Reciprocal insurance among Kenyan pastoralists
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DOI: 10.1007/s12080-012-0169-x
- Cite this article as:
- Dixit, A.K., Levin, S.A. & Rubenstein, D.I. Theor Ecol (2013) 6: 173. doi:10.1007/s12080-012-0169-x
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Abstract
In large areas of low and locally variable rainfall in East Africa, pastoralism is the only viable activity, and cattle are at risk of reduced milk output and even death in dry periods. The herders were nomadic, but following the Kenyan government’s scheme of giving titles to group ranches, they are evolving reciprocity arrangements where a group suffering a dry period can send some of its cattle to graze on lands of another group that has better weather. We model such institutions using a repeated game framework. As these contracts are informal, we characterize schemes that are optimal subject to a self-enforcement or dynamic incentive compatibility condition. Where the actual arrangements differ from the predicted optima, we discuss possible reasons for the discrepancy and suggest avenues for further research.
Keywords
KenyaPastoralismVariable rainfallInsuranceSelf-enforcementIntroduction
Public-good and common-pool resource problems are fundamental to sustainability and ineluctable features at the interface between ecological and socioeconomic systems (Ostrom 1990; Sethi and Somanathan 1996; Weissing and Ostrom 1993; Dasgupta 1997). More generally, the challenges addressed in dealing with such problems are also widely found in biological systems even in the absence of humans: bacteria produce extracellular polymers that provide benefits to others, plants fix nitrogen, collective foraging and defense are widespread, and indeed the prudent use of common resources emerges in a number of different contexts. Thus, not only can approaches for dealing with human–environment interactions help manage these situations but such approaches also can help to elucidate analogous problems throughout ecology and evolutionary biology. This paper chooses as an example collective insurance arrangements in herder systems, but the hope is that the framework developed will serve as a starting point for dealing with a much wider set of phenomena.
Pastoral herding appeared thousands of years ago when hunter-gatherers domesticated wildlife, selectively breeding livestock that could convert inedible vegetation of previously underutilized arid and semiarid lands into useable foodstuffs such as milk and meat. The lands are characterized by rainfall that has a low average, but high spatial and temporal variation. Pastoral herders coped with the resulting uncertainty in rangeland productivity by migrating large distances following the rains. Since productive areas were often controlled by resident tribes, the mobility of wandering tribes was constrained. Warrior-enforced encroachment, tempered by informal rules of land tenure as well as wife exchange among tribes, created a variety of mechanisms that fostered short-term sharing by the occupiers of productive lands with those whose land was currently, but temporarily, unproductive (Homewood 2008).
Generally, the drier the region, the more pastoral herders subsist on foodstuffs derived from livestock. Some of the purest pastoralists—the Maasai, the Samburu, the Turkana, and the Boran—live in East Africa where annual rainfall is less than 400 mm. Traditionally, families in these tribes survived mostly on milk from their herds. Milk is virtually a perfect food supplying protein, calories, and vitamins. But sufficient production to sustain families depends on herds consuming vegetation from pastures not degraded by excessive livestock grazing and browsing.
Even though no tribe can control enough rangeland to sufficiently reduce the effects of rainfall variability, the pressure to control as large a tract as possible results in rangelands being managed as a common-pool resource. Since the costs of excluding groups arriving from unproductive land are likely to be greater than the gains of defending productive land, rules based on reciprocity and kinship often develop to reduce violence and foster long-term gains of wandering and defending groups. But such relationships are prone to cheating. If reneging for short-term gain limits future movement, then staying put during “bad times” with large herds that were appropriate when times were good is likely to lead to degradation of the land, unless Hardin’s idea of “mutual coercion, mutually agreed upon” is practiced.
The Kenya Government’s new land tenure policy during the 1970s (see ILRI 1995) compounded the problem of limited movement and resulting land degradation. When communities received title deeds to exclusive areas, pastoral herders who had relied on transhumance for thousands of years were essentially sedentarized, living on parcels of land that became known as “group ranches” and which averaged 15,000 ha (37,000 acres or 60 square miles) in size, much too small to average out rainfall variability within, or even among neighboring clusters of, communities.
