Keywords:

Specifying agency relationships between the different actors in ambulatory care -the patient, the physician, the insurance and public authorities -allows to render an account of the complexity and the specificity of the health system. After a presentation of the normative approach of the agency theory, we will focus on two agency relationships : the relationship between the insurance and insured people and the relationship between the patient and the physician. The driving part of supply appears through the analysis of the relationship between the physician and the others : he is the agent of both the patient and public authorities. The issue is then the hypothesis of supplier induced demand that is subjected to an empirical estimation, based on French data, which of the methodological limits are inevitably stressed. Some rules of the game likely to be enacted in ambulatory care are at last cautiously brought forward.

Résumé

La spécification de relations d'agence entre les différents acteurs de la médecine de ville -le malade, le médecin, l'assurance et la tutelle -permet de rendre compte de la complexité et des spécificités du système de santé. Après une présentation de l'approche normative de la théorie de l'agence, l'accent est mis sur deux relations : la relation assurance assuré et la relation patient médecin. Le rôle moteur de l'offre apparaît à travers la relation du médecin avec les autres acteurs du système : agent du patient et agent des pouvoirs publics dans un jeu à trois protagonistes inégalement détenteurs d'information. On débouche alors sur l'hypothèse de la demande induite par l'offre, développée indépendamment de la théorie de l'agence, qui fait l'objet d'un modélisation économétrique et de tests à partir de données françaises dont on ne manque pas de souligner les limites méthodologiques. Quelques règles du jeu susceptibles d'être édictées en médecine ambulatoire sont alors prudemment avancées.

Mots clés : relations d'agence -information -médecine de ville -induc tion de la demande par l'offre -régulation -incitation.

In order to understand the functioning of the health system, the traditional approach to ambulatory care by the market considers the specific characteristics of the health sector as market imperfections. In this market, it encounters some limits such as, for instance, the lack of consensus on the nature of the medical services market : is it a competitive market, a monopolistic competitive one, and moreover, is it a discriminating or an increasing monopoly ? From another point of view, this approach considers the practitioner as an individual manager and, therefore, it doesn't take into account the deontology concern of medical practice, neither the driving force of supply in the conversion process of need into demand.

Finally it neglects the interaction between the medical services market and the medical insurance market. With regard to public authorities, they appear as being a more or less necessary evil, guarantor of the unquestionable rules of the game.

The agency theory allows to overtake some of these limits. In this paper, ambulatory care is analysed through the specification of complex agency relationships which exist between different actors : patient, physician, insurance and public authorities. Information is then in the heart of the processes of decision and of optimal resource allocation, with respect to the classical assumptions of rationality, which implies that agents (actors) will have the best possible use of the information they get. The dysfunctioning inherent to information assymetry is considered as adverse selection and moral hazard in which interaction drives to supplier induced demand. The inducement hypothesis is subjected to an econometric modelling and to an original empirical estimation, based on French data in which conjonctural and intrinsic methodological limits are underlined.

As a conclusion, some rules of the game are carefully suggested. They are susceptible to be applied to French ambulatory care in order to counter the dysfunctioning by incentive scheme in a context where the economic growth decline endangers the achievement of the three targets that make the originality of the French system : the guarantee in care access equity, the keeping of liberal medical practice principles and the health care cost-containment.

The observation of information structures brings authors as S. [START_REF]The Economic Theory of Agency. The Principal's Problem[END_REF], S. Shavell (1979aShavell ( et 1979b)), S.J. [START_REF] Grossman | An Analysis of the Principal-Agent Problem[END_REF] to interpret economic agents relationships in terms of agency relationships that are consequences of incomplete information allocation : the principal sollicits the services of an agent who gets specific knowledge.

Whenever information is lastingly asymmetric, whether the behaviour of some actors is hidden, or, suppliers and demanders cannot use the same information related to exchanged goods' characteristics, strategical behaviours emerge, implying resources misallocations called respectively moral hazard (K.J. [START_REF] Arrow | Uncertainty and the Welfare Economics of Medical Care[END_REF] and adverse selection (G.A. [START_REF] Akerlof | The Market for "Lemons" : Quality Uncertainty and the Market Mechanism[END_REF].

Framework of reference : perfect agency relationships

With S. Ross (1973 pl34) "we will say that an agency relationship has arisen between two (or more) parties when one, designated as the agent, acts for, on behalf of, or as representative for the other, designated the principal, in a particular domain of decision problems". The agent's intervention brings out outcome (income, profit or consumption) which should be devided up between principal and agent according to the conditions of implicit or explicit contract.

In an uncertainty context, the principal-agent problem is set up in the following terms : what is the risk-sharing, implying an expected outputsharing, which maximizes the principal expected utility under the agent rationality constraint ? The principal expected utility is function of the outcome of the agent's action. The agent's rationality constraint implies that the agent expected utility is above the one he will get without power delegation. The agent expected utility is function of the relative importance of the income he expects to receive and function of his effort.

