Coexistence of GM and non-GM crops with endogenously determined separation

Ecological Economics 70 (2011) 2486–2493

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Analysis

Coexistence of GM and non-GM crops with endogenously determined separation Emily Gray 1, Tihomir Ancev ⁎, Ross Drynan Agricultural and Resource Economics, Faculty of Agriculture, Food and Natural Resources, University of Sydney, Australia

a r t i c l e

i n f o

Article history: Received 1 December 2010 Received in revised form 5 August 2011 Accepted 11 August 2011 Available online 8 September 2011 JEL classification: D81 D02 C61 Q57 Q58 Keywords: Coexistence GM crops Institutions Pollen barrier

a b s t r a c t The possibility that genetically modified (GM) crops may contaminate non-GM crops through pollenmediated gene flow presents a challenge to coexistence of GM agriculture with conventional and organic farming systems. In this paper an analytical model of coexistence is developed that allows for endogenous derivation of efficient widths and allocation of pollen barriers to limit contamination of non-GM crops. To reflect the uncertainty that surrounds pollen dispersal mechanisms the model contains a stochastic contamination function and safety rule decision mechanism, constraining the level of contamination to remain below a tolerated adventitious presence with a given probability. Two policies are considered and their performance is tested: the tolerance level of adventitious presence, and the allocation of responsibility for implementing coexistence measures to either GM or non-GM farmers. The relative size of GM rents (the value of productivity gains and the non-pecuniary benefits from GM crops), rents for identity preserved non-GM crops (price premiums realised over the GM crop price), characteristics of farms, and possible variation in agricultural landscapes are also taken into account. The findings indicate that conventional adventitious presence tolerances can be met without ex ante mandating large widths of pollen barriers. At the policy level, the findings of this paper are relevant for setting region-specific pollen barriers widths, and/or for establishing institutions that facilitate cooperative coexistence. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The possibility of continued consumer opposition to genetically modified food crops (GM crops) has significant implications for the production and marketing of agricultural commodities. Heterogeneous consumer preferences for GM and non-GM foods make it necessary for GM and non-GM production systems to coexist. Coexistence is compromised by the possibility of GM adventitious presence: the likelihood that GM material would inadvertently mix with non-GM crops, preventing non-GM producers from marketing their crop as GM-free. If GM-free products command a price premium, GM adventitious presence (hereafter, adventitious presence) and the consequent loss of GM-free identity (and the related price premium) may constitute a negative spatial externality (Beckmann and Wesseler, 2007). Adventitious presence due to cross pollination may also have aggregate consequences for the organisation of agricultural landscapes. If non-GM farmers' cropping decisions are shaped by the economic consequences of adventitious presence to the extent that farmers relocate or switch to GM varieties to avoid the externality, then cultivation

⁎ Corresponding author. E-mail address: [email protected] (T. Ancev). 1 Present address: Australian Bureau of Agricultural and Resource Economics and Sciences. This research was conducted as a part of Emily Gray's PhD dissertation at the University of Sydney. This paper does not necessarily reflect the views of ABARES. 0921-8009/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2011.08.005

of GM crops may be clustered spatially (Beckmann and Wesseler, 2007; Lewis et al., 2008). Simulation studies of pollen dispersal and adventitious presence patterns over real and hypothetical agricultural landscapes suggest that the ability to produce and market non-GM crops will be compromised by an increasing share of GM crops and spatial clustering of GM and non-GM fields (Belcher et al., 2005; Ceddia et al., 2007; Ceddia et al., 2009; Munro, 2008). The welfare effects of this possible re-organisation of cropping patterns are central to the coexistence problem and to the institutional arrangements intended to ensure that farmers and consumers have a genuine choice between GM and non-GM crops. The principle of coexistence states that farmers should be able to cultivate the crops of their choice, whether conventional, organic or genetically modified, and coexistence policies are aimed at ensuring non-GM crops can be grown, marketed and consumed in the presence of GM crops. To this end, coexistence institutions range from crop stewardship guides in Australia and North America (Brookes and Barfoot, 2004), to mandatory labelling of GM products, strict separation and special liability regimes in some EU-27 member states (Beckmann et al., 2006). While coexistence policies may reduce the risk of adventitious presence faced by non-GM farmers or provide for redress of economic losses, simulations suggest that farmers' GM adoption decisions are influenced by institutional arrangements for coexistence (Demont et al., 2008b). Whether GM crop cultivation remains feasible given spatial ex ante coexistence regulations and ex post liability regimes depends not only on the accepted tolerance thresholds for GM adventitious