Consequently, new methods of organizing livestock movements from areas of low rainfall to high rainfall had to be developed. In theory, herders with cash could buy grazing rights on more productive land, a practice that is common in Australia and other areas of the world. Renting land for transferred herds is known as agistment and relies on trust since receivers of herds are expected to care for them well and senders of the herds are expected to send only easy-to-manage animals (McAllister et al. 2006). But incomes among pastoral herders in East Africa rarely exceed $1 per day, so agistment practices are rare. Instead, pastoral herders are developing reciprocity arrangements with other communities so that when conditions are poor for one community, a fraction of that community’s herds can be moved to the more productive lands of the distant partnering community. Unlike arrangements under the agistment system, transferred livestock by African pastoralists are managed by their owners. For this system to be stable, when the conditions are reversed, communities that previously received herds should be able to send a similar fraction of their herds to the former sending communities. But if the former sending communities renege on their agreement or have not managed their lands well by setting enough rangeland aside to sustain their own returning herds as well as herds of former receivers that will be expected in the future, the payoffs will not be equal and offsetting, and reciprocity arrangements will collapse.
In this paper, we consider the viability of such arrangements. For this initial exploration, we use a very simple model. We assume that the groups are symmetric except for the weather realizations: they have the same production and cost functions and the same marginal probability distributions of weather realizations. When we consider self-enforcing cooperation in Section “Self-enforcing second-best,” we will assume that identical periods of this kind repeat indefinitely, ignoring serial correlation of weather and ignoring the dynamics of cattle population through birth and death, and that of land quality through gradual degradation or restoration. While this model serves to yield some useful results and insights, we will later list many dimensions along which it can be generalized; these generalizations are part of our ongoing work.
The basic model
- 1.
It should be an increasing function of each argument: the partial derivatives \({{\partial {C}}/{\partial {x}}}\) and \({{\partial {C}}/{\partial {z}}}\) should both be positive. It is more costly to farm more animals (including both direct costs and those of any land degradation that has to be restored so x can be increased while keeping z constant) and it is more costly to maintain higher quality of land while raising a given number of animals.
- 2.
The second-order own partials \({{\partial^2 {C}}/{\partial {x}^2}}\) and \({{\partial^2 {D}}/{\partial {z}^2}}\) should both be positive, i.e., the incremental or marginal costs of keeping more cattle should be increasing as an increasing number of them crowd more on the given amount of land, and the marginal or incremental cost of sustaining higher land quality should be also be increasing as the desired quality increases, because the cheapest quality-increasing measures will be undertaken first and successive steps to improve quality further will require resort to successively more costly methods.
- 3.
The second-order cross-partial \({\partial^2 {C}/\partial {x}\partial {z}}\) should be positive: the more cattle on the land, the harder it is to make any incremental improvement in land quality. Then, the quadratic we use is the simplest function that meets these requirements while combining flexibility and parsimony: it employs just one free parameter c. We could make the cost proportional to (ax + bz)^{2} where a and b are free parameters, but that is redundant because we can choose units of x and z to make a = b = 1.
The two groups’ weather outcomes are perfectly positively correlated if p_{1} = 0; in this case, reciprocal arrangements will not help. The opposite case of perfect negative correlation corresponds to p_{2} = p_{0} = 0 and \(p_1 = {\frac{1}{2}}\); this is when reciprocal arrangements have the greatest potential. The case of independent outcomes (zero correlation) requires p_{1} = p_{H}p_{L} = (p_{2} + p_{1}) (p_{1} + p_{0}), which then simplifies further to \(p_1 = \sqrt{p_0\,p_2}\).
One group’s optimum
The full or first-best optimum
The two groups together can achieve better outcomes. If one has the good weather realization H and the other has the bad weather realization L, the total output can be raised by transferring some cattle to graze on the land that is more productive in this weather realization. We emphasize that the “transfer” is not a change of ownership, it is merely a temporary move to better grazing grounds. Some people from the home group travel with the cattle to manage them, and at the end of the season, the cattle will return to the home ranch. No net cost to transport is assumed since the cows graze while walking between sites. Also, the fortunate group, which enjoys more favorable weather, can share some of the output of its own cattle with the unfortunate group. The good and bad weather conditions fluctuate probabilistically, so these are mutual insurance arrangements and not one-way gifts.
The implementation of the optimum may be problematic. A group that has a good weather realization may be tempted to renege on its agreement and refuse to accept cattle from the other group that has had a bad weather realization, instead using its greener land for its own herd. And it may be tempted to refuse to share output with the other. If the social planner has enforcement power, or if a formal enforceable contract can be written by the groups, the problem can be solved. We will call this a full or first-best optimum and characterize it in the rest of this section. But if enforcement power is lacking, the arrangement has to be self-sustaining, based on repeated relationship where the lucky group realizes that some time in the future it may need a return of the favor and therefore that its short-run gain from reneging has a long-run cost. We will take up this self-enforcing or second-best optimum in the next section.
