Does Health Insurance Encourage the Rise in Medical Prices? A Test on Balance Billing in France

Our purpose is to evaluate the influence of health insurance coverage on the use of specialists who balance bill. We estimate the impact on patients' behavior of a shock consisting of better coverage of balance billing, while controlling for supply side drivers. We use a panel data set of 43,111 French individuals observed between January 2010 and December 2012. Individuals are observed when they are all covered by the same supplementary insurer, with no coverage for balance billing, and after 3,819 of them switched to other supplementary insurers which offer better coverage. Our estimations show that better coverage contributes to a rise in medical prices by increasing the demand for specialists who balance bill: for individuals who enjoy better coverage the proportion of consultations of specialists who balance bill is increased by 9%, and balance billing charged per consultation by 32%. However, the impact of the coverage shock depends on local supply side organization. When the proportion of specialists who do not balance bill their patients is high enough, patients have a real choice between specialist type: there is neither evidence of an inflationary effect of supplementary coverage, nor of limits in access to care due to balance billing.


Introduction
Designed to favour equity in access to care, social health insurance is widespread in the European Union and most developed countries. Many debates have focused on its sustainability, which relies on the ability of health care systems to contain health expenditure growth. But little attention has been devoted to the fact that the eectiveness of coverage depends on the regulator's ability to control medical prices. As concerns ambulatory care, national health insurance systems usually set prices or sign agreements with physicians to set a regulated fee, which is the basis for public reimbursement.
Nevertheless, physicians can generally "balance bill" their patients, i.e. charge them more than the regulated fee. Since balance billing can lead to high out of pocket expenditures, patients often purchase supplementary health insurance (SHI) to cover this nancial risk. However, generous health insurance coverage can cause welfare loss, not only because it might favour excessive consumption of care, but also because health care providers can increase their prices (Pauly (1968), Feldstein (1970), Feldman and Dowd (1991)). Hence comprehensive coverage might favour demand for expensive physicians, resulting in an increase in balance billing. This increase leads to a rise in SHI premiums for patients who have subscribed to such insurance, and jeopardizes coverage for patients who are covered by social health insurance only.
Balance billing was already a political issue in the United States in the late 1980s. Physicians were allowed to charge their Medicare patients more than the copayment set by the federal health insurance for the 65+ years old. In 1984, balance billing amounted to 27% of the total out-of-pocket payments charged to Medicare beneciaries for physician consultations.
Concerns about possible degradation of health care coverage led several states to restrict balance billing, and the federal government followed suit. The Omnibus Budget Reconciliation Act of 1989 imposed restrictions on balance billing. It was eventually limited to a maximum of 9.25% of the Medicare fee in 1993 (see McKnight (2007) for a full description of Medicare's balance billing reform). Similar decisions were taken in Canada at the end of the 1980s.
In France, a large proportion of specialists are allowed to balance bill their patients. The population is covered by mandatory National Health Insurance (NHI) and for each service provided, there is a reference fee set by agreement between physicians and the health insurance administration. The NHI covers 70% of the reference fee for ambulatory care. In addition, individuals can take out supplementary private insurance: either voluntarily on an individual basis, or through occupational group contracts. Currently, 94% of the French population is covered by a supplementary health insurance contract. Supplementary insurance contracts cover the 30% of ambulatory care expenses not covered by National Health Insurance. In addition they can oer coverage for balance billing.
Concern about balance billing is rising in France because it has doubled over the last 15 years and now represents 2.3 billion euros. This expansion is due to an increase in both the average amount of balance billing (a 1.7% increase by year between 2004 and 2011) and the share of doctors (mostly specialists) who balance bill their patients. On the one hand, policy makers can take advantage of balance billing which permits an increase in physicians' earnings with no additional burden on social health insurance. On the other hand, balance billing raises out-of-pocket payments and might lead to a two-tier health care system where only rich people can aord specialists who balance bill their patients. Moreover, the last ten years have been marked by a continuous extension of balance billing coverage by SHI, together with a continuous increase in the amounts of balance billing, suggesting that coverage encourages balance billing. In keeping with this idea, the French government has recently introduced tax reductions to favour insurance contracts that limit their coverage of balance billing.
Balance billing in the context of social health insurance raises the following policy questions: should it be forbidden or restricted (as for Medicare patients in the USA)? Should coverage of balance billing be restricted (as recently decided in France)? On the contrary, should the government favour balance billing to promote a higher level of care quality? Or should the government only monitor the supply of care, to see that all patients have a real choice, i.e. eective access to physicians who do not balance bill their patients?
The purpose of this paper is to measure the causal impact of a positive shock on supplementary health insurance coverage on recourse to physicians who balance bill. The econometric analysis is performed on a French database of 43,111 individuals observed between 2010 and 2012 and covers the use of specialist consultations in ambulatory care. In addition to measuring the impact of insurance coverage on balance billing, we address two related issues: the inuence of supply organization on balance billing (i.e. distance to physicians, and access to physicians who do not balance bill), and the possible impact of balance billing on access to care.