E. Gray et al. / Ecological Economics 70 (2011) 2486–2493

presence and on consumer demand that translates into price premium for GM-free products, but also on landscape and field geography: specifically, the proportion of the landscape planted to the relevant crop, field size and proximity to neighbouring fields, and the extent to which fields are scattered in the landscape. Further, published findings suggest that not all farmers will be equally affected by uniform spatial ex ante coexistence regulations, with farmers in agricultural landscapes characterised by small fields, monoculture, and GM crops adopted on randomly dispersed fields likely to be disproportionately affected (Devos et al., 2007; Devos et al., 2008b; Sanvido et al., 2008; Skevas et al., 2010). Other studies suggest that compliance with mandatory isolation distances can manifest at the landscape scale as a ‘domino effect’ (Demont et al., 2008a,b; Demont et al., 2009; Lewis et al., 2008). In addition, the existence of stringent coexistence measures in some jurisdictions have prompted researchers to question whether the underlying purpose of coexistence regulation might be deterrence of GM crop adoption (Beckmann et al., 2006; Devos et al., 2008a; Devos et al., 2009). In response, the literature has increasingly argued for alternative, more flexible coexistence regulation based on negotiable measures that are proportional to the economic incentives of coexistence (for example, see Messean et al., 2006; Demont et al., 2008b; Devos et al., 2009). The objective of this paper is to add to this literature by: (i) endogenising the width of non-GM pollen barriers planted on the borders of GM and non-GM fields to trap GM pollen; (ii) relaxing the assumption of deterministic adventitious presence; and (iii) testing a system of alternative property rights for growing GM crops. This is pursued by adopting a decision framework for regulating environmental and health risks with stochastic pollution-generating process (Lichtenberg and Zilberman, 1988), and applying it to the problem of coexistence. This framework has been extensively used in the context of nutrient contamination of groundwater, including by nitrates (Kampas and White, 2003; Lichtenberg and Penn, 2003), and by pesticides (Harper and Zilberman, 1992; Lichtenberg et al., 1989), and to the regulation of the health or environmental risks of GM crops (Lichtenberg, 2006). However, to the best of authors' knowledge, the current paper is the first application of this framework to the problem of coexistence of GM and non-GM cropping. Specifically, the model developed in the paper allows efficient widths of pollen barriers to be derived endogenously, rather than using exogenously-specified isolation distances. Adventitious presence in non-GM crops is modelled by a stochastic, distancedependent function, such that the efficient width of pollen barriers is determined according to a safety rule that ensures the adventitious presence tolerance is not exceeded with some probability. The model is used to test a system of alternative property rights based on scenarios where: (i) property rights for growing GM crops are assigned ex ante to GM or non-GM farmers; and (ii) GM and non-GM farmers engage in bargaining to determine whether pollen barriers are planted in the GM or non-GM field. The latter represents a Coasean setting, introduced in the coexistence literature by Beckmann et al. (2011), Demont et al. (2008b) and Demont et al. (2009). Unlike ex ante regulations, negotiations on pollen barriers will depend on the assignment of property rights, and on whether the opportunity costs of coexistence are proportional to the relative ‘GM’ and identity preservation ‘IP rents’. 2 2. Methods

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and access to markets. Farmers of the first type have a comparative advantage in producing a GM crop (GM farmers), while farmers of the second type have a comparative advantage in producing a nonGM crop (non-GM farmers). In the absence of a coexistence problem, GM farmers earn a higher profit from cultivating the GM variety of a crop than the non-GM variety (or an alternative crop). Similarly, in the absence of a coexistence problem, non-GM farmers earn a higher profit from cultivating the non-GM variety of a crop than the GM variety (or an alternative crop). Let the index for GM farmers in the landscape be g = 1, 2, …, G, and that for non-GM farmers be n = 1, …, N. Assume further that i (i = 1, …, I) of a given GM farmer's neighbours are growing non-GM crops, where I ≤ N. Also assume that m (m = 1, …, M) of a given nonGM farmer's neighbours are growing GM crops, where M ≤ G. Coexistence of GM and non-GM farmers in the landscape is compromised when the level of adventitious presence of GM material in non-GM crops (due to cross pollination by GM crops) prevents nonGM farmers from marketing identity preserved non-GM crops and from realising the associated price premiums. The spatial externality manifests as a threshold effect on non-GM farmers' profits (Ceddia et al., 2007). Denoting the level of adventitious presence in the nth farm by Cn, a non-GM farmer will only be able to market the produce as non-GM and realise the price premium awarded for identity preserved non-GM crops if adventitious presence is less than or equal

