The growing medical desertification in most OECD countries driven by an increasing spatial concentration of physicians (Pál et al., 2021) is a prominent concern for policy-makers. If medical desertification is an important issue for accessibility to care services, then another dimension that has received less attention from economists is the consequences of the pricing of physician services (see Gaynor and Town, 2012). This could be another major concern, especially in OECD countries.1 which allow some or all of their physicians to set their prices freely. Indeed, in these countries, the pricing of physician services is an important factor that influences the healthcare affordability.

France is an interesting context in which to explore physicians’ pricing decisions and their consequences. Approximately 40% of physicians (CNAMTS, 2017), mainly specialists, are able to balance bill their patients based on no other limit than their evaluation of “tact and moderation”. The part of the bill that is above the regulated fee is not covered by National Health Insurance (NHI)2. Moreover, as physicians in France are free to choose their location, the geographical concentration of free-billing physicians reinforces concern for healthcare access. There is a well-known risk that free-billing physicians are located in similar attractive locations characterized by excess demand at regulated prices, high income and amenities (see Feldman and Sloan, 1988). The study on the location of liberal health professionals in France proposed by Barlet and Collin (2009) supports this idea as physician specialists such as gynecologists, pediatricians or ophthalmologists are strongly spatially concentrated in large metropolitan areas.

The objective of this paper is to provide new robust evidence on free-billing physicians’ pricing behavior by developing a structural approach. This is an important and necessary step to better understand which kind of policy tools could limit additional fees and improve care affordability. To achieve this objective, we make several contributions to the existing literature. First, we develop a closed-form solution of a circular city model with heterogeneous physicians where consultation quality influences both patients’ utility and physicians’ costs. This allows us to highlight and discuss how individual and competitors’ quality influence equilibrium prices but also to provide new insights concerning the effects of competition. Second, we are able to structurally identify core parameters of the model by building a unique geolocalized database of more than 4,000 free-billing physicians from three specializations (ophthalmology, gynecology and pediatrics). We develop a general two-step spatial generalized method of moments (GMM) procedure allowing us to control for sample selection bias, endogeneity and an unknown distribution of errors. As shown by Fingleton and Le Gallo (2010) and Kelejian and Prucha (2010), a general GMM estimator allows flexible assumptions for identification in the presence of these issues. Indeed, unlike the quasi-maximum likelihood (Q-ML) estimator, it does not require complete knowledge of the distribution of the spatial data. The different robustness checks and the sensitivity analysis to measurement error reinforce the reliability of our findings. Finally, our empirical results provide important insights. We find for all specialties a significant positive spatial autocorrelation (dependence) in prices. This means that physicians’ prices are strategic complements as a physician’s price increases with its competitors’ prices. Moreover, we validate our prediction that the strength of strategic complementarity in prices increases with physician density. According to our theoretical model, a positive spatial dependence in prices also reflects a market where incentives to compete for quality are low. Our findings corroborate this, as we do not find a significant impact of consultation quality on physicians’ prices. Our empirical results also suggest the potential existence of noncompetitive behavior, especially for ophthalmologists and gynecologists. Indeed, for these two specialties, prices increase with both the competition intensity measured by the average distance to first-degree contiguity competitors and the effective level of competition measured by the proportion of free-billing physicians among competitors.

The body of evidence collected in our study points towards a type of market that provides weak incentives to react to classical competitive mechanisms (both vertical and horizontal differentiation). In the context of increasing spatial concentration of physicians in metropolitan areas, our results highlight key mechanisms to explain the continuous (and heterogeneous) rise of additional fees in France.

The rest of the paper is organized as follows. In Section 2, we introduce core related literature and present the French primary care system. Section 3 develops the circular city model with heterogeneous free-billing physicians. In Section 4, we detail the construction of our database and introduce descriptive statistics. Section 5 presents the structural spatial econometric models tested and our identification strategy. Section 6 provides our empirical results and simulations. Conclusions are presented in Section 7.