By William H. Dow
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Additional resources for Unconditional demand for health care in Côte d'Ivoire: does selection on health status matter?
Unfortunately, decomposing Pjk into two parts, each of which has the logit form, is only valid when there is correlation between unobservables within branches. If instead there is correlation between unobservables in different branches, then the resulting conditional probability f(Med¦Sick) will no longer have an NMNL form. This would arise, for example, if there is correlation between the alternatives in which care is not demanded (Îws is non-zero). Thus when demand is estimated as an NMNL conditional on sickness, the implicit assumption is that Îws is zero.
As argued earlier, the dynamic model in Section 2 implies that the health care demand decision can be modeled for the entire unconditional population. This implies that the choice set can be redefined to consist of hospital h, clinic c, and none n, where now no distinction is made between whether non-demanders consider themselves as sick or not. This marginal procedure still yields consistent estimates of unconditional health care demand, assuming that the error distributions are appropriately specified (as discussed below).
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