Step 1
Observe that m_{ij}, the number of cattle of group 2 moved to graze on group 1’s land in state (i,j), is higher if (1) A_{i} is high relative to A_{j}, (2) z_{1} is high relative to z_{2}, and (3) x_{2} is high relative to x_{1}. The first of these serves the purpose of the reciprocity arrangement: to insure or smooth out fluctuations in income. But the other two can create moral hazard. Each group may be tempted to allow its land to degrade (lower z) and stock more cattle (raise x) beyond the optimum and then transfer some cattle to benefit from the other’s better and less-intensively grazed land. With both groups so tempted, this will turn into a prisoners’ dilemma. Since x_{i} and z_{i} must be committed before the weather condition is realized, if the two magnitudes are publicly observable, the ability to send cattle can be made contingent on the group having adhered to the optimum, and the moral hazard of cheating on x_{i} and z_{i} can be thus overcome. We will throughout assume this to be the case and, in the next section where we consider implementation of the optimum, will focus only on the moral hazard of refusing to accept the other group’s cattle (m_{ij}). In the symmetric solution we consider below, the two x’s will be equal, as will the two z’s, and optimal transfers will depend only on the weather conditions. But in asymmetric situations, monitoring moral hazard will be more problematic. In addition, the issue of allowing transfers to disadvantaged groups for redistributive reasons will have to be considered.
Step 2
Step 3
Gains from reciprocity arrangement
If ρ > 1, each of the two steps leading to Eqs. 25 and 26 reverses the direction of the inequality. With this even number of reversals, the same final result remains valid.
Other properties of the full optimum
Fraction of herd transferred to better-weather land
A_{H}/A_{L} | α | ||||
---|---|---|---|---|---|
0.1 | 0.3 | 0.5 | 0.7 | 0.9 | |
1.5 | 0.222 | 0.282 | 0.385 | 0.589 | 0.966 |
2.0 | 0.367 | 0.458 | 0.600 | 0.820 | 0.998 |
5.0 | 0.713 | 0.818 | 0.923 | 0.991 | 1.000 |
10.0 | 0.856 | 0.928 | 0.980 | 0.991 | 1.000 |
In reality, we typically find around 90 % of herds moved in bad weather conditions.^{4} Therefore, the combinations A_{H}/A_{L} = 2, α = 0.7, and A_{H}/A_{L} = 5, α = 0.5, seem reasonable. This will guide our numerical calculations in what follows.
Ratio of herd size in full optimum to that in isolation
A_{H}/A_{L} | ρ | |||||
---|---|---|---|---|---|---|
0.0 | 0.5 | 1.0 | 1.5 | 2.0 | 20 | |
1.5 | 1.028 | 1.011 | 1.000 | 0.992 | 0.985 | 0.968 |
2.0 | 1.069 | 1.027 | 1.000 | 0.979 | 0.962 | 0.968 |
5.0 | 1.201 | 1.087 | 1.000 | 0.931 | 0.887 | 0.968 |
10.0 | 1.265 | 1.127 | 1.000 | 0.897 | 0.847 | 0.968 |
We see that if ρ < 1 (low risk aversion), the ratio is > 1 and rises with A_{H}/A_{L}, and if ρ > 1 (high risk aversion), the ratio is < 1 and falls as A_{H}/A_{L} rises. This numerical finding can be proved rigorously using some complicated algebra. The result goes against the intuition stated above: optimum herd sizes under the reciprocal arrangement are smaller, not larger, when traders are highly risk averse. Also, the ratio is not monotonic in ρ at high end, but the intuition for that is unclear.
When is the full optimum self-enforcing?
Upper bound on r for self-enforcement of full optimum
ρ | Case (1) | Case (2) |
---|---|---|
α = 0.75, β = 0.25, A_{H} = 2 | α = 0.5, β = 0.5, A_{H} = 5 | |
\(\overline r\) | \( \overline r\) | |
0.0 | 0.2771 | 0.1685 |
0.5 | 0.3687 | 0.3299 |
1.0 | 0.4767 | 0.5845 |
2.0 | 0.7505 | 1.5560 |
5.0 | 2.3637 | 30.4185 |
The full optimal degree of reciprocity is self-enforcing if the actual time-discount rate of the groups is below this upper bound \(\overline r\). We see that as risk aversion increases, the bound increases, increasing the chances of the condition being fulfilled; this accords with intuition.
