# **Section II.1. Empirical Framework**

# _The Empirical Model_

The empirical framework relates patient satisfaction to the effort exerted by the doctor in the interaction. Since most of the variation in satisfaction is between those who report being “verysatisfied” and those who report being “satisfied”, we retain the binary classification of Table 1 in the econometric analysis. There is some evidence that this distinction resonates with patient’s qualitative assessment of care and that the difference between the two categories corresponds to a very clear distinction in the patient’s feelings about the interaction (Collins and O’Cathian, 2003). The dependent variable, Sij, the satisfaction reported by patient i in her interaction with doctor j, is therefore coded as: Sij = 0 if reported satisfaction ≠ “very satisfied” and Sij = 1 if reported satisfaction = “very satisfied” Since the use of fixed-effect estimations leads to substantially different results, two simple tables highlight the main contribution of this methodology. Table 3a and 3b show the (hypothetical) effort exerted by Doctors A and B in their (hypothetical) interactions with four patients. Doctors can either exert high effort (1) or low effort (0.5); likewise patients can report either high satisfaction (1) or low satisfaction (0). In our example, Doctor A generically exerts greater effort while Doctor B exerts less.

In Table 3a, there is a strong association between effort and satisfaction across the two doctors but there is _no association between effort and satisfaction “within” doctors_ —that is, neither for Doctor A nor for Doctor B do patients report more/less satisfaction when each doctor exerts more or less effort. The association between effort and satisfaction is driven by the relatively greater use of Doctor B by patients who always report low satisfaction and of Doctor A by patients who always report high satisfaction. In contrast, Table 3b depicts the situation where there is both a correlation across doctors and “within” doctors. In a normal OLS regression both Tables 3a and 3b would show the same positive correlation between effort and satisfaction due to the correlation across doctors. A fixed-effect specification would reveal that there is no correlation between effort and satisfaction _within each doctor_ .

One requirement for “within” doctor estimations of the kind in Table 3b is that there is substantial variation in effort for every doctor; indeed, the regression with a “within” doctor estimator, which is akin to including a separate dummy variable for every doctor, will not be estimable when every doctor exerts the same effort for every patient. In this case, the doctor fixed-effects will be fully collinear with effort; fortunately, as we saw above, close to 50 percent of the variation in total effort is within rather than across doctors.

The estimation strategy can be presented formally as follows. The multivariate regression framework is given by an equation of the form: Sij = α + β Effortij + γ Xj + δ Xi + ( η j + μ i + ε ij)

[Equation 1] where Effortij is the effort for doctor j in her interaction with patient i, Xj are observed doctor characteristics (such as age and gender), Xi are observed patient characteristics (such as wealth, education and health-status) and the terms in the parenthesis (.) are doctor and patient characteristics that we did not measure but are correlated with reported satisfaction. The ηj corresponds to unmeasured intrinsic attributes of the doctor (for example courtesy); μ i are unmeasured 6