### 4.2.2 Facility Fixed Effects

Our fi nal speci fi cation tackles the matching problem from a different angle. The key to this speci fi cation is the allocation of patients to practitioners in hospitals and smaller clinics. Most private and public sector clinics are manned by a single provider. Thus, when a patient chooses to visit such a clinic, she chooses to match to the provider who staffs the clinic. In contrast, all hospitals are staffed by multiple doctors in the out-patient departments where we observed them. Like most out-patient departments, once a patient chooses to visit the institution, there is no further matching. Patients wait in a single queue and visit the doctor free at the time they come to the front of the line (similar to a queue with multiple counters). When patients visit hospitals they do not count on visiting a particular doctor; consequently within facilities patients are randomly matched to providers.

The relationship between competence and observed patient characteristics within the same facility is consistent with the hypothesis of random matching. In a regression context, a test that observed patient characteristics are correlated to provider competence within facilities is rejected at the 5 percent level and is barely signi fi cant at the 10 percent level. We exploit this "random-matching" component of hospitals by including facility-level fi xed effects in the regression of effort on competence. In comparing effort levels of providers of differing competence who practice in the same facility, we purge the estimated coefficient of biases arising from non-random matching.

## 4.3 Interpreting the Impact of Institutions on Effort

Estimates of β2 from Equation (7) confound the effects of selection into the public sector and the adverse impact of incentives. To some extent, the inclusion of clinical competence as an additional explanatory variable is novel and likely controls for the bulk of the selection effects. In addition to including provider competence, we ensure that our estimates are robust to all observed characteristics of providers and patients, both in regression and more fl exible matching speci fi cations (propensity score matching). This assumes that there is no selection on unobserved variables. An alternate interpretation is that the estimate coefficient re fl ects the joint effect of incentives and selection on unobserved characteristics in the public sector. Table 3 summarizes our empirical strategy and the assumptions required for the estimates to be unbiased in Equation (7).<sup>23</sup>

# 5 Results

Following Table 3, we present results on the relationship between effort and competence and the difference between the public and private sector for three speci fi cations. The fi rst controls for observed doctor and patient characteristics, the second accounts for patient matching by including average patient income or neighborhood fi xed effects and the third accounts for patient matching by including facility fi xed effects.

> 23 We require that competence is strictly exogenous for all the speci fi cations. This may not be true if more motivated/altruistic doctors also seek more training. We are less worried about this source of omitted variable bias, since policy changes that would have to tackle this issue relate to greater training and education for providers. At this point, we stick to the pool of available doctors and look for policies that may affect the distribution of such providers or those that may lead them to exert greater effort-in-practice.

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