International security, insurance, and protection: Negative spillovers within alliances

Over forty years ago Olson and Zeckhauser (1966) proposed a now famous theory of security alliances that has evolved into a general paradigm of group good allocation behavior. We consider multiple pure public goods where “defense” or “security” is disaggregated into the more realistic categories of self insurance and self-protection.

Among the first to examine combinations of instruments open to individuals to manage risks to their well-being were Ehrlich and Becker ("EB 1972).  EB identified several types of preparation available to expected utility maximizing agents faced with what we will call "costs of emergency."  These costs consist of any mix of (a) probability of loss and (b) magnitude of loss (hereafter together referred to as "risk profile"). Among such preparations were (a) "self insurance" to compensate for or reduce the magnitude of loss and (b) "self-protection" to reduce the probabilities of loss.

It would now be generally agreed that these ideas apply to entire societies attempting to cope with diverse conflicts.  Governments need not passively accept risks when production and/or consumption decline creating unwelcome situations. More and more countries face a common risk of a disastrous event as an alliance and jointly avoid that risk. Examples of such events include invasion, terrorist attacks, environmental disaster, and pandemic of infectious disease. Nevertheless, utilization of EB to model collective improvements to the entire "risk profiles" as international public goods is sparse

We show how each of the two public goods provided by the countries in alliance critically influences the impact of a change in their incomes at positions of simultaneous optimization. When disaggregated into these two components, inferiority of public goods is no longer exceptional or unusual. An increase in income in one country may reduce the provision of the public goods, and diminish the welfare of its allies. Due to the goods inferiority, negative spillovers are more likely to occur than under the conventional analysis. We show how economic growth and redistribution create negative spillovers and related difficulties among allied countries managing insurance and protection with emphasis on analysis of corner solutions.