Here eij is the effort exerted by the doctor in the interaction between doctor i and patient j. θi is the competence of the practitioner, publici is a dummy variable that indicates whether the doctor is in the public sector, Xi a vector of other observed provider characteristics, and Yj a vector of observed patient characteristics. The error term in the parenthesis consists of the patient’s (unobserved) willingness to pay, vj, an interaction speci fi c error μij and a doctor speci fi c error term εi.

In addition to the effort equation, there is a relationship that speci fi es the structure of matching in the market.

This problem is hard to estimate due to the matching of patients to providers. Since the willingness-to-pay is not observed, it enters in the error term of Equation (7). As discussed above, if the doctor is a perfect price discriminator, patients are indifferent between less and more competent providers (the doctor can extract all surplus) so that σ = 0 in Equation (8) . In this case, the coefficient β1 re fl ects the average valuation of cure as per the bargaining model. In all other cases, we have to worry about matching patients to providers. The matching equation implies that the patient’s willingness-to-pay for quality is correlated with the competence of the provider. The likely direction of this bias is upward as patients with a higher willingness-to-pay will match with more competent providers. The complementarity between effort and competence may be entirely because better doctors see richer patients and effort depends on the price of the transaction.<sup>19</sup> Attributing β2 entirely to incentives in the public sector is also problematic if particular types of providers prefer the public sector. The direction of this bias is difficult to determine–there are arguments that more altruistic doctors or those building up a reputation locate in the public sector, which biases the estimate towards zero (see for instance, Chawla 1997). On the other hand, doctors with higher costs of effort may locate in the public sector, biasing the coefficient upwards.

# 4.1 Interpreting the Relation between Effort and Competence: The Structure of Sorting

To understand how patients match to doctors, we matched household visits to doctors in the parallel household survey to providers in the doctor survey. We completed this matching for all visits over a 2 year period, during which households were administered surveys on a weekly basis for 35 weeks. This data yielded close to 4,000 doctor visits; in 65 percent of these visits, we were able to match the provider visited to a practitioner in our study (recall the sampling scheme gave greater weight to doctors who were visited more). Since all households were administered a consumption-expenditure survey, we then computed the "average income of a patient" as the average income of households matched to providers, weighted by the number of visits over the 2-year period. By construction, the sample of practitioners also includes those who were never visited.

> 19 Our attempt to address the matching issue differentiates this paper from Leonard’s (2005) work. While Leonard (2005) tries to address the selection issue, he does not present a synthesis of how the market operates in equilibrium; as such, it is hard to tell what portion of his results are driven by the selective sorting of patients to doctors. This problem be partially solved with information on patient characteristics. Given the particular environment (crowded urban streets and clinics that consist of a single room open to the outside) both patients and doctors were reluctant to give permission for this exercise and we explore other options for identi fi cation purposes.

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