market alternatives may be in greater supply. This feature introduces portfolio aspects to the decision to participate in the formal system - that is, relative to the choices available to workers in developed countries where governments have capacity to enforce the mandate to participate, individuals in developing countries can pick and choose between a range of publicly provided, market and non-market (informal, family based) instruments to mitigate the loss of earnings ability in old age. Thus, an analytical framework that is sufficiently broad to encompass preferences with respect to a variety of instruments is required to motivate this empirical analysis.

Such a framework is available in the early articles on the economics of insurance. In their 1972 paper Ehrlich and Becker combine expected-utility and indifference curve analysis within the context of a "state preferences" approach to behavior under uncertainty. Although their model abstracts from the important inter-temporal life-cycle element of insurance decisions, it provides several predictions of optimal risk-mitigating behavior that lend themselves to empirical tests using cross section survey data.

Their model is straight forward. In the face of a prospective loss, individuals can either insure against the loss, or take steps to lower the likelihood that the loss will occur. The _"comprehensive insurance"_ problem of the individual is to determine their optimal expenditure on a set of alternative instruments - _"market insurance", "self-insurance"_ and _"self-protection "._ Both market and self-insurance transfer income from the "good" states to the "bad" states of the world, lowering the size of losses in the bad states. Where it is available, market insurance can be purchased at a price - the "premium". Self-insurance differs from market insurance in that there is no market for it and therefore no explicit price. However, a shadow price can be imputed from the costs incurred by the individual in self-insuring. The critical difference between the two ways of insuring is that market insurance _pools_ risk across individuals, while self insurance does not. Individuals who neither insure through a market nor self insure - whether by choice or because both instruments are missing - must cope with the losses in any bad states that occur. The third instrument, self-protection, reduces the probability of the bad state, although since it does not transfer income from good to bad states, it does not affect the size of the loss should the bad state come about.-<sup>2</sup> Within the Ehrlich and Becker framework, individuals smooth consumption over good and bad states of the world. Where insurance markets are missing the individual smoothes consumption using only self-insurance and self-protection. In a world where the option of both market insurance and self-insurance exist, they are substitutes. Market insurance - available at or near actuarially fair prices'<sup>3</sup> - reduces the take up of self12 The authors admit that, "... it is somewhat artificial to distinguish behavior that reduces the probability of the loss from behavior that reduces the size of a loss, since many actions do both." (Erlich and Becker, 1972, p. 634) However, they find it helpful to separate _selfprotection_ from _self insurance_ since the latter clearly performs the insurance function of redistributing income from good to bad states.

13 Conventionally, the price of market insurance X is said to be "actuarially fair" if or = _p /I - p,_ where p is the probability of the bad state occurring.

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