Whenever the agent's effort is perfectly observed, the principal, solving his optimization programme, can control the agent at the time of the contract elaboration. It has been proved that:

-if the principal is risk neutral and the agent is risk adverse, the solution of the principal-agent problem, that is the optimal risk-sharing, is such as the principal takes over the whole risk ; the agent is completely "insured" by the principal. "This Pareto-optimal risk-sharing however has a m ajor disadvantage : the agent is no more incited to make efforts since his income is not function of this effort" (JJ. Laffont 1987 p6) : the agent chooses consequently a minimal effort level. Which means, a contrario, that any incentive scheme, implying that the agent is not completely "insured", will then make the equilibrium diverge from the Pareto-optimal one. -if the principal and the agent are both risk adverse, the optimal risk-sharing is such as the respective outcomes of the principal and of the agent are increasing functions of the action's output (cf diagram n°l from J.J. [START_REF] Laffont | Le risque moral dans la relation de mandat[END_REF].

1.2.The agency relationship with moral hazard.

Whenever the agent's behaviour is imperfectly observed, that is whenever the principal observes only the action's output, but not the achieved effort, the agent adopts a strategical behaviour : moral hazard makes consequently the agent's interest diverge from the one of the principal and deviate the equilibrium from a Pareto optimal situation.

The uncertainty is due not only to the intrinsicly stockastic characteristic of the output, but also to the interest divergence between the principal and the agent.(G. Charreaux, 1987, p 24). The information which the agent knows to be asymetric plays a similar part in wealth, and is a significant argument in agent's strategies (M. Mougeot, 1989, p 294).

A new constraint is added to the previous principal-agent problem: it reflects the fact that the agent chooses himself his effort level without the principal observing. It comes to include in the principal's programme a constraint equivalent to the first order condition of the agent's programme.

This representation, called "first order approach", is developped especially by S. [START_REF]The Economic Theory of Agency. The Principal's Problem[END_REF]), B. Holstrom (1979), S. Shavell (1979 b) and J. Mirrlees (1979). It has been proved (cf diagram n° 2) that the solution to the principal-agent's problem allows a second best sub-optimal situation, about which we have very little information (without restrictive assumptions), but it implies arbitration between effort incentive and "good" risk-sharing * Notations and assumptions y : a stochastic variable, result of the agent's action e : the level of the agent's effort F(y ; e ) ; f(y ; e) ; respectively the cumulative probability function and the probability distribution of y, influenced by e t(y): grants from the principal to the agent -The agent's utility function is supposed to be separable : 11] V(t(y) ; e) = v(t(y)) -w(e) v' > 0 ; v" < 0; w' > 0 ; w" > 0

-The individual rationality level of the agent, fixed to zero, is exogeneous. His individual rationality constraint is :

[2] EV(t(y) ; e) > 0 that is [3] Ev(t(y)) -w(e) > 0
-The principal's utility is function of his net reward :

14] U = U(y -t(y)) U' > 0 U" < 0 * Principal maximization programme :

The principal's programme is to maximize his expected utility under the constraint that the agent gets a minimum expected utility : [5] Max EU(y -t(y» e ; t(.)

Ev(t(y)) -w(e) > 0

The function of Lagrange is :

[6] L = J U(y -t(y)) f(y ; e) dy + X [f v(t(y)) f(y; e) dy -w(e)]

The first order conditions are the following :

[7] -= -U'(y -t(y)) f(y ; e) + X v'(t(y)) f(y ;e) dy = 0 d t

[8] = J*u(y -t(y)) fe(y ; e) dy + X v(t(y)) fe(y ; e) -k w'(e) = 0 de 191 [7] can be written :

U ' ( y -t ( y ) ) _ x v ' ( t ( y ) )
a) If the principal is risk neutral: U" = 0 and if the agent is risk adverse : v" <0. We can observe, by differenciating [9] :

[10] 4 ^= ° that is dy [111 U"(y -t(y)) [1 -t'(y)] v'(t(y)) -v"(t(y)) t'(y) U'(y -t(y)) = 0
[121 or t'(y) v"(t(y)) U'(y -t(y)) = 0 well v" < 0 and U' > 0 then

[13] t'(y) = 0 => t(y) = constant

The agent has constant reward : the principal undertakes the whole risk. b) If the principal and the agent are risk adverse : U" < 0 and v" < 0. From [11] : fl4] t'(y) = -------»"(y -t(y» v'(t(y))

U"(y -t(y)) v'(t(y)) + v"(t(y)) U'(y -t(y))

Then : [15] 0 < t'(y) < 1. This implies that: t(y) is an increasing function of y and y -t(y) is also an increasing function of y. The rewards of both the principal and the agent are rising with y, output of the agent's action._________________ * Notations and assumptions Recovery of the notations of the first diagram. A new assumption : -the effort level e of the agent is not observable by the principal * Principal maximization programme

The principal has to include in his own maximization programme a new constraint which means that the agent chooses his effort level by himself and that this effort is not observed ; this constraint expresses that e maximizes the agent's programme :

[16] e G arg max J [v(t(y)) f(y ; e)dy -w(e)] e

The principal then includes in his maximization programme, according to the "first order" representation, the first order condition of the agent's programme, that is : [17] = Jv(t(y)) fe(y ; e)dy -w'(e) = 0 de The principal's programme is then : [18] Max J U(y -t(y)) f(y ; e)dy e ; t(.) [19] sous Jv(t(y) f(y ; e)dy -w(e) > 0 (A,) [20] Jv(t(y)) fe(y ; e)dy -w'(e) = 0 (\i) . .