to a tolerated adventitious presence threshold (C ), that is if Cn ≤C : To protect non-GM farmers and consumers, governments commonly impose mandatory isolation distances between GM and nonGM farms. These are thought by many to be overly stringent. A more flexible approach would be for GM farmers and their non-GM neighbours to engage in negotiations about cultivating a pollen barrier to reduce cross pollination (Beckmann and Wesseler 2007; Demont et al., 2008b). In this case, pollen barriers with width that is corresponding to the economic incentives of coexistence may be put in place subject to the allocation of initial property rights for growing GM and non-GM crops, the income effects, and transactions costs. Assuming transaction costs are not so high as to impede the voluntary exchange of property rights, the resulting allocation of land to GM and non-GM crops and pollen barriers will be efficient, by virtue of the Coase theorem, reflecting consumer preferences for non-GM foods (as transmitted by prices to farmers), and the pecuniary and non-pecuniary gains from cultivating GM crops. Because adventitious presence in the non-GM field depends on distance from the GM pollen source, the cross pollination can be termed an ‘edge-effect externality’ (Parker and Munroe, 2007). The frequency of cross pollination is expected to be highest at a common boundary of the GM and non-GM fields and then to rapidly decline with distance from the GM pollen source (the edge-effect). Let cn(x) denote the rate of cross pollination of the nth non-GM field occurring at distance x from the GM field. To meet the adventitious presence tolerance, a non-GM farmer may cultivate pollen barriers of width xn on the edge of their field closest to the GM field, thereby removing the crop with the highest levels of adventitious presence, as demonstrated in Fig. 1. Adventitious presence in the non-GM crop may also be reduced by cultivating a pollen barrier of width xg in the GM field, as demonstrated by Fig. 2. Average adventitious presence (Cn) across the non-GM field can be described by a general function (Damgaard and Kjellsson, 2005) that takes into account the width of the non-GM field and widths of pollen barriers cultivated in the GM (xg) and non-GM fields (xn):

Assume that there are two types of farms in a hypothetical landscape. These differ with regard to pest pressure, managerial expertise


 Cn xn ; xg ¼

2 In this context, the term ‘GM rents’ represents the value of productivity gains and the non-pecuniary benefits from adopting GM crops (see Marra and Piggott, 2006). ‘IP rents’ are the increases in revenue from realising price premiums for identity preserved non-GM crops over the GM crop market price.

where Xn is the width of the whole non-GM field. The integral in Eq. (1) represents total adventitious presence. Average adventitious presence is derived by averaging the value of this

Xn þxg 1 ∫ c ðxÞ Xn −xn xn þxg n

dx

ð1Þ

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E. Gray et al. / Ecological Economics 70 (2011) 2486–2493

Frequency of cross-pollination over the non-GM Field (%)

cn(x) GM Field

Xn

Xg

Non-GM Field

0

xn

Fig. 1. Pollen barriers in the non-GM field (xn).

Frequency of cross-pollination over the non-GM Field (%)

cn(x)

GM Field

Xn Non-GM Field

Xg

xg 0 Fig. 2. Pollen barriers in the GM field (xg).

integral over the entire width of the non-GM crop. The width of the GM field, Xg, does not explicitly affect adventitious presence levels but would do so implicitly and indirectly via the function cn(x) describing the frequency of cross pollination. 3 On the other hand, the width of the recipient field (Xn) has a direct effect on adventitious presence due to the dilution effect of competition between the incoming GM pollen and non-GM pollen produced in the recipient field (Damgaard and Kjellsson, 2005). A general model of coexistence is described in Eqs. (2) and (3) below. Suppose that initially non-GM farmers hold property rights to cultivate their crops without being affected by cross pollination from surrounding GM crops. In that case, the gth GM farmer with i neighbours growing non-GM crops (i = 1, …, I) will have to take into account that the level of adventitious presence in the non-GM crops grown by each of his neighbours be kept below the tolerated ad must
 ventitious presence threshold Ci ≤C . The GM farmer can either cultivate a pollen barrier in his own field (denoted by xgi) at the boundary with the ith neighbour's non-GM field to limit adventitious presence in neighbour's crop, or can compensate i neighbours for cultivating pollen barriers xi in their non-GM fields. If the profit earned from cultivating a GM crop with the necessary pollen barriers is less

3 The width of a pollen barrier in the GM field effectively reduces the width of this field and thereby indirectly affects cn(x), and consequently the average level of adventitious presence. This second order effect of xg on average adventitious presence is not explicitly treated in this paper.

than the profit from cultivating a non-GM variety (πgNGM N πgGM), the GM farmer switches to cultivating the non-GM variety. This problem of choice among GM and non-GM crops from the perspective of a GM farmer may be represented as 4: h i max xmax π ; πgNGM gi xi ∀i gGM


subject to Ci ≤C xgi ≤ Xg x i ≤ Xi xgi ; xi ≥ 0

∀i

ð2Þ

∀i ∀i

Suppose, conversely, that GM farmers have the right to grow GM crops, without liability for cross pollination of neighbouring non-GM crops. In that case, a non-GM farmer with m neighbours growing GM crops (m = 1, …, M) will himself have to ensure that total adventitious presence in his non-GM crop is less than the tolerated adventitious presence threshold, if he intends to continue growing a nonGM crop and thereby earning IP rents. 5 Assuming that adventitious presence is additive across sources, the constraint the nth non-GM 4 Note that i refers to the subset of all non-GM farmers who are immediate neighbours of the gth GM farmer. Farmers also face the constraints that pollen barriers cannot exceed field widths. 5 The scenario where the GM farmers hold the property rights may not be easily applicable in practise, especially in the light of the so-called ‘newcomer principle’ (Demont and Devos, 2008). However, it is important to consider this scenario for conceptual purposes.