What is the impact of balance billing on social welfare? After restrictions on balance billing were decided on in the USA, several theoretical papers attempted to predict the eects of such a reform on social welfare. The papers by Paringer (1980), Mitchell & Cromwell (1982) and Zuckerman and Holahan (1989), assume that physicians face a downward-sloping demand curve and do not dier in the quality of care they provide but are able to price discriminate their patients. If physicians accept to treat fee-only patients, social welfare is unchanged: balance billing results in a transfer of surplus from patients with a high willingness to pay to physicians. More recent papers assume that physicians are not homogeneous, and can discriminate between patients in price and quality (Glazer and McGuire (1993); Kifmann and Scheuer (2011)). These papers conclude that balance billing contributes to an improvement in welfare because quality is higher both for fee-only and balance-billed patients. A key assumption is that physicians have perfect information about patients' willingness to pay and are able to price discriminate perfectly. Jelovac (2013) points out that this assumption is unrealistic. She assumes that physicians do not have perfect information about patients' ability to pay. On this basis, she nds that balance billing can reduce access to care and consequently lower social welfare.
Empirical evidence about limits on access to health care that are attributable to balance billing is rather scarce and inconclusive. Using US data, McKnight (2007) nds that the restrictions imposed on balance billing reduced out of pocket payments by 9%. However, she does not nd any evidence of an increase in health care use, which supports the idea that balance billing acts solely as a mechanism of surplus extraction and does not hinder access to care. On the other hand, a rather descriptive analysis on French data shows that reductions in recourse to health care are more frequent in regions where balance billing is more widespread (Desprès et al. (2011)).
The literature devoted to the impact of health insurance on the market for health care can shed light on the question of the impact of health insurance on balance billing. If more insurance raises demand, this should increase medical prices. On the supply side, early papers studying the inuence of health insurance on medical prices date from the 1970s. According to Feldstein (1970Feldstein ( , 1973 physicians respond to health insurance coverage by increasing their fees. Using US data, Sloan (1982) showed that a 1$ increase in health insurance coverage results in a 13 to 35 cent increase in physicians' fees. These results are in line with theoretical predictions (see for instance Chiu (1997) and Vaithianathan (2006)). On the demand side, moral hazard relies on the sensitivity of demand to prices (Einav, Finkelstein et al.(2013)): assuming a negative price-elasticity of demand, better coverage leads to an increase in health care use.
In this paper, we examine the impact of the generosity of supplementary insurance coverage on the amount of balance billing per consultation, on patients' propensity to use specialists who balance bill, and on patients' recourse to specialists.
For that purpose, we evaluate the impact on patients' behavior of a shock consisting of better coverage of balance billing, while controlling for supply side drivers, i.e. proportions of physicians who balance bill and physicians who do not. In our framework the impact of coverage on health care use is mostly linked to the inuence of insurance coverage on demand for care quality and as a result, on prices set by care providers. It depends on patient's belief regarding the quality of care provided by physicians who charge balance billing and on the cost of access to physicians who do not balance bill their patients. In a way, focusing on balance billing enables us to investigate the content of moral hazard in one specic case.
Our database stems from administrative data provided by the Mutuelle Générale de l'Education Nationale (MGEN ). We use a panel dataset of 43,111 individuals observed between January 2010 and December 2012, which provides information, at the individual level, on health care claims and reimbursements provided by basic (NHI) and supplementary (SHI) insurance. Our data makes it possible to observe enrollees when they are all covered by the same supplementary insurer (MGEN ), with no coverage for balance billing, and after some of them switched to other supplementary insurers which oer better coverage. So, we have at our disposal a treatment group, the "switchers", and a control group, the "stayers", made up of those who did not leave the MGEN SHI. Our question is the following: Does an improvement in supplementary coverage induce an increase in balance billing per consultation or only an increase in the number of consultations? In the former case, patients would choose more expensive care thanks to their better coverage. In the latter, their would not really have a choice between physicians who balance bill and physicians who do not: the main impact of balance billing would be to limit access to care.
On the whole sample, we nd that better coverage leads individuals to raise their proportion of consultations of specialists who balance bill by 9%, which results in a 32% increase in the amount of balance billing per consultation.
However, the impact of the coverage shock depends on the organization of supply for care, more precisely on conditions of access (or distance) to physicians who balance bill and to physicians who do not. We can measure physician availability by the local specialist:population ratio. When this ratio is high for physicians who balance bill, the sensitivity to a coverage shock depends on whether the local specialist:population ratio (availability) of local physicians who do not balance bill is high or not. When it is high, then a coverage shock has no eect on recourse to expensive physicians or on the amount of balance billing. On the contrary, when it is low (physicians who do not balance bill are scarce), a coverage shock has a strong impact: individuals raise their proportion of consultations of specialists who balance bill by 22%, which results in a 92% rise in the amount of balance billing per consultation; in addition, there is evidence of limitation in access to care for a minority of individuals in this situation (10% of the sample). On the other hand, when there are very few physicians who balance bill, a coverage shock has no impact on patient behavior (10% of the sample). These results are obtained with instrumental variable estimates on models with individual xed eects, hence controlling for unobserved individual heterogeneity and for non exogeneity of the decision to switch to a more generous SHI.
