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Y = X[beta] + [y.sub.1][I.sub.d] + [y.sub.2][I.sub.s] + [mu]where X represents the vector of predisposing, needs, and other enabling factors. Incorporating the selection west using the control function model, we haveY = X[beta] + [y.sub.1][I.sub.d] + [y.sub.2][I.sub.s] + [[alpha].sub.0](1 - [I.sub.d] - [I.sub.s])[[lambda].sub.0] + [[alpha].sub.d][I.sub.d][[lambda].sub.d] + [[alpha].sub.s][I.sub.s][[lambda].sub.s] + vThe [lambda]''s are the transformations of the probabilities predicted from the first stage (Heckman 1978; 1979; 1990; Lee 1982; 1983). They are the correction factors similar to the correction factor (inverse Mill''s ratio) in a Heckman correction model where the response variable in the first stage is binary rather than multicategorical (Heckman 1979; 1990). Vella and Verbeek (1999) showed that testing for the presence of endogeneity is equivalent to testing whether [alpha]''s are zero. With the incorporation of the endogeneity control, the effects of having a regular doctor ([I.sub.d]) and having a regular site ([I.sub.s]), conditional on the choice of a usual source of care, are [y.sub.1]+([[alpha].sub.d][[lambda].sub.d]- [[alpha].sub.0],[[lambda].sub.0]) and [y.sub.2]+([[alpha].sub.s][[lambda].sub.s] - [[alpha].sub.0][[lambda].sub.0]), respectively.* A single-equation estimation that regresses utilization over having a usual source of care would provide biased results of the effect of having a usual source of care because of the omitted correction terms. The fourth and fifth columns are the counterparts of columns one and two in single-equation estimations. For blood pressure and cholesterol level checkups, in which endogeneity of having a usual source of care was found, estimations without endogeneity control overestimated the relative effects of having a regular doctor to having a regular site. The comparative advantage of having a regular doctor (relative to having a regular site) estimated by the single-equation approach is shown in the last column of Table 4. Except for blood pressure and cholesterol level checkups, no significant differences were found in the effects of having a regular doctor and having a regular site.
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