E. Gray et al. / Ecological Economics 70 (2011) 2486–2493

  max max πnNGM ; πnGM


ρ1

0.8

ρ2

0.6 0.4 No Buffer Buffer

0.2 0

A

Adventitious Presence in the non-GM crop (%)

ð3Þ

3. Stochastic GM Adventitious Presence Function Uncertainty about the physical processes affecting pollen movement, whether due to the natural variability of biological processes and landscape properties or the limitations of available data and models used to estimate adventitious presence, can play a significant role in modelling cross pollination between GM and non-GM crops. A mechanism is needed to take uncertainty into account. This can be achieved by modelling both the mean rate of cross pollination and the frequency of more extreme cross pollination events (Kuparinen et al., 2007). Let the function cn(x) showing the frequency of cross pollination in the nth non-GM field at distance x from a GM field be a stochastic function that can be designated c˜ n ðxÞ. For any value of the function, there will be a corresponding function (see Eq. (1)) defining average adventitious presence in a non-GM field as a function of pollen barrier   widths. This function will itself be stochastic, C˜ n xn ; xg . For any pollen barrier widths, the stochastic function defining average adventitious presence
in a non-GM field will have an associated probability density  function f C˜ n ð·Þ , and correspondingly, a cumulative distribution func
  tion, F C˜ n xn ; xg . When adventitious presence is stochastic, pollen barriers increase the probability that adventitious presence in the non-GM crop is below a given tolerance level. This is demonstrated in Fig. 3 where adventitious presence must be below a given threshold (A), and adventitious presence levels are represented by a probability distribution function that is conditional on the width of the pollen barriers (Segerson, 1988). In the absence of a pollen barrier, the threshold (A) is met with probability ρ2. Cultivating a pollen barrier shifts the cumulative distribution function (CDF) of adventitious presence to the left. The threshold is met with higher probability (ρ1). The framework developed here respecifies the deterministic adventitious presence constraints in Eqs. (2) and (3) using a safety rule decision mechanism (Kataoka, 1963; Lichtenberg, 2006; Lichtenberg and Zilberman, 1988). The safety rule mechanism constrains the level of adventitious presence in non-GM crops to remain below a maximum allowable level (the tolerated threshold) to an exogenously set probability or reliability. The safety rule is specified via chance or probabilistic constraints in a stochastic programming model. 6

1

Fig. 3. Control of stochastic pollen-mediated adventitious presence Source: Adapted from Kampas and White (2004).

xm ∀m;xnm

subject to ∑m Cm ≤ C xm ≤ Xm ∀m xnm ≤ Xn xnm ; xm ∀m ≥ 0

A

Cumulative Probability of C n

farmer faces is to ensure that the sum of adventitious presence in his field attributable to m GM neighbours is no greater than the specified
tolerance, i.e. ∑m Cm ≤C . The non-GM farmer can either cultivate a pollen barrier in his own field (denoted by xnm) at the boundary with the mth neighbour's GM field to reduce cross pollination by neighbour m's GM crop, or can (at least in theory) pay the GM neighbours for cultivating pollen barriers (xm) in their GM fields. If the profit earned from cultivating a non-GM crop with the necessary pollen barriers is less than the profit when IP rents are forfeited due to adventitious presence being greater than the specified tolerance (πnNGM b πnGM), the nonGM farmer switches to cultivating the GM variety. This problem of choice among GM and non-GM crops from the perspective of a nonGM farmer may be represented as in Eq. (3)6:

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Note that in Eq. (3), m refers to a subset of a GM farms who are immediate neighbours of the non-GM farmer and farmers also face the constraints that pollen barriers cannot exceed field widths.

When non-GM farmers have the right to be free of cross pollination, a GM farmer that has i non-GM neighbours faces a stochastic constraint of the form: n o
Pr C˜ i ≤C ≥ ρi ∀i

ð4Þ

When property rights for growing GM crops are with GM farmers, a non-GM farmer that has m GM neighbours faces a stochastic constraint of the form: n o
Pr ∑m C˜ m ≤C ≥ ρn

ð5Þ

Although the chance constraints take the risk of exceeding the tolerated adventitious presence into account explicitly (via an upper limit ̃ ≰ C¯ } b 1 − ρn), placed on this probability, Pr{Cĩ ≰ C¯ } b 1 − ρi; Pr{ΣCm the chance constraint is a qualitative measure of risk. The probability (1− ρ) of violating the adventitious presence threshold can be interpreted as the farmer's aversion to uncertainty about staying within the threshold (Kampas and White, 2003; Lichtenberg, 2006). However, only the probability (1− ρ) of exceeding the threshold is controlled, and not the magnitude of a violation. In this case, the threshold effect of the spatial externality means that the economic consequences are unaffected by the magnitude of a violation. When non-GM crops are tested for adventitious presence at the farm level, adventitious presence P in excess of C is sufficient to cause economic loss.7 3.1. Solution to the Stochastic Problem The problem is solved as a nonlinear programming problem. One issue is whether the feasible space defined by the chance constraint is convex, as needed to ensure that there is a single maximum profit point. The feasible set (D) is defined as in Henrion (2004):  n 

 o
 n o o n
  D xn ; xg ¼ xn ; xg Pr C˜ ≤C ≥ρ ¼ xn ; xg FC˜ C ≥ρ

ð6Þ



where FC˜ C is the cumulative distribution of C˜ evaluated at C and ˜ the distribution of C is dependent on xn and xg. Consider a random variable that is a convex function of underlying deterministic variables and stochastic variables. It can be shown that the probability of this random variable being less than any defined 7 The analysis of this paper is only conducted at the farm level. It is entirely possible that some ‘dilution’ of adventitious presence occurs when the produce from various farms are combined together, for example at a silo or other receiving point. We thank the reviewers for pointing this out.