However, the numerical results present an ambiguous picture about the likelihood of it being met in reality. A rough proxy for the groups’ time-discount rate is the interest rate at which they can borrow or lend. We have some evidence about the magnitude of the actual interest rates r for these herders. In principle, they can borrow from cooperatives and banks at rates in the range of 12 to 20 % per year.^{6} But the availability of such loans is quite constrained, so the implied or shadow interest rates are significantly higher. Second, there is some anecdotal evidence that farmers in neighboring areas borrow to buy equipment only if the loans pay back in one season, suggesting a rate of around 100 % (but this may contain an option value component). Thus, the likely range of actual values of interest rates overlaps with the range of upper bounds we have calculated.
If the condition (28) is not met, fully optimal reciprocity cannot be sustained on the basis of the groups’ long-run self-interest. More limited reciprocity can be sustained, and we will examine such constrained or second-best solutions in the next section. But the groups may also attempt to sustain the full optimum by cultivating ties such as intermarriage that lead them to take the other group’s welfare directly into account in their own benefit-cost calculation. Such ties do exist, and it will be interesting to see whether they are selectively more prominent in situations where Eq. 28 is less likely to be fulfilled.
Self-enforcing second-best
The fact that the transfer rule is not affected by the imposition of the self-enforceability constraint has a useful implication. Our earlier result (Eq. 27) on the fraction of herds transferred in the full optimum remains valid for the constrained optimum. Therefore, so does our inference about the plausible values of α, A_{H}, etc. based on observations for the fractions transferred in reality.
Sample numerical solution for constrained optimum
r | 0.3687 | 0.4000 | 0.6000 | 0.8000 | 1.0000 |
---|---|---|---|---|---|
μ | 0.00000 | 0.00656 | 0.02299 | 0.02469 | 0.02339 |
\(\overline{Y}\,/\,(\,\overline{Y}+\underline{Y}\,)\) | 0.5000 | 0.5065 | 0.5326 | 0.5459 | 0.5539 |
x | 0.7519 | 0.7518 | 0.7515 | 0.7514 | 0.7513 |
EU | 1.5077 | 1.5077 | 1.5073 | 1.5069 | 1.5066 |
The first column is for the value of r exactly at the upper bound that is consistent with the full optimum being self-enforcing. Therefore, the multiplier μ on the self-enforcement constraint is zero. For higher values of r, the constraint does affect the solution, but remarkably little. Even when r is substantially above the upper bound, the Lagrange multiplier on the constraint is quite small (in fact, μ decreases slightly as r increases to very high levels, but as Eq. 35 shows, the product rμ has an independent influence that keeps substantive magnitudes like the output share monotonic). Only a little more than 50 % of the output suffices to keep the lucky group in line. The size of the herd decreases very slightly, as does the expected utility.
In our context, giving a larger share of output to the hosting group may need to be managed in subtle ways. The herds are transferred over large distances, as much as 100 km. It is impractical to send any of the milk back to the owner group’s home ranch. Some members of that group have traveled with the herd to manage it, and they can consume the milk. They can also sell some milk locally on the host groups’ land but probably have to do so at an unfavorable price. Thus, the hosting group may de facto get a large share of the milk. That may overfulfill the host group’s no-reneging condition but may call into question the owner group’s incentive to send animals. In fact, there are other dimensions of output, namely, blood, meat, and any calves born during the stay at the host ranch. Herders from the owner group that have traveled with the herd to manage it can decide whether to draw blood and how much and how many cattle (if any) to kill for meat, so they can ensure that more goes back to the owner group with the cattle at the end of the dry spell. Also, the owner group retains rights to calves. Then, a suitable combination of these four dimensions of output can be constructed to meet the relevant no-reneging condition (32) or (33) with equality, even though the single dimension of milk may not be capable of being split up in just the right proportions.
Another and perhaps stronger reason for sending to a ranch with better rainfall may be to improve the prospects for survival of the animals themselves. A proper treatment of that aspect requires a richer dynamic model; that is a part of our future research plans.
