Ducks and Economics

Wolfson, Puri, and Martinelli write in the Journal of Conflict Resolution in 1992:

We propose a dynamic model of the interaction between two rival powers. It is not an easy model, because it involves nonlinear difference equations; yet it is simple in the sense that it involves only a few variables. Parsimony shows that complexity and apparent paradox need not arise from the multiplicity of factors but from their nonlinear connections. Complications certainly may be introduced such as considering more than two states and alliances among them (Wolfson 1973) as well as further specification of expectation formation. They might improve some future statistical investigations, but the theory has no need for those hypotheses to explain the complexity of the historical record. Occam’s razor suggests that small is beautiful.

The present model is only a prototype; nevertheless, it is well defined. It runs on the computer with plausible hypothetical parameters; it generates scenarios that make sense; and it presents endogenous regime switches between war and peace, balance of power and preponderance of power, stability and instability.

The model traces out the interaction over time of the antagonism between two rival powers. They are assumed to be rational and to maximize their utility subject to both economic and political constraints.

The economic constraint is a convex guns-versus-butter production possibility frontier: with given resources, a nation can produce various combinations of civilian and military goods with diminishing returns to specialization in either product. The rate of trade off between civilian and military goods is negative and declines monotonically, that is, without change in sign.

The political constraint is more complex. It reflects the choice between military power on one hand and the probability of peace on the other. Like economic agents, political leaders must also choose between the goals of peace and power that sometimes reinforce and sometimes oppose each other. The complexity of international politics arises from the fact that the acquisition of military capability might raise or lower the probability of peace, so that the set of feasible political states is not convex. Both the preponderance of power and balance of power correspond to a high probability of peace. These regions are separated by intermediate regions where war is more likely.

In the literature, balance of power and preponderance of power are frequently regarded as mutually exclusive (Organski and Kugler 1980), but in this model they are synthesized by restricting them to their own domain. The resulting nonconvexity is the key to understanding the complex dynamics of international conflict. The consistent sign of the slope of the convex economic constraint makes it generally possible to approximate its dynamics by linear expressions, but this is not possible for the political relationship where the slope varies in sign. The political relationship is inherently non-linear. We are, therefore, confronted with a situation that is substantially different from the standard cases.

The contradictory results reported by researchers do not necessarily stem from the limitations of measurement. They are systemic and follow from the attempts to apply linear methods to the nonlinear dynamic nature of conflicts (Most and Starr 1989).

Linear models presume that small changes in causes-be they errors in measurement, rounding errors of digital computers, or incremental changes in public policy-give rise to small variations in the consequences. If this were so for our problem, the pattern of events leading up to war would be very similar across history, and statistical investigations would yield consistent results. But this is not the case. It is therefore likely that international politics is a nonlinear system in which small variations in initial conditions may lead to large, sometimes discontinuous, even chaotic changes in outcome.