Traditional explanations of overgrazing based on property rights are not consistent with the stylized facts of pastoralism in developing countries which indicate that it is the destruction of traditional property rights systems rather than their existence which is the root cause of the problem of overgrazing. Static models of common property have attempted to address this issue by arguing that common property has advantages in terms of risk management. Alternatively, our understanding of traditional pastoral property rights may have failed to capture some basic features of traditional property rights. First hand observation of traditional pastoral economies suggests that economic theory has, by characterising property rights as either open access or common property, failed to adequately capture the nature of traditional pastoral economies. Traditional pastoral property rights are mixed, but mixed in an interesting way. In reality many pastoral property rights systems appear to fluctuate seasonally, that is the right to access a patch of land changes from season to season. Can one mathematically model such a system, how would such a system perform when compared with private property or common property, and why is this mixed system apparently so robust compared with the alternatives? In this thesis I attempt to address some of these questions.
This thesis applies Ito stochastic control theory to the study of the economics of pastoralism in developing countries. Numerical simulation models are developed to compare near-optimal paths of the mean and variance of livestock and pasture biomass between different property rights regimes.
The solution procedure employs Monte-Carlo optimization in conjunction with numerical solution of the underlying stochastic differential equations and numerical integration of the objective function. This global optimization approach avoids the “curse of dimensionality" that arises with grid based methods such as finite difference and Markov chain approximation by employing randomization. The approach is a more direct way of using randomisation to break the curse of dimensionality than other methods suggested in the literature that are in general based on random grid generation.
The modelling method employed compares different property rights regimes, based on analysis of mean first exit times from a sustainable region of pasture-livestock space. The comparison takes the form of a thought experiment, in which an attempt is made to determine whether one property rights regime is in some sense "better, than another without relying on notions such as transactions costs. The analysis as conducted is essentially a form of "dynamic" mean-variance analysis, although an approach to dynamic stochastic efficiency analysis via Fokker-Planck theory and mean first exit time analysis is discussed. This leads to a theory of the evolution of property rights that is based solely on the dynamic stability of a given property rights regime in the presence of environmental uncertainty and which does not in any way rely on concepts such as transactions costs. Three property rights regimes, namely private property, common property and mixed regime referred to in the thesis as transhumance are compared. The analysis of transhumance as a property rights regime involving seasonal switching between private and common property is, to the best of my knowledge, novel. It is concluded that while most of the results reported in the literature on static economic models of common property grazing are robust to a dynamic extension, common property grazing does not manage uncertainty as well as private property. The modelling results suggest that, as expected, the most stable property rights regime is transhumance.