푋푡 푋푡

18 This first-order necessary condition can be solved numerically using a non-linear solver to equate it to zero by finding the harvest 푌푡, with 푋푡 treated as a parameter. Once again, the initial resource stock is 푋0 = 35 tigers. Once the solver yields the initial harvest, 푌0, the iterative map

[푋푡+1 = 푋푡 + 퐹(푋푡) − 푌푡] is called upon to derive 푋1, and the exercise is repeated for 푡 =

1, 2, … , 푇. In the approach path shown in Figure 3, we observe that the resource stock 푋푡 → 0 and tiger extinction in the BRT occurs in 49 years. Extinction is optimal in this scenario in consonance with the implicit function 휙1(푋, 푌; 훿, 퐵) (Figure 1). The presence of a poaching penalty delays extinction by 11 years compared to what was observed in the approach path in Figure 2.

40 35 30 25 20 15

10 Tiger Populatoin (Xt) Populatoin Tiger 5 0 0 5 10 15 20 25 30 35 40 45 50 Time (t)

Figure 3: Approach path of 푋(푡) without secure property rights to sacred tigers and penalty imposition.

19 3.1.3. Secured property rights

The third policy scenario that we consider is one where the resident Soligas tribe has secure property rights to the tiger resource. The parameter values in Table 1 are substituted into Equation

(5) to numerically solve for the steady-state values of resource stock (푋∗) and harvest (푌∗) by using a non-linear solver. The steady-state equilibrium values we derive are 푋∗ = 52.246 and

∗ ∗ 푌 = 퐹(푋 ) = 1.025. This situation would correspond to the implicit equation 휙2(푋, 푌; 훿) or

휙3(푋, 푌; 훿) in Figure 1 that yielded steady-state equilibriums over time. We use the solver at the same time to derive a spirituality weight of 훽 = 146.31, which yields a steady-state existence or spiritual value of 훽 ln(푋∗) = 578.83. We will now examine if the approach paths of 푋(푡) and

푌(푡) eventually reach these equilibrium values, given that the initial resource stock is not at the

∗ steady-state, i.e. 푋0 ≠ 푋 . In order to simulate our infinite-horizon problem we will use the concept of a final function (Conrad, 2010). A correctly specified final function allows one to approximate the approach to a steady-state in an infinite-horizon problem by converting it to a finite-horizon problem. Let us revisit our optimization problem. We rewrite the problem as follows.

푇−1 maximize 푊푓 = ∑ 휌푡[푝푌 − (푐⁄2) 푌2⁄푋 + 훽 ln(푋 )] 푇−1 푡 푡 푡 푡 {푌푡} 0 푡=0

푇−1 푐 2 + 휌 {푝푟푋푇(1 − 푋푇⁄퐾) − [푟푋푇(1 − 푋푇⁄퐾)] + 훽 ln(푋푇)}⁄훿 2푋푇

subject to 푋푡+1 = 푋푡 + 푟푋푡(1 − 푋푡⁄퐾) − 푌푡 and 푋0 > 0.

The objective function 푊푓 is the sum of the present value of net benefits over time 푡 =

0, 1, 2, … , 푇 − 1 and some final function, 휓(푋푇):

20

푇−1 푐 2 휓(푋푇) = 휌 {푝푟푋푇(1 − 푋푇⁄퐾) − [푟푋푇(1 − 푋푇⁄퐾)] + 훽 ln(푋푇)}⁄훿 2푋푇

The final function can be thought of as the value of maintaining 푋푇 for 푡 = 푇, 푇 + 1, … , ∞ by harvesting 푌푡 = 푟푋푇(1 − 푋푇⁄퐾) for the rest of time in steady-state. With 푌푡 = 푟푋푇(1 − 푋푇⁄퐾) being a constant, it can be factored out of the infinite series with the present value converging to

휓(푋푇). Using the parameters in Table 1, assuming an initial value of 푋0 = 35, 푇 = 70 years, and

푡=69 assigning initial value guesses for {푌푡}푡=0 = 0.10, we numerically estimate the approach paths of

푋(푡) and 푌(푡) over the horizon of 푇 = 70 years. Using the programmable non-linear Solver, we find convergence to a maximum value for the objective function, 푊푓 = 7609.43. Moreover, we note that (푋푡, 푌푡) = (52.2, 1.02) as 푡 → 70, which implies that the approach paths of the resource stock and harvest approach the steady-state values (푋∗, 푌∗) derived using Equation (5). The approach path of 푋푡 with the inclusion of existence value is shown in Figure 4 as the solid line.

The dotted line in Figure 4 depicts the approach path of 푋푡 without the inclusion of existence or spiritual value (i.e., the myopic manager’s framework). In this scenario the existence value,

훽 ln(푋푡), drops out of the optimization framework as derived in Equation (5.1). The dotted line approach path provides us with a reference baseline for examining the effect of explicitly including existence value (i.e., the social planner’s framework).