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E. Gray et al. / Ecological Economics 70 (2011) 2486–2493

value will be a log-concave function of the underlying deterministic variables if the probability distribution of the underlying stochastic variables is log-concave
 (for example, Theorem 9, Prékopa, 1980). Hence, if C˜ ¼ g xg ; xn ; θ˜ , where θ˜ is a vector of underlying sources 
 of random variation (e.g. wind speed and direction), then FC˜ C will be log-concave in xn and xg, provided the function g(⋅) is concave in all variables and provided the distribution of θ˜ is log-concave. 
 
 If FC˜ C is log-concave, the constraint, FC˜ C ≥ρ defines a convex feasible space of xn and xg values. This follows immediately since after taking 
the logarithm of both sides the constraint is equivalent to ln FC˜ C ≥ lnðρÞ, which is sufficient for convexity. 8 Further, certain assumptions need to be made about the cross pollination function and the source of uncertainty in the cross pollination rate to ensure convexity. Suppose that the uncertainty surrounding cross pollination can be modelled multiplicatively:

with width xi cultivated in the ith non-GM field; and all other variables are as previously defined. The Lagrangean of Eq. (9) is as follows, where ϕi, μi and νg are Lagrangean multipliers:

c˜ n ðxÞ ¼ θ˜ cn ðxÞ

∂Lg

ð7Þ

Lg ¼ πgGM −∑i ωxi −∑i τxgi

  −∑i ϕi FC˜ C −ρi

The Kuhn–Tucker conditions for optimality can be derived as: ∂Lg ∂xi

∂xgi

where cn(x) is a function defining the deterministic rate of cross pollination in the absence of uncertainty, and θ˜ is the ratio of the actual cross pollination rate to that deterministic rate, assumed to be independent of the distance x. Correspondingly, overall adventitious presence in a non-GM crop will be:

∂ϕi



 C˜ n xn ; xg ¼ θ˜ Cn xn ; xg

∂μi

ð8Þ

Provided cn(x) is convex in x, as reflected   in Fig. 1, then Cn(xn, xg) will be convex in xn and xg, and C˜ n xn ; xg will be convex in xn, xg ˜ The requirement for θ˜ to be a log-concave probability distribuand θ. tion is satisfied by a number of common probability distributions such as the uniform, normal and exponential distributions (Bagnoli and Bergstrom, 2005). For example, suppose that random
 variable θ˜ has an exponential h i distribution: a density function f θ˜ ¼ λe−λθ and mean E θ˜ ¼ λ−1 . For given xn and xg, the variable C˜ n also has an exponential distribu
 h i ˜ tion, with density f C˜ n ¼ ðλ=Cn Þe−λC n =Cn and mean E C˜ n ¼ Cn =λ. With GM cross pollination from multiple sources, overall adventitious presence is the simple sum of one or more exponential (adventitious presence) variables, each of which is a convex function of the decision variables (xn and xg). 3.2. Kuhn–Tucker Conditions When property rights are with non-GM farmers, the deterministic equivalent of the stochastic optimisation problem facing the GM farmer is:  
 max max πgGM −∑i ωxi −∑i τxgi ; πgNGM

i

xi ≤ Xi

∂Lg

∂Lg ∂νg

xi ·



 0 ¼ −τ−ϕi ·F xgi C −νg ≤0

xgi ·




  ¼ − FC˜ C −ρi ≥0

ϕi ·

¼ −ðxi −Xi Þ≥0

μi ·


 ¼ − ∑i xgi −Xg ≥0

νg ·

i

∀i ∀i

i ¼ 1; …; I

ð9Þ

i ¼ 1; …; I

¼0

∂xi ∂Lg

∀i

i ¼ 1; …; I ð12Þ

¼0

∀i

i ¼ 1; …; I ð13Þ

¼0

∀i i ¼ 1; …; I

∂xgi

∂Lg ∂ϕi ∂Lg ∂μi ∂Lg

∂νg

¼0

∀i i ¼ 1; …; I ð11Þ

¼0

ð14Þ

ð15Þ

From Eq. (11) and assuming zero transaction costs, when a GM farmer negotiates a pollen barrier (xi N 0) in his ith non-GM neighbour's field the optimal width of the pollen barrier xi will be such that the value of increasing the probability that adventitious presence in the non-GM neighbour's crop is less than the tolerated threshold