To sum up, we nd evidence of moral hazard and, for some individuals, of limits in access to care due to balance billing. However, our main result is the absence of impact of a coverage shock when people can choose between physicians who balance bill and physicians who do not. On the basis of these results, the appropriate policy is not to limit the extent of coverage, but to monitor the supply of care in order to guarantee patients a real choice of their physicians. This paper is organized as follows. Section 2 describes French regulation of ambulatory care, and formalize, in this context, patients' decisions to consult a physician who balance bill. In section 3, we present our data and empirical strategy.
Section 4 makes explicit the empirical specication. Results and robustness checks are presented in Section 5 and section 6 concludes. Tables and gures are displayed in Appendix.
2 French regulation of ambulatory care and balance billing In France ambulatory care is mostly provided by self-employed physicians paid on a fee-for-service basis. Since 1980, physicians can choose between two contractual arrangements with the regulator. If they join "Sector 1", physicians are not permitted to balance bill. They agree to charge their patients the reference fee (23e in 2012 for a routine visit), and get scal deductions in return. If they join "Sector 2", they are allowed to set their own fees. Access to Sector 2 being strongly limited for GPs since 1990, most of them belong to Sector 1: they are 87% in 2012. Hence the issue of balance billing concerns mostly specialists. Balance billing adds 35% to the annual earnings of Sector 2 specialists. The average proportion of specialists operating in Sector 2 amounts to 42% in 2012. However, this proportion varies dramatically across regions and specialties: for instance, the proportion of specialists operating in Sector 2 is 19% for cardiologists, 73% for surgeons and 53% for ophthalmologists.
The net price faced by patients for a consultation depends on whether or not they consult a Sector 2 specialist, and on their SHI coverage. Currently, coverage of balance billing varies between SHI contracts: on the one hand, a sizeable proportion of SHI subscribers are not covered for balance billing (52% of subscribers on an individual basis). One the other hand, 48.5% of all SHI policyholders (individual contracts and occupational group contracts altogether) state that they are well covered for balance billing (Celant and alii (2014)).

The decision to consult a Sector 2 specialist
Sector 1 and Sector 2 specialists are supposed to provide the same medical service and balance billing amounts to charging a higher price for the same thing. However, access to Sector 2 is restricted from 1990 on to physicians who are able to demonstrate a qualifying hospital practice, which suggests that they have a higher education and more ability.
Apart from this fact, patients have no information on possible dierences in quality of care provided by physicians. In this context, physician's choice to belong to Sector 2 can be seen as a signal about his ability (Spence (1973)) and patients might prefer to consult a Sector 2 physician to have a better chance to get high quality of care (see also Batifoulier and Bien (2000)). Nevertheless, besides the issue of care quality, other potential dierences between Sector 1 and 2 specialists are observable: if there is a local shortage in Sector 1 specialists, consulting a sector 1 specialist exposes the patient to search costs, waiting time and transportation costs, whereas Sector 2 specialists can be more accessible. 1 Consider a utility maximizing patient: he/she chooses the levels of consumption of non-medical goods (z) and of specialist consultations to Sector 1 and Sector 2 physicians (x 1 and x 2 ) in order to maximize U (z, h(x 1 , x 2 )) under a budget constraint. h is the level of patient's health, given by a subjective health production function: where h 0 is the level of health without any specialist consultation. The ouput provided by g(x 1 , x 2 ) depends on a patient's beliefs regarding the productivity and quality of consultations to Sector 1 and Sector 2 specialists.
Consider p the regulated fee and bb the level of balance billing. As stated above, all supplementary insurance contracts cover the share of the regulated fee which is not covered by National Health Insurance (NHI), i.e. 30 % for a consultation. 2 In addition some SHI contracts oer coverage of balance billing. We denote γ the rate of coverage by the mandatory National Health Insurance (NHI), c the minimal rate of coverage oered by all supplementary health insurers (copayment coverage), and s the balance billing coverage oered by some SHI. The cost of access to Sector 1 or 2 specialists is also inuenced by their availability, which can be measured by the local specialist:population ratio. We denote d 1 and d 2 the search costs, as well as transportation and waiting time costs associated to the access to a Sector 1 or a Sector 2 specialist. d 1 and d 2 are linked to the local specialist:population ratios of Sector 1 and 2 specialists.
Hence, the total cost of a consultation of a Sector 1 specialist is: p 1 = p(1 − γ − c) + d 1 ; and the total cost of a consultation of a Sector 2 specialist is: Given that all individuals in our sample are fully covered for copayments, 3 the relative price of a Sector 2 consultation is given by: 4 Given this formalization, the decision to consult a Sector 2 specialist is described in Figure 1, where the curves are isoquants relative to patient's subjective health production function. The iso-cost lines have a slope equal to the relative price p 2 p 1 . The graph assumes that the patient believes that consultations of a Sector 1 and Sector 2 physician are substitutable. In this framework, an increase in balance billing coverage (say, from s = 0 to s > 0) induces an increase in the use of Sector 2 physicians. The magnitude of the impact depends on the availability of Sector 1 physicians. Indeed, the variation of the relative price with respect to s is Note that Figure 1 does not represent the case where Sector 2 physicians are very scarce. In this case, p2 p1 → ∞ whatever the value of s: in this situation, a change is SHI coverage should have no eect on recourse to Sector 2 physicians. Another specic case is when the patient believes that Sector 1 and Sector 2 physician are perfectly substitutable: this leads to corner equilibria, with only Sector 1 or only Sector 2 consultations, depending on the value of p 2 p 1 and on g(.) parametrization.

