The authors assume that physician and non-physician hours, capital, and other factors are measurable but effort is not. What determines physician effort? Physicians get utility from income, y, and disutility from exerting effort and working more hours. The authors assume physicians have the following utility function, u i:
u i = y i - v i (e i, h i )
y i = α(P-C)q i + n -1 (1-α)(P-C)Σ (1 to n) q i
The variable α represents the percentage of work that physicians receive 100% of the net profit they generate and (1-α) represents the net profit generated shared among the n physicians in the group.
∂u i /∂e i = [α + n -1 (1-α)](P-C)(∂f i /∂e i ) - ∂v i /∂e i ) = 0
So know we’ve done some math. Who cares? What do we get out of all these equations? The first order equation, ∂u i /∂e i, shows that when physicians optimize their effort level, they trade off the benefit from extra effort (more money) versus the cost of more effort (they’d rather be golfing). The authors can also use comparative statics to to predict how they will affect physician effort.
α: An increase in the percentage of work where the physician receives 100% of the profit generated will increase effort.
P: An increase in the price of a medical service will increase physician effort.
C: An increase in the cost of a medical service will decrease physician effort
n: As the number of physicians increase, effort decreases. This is because physicians will have to share more of their income with other doctors. This results falls in line with the finding of Newhouse (1973). This paper found evidence of “behavioral diseconomies of scale” whereby physicians shirk more as the number of physicians in the group increases.
How do Pauly and Gaynor test this hypothesis. First, they used data collected by the Mathematica Policy Research on 957 medical groups and 6353 physicians. They have data on physician and assistant hours, capital, and other information. They estimate effort using a maximum likelihood production frontier estimation.
One problem is that physician compensation structure may be endogenous. Physicians who are more active may decide to choose medical groups where α is large and n is small. To try to correct this problem, the authors use physician tastes as an instrument.
The authors find that “incentives affect the quanity [of medical services] produced but not measured technical efficiency…Specifically, relating compensation to productivity does increase production as theory would suggest. The number of members in a group decreases the quantity produced, and experience leads to greater productivity.”