The self selection constraint reveals that, in equilibrium, the high risks will be indifferent between (a) spending s.
Now, defining [s.sub.U] as the level of treatment chosen ex post by a known high risk if offered policy U (obtained by conditions equivalent to those in equations (6a) and (6b)), the self selection conditions for such a separating equilibrium are:
expected utility if uninformed (in which case, the individual cannot avail himself of opportunities for reducing hazard and the low risk policy is selected from the self selection menu).
Using the self selection constraint, v(H, [p.sub.H]([s.sub.H])) - [s.sub.H] = v([L.sup.2], [p.sub.H]([s.sub.L])) - [s.sub.L],
Using the self selection constraints (9a) and (9b), this becomes:
In the prior information regime, low risks will hold contract [L.sup.3] which is defined by contract H and the binding self selection constraints (9a) and (9b).
The initially informed low risks are strictly better off when the uninformed become informed because of the weaker self selection constraint in the two contract menu (as is the case with the treatment option).
The empirical techniques developed by Mincer (1983) and Mellow (1981) to measure the wage effects of unionization can be adapted to the issue of migrant self selection. In essence, a longitudinal wage model can be specified which compares the wages of prospective migrants and nonmigrants.
For prospective migrants to rural areas, however, we find no evidence of favorable self selection.