Availability of Sector 1 and Sector 2 specialists
As stated above, supply side organization can inuence the recourse to Sector 2 specialists. Figure 2 provides geographical information about the specialist:population ratio of Sector 1 and Sector 2 specialists by département (there are 95 départements in France). The specialist:population ratio is an indicator of physicians' availability, i.e. of search, transportation and waiting time costs associated to access to a Sector 1 or a Sector 2 specialist. Figure 2 shows that there is not always an inverse relation between the specialist:population ratio of Sector 1 specialists and the specialist:population ratio of Sector 2 specialists: on the Mediterranean cost, there are many of both types of specialists. Conversely, in Brittany (North-West of France), there are many Sector 1 specialists and very few Sector 2 specialists. It is the reverse in the Parisian region, with many Sector 2 specialists and very few Sector 1 specialists. Figure 3 gives for each département, the proportion of Sector 2 specialist consultations and average balance billing per consultation, as computed on our sample. The comparison with gure 2 suggests a strong impact of supply side drivers on both propensity to see a sector 2 specialist and the amount of balance billing.

Data and empirical strategy
We use a panel data set from a French supplementary insurer: Mutuelle Générale de l'Education Nationale (MGEN ).  Switchers' decision to leave in 2011 creates a positive shock on their SHI coverage. Therefore, we can use Stayers and Switchers as control and treatment groups [see Figure 4].
Actually, we do not observe switchers' coverage for balance billing after they quit MGEN. However, since MGEN coverage on balance billing is zero we know that their new coverage will be at least equal and probably better than before.
Hence our estimated impacts should be interpreted as "intent-to-treat" (ITT) eects. These are likely to understate the real impacts of a better insurance coverage and should be interpreted as lower-bounds.
The original sample was made of 91,629 stayers and 8,249 switchers. For the purpose of the study, we decided to over-represent switchers: in our data the proportion of switchers is not representative of the actual switching rate, which amounts to 0.5%. We excluded the people who lived in départements or territoires d'outre-mer (outside territories such as Guadeloupe, Martinique, etc.) and the 1% top care users in 2010 or 2012 (more than 28 consultations a year for stayers, 30 for switchers). As stated above, balance billing is not an issue for GPs ; hence we focus on specialist consultations.
More precisely, we measure the eect of insurance coverage on the decision to visit a specialist who charges balance billing, conditional on the use of specialist consultation. Therefore, we restricted the sample to individuals who had at least one specialist consultation in 2010 and 2012 (Spe=1). They represent 45% of stayers and 48% of switchers. To sum up we will use a sample of 43,111 individuals whose 39,292 are stayers and 3,819 switchers; they are observed in 2010-2012 and have at least one specialist consultation.

Variables
Our data provide information at individual level about the total number of specialist consultations (denoted Q), the number of consultations of a Sector 2 specialist (Q2) and the total amount of balance billing (BB). Our variables of interest are the number of specialist consultations Q, the proportion of consultations of Sector 2 specialists Q2/Q, the average balance billing per consultation, BB/Q and the average balance billing charged per Sector 2 consultation, BB/Q2 (this latter indicator is computed on individuals who had at least one visit to sector 2 specialist (Spe2=1)).
Using these four indicators allows us to distinguish between patients' use of specialists, patients' decision to consult a Sector 2 specialist, and the level of balance billing charged which depends on price setting by specialists on the supply side, and on demand for expensive specialists (as a signal of quality) on the demand side. Of course, the average amount of balance billing per Sector 1 or 2 consultation (BB/Q) is inuenced both by the proportion of Sector 2 consultations and the associated balance billing level.
At the individual level, we can only compute an indicator of average balance billing. Indeed, our data provides information on the number of consultations for each specialty in Sector 1 and Sector 2 but not on the fees associated to each consultation. However, we can take advantage of the specialty needed by patients to control for the extent of their choice as concerns Sector 1 or 2 specialists. In France, gynaecologist, ophthalmologist, surgeon and ENT specialists charge balance billing in a much larger proportion than their colleagues. As a result, it is much more dicult to avoid a Sector 2 physician for a patient whose health care needs imply a recourse to one of these specialists, and the balance billing per consultation is inuenced by patient's care needs. To deal with this heterogeneity, we introduce a dummy variable referring to "expensive physicians" (Exp.P hy), which is equal to 1 when the individual visits at least one of these specialists.