Concluding comments
We have developed a model of the reciprocal arrangements that enable Kenyan cattle herders to cope with weather fluctuations across their group ranches. The key mechanism is repeated interaction—the short-term gains from reneging on your promise to take in a less-fortunate partner group’s cattle must be weighed against the long-term costs from collapse of the mutual insurance arrangement. We made many special assumptions to simplify or ignore other aspects of the situation and to produce a tractable model. Even this extremely simple model yields some insights. Some key parameters can be calibrated by comparing the results with observations. Then, it appears that the degree of patience required for successful self-sustaining reciprocity is right in the range of the rates of time discounting that the herders face. Therefore, we should expect to see success in some instances and not others. In the latter cases, the groups may create supplementary supporting mechanisms such as intermarriage to improve the prospects of cooperation, or they may modify the scheme to reduce the temptation to renege. We find that the optimal modification is to give the host group a larger share of the milk produced by the transferred cattle and argued that this may happen naturally because of the difficulty of transporting milk back for consumption by the owner group.
Thus, the model appears to be a promising start, but many features must be added for better and deeper understanding. These are among our plans for future work.
Dynamics
Successive periods in our simple model are linked only by the repeated game. In reality, there are many other links. The quantity of cattle is not a matter of totally independent choice each period but evolves as a state variable. New purchases and births add to the stock, and sales and deaths reduce the stock. The births and deaths can be functions of the quantity and quality of land in relation to the size of the herd, and also the weather outcome. The quality of land is also a state variable, increased by better maintenance effort and degraded by grazing, which depends on the size of the herd that grazes on the land. Weather can also be correlated over time. These modifications will turn our repeated game into a dynamic game, which is far harder to analyze.
Unequal sizes
We assumed the two groups to be identical (except of course in the actual realizations of weather outcomes in any one period) and found symmetric solutions. In reality, land endowments of groups differ widely. Recognition of these asymmetries will alter the analysis in several ways. Smaller groups generally have bigger incentives to renege, making self-enforcement harder. If one group has land of naturally better quality or permanently better weather conditions than the other, we will have to consider ethical issues of whether the unfortunate group should somehow be given a redistributive transfer from the fortunate group’s output and, if so, the practical policy issues of how such transfers can be implemented.
Multiple groups
We considered only two groups. In reality, the region has several groups and group ranches. Each has ties with many other groups and can in principle have multiple reciprocity agreements in place. This can however make it harder to sustain any one such agreement. If group A can renege on promise to accept B’s cattle but then use a separate arrangement with C when the need arises, this threatens the viability of the arrangement with B. The system needs multilateral punishments whereby C will refuse to deal with A if A has previously reneged on its arrangement with B. Theoretical analyses as well as case studies of such arrangements exist, for example, Kandori, (1992), Greif (1993) and Dixit (2004), but Kenyan herders may not have the necessary multilateral communication, norms, and sanctions to sustain them.
Other insurance
In recent years, international organizations have developed and experimented with more formal insurance schemes, based on objective indexes of weather and rangeland conditions, to cover ranchers against livestock mortality caused by droughts (Mude 2012). In future research, we will study how these relate to the relation-based informal and self-enforcing arrangements examined here.
Empirical research and evidence
- 1.
Conducting questionnaire and experimental studies to estimate r, ρ, etc.
- 2.
Gathering data for systematic statistical estimation of α, β, A_{H}, A_{L}
- 3.
Relating the success or failure of such arrangements of individual groups or pairs to their specific circumstances including the interest rates they face, whether they have made supporting arrangements like intermarriage, etc.
See http://en.wikipedia.org/wiki/Cobb-Douglas_production_function, for a summary, and Douglas (1976) for a survey.
This can be interpreted as follows: to induce an individual to agree to a bet where he/she may win or lose a fraction f of his/her wealth, the probability of winning would have to be \({\frac{1}{2}} + \frac{1}{4} \rho\). See p. 95 Arrow (1971). When ρ = 0, the group is risk neutral and willing to take a fair bet. When ρ > 0, the bigger it is, the more risk averse the group and demands better odds to be induced to take the bet.
More generally, the (Pareto) efficient frontier of negotiation between the two groups will maximize the expected utility of one group for each given level of the expected utility of the other, and the location of the chosen point on this frontier will depend on the relative bargaining strengths of the two.
For those unfamiliar with this usage in economics, it means that a unit of utility accruing one period later is worth only 1/(1 + r) of a unit accruing in the immediate or current period.
Acknowledgements
The authors thank seminar audiences at the Institute for Advanced Study, Princeton, MIT, Oxford, and Yale for the useful comments and Linda Woodard for the computational assistance.