Does an increase in family physicians (FPs) increase individual health? A naive research might believe that we could uncover whether or not this was true by comparing the average health levels of areas with lots of doctors with the average health levels of areas with few doctors. However, doctors often work where there are lots of sick people. Thus we can find a spurious correlation between FP quantity and individual health level.
Gravelle, Morris and Sutton (HSR 2008) aim to find the true relationship between FP quantity and individual health. They use data from the Health Survey for England and the General Medical Services (GMS) Statistics database. The authors note that family physicians may be attracted to areas where healthy patients live if these areas have attractive amenities not captured in the data. On the other hand, FPs might be attracted to areas where lots of sick people live since FP compensation is based on an age-related capitation payment. The authors claim that the following 2 instruments will be correlated with physician supply but uncorrelated with individual patient health: semidetached house prices and age-related capitation payments.
In the first stage, Gravelle and co-authors find that a larger age-related capitation payment attracts more FPs while increased house price decreases FP supply. The authors conclude the following:
“FP supply is positively associated with individual self-assessed health. If no allowance is made for the endogeneity of FP supply, the effect is not statistically significant…When FP supply is instrumented by age-related capitation, a 1 SD increase in FP supply increases the probability of reporting very good health by 4.1 percent. The results are robust to transformations of the health variable and to alternative specifications of the effects of individual age on health.”
- Gravelle, Morris and Sutton (2008) “Are Family Physicians Good for You? Endogenous Doctor Supply and Individual Health” HSR, 43(4) 1128-1144.
In the paper, the authors use the ln(FP supply) as the key dependent variable. However, ln(FP supply) is an estimated figure. Thus, when the authors calculate the standard errors, they use a bootstrap methodology as follows:
- Draw a sample of 351areas (local authorities) with replacement from the area-level data set.
- Estimate the ln(FP supply) equations for each of the 3 years—1997, 1998, and 1999.
- Estimate the individual-level health equation using predicted ln(FP supply) plus the individual and area-level covariates. The individual observations are weighted by the number of times the LA in which an individual lives was drawn in the first stage bootstrap sample.
The reported standard error of the instrumented ln FP supply coefficient is the standard deviation of the estimated coefficients on ln FP supply from 200 replications of this procedure.