Demand characteristics include gender, age, income and health status. Our income variable refers to the individual's wage. It is computed using the fact that premiums are proportional to individuals' wages. Because premiums are limited by lower and upper bounds for monthly wages lower than 1,000 and higher than 4,900e, this proxy is close to a truncated individual wage. As concerns health status, we know if the patient has a chronic disease (CD = 1). Supply side characteristics include consultations to a GP, specialist:population ratios and the Exp.P hy dummy variable. In France, one can visit a specialist without seeing a GP before. More exactly, patients do not need their GP's agreement to consult gynaecologists or ophthalmologists. For other specialties GPs are gatekeeper and their consent determines the extent of national health insurance reimbursement. 5 We control for this specic feature with a dummy indicating that the patient had at least one visit to a GP in the current year (GP = 1). Supply side organization is taken into account using specialist:population ratios, at the départment level in Sector 1 (SPR1) and 2 (SPR2). We introduce an interaction between Sector 1 and 2 specialist:population ratios to allow for non linear eects. Information on specialist:population ratios comes from data provided by the NHI, 6 which are available only for 2010 and 2011. Waiting for a forthcoming update, we use information relative to 2011 for year 2012.

Basic features of the data
Since MGEN enrollees are mostly teachers, the sample is not representative of the French population [ Table 1]. They are mostly women (65%), their average age is 55, and the average monthly wage is equal to 2434e, which is higher than the average wage in France. We caution against generalizing our results to dierent settings, because we are likely to deal with a specic population as far as health habits, values and risk aversion are concerned.
A result common to many papers devoted to competition in health insurance is the higher propensity of young, healthy and highly educated individuals to switch companies (Dormont et al. (2009)). We nd the same characteristics for people who decided to leave MGEN SHI: they are much younger (42.5 versus 55.4) and healthier than stayers (only 6.8% have a chronic disease, versus 17.5%). Contrary to results found in the literature, switchers have lower income than stayers. This is due to the fact that MGEN enrollees are all teachers: hence wage variability is reduced in comparison with a sample which would be drawn on the whole population; in addition, the remaining variability is strongly correlated with age because promotions are mostly decided on the basis of seniority. So, in our case, switchers have a lower income because they are on average thirteen years younger than stayers. Table 2 displays statistics about recourse to specialist, proportion of Sector 2 consultations and amount of balance billing for stayers and switchers in 2010, i.e. when both had no coverage for balance billing. These statistics depict heterogeneity in preferences and situations for individuals who have the same coverage. On average, stayers and switchers use respectively 3 and 3.2 specialist consultations in 2010. The proportion of Sector 2 consultations is signicantly higher for switchers than for stayers: 51.6% instead of 44.6%. As a result, switchers pay signicantly more balance billing, in total (41e versus 30e), per consultation and per Sector 2 consultation. So, even when they had no coverage for balance billing, switchers consumes more Sector 2 specialists and paid more balance billing than stayers.
The second column of table 2 gives, for each indicator, the mean and standard deviations for observations that are higher than the 99 percentile (average of the top 1%). The top 1% average values of balance billing show that, even with a SHI contract, individuals are not protected against high out-of-pocket expenditures: 433e for stayers and 505e for switchers. This is especially true because these gures are computed on a sample, whose top 1% consultation users have been already excluded: on the whole sample, we nd top 1% average balance billing that are equal to 638e for stayers and 914e for switchers. 6 SNIR (Syndicat National Inter Régimes), provided by CNAMTS (Caisse Nationale d'Assurance Maladie des Travailleurs Salariés) .
The two last columns of table 2 display, for each indicator, the mean and standard deviations computed for individuals living in places characterized by low or high levels of Sector 2 specialist:population ratio. We nd a strong inuence of supply side organization: dierences between stayers and switchers are signicant only in places where Sector 2 specialists are numerous (in last column).

Empirical specication
The Y it denotes the dependent variable, which is one of the four indicators of interest: log(Q), log(Q2/Q), log(BB/Q) and log(BB/Q2). We introduce individual xed eects α i . The disturbance ε it is supposed to be iid (0, σ 2 ε ).
Specifying a xed eect α i enables us to allow for a potential non exogeneity of the decision to leave MGEN that would arise from a correlation with individual unobserved heterogeneity. These eects are likely to be connected to switchers' permanent beliefs in better quality of care in Sector 2, or specic disutility of time consuming transportations and search eort. Decision to leave MGEN might also be induced by a transitory shock on health care needs (illness onset, that we cannot observe perfectly, although we observe and control for the onset of chronic diseases) or by an information shock that aects beliefs regarding quality of care in Sector 2. In this case, there is a correlation between it and the decision to leave MGEN. For this reason, we have performed an instrumental variable estimation of equation (2), in order to obtain a consistent estimation of the causal impact of an improved coverage on Y it (i.e. the use of specialist consultations, the proportion of sector 2 consultations and the amount of balance billing per consultation).
A reliable instrument has to be correlated with the decision to leave MGEN (QU IT ) and must not aect directly the dependent variable Y it . We have at our disposal two variables that are good candidates to be relevant instruments, and appeared to be exogenous and well correlated with QU IT . We used the decision to retire in 2011 for people younger than 55 and the decision to move in 2011. The threshold chosen for retirement age refers to a specic right for teachers that allowed those who raised three kids to retire before they were 55. This right has been revoked recently and eligible teachers had to use this opportunity before January 2012. Hence the propensity to retire before 55 rose strongly between 2010 and 2011, as shown in Figure 5. This policy decision creates an exogenous shock that gives us a good instrument.
Indeed, a high number of teachers retired in 2011 before they were 55 and decided to leave MGEN SHI the same year.