 
C˜ i ≤C , −ϕi ⋅F 0xi C N0 , is equal to the sum of the compensation payment (ω) and the shadow price of land in the non-GM farm (μi). From Eq. (12), if the gth GM farmer cultivates a pollen barrier in his own field (xgi N 0) to limit the level of adventitious presence in his ith non-GM neighbour's crop, the optimal width of the pollen barrier xgi will be such that the value of increasing the probability that the level of adventitious presence in his neighbour's crop is less than the tolerated threshold is equal to the sum of GM rents forfeited on the land cultivated with a pollen barrier (τ) and the shadow price of land in his GM farm (νg). Eqs. (13) to (15) are the complementary slackness conditions. When property rights are with GM farmers, the deterministic equivalent of the stochastic optimisation problem facing the nonGM farmer is:

subject to : FC˜

n



 C ≥ρ

ð16Þ

∑m xnm ≤ Xn ∀i

i ¼ 1; …; I

where τ is the opportunity cost (forfeited GM gains) of a pollen barrier with width xgi cultivated in the gth GM field at the boundary with the ith non-GM neighbour's field; ω is the opportunity cost (the forfeited IP premiums due to harvesting the pollen barrier crop separately to be sold as ‘genetically modified’) of a pollen barrier

xm ≤ Xm ∀m m ¼ 1; …; M xnm ; xm ≥ 0 ∀m m ¼ 1; …; M where all variables are as previously defined. The Lagrangean of Eq. (15) is as follows, where φn, ψn and γm are Lagrangean multipliers: Ln ¼ πnNGM −∑m ωxnm −∑m τxm

  −φn FC˜ C −ρ n

8

∂Lg

xnm ;xm

∑i xgi ≤Xg xi ; xgi ≥0

∂Lg



 0 ¼ −ω−ϕi ·F xi C −μi ≤0

 
 max max πnNGM −∑m ωxnm −∑m τxm ; πnGM

xi ;xgi

subject to :

FC˜ C ≥ρi

ð10Þ

i

−∑
i μi ðxi −Xi Þ  −νg ∑i xgi −Xg

A sufficient requirement for a convex feasible space is that the constraint is of the form, “concave function of the decision variables ≥ constant”.

−ψn ð∑m xnm −Xn Þ −∑m γm ðxm −Xm Þ

ð17Þ

E. Gray et al. / Ecological Economics 70 (2011) 2486–2493

and the Kuhn–Tucker conditions are:

 ∂Ln 0 ¼ −ω−φn ⋅F xnm C −ψn ≤0 ∂xnm

xnm ·

∂Ln ¼0 ∂xnm

∀m m ¼ 1; …; M ð18Þ



 ∂Ln 0 ¼ −τ−φn ⋅F xm C −νg ≤0 ∂xm

xm ·

∂Ln ¼0 ∂xm

∀m m ¼ 1; …; M ð19Þ




  ∂Ln ¼ − FC˜ C −ρ ≥0 n ∂φn

φn ·

∂Ln ¼0 ∂φn

ð20Þ

∂Ln ¼ −ð∑m xnm −Xn Þ≥0 ∂ψn

ψn ·

∂Ln ¼0 ∂ψn

ð21Þ

∂Ln ¼ −ðxm −Xm Þ≥0 ∂γm

γm ·

∂Ln ¼ 0 ∀m m ¼ 1; …; M ∂γm ð22Þ

From Eq. (18), if the non-GM farmer cultivates a pollen barrier (xnm N 0) in his own field to limit adventitious presence from neighbour m ' s GM crop, he will equate the value of increasing the probability that adventitious
presence in his non-GM crop is less than the 
  tolerated threshold −φn ⋅F 0xnm C N0 to the sum of the IP premiums forfeited on the land allocated to the pollen barrier (ω) and the shadow price of land in his non-GM farm (ψn). From Eq. (19), when the non-GM farmer negotiates with his mth GM neighbour to put a pollen barrier, the optimal width of the pollen barrier xm will equate the value of increasing the probability that adventitious presence in
the non-GM crop is less than the tolerated threshold C˜ n ≤C ,
  
−φn ⋅F 0xm C N0 , to the sum of the compensation payment (τ) and the shadow price of land in the GM farm (γm). Eqs. (20) to (22) are the complementary slackness conditions. 4. Empirical Application This model was applied to a case study of Roundup Ready® canola (oilseed rape) in Australia (Gray, 2010). A function describing the frequency of cross pollination at distance x from the GM field was estimated using data on the frequency of herbicide tolerance in commercially farmed non-GM canola, published in Rieger et al. (2002). The steps followed to estimate the parameters of this function were similar to the double-hurdle or Two-Part Model described by Wooldridge (2002). 9 This involved estimating a Probit model of the probability of observing cross pollination, and then, conditional on this probability, a model of the rate of cross pollination as an exponential decay function of the distance was estimated: h n h

 ˆ 1x E cjx ¼ Pr c N 0jxgE cjx; c N 0 ¼ Φ δˆ 0 α ˆ exp β

ð23Þ


 2 2 ˆ 0 þσ ˆ =2 ¼ 0:048 and σ ˆ is the variance of the frewhere α ˆ ¼ exp β ˆ 1 ¼ −0:0002 is quency of cross pollination from the OLS regression, β the estimated coefficient on distance from the OLS regression, and δˆ 0 ¼ −0:37 is the estimated constant from the Probit model. Distance x from the GM field was not significant in either the Probit model or the exponential decay function, possibly because the edge-effect was not clearly evident in the Rieger et al. (2002) dataset. Many of the non-GM canola fields in the dataset were not adjacent to the GM canola fields, and samples were taken from only three locations in each field: at the edge nearest the source field, at the middle,

9

Details on estimation can be obtained from the authors on request.