< Figure 4 >

21 60

50

40

30 X(t) with Existence Value 20 X(t) without Existence Value

Tiger Population (X) Population Tiger 10

0 0 10 20 30 40 50 60 70 Time

Figure 4: Approach paths of 푋(푡) with and without existence value in the presence of secure property rights for Soligas to sacred tigers.

3.1.4. Secured property rights and poaching penalty

With secure property rights and penalty imposition, Equation (6) can be numerically solved to derive steady-state values (푋∗, 푌∗) for the parameters in Table 1. 퐵 = $769 and 휃 = −5 are the penalty function parameters where 퐵 is the penalty amount and 휃 < 0 facilitates a positive probability, i.e. 푒(휃(1−푌푡⁄푋푡)) ≥ 0. We accordingly derive 푋∗ = 56.557 and 푌∗ = 퐹(푋∗) = 0.968.

We also derive a spirituality weight of 훽 = 167.50 that yields a steady-state spiritual value of

∗ ∗ 훽 ln(푋 ) = 675.92. Next, we examine the resource’s approach path when 푋0 ≠ 푋 by using the final function method described earlier.

22 maximize 피[푊퐵] = ∑푇−1 휌푡[푝푌 − (푐⁄2) 푌2⁄푋 − (푌 ⁄푋 )푒(휃(1−푌푡⁄푋푡)). 퐵 + 훽 ln(푋 )] + 푇−1 푡=0 푡 푡 푡 푡 푡 푡 {푌푡}0

푇−1 푐 2 푋푇 (휃(1−푟(1−푋푇⁄퐾))) 휌 {푝푟푋푇(1 − 푋푇⁄퐾) − [푟푋푇(1 − 푋푇⁄퐾)] − 퐵. 푟 (1 − ) 푒 + 훽 ln(푋푇)}⁄훿 2푋푇 퐾 subject to 푋푡+1 = 푋푡 + 푟푋푡(1 − 푋푡⁄퐾) − 푌푡 and 푋0 > 0 given.

Under the policy scenario of secure property rights for the Soligas tribe we find that with

푡=59 푇 = 59, and initial guesses for {푌푡}푡=0 = 0.10, the solid line approach path of 푋푡 reaches the optimal steady-state value of 푋∗ = 56.5 as shown in Figure 5, with a steady-state harvest of 푌∗ =

0.96. This policy result would correspond to the implicit equation 휙2(푋, 푌; 훿) or 휙3(푋, 푌; 훿) in

Figure 1 that yielded steady-state equilibriums over time. The dotted line in Figure 5 depicts the baseline approach path of 푋푡 without the inclusion of existence value, 훽 ln(푋푡), in this policy scenario.

< Figure 5 >

60

50

40

30 X(t) with Existence Value 20 X(t) without Existence Value

Tiger Population (X) Population Tiger 10

0 0 10 20 30 40 50 60 70 Time

Figure 5: Approach paths of 푋(푡) with and without existence value in the presence of secure property rights for Soligas and poaching penalties.

23 < Table 2 here >

Table 2: Summary of Results

Policy Secure rights to Inclusion of spiritual Tiger population (푿∗), Harvest (풀∗), and Existence or Figure tiger resource? value in social Spiritual value (휷 퐥퐧 푿∗) reference planner’s decision? Exclusion; no No No; myopic manager Localized extinction as 푡 → 38 years; open access harvest Figure 2 poaching penalty. drives down population (and the related existence value) as

푋푡 → 0. Exclusion; with No No; myopic manager Localized extinction as 푡 → 49 years; open access harvest Figure 3 poaching penalty. drives down population (and the related existence value) as

푋푡 → 0; poaching penalty delays extinction by 11 years. ∗ ∗ Inclusion; no Yes Yes; social planner (푋푡, 푌푡) → (푋 , 푌 ) = (52.24, 1.025) as 푡 → 70 years; Figure 4 poaching penalty. 푌∗ = 퐹(푋∗) in steady-state. Existence or spirituality value weight 훽 = 146.31, yielding an existence value of 훽 ln(푋∗) = 푈푆$ 578.83. ∗ ∗ Inclusion; with Yes Yes; social planner (푋푡, 푌푡) → (푋 , 푌 ) = (56.55, 0.968) as 푡 → 59 years; Figure 5 poaching penalty. 푌∗ = 퐹(푋∗) in steady-state. Existence or spirituality value weight 훽 = 167.50, yielding an existence value of 훽 ln(푋∗) = 푈푆$ 675.92

24 4. Discussion and Conclusion

The simulation of the various conservation management scenarios in our model yields several key policy results. In the policy scenario depicted in Figure 4, where the Soligas have secure property rights in the BRT tiger reserve, we observed that the stock, 푋(푡), converges to its steady-state

∗ equilibrium value of 푋 = 52.24 from the initial value of 푋0 = 35. The spiritual value that we derived numerically using Equation (5) equals 푈푆$ 578.83 in steady-state equilibrium. By explicitly accounting for the existence value of spirituality for the Soligas, the social portfolio manager’s decision is to either harvest zero amount or at most to harvest a sustainable amount into the future. In Figure 2, however, we observed that when property rights are taken away from the

Soligas, extinction is rendered an optimal outcome in our model. Extinction is optimal because the

Soligas’ beliefs on tiger spirituality do not feature in the myopic manager’s decision-making process. The public benefit of tigers for the Soligas, underestimated by the myopic manager, is inadequate to sustain a population of tigers beyond 38 years in this situation. With a rapidly declining tiger population the spiritual value is eroded quickly. This in turn lowers the public good benefit for the Soligas and increases the incentive to harvest the last tiger surviving in the wild.