Moreover, the rules dening the MGEN premium entail a rise in the proportion of income from 2.97% before retirement to 3.56% after. This shock on premium is likely to be a reason to leave which is uncorrelated with health care needs or beliefs in the quality of care is Sector 2. We also use the decision to move in 2011 as an instrument for the decision to quit MGEN for SHI. Indeed, moving always induces high administrative costs that are likely to reduce the reluctance to face the relatively limited costs associated to a switch of SHI. The results of the Sargan tests we have performed show that these two instruments, "moving in 2011" and "retired before 55" are compatible. Used together, they increase the estimator's precision on the whole sample. Note that we have no accurate information on individuals' adresses: we observe the occurrence of a move only when people have moved in another département. Actually the instrument "moving in 2011" cannot be used for the estimations we performed on sub-samples: the move must occur within the sub-sample, which eliminates too many observations.

Results
Our results are displayed in tables 3 and 4. Table 3 gives the estimates of the causal impact of better coverage on the four indicators Y it . Table 4 presents the estimations of the other regressors' inuence and of individual xed eects.
Several tests support the consistency of our instrumental variable estimates. For estimations performed on the whole sample, it was possible to perform Sargan tests which all led to a non rejection of instrument compatibility. 7 In addition, we examined whether our estimations could be subject to the weak instrument problem. For this purpose, we tested for the signicance of the excluded instruments in rst stage regressions. We found a large signicance of the partial correlation between the excluded instrument and QU IT , with high F statistics 8 . Following Bound, Jaeger and Baker (1995), this suggests that we can rule out instruments' weakness. We rely on IV results when Hausman tests led to a rejection of QU IT exogeneity. Otherwise we can rely on OLS estimates, which are consistent with IV estimates when QU IT is exogenous. Recall that all estimations include individual xed eects. Of course, IV estimates provide local average treatment eects (LATE).
5.1 Impact of better coverage on recourse to Sector 2 specialist and balance billing Table 3 provides the OLS and IV estimates of parameter τ , which is the impact of the coverage shock for the whole sample (line 1) and various sub-samples (lines 2-9), on recourse to specialist, the proportion of sector 2 consultations and the amount of balance billing per consultation. For each line and dependent variable we also provide the Hausman test p-value (rejection of QU IT exogeneity when it is lower than 5%). As stated above, we control for unobservable individual heterogeneity and potential non-exogeneity of QU IT . Note that a more simple dierence-in-dierences approach which compares stayers and switchers between 2010 and 2012 led to the same results than our OLS with xed eect estimates.
On the whole sample (line 1), better coverage has no impact on recourse to specialist (log(Q)) but increases by 9% the share of Sector 2 consultations, which results in a 32% increase in the amount of balance billing per consultation. Hence, because it raises demand for Sector 2 physicians, better coverage by SHI is likely to encourage the rise in medical prices.
However, we do not nd a signicant eect of better coverage on the price for S2 consultations (log(BB/Q2)): patients who used to visit S2 specialists do not take advantage of their better coverage to visit even more expensive physicians.
This suggests also that physicians do not adjust their prices to their patients' coverage, at least in the short run.
As concerns signicant coecients, we nd 2SLS estimates that are larger than the OLS estimates (see, for instance, table 3, line 1). At rst view, it seems surprising to nd a negative endogeneity bias, given that people are supposed to quit to enjoy a better coverage for balance billing. In fact, such negative bias is quite possible: given that our specications allow for an individual xed eect, the IV estimation mostly corrects bias due to transitory health shocks. These shocks can be positively or negatively correlated over time, but a negative correlation is more likely because the onset of a chronic disease is captured through a dummy variable in the regressors. Taking the example of a tibia fracture, the patient experiences a lot of consultations with large balance billing and decides to quit MGEN in 2011 for better coverage. In 2012, her needs in sector 2 specialist consultation are lower because she has recovered (however, our IV estimates show that for a given level of needs she uses more sector 2 specialists than before quitting, because of the improvement in coverage). 9 9 A simple model enables us to compute the bias. For individual i, denoting the year by t = 10, 11 or 12, we have: where bb is the use of balance billing and quit is the decision to quit in 2011. We suppose a > 0: people are likely to quit for better coverage in relation to the balance billing they were charged during the previous year (side regressions we have performed give empirical support to a > 0, results are available on request). Formally, the model above removes all control variables (density levels, income, chronic disease indicator, etc.) by taking the residuals of the projections of balance billing and quit on these control variables (Frish-Waugh theorem). v i (respectively, u i ) is an individual xed eect referring to the disutility of transportation costs for i (respectively, to i s risk aversion). u i and v i are supposed to be uncorrelated. ε and η are transitory health shocks inuencing decision to quit and the use of specialists who balance bill their patients. ξ is the transitory policy shock related to the repeal after 2011 of the possibility to retire before 55. ξ is supposed to be uncorrelated with v, ε and η. Denoting τ ols the OLS estimator of τ , one has: p lim τ ols = τ + a σ 2 v σ 2 q + σεη σ 2 q , where σ 2 v and σ 2 q denote the variances of v and quit , and σεη denotes the covariance between ε i,11 and η i,12 . In xed eect estimations, v i is removed from the specication and the asymptotic bias becomes: p lim τ ols,F E = τ + σεη σ 2 q . It has the same sign as σεη, which can be positive or negative. 5.2 The eect of supply side organization on the impact of better coverage As stated above the relative price of a Sector 2 consultation is not only inuenced by balance billing coverage s, but also by search and transportation costs d 1 and d 2 to reach a Sector 1 or 2 specialist. One has: p2 p1 = (bb−s)+d2

d1
. Hence supply side organization should have a strong impact on recourse to Sector 2 specialists and balance billing. As shown in gure 2, local availability of Sector 1 and 2 specialists varies dramatically across départements. This is likely to induce an heterogeneity in the impact τ of better coverage, that we examine in what follows 10 .