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and at the edge furthest from the source field. As a result, it is possible that the relatively flat tail of the leptokurtic distribution of cross pollination was over-represented in the dataset, resulting in insignificant coefficient on distance. However, since theory and other empirical studies indicate that distance from pollen source influences the rate of cross pollination, the distance variable was retained in the estimated model. Therefore, caution is advised before drawing general conclusions about coexistence of GM and non-GM canola (or other crop species) based on the results derived from the empirical analysis presented below. To obtain the level of GM adventitious presence in a non-GM canola field, Eq. (23) is integrated over the width of the non-GM field (Xn − xn) that is harvested and sold as non-GM. As it is assumed that grain harvested from the non-GM field is sold as one lot, average adventitious presence is found by dividing the integral of Eq. (23) by the width of the non-GM field, Xn. Uncertainty was modelled as described previously in Section 3.1. The estimated adventitious presence function was multiplied by an

exponentially distributed random deviate θ˜ , where E θ˜ ¼ 1. The deterministic equivalent of the chance constraint was derived following Biswal et al. (1998). When property rights are with nonGM farmers, the chance constraint given previously in Eq. (4) becomes:


−C =Ci

e

≤1−ρi

∀i i ¼ 1; …; I

ð24Þ

and when property rights are with GM farmers, the chance constraint in Eq. (5) becomes: 2

3

6 ∏ 6 4∑ M

m¼1

M




M−1 −C =Cm Cm e

m¼1 ∏I m¼1 m≠j




Cm −Cj

7 7 5≤1−ρ

m; j ¼ 1; …; I ; m≠j

ð25Þ

where the left hand side of Eqs. (24) and (25) are the complementary cumulative distribution functions of Ci and ∑m Cm , respectively. The deterministic equivalents of the chance constraints in Eqs. (24) and (25) can be interpreted as placing an upper bound of (1 − ρ) on the probability of exceeding the adventitious presence tolerance level
C . The probability of exceeding the adventitious presence tolerance is represented by the complementary cumulative distribution functions of C˜ i ¼ θ˜ i :Ci when property rights are with non-GM farmers, and by ∑m θ˜ m :Cm when property rights are with GM farmers. The nonlinear programming model was solved using the GAMS/ CONOPT3 solver. The model was solved for a range of scenarios: a base case that was independent of responsibility for implementing coexistence measures (one GM and one non-GM canola field—Eq. (5) simplifies to Eq. (4) when i = 1). Subsequent scenarios examined the implications of increasing the number of neighbours under both property rights scenarios. In each scenario, a range of adventitious presence 
 tolerances C and reliability levels (ρ) were considered. Sensitivity analyses considered the implications of alternative distributional assumptions on adventitious presence, premiums for IP non-GM canola, and larger and smaller canola fields (reported in Gray, 2010). Fig. 4 presents the CDFs of GM canola adventitious presence with one, two and four neighbours growing GM canola (obtained by rearranging Eqs. (24) and (25)) without pollen barriers in GM or non-GM fields. As in Fig. 3, the CDFs are graphical representations of the chance constraints when there is one source of GM pollen (the solid line), two sources of GM pollen (the dashed line), and four sources of GM pollen (the dotted line). As the number of neighbours growing GM canola increases, the probability that adventitious presence in the non-GM canola is less than or equal to a given adventitious presence tolerance decreases. However, as the CDF is conditional on the width of pollen barriers, as described in Fig. 3, planting pollen barriers will shift the

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Fig. 4. Cumulative distribution functions of GM canola adventitious presence (adventitious presence exponentially distributed).