Another conventional management practice is to penalize illegal harvesting within a protected area. We explore this policy scenario when a penalty of $퐵 is imposed upon the harvester if she is caught by conservation authorities – with some positive probability – harvesting the resource illegally. In Figure 5, with secure property rights for the Soligas and 퐵 = $769, our model yields a convergence of the stock to its steady-state equilibrium value of 푋∗ = 56.55 from the initial value of 푋0 = 35. This steady-state stock is higher than the case with no penalties depicted in Figure 4 where we derived 푋∗ = 52.24. Moreover, the steady-state harvest with penalty imposition is 푌∗ = 0.96 and steady-state spiritual value is 훽 ln(푋∗) = 푈푆$ 675.92. The latter

25 value is higher than in the case of no penalty imposition where we derived a spiritual value of

푈푆$ 578.83. The expected payment of a penalty raises the stakes of harvesting the protected resource illegally, and this is demonstrated in the harvester reducing offtake in steady-state perpetuity. The public benefits of tiger spirituality for the Soligas are reinforced via this penalty policy for illegal harvest.

However, one must keep in mind that the monitoring and enforcement involved in such a penalty policy has its own cost for conservation authorities, which does not form a part of the social portfolio manager’s decision framework. If achieving a sustainable tiger population is the principal aim of conservation policy, the explicit accounting of the existence value of spirituality appears to work very effectively without the need for imposing a penalty policy. Of course, this inference is based on the assumption that secure property rights are granted to the Soligas. Steady- state stock values in these cases correspond to the phase diagrams associated with 휙2(푋, 푌; 훿) or

휙3(푋, 푌; 훿) in Figure 1. Taking away property rights, by evicting the Soligas from the BRT, would likely result in localized tiger extinction in 49 years as depicted in Figure 3. One advantage of having this penalty policy is that localized tiger extinction takes longer to occur than in the no penalty scenario (38 vs. 49 years; Figure 2 and Table 2). Inclusionary policies without penalty provide policymakers the advantage of securing a higher stock and spiritual values while avoiding the burden of monitoring and enforcement associated with harvesting penalties.

The incentive to harvest the tiger resource for private gain would potentially increase with a higher poaching price, 푝. If the ratio of price to harvest costs were to increase such that (푝⁄푐) ≫

1, then resource extinction would likely be rendered optimal since 푝 would be much higher than 푐 for the last resource unit (Conrad, 2010). This situation would correspond to the implicit equation

휙1(푋, 푌; 훿) that yielded localized tiger extinction in the phase diagram of Figure 1. One can infer

26 that if poaching prices were to become higher over time with reductions in tiger population then, along with conferring of secure property rights to the Soligas, it would be especially prudent to explicitly account for the spiritual value of tigers in resource management practices.

The novelty of this paper is in the non-market valuation of an important, but often overlooked, aspect of species conservation. Non-consumptive values are vital to an endangered species’ survival and existence value must be explicitly associated with the resource to avoid sub- optimal policy decisions with high social and ecological costs. Zabel et al. (2011) identify a research gap in the literature on what function types might be appropriate for modeling tiger existence value. The bioeconomic model developed in this paper attempts to fill this gap by using a specification of an existence value function and estimating spiritual values, as opposed to identifying a range for such values. The simulations presented here have incorporated existence value and ascertained likely approach paths for tigers in the BRT based on the Soligas’s spiritual traditions. Our model is general enough to be applied to examine the resource dynamics of several other endangered species – both fauna and flaura.

Spirituality associated with natural resources stretches to many other species as they are revered by native tribes and forest dwellers around the world. Securing tribal property rights as a conservation policy tool is costly and government bodies face limited financial and human resources. Having estimates of the existence values placed by tribes in different parks through a framework like the one presented here can offer policymakers information to efficiently allocate scarce conservation resources to parks with the highest potential for desired conservation outcomes. For instance, the spiritual values estimated here can be used as inputs for conservation reserve site planning using tools such as the InVEST model (e.g., Polasky et al. (2011)) or for conservation portfolio design models (e.g., Mallory & Ando (2014)). Spiritual value estimates can

27 help prioritize where policy efforts should be focused to maximize conservation return on investment, in ways that do not ignore tribal traditions and the public good values they generate.

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