To check this prediction, we have performed separate estimations of model (2) on regions dened as groups of départements. On the basis of gure 2, three regions are considered: Ile-de-France (in the center of France including Paris), PACA-Aquitaine-Alsace-Rhône (Côte d'Azur, East and South-West of France), and Normandie-Bretagne-Pays de Loire (West and North-West). We nd very dierent impacts between regions. In Ile-de-France and PACA-Aquitaine-Alsace-Rhône, (lines 2 and 3 on Table 3), where there is a lot of Sector 2 specialists, better coverage induces more Sector 2 consultations and balance billing. On the contrary, in Normandie-Bretagne-Pays de Loire, where there are very few Sector 2 specialists, we nd no signicant impact of better coverage on any indicator of care use or recourse to Sector 2 specialists (line 4 on Table 3).
To investigate more thoroughly the inuence of local availability of Sector 1 and 2 specialists on the impact of QU IT , we have dened sub-samples on the basis of the local levels of Sector 1 and Sector 2 specialist:population ratios. Lines 5 and 6 of Table 3 oppose areas with low and high Sector 2 specialist:population ratios, a low (resp. a high) level of specialist:population ratio being dened as belonging to the rst (resp. the last) quartile of SP R2 distribution across départements. We nd no eect of better coverage when there are very few Sector 2 specialists (line 5). In this case, better coverage does not change the main reason why patients do not visit Sector 2 specialists: they cannot manage to nd or reach one ( p2 p1 → ∞). On the contrary, when there is a lot of Sector 2 specialists (line 6), better coverage induces a 18% increase in the proportion of consultations of Sector 2 specialists, which results in a 75% increase in the amount of balance billing per consultation. This is pure substitution: the total number of consultations in unchanged.
However, these estimated impacts could again hide heterogenous impacts within the areas with a high level of Sector 2 specialists. Indeed, when d 2 is nite, we have: , suggesting that the impact should depend on the availability of Sector 1 specialists. To investigate this, we split the areas characterized by a high level of Sector 2 into two sub-samples: the one with a high level of Sector 1 specialist:population ratio, the other one with medium and low levels of SP R1. The results are striking: when Sector 1 specialists are numerous (line 7, Table 3), a coverage shock has no impact on recourse to Sector 2 specialists and balance billing. In other words, when patients have a real choice, we do not nd evidence of moral hazard. Conversely, when Sector 1 specialists are not numerous (line 8), we nd larger impacts: better coverage induces a 22% increase in the proportion of consultations of Sector specialists, and a 92% increase in balance billing.
Finally, we nd evidence of limits in access to care on a restricted sub-sample (line 9), relative to areas characterized by both profusion of Sector 2 specialists and scarcity of Sector 1 specialists. This is the only case where we nd a signicant impact of better coverage on the quantity of specialist consultations Q, with a 55% rise, in addition to impacts on the share of Sector 2 consultations and on the average balance billing per consultation. This result suggests that due to the lack of Sector 1 specialists in these areas, aordable care is restricted and leads some individuals to give up on specialist consultations. Note that this evidence of limits in access to care concerns a small proportion of individuals in our sample (10%).

Adverse selection eects and other determinants of balance billing
We now focus on the respective eects, ceteris paribus, of supply side organization, income and chronic diseases on specialist visits, use of S2 specialists and average amount of balance billing per S2 consultation. Table 4 presents the estimates of parameters λ, β 1 and β 2 resulting from OLS applied to equation 2 with xed eects, for the four indicators Y it . For these coecients, magnitude and signicance of 2SLS estimates are indeed similar. Supply side organization directly impacts the amount of balance billing through two mechanisms: the more or less constrained choice to consult a S1 or a S2 physician and the price of S2 consultations. For some specialties such as gynaecologists, surgeons, ophthalmologists or ENT specialists, the proportion of S2 specialists is especially high (above 50%) making the choice to visit a S1 or a S2 specialist heavily constrained. Indeed, we nd that a visit to one of these specialists is likely to increase by 79% the average amount of balance billing per consultation. Competition between S2 physicians seems to lead to an increase in the price of S2 consultations. For the average value of S1 specialist:population ratio (50 physicians for 100,000 people), a 1% increase in S2 specialists:population ratio increases the average price of a Sector 2 visit by 1.4%.
Contrary to supply side eects, other determinants such as income or health status do not impact the consumption of balance billing. An increase in income does not change the recourse to S2 specialists. However, we nd a signicant eect on the total number of visits to a specialist: a 1% increase in income increases the total number of visits by 0.16%.