 
 CDF of the adventitious presence 1− exp − C =Ci , until a given adventitious presence tolerance in the non-GM canola is met with a probability that is in line with farmer's aversion to uncertainty, ρ. It is evident from Fig. 4 that commercial tolerances of 0.9% adventitious presence can be met in non-GM canola without requiring pollen barriers to be planted, whether property rights are with GM or non-GM farmers. The CDFs of GM canola adventitious presence with one, two and four neighbours growing GM canola approach unity
for adventitious presence tolerances (C ) of 0.2% (meaning an adventitious presence tolerance of less than 0.2% can be met with a reliability close to 100%). Moreover, sensitivity analyses demonstrated that this result holds independent of the size of canola fields, and of distributional assumptions about the adventitious presence (Gray, 2010). In contrast, to satisfy a more stringent standard of 0.1% adventitious presence in non-GM field with high reliability, extensive pollen barriers were found to be necessary if a non-GM farmer has several neighbours cultivating GM canola. For example, if there are four neighbours, the probability of not exceeding adventitious presence of 0.1% without any barriers falls to 0.85 (Fig. 4). This is in part due to a reduction in the dilution effect, as a greater share of the nonGM field is planted to pollen barriers. However, as noted above, these results should not be used to draw general conclusions about coexistence of GM and non-GM canola (or other crop species), given data limitations indicating that cross pollination rates do not display a pronounced edge-effect. On the other hand, the proposed model of coexistence may be used to examine the aggregate consequences of farmers' land-use decisions in the event of more stringent adventitious presence tolerances. Estimates of the efficient widths and allocations of pollen barriers can be used to evaluate farmers' optimal land-use decisions by comparing the opportunity costs to farmers of: (i) cultivating pollen barriers; (ii) switching from GM to non-GM crops or forfeiting price premiums for GM-free crops; and (iii) compensating neighbour(s) for cultivating pollen barriers. In this way it is also possible to examine the extent to which farmers' incentives to cluster production, and thereby the efficient distribution of land between GM and non-GM production in an agricultural landscape is influenced by: (a) uncertainty over the extent of pollen-mediated adventitious presence; (b) the opportunity costs of farm-level coexistence measures to limit cross pollination by GM crops; and (c) the system of property rights for growing GM crops. 5. Summary and Conclusion Endogenously determining the widths of pollen barriers with the safety rule decision mechanism has several advantages over setting ex ante mandatory isolation distances. Factors that predict adventitious

presence—such as the size and alignment of GM and non-GM fields and distances between fields—can be included by utilising a simple model of pollen-dispersal as a function of distance. The efficient width of pollen barriers is established based on two key parameters that are central to coexistence policy and risk assessment, respectively: (i) the
tolerance for GM adventitious presence, C , which depends on market and labelling thresholds for GM adventitious presence; and (ii) the reliability level of satisfying the adventitious presence constraint, ρ, which is equivalent to the confidence level of hypothesis testing (Lichtenberg and Zilberman, 1988), and allows the decision maker (individual farmers or coexistence policy makers) to adjust estimates of the risk of exceeding adventitious-presence tolerances in a meaningful way. Marginal adjustments in these two policy parameters can then be related to changing widths of pollen barriers and their associated opportunity costs. Moreover, unlike mandatory isolation distances, the endogenously determined widths of pollen barriers will be efficient, conditional on property rights, the risk of GM adventitious presence, and the tolerance for GM adventitious presence, and given the opportunity costs of coexistence and the relative magnitude of IP and GM rents. Assuming transaction costs are minimal, endogenously derived pollen barrier widths will be preferable to mandatory ex ante isolation distances and their associated compliance burden. This result conforms to findings reported elsewhere (for example, Demont et al., 2008b; Devos et al., 2009), effectively calling for greater flexibility in coexistence regulations. The assumption of minimal transactions costs applying to scenarios of negotiated outcome may be too great an abstraction. If transaction costs are high, the efficiency gains from endogenously determined pollen barriers may be dissipated by the costly process of negotiation. For example, access to the necessary information to determine the efficient width of pollen barriers, and monitoring of their implementation, may be costly. The stochastic framework is an additional complication, assuming that farmers have sufficient knowledge of the distribution function of cross pollination. These are limitations of the outlined models. However, if farmer organisations and networks take on a role in facilitating negotiations, as Skevas et al. (2010) found to be the case in Portugal, transaction costs and even coexistence compliance costs may be significantly reduced. Nevertheless, the value of the model of endogenous coexistence lies in its potential use by authorities to establish guidelines for coexistence of GM and non-GM agriculture. Policy makers have greater access to the information necessary to determine the efficient width of pollen barriers. Rather than mandating uniform isolation distances, policy makers can set region-specific measures (or ideally at an even finer spatial scale, such as a shire) that take into account average farm characteristics (such as the size of fields), the characteristics of the agricultural landscape in a region (such as likely GM adoption rates, extent of monoculture and planting patterns), and the marketing strategies predominant in the region (for example, grain intended for organic markets or for varietal seed). Alternatively, policy makers may establish institutions that facilitate a limited form of cooperative coexistence. These may take the form of guidelines for the appropriate width of pollen barriers and a specified reliability level. Foremost among these institutions, policy makers should be explicit about the initial assignment of property rights to either GM or non-GM farmers. For example, the European Union position is that farmers who introduce a new production technology should bear the responsibility of implementing the farm-level measures necessary to limit adventitious presence (the newcomer principle). Contrary to this position, Beckmann et al. (2011) conclude that a system that assigns property rights to GM farmers is more efficient when transaction costs are positive (but not prohibitive) and there are costs to using the legal system for claiming damages. Findings from this paper add to this debate by demonstrating that the level of protection provided to nonGM farmers, as provided by an endogenously determined width of pollen barriers, is dependent on the system of property rights.

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