Individuals with higher health care needs do not change their use of S2 specialists either. Indeed, patients who suer from a chronic disease are likely to increase by 19% the number of visits but do not change their proportion of S2 visits.
Demand for S2 consultations can also be explained by unobservable individual preferences (beliefs in S2 quality, willingness to avoid waiting lists). Actually, we nd strong evidence of individual heterogeneity between Stayers and Switchers. To do so, we regress the dummy Switcher i on the estimated individual xed eects obtained in the panel data estimation. Obviously, with a two-year panel, we cannot expect our estimates of α i to be consistent. Nevertheless, we think relevant to examine the relation of these estimates with the propensity to use S2 specialists. Indeed, the average amount of balance billing per visit is 18% higher for Switchers than for Stayers. Regardless of their health insurance coverage, Switchers visit more often S2 specialists (the share of S2 is 3% higher for switchers) and those specialists charge them higher fees (+7%). This means that individuals with higher preferences for S2 visits are more likely to ask for better coverage. This nding is consistent with classical results on adverse selection.

Robustness checks
On the whole sample, our IV estimates are performed with two instruments ("retired before 55" and "moving") contrary to sub-samples estimates where only "retired before 55" is used. We have to check that IV estimates on the whole sample and on sub-samples remain comparable. So we checked that coecient magnitudes are similar when using only the "retired before 55" instrument on the whole sample, as for the sub-sample estimations. Results are similar in magnitude, with smaller precision (with no change as concerns impact signicance).
Moreover, our IV estimates measure the eect of a better coverage on a specic population which concerns mostly women between 40 and 55 years old. In addition to the fact that only a LATE is estimated here, we have to check the robustness of the results when restricting the sample of untreated to people that are similar to the treated that are captured by the instrumental variable. This is the case: our results are robust when we restrict the sample to women between 40 and 56 years old. Therefore, the eect of better coverage is not driven by compliers' demographic characteristics.

Conclusion
In this paper we evaluate the causal impact of a positive shock on supplementary health insurance coverage on the use of specialists who balance bill. We use panel data to control for unobservable individual heterogeneity and rely on instrumental variable methods to deal with the possible non-exogeneity of the decision to switch to a supplementary insurer that oers better coverage for balance billing.
In France, recourse to Sector 2 specialists (who balance bill) can be due to a belief that they provide better quality of care, or to diculties in access to Sector 1 specialists that include search, waiting time and transportation costs. We nd heterogeneity in preferences and beliefs that lead to more recourse to Sector 2 specialists. In particular, people who decided to leave MGEN, i.e. the switchers, are more likely to use Sector 2 specialists, ceteris paribus.
Our estimations show that better coverage contributes to a rise in medical prices by increasing the demand for specialists who balance bill. On the whole sample, we nd that better coverage leads individuals to raise their proportion of consultations of specialists who balance bill by 9%, which results in a 32% increase in the amount of balance billing per consultation. However, the eect of supplementary health insurance clearly depends on supply side organization. As might be expected, geographical areas where there are few sector 2 specialists are not aected by such moral hazard.
Interestingly, we nd no evidence of any impact of a coverage shock on recourse to Sector 2 specialists in areas where there are many Sector 1 specialists. About 34% of the sample are in these two cases (scarcity of Sector 2 specialists or availability of Sector 1 specialists) and therefore would not increase their use of expensive physicians if their coverage for balance billing were better.
On the contrary, when the Sector 2 specialist:population ratio is high and when Sector 1 specialists are not numerous, a coverage shock has a strong impact: individuals raise their proportion of consultations of Sector 2 specialists by 22%, which results in a 92% rise in the amount of balance billing per consultation (this concerns 25% of the sample). In addition, there is evidence of limitation in access to care due to balance billing for individuals living in areas characterized by both profusion of Sector 2 and scarcity of Sector 1 specialists. Indeed, better coverage enables them to increase their number of consultations. Although evidence of such limitation concerns only a minority of people (10%), it is worthwhile to stress that low-income individuals are under-represented in our sample because MGEN covers mostly teachers. Hence, our estimated eect of better coverage on access to health care should be interpreted as a lower-bound.
Our results enable us to tackle some current policy questions about balance billing regulation. We have found that generous supplementary coverage can encourage balance billing, and consequently have an inationary eect on medical prices. However, this inationary impact appears only when Sector 2 specialists are numerous and Sector 1 specialists relatively scarce. When people can choose between physicians who balance bill and physicians who do not, a coverage shock has no impact on the use of Sector 2 specialists. When the number of specialists who charge the regulated fee is suciently high (i.e. more than 56 specialists for 100,000 inhabitants), there is neither evidence of limitation in access to care, nor of inationary eect of supplementary coverage. As a consequence, the most appropriate policy is to monitor the supply of care in order to guarantee patients a real choice of physicians. Given that we have found heterogeneity in preferences such that some individuals prefer Sector 2 specialists, this policy allows for an improvement in welfare through a supply of insurance contracts oering balance billing coverage for those who want it. On the contrary, if policy makers are not able to ensure a sucient supply of sector 1 specialists, limiting insurance coverage can be a second best solution to contain the increase in medical prices.