--rr-r increasing m y.

f(y ; e)

This last assumption shows that the agent's reward rises with y. As a matter of fact, by differenciating [21], we obtain : U"(y -t(y)) v'(t(y)) -u. d [fe(y ' e) 1 f(y ; e)l [23] t'(y) = ------------------------Û "(y -t(y)) v'(t(y)) + v"(t(y)) U'(y -t(y)) U" < 0 ; v" > 0 ; n > 0 (B. Holtsrom 1979 andS. Shavell 1979) ; v1 > 0 ; U'. > 0 imply that t'(y) > 0 and that t(y) rises with y._____________ (J.J. Laffont, 1987, p 14). The duality of the action's role, of which the conflictual characteristic is underlined by S.J. [START_REF] Grossman | An Analysis of the Principal-Agent Problem[END_REF] clearly appears : the action produces outcome, shared between principal and agent, and at the same time it produces a signal of the agent's effort level.

The agency relationship with the adverse selection.

Developped by G.A. [START_REF] Akerlof | The Market for "Lemons" : Quality Uncertainty and the Market Mechanism[END_REF], the adverse selection concept defines an agency relationship where some characteristics of the agent's belongings are imperfectly observed by the principal (cf J.J. [START_REF] Laffont | Using Cost Observability to Regulate Firms[END_REF], for an application to regulate firms).

Imagine for instance the relationship between insurance-principal and insured-agents : let's assume that the agent's group, heterogeneous according to individual risks, is homogeneous according to the other characteristics (initial wealth, risk-aversion level...).

It has been proved (cf diagram n° 3, from J.P. [START_REF] Cresta | Théorie des marchés d'assurance[END_REF][START_REF] Laffont | Cours de théorie micro-économique[END_REF] that whenever insurance knows agent's individual risk levels (and if it is risk-neutral), the solution of the principal-agent problem (constrained by the agent's individual rationality) implies that the agent is completely insured. It implies also that insurance premium is equal to the probability of the insured event, that is the whole cost of insurance is equal to the expected loss.

On the contrary, whenever the insurance cannot observe the individual probabilities of the insured event (individual characteristics imperfectly observed), insurance applies the same premium to each insured patient. This premium is equal to the average risk level supposed to be known by insurance.

In the agent's group where the individual risk level is below the average, it has been proved (cf diagram n° 3) that the individual rationality constraint is not carried o u t: the agent's expected utility is below the one he will get without power delegation. Those agents do not contract insurance policy. Only the agent whose risk level is above that average will contract an insurance policy : their rationality constraint is carried out, they will establish a relationship with the principal. This phenomenon, called adverse selection because "bad" risks drive out "good" ones, has two consequences : on one side, a "lack" of transactions and therefore, inefficiency since better information Diagram n°3 : The agency relationship with adverse selection applied to the insurance market (From J.P. Cresta 1984 and J.J. [START_REF] Laffont | Cours de théorie micro-économique[END_REF].

* Notations and assumptions

Consider a population of potential agents i = 1 ; I heterogeneous up to their individual risks and homogeneous up to their other characteristics :

x : loss in the occurrence of the insured event, x > 0 Yo : initial wealth V : utility function of the potential agent such as : V' > 0 and V" < 0 tc\ : individual probability to undergo damage 0i : individual insurance premium by indemnity unit zi : indemnity paid to the agent i * Solution of the problem a) In the context of perfect information, the insurance-principal lets the insured-agent choose his insurance coverage level zj. The balance budget constraint of the insurance (supposed to have no profit) is :

[24] 2 0i ^ = 2 Jii Zj In order to complete this constraint, the insurance proposes to the agent i premium such as 0i = 3ti by indemnity unit. The insured-agent's programme is the maximization of his expected utility :

[25] Max EjV = m V(Y0 -0j z, + zj -x) + (1 -m) V(Y0 -0j n) V(with event) V(without)
For which the first order condition is :

[26] 3ti (1 -0i) V'(Y0 -6i Zi + Zi -x) = (1 -3ti)0i V'CYo-eizO When 0i = 3T i it is : [27] V'(Y<> -0i z, + Zi -x) = V'(Y0 -0i z,)
That is full insurance coverage : zj = x. The agent's expected utility is then :

[28] EiV(with) = V(Y0 -m x)
His individual rationality level is equal to the expectation of his utility when not insured, that is :

[29] EiV(without) = jij V(Yo -x) + (1 -atj) V(Y0) If he is risk adverse (V" < 0), his individual rationality constraint is completed : l30] V(Yo -Jtix) * * V(Y0 -x) + (1 -Jti) V(Y0) b)
In the context of imperfect information, the insurance-principal only observes the whole population's average probability n of undergoing the loss x ; then insurance proposes premium equal to the expected average loss jtx. The individual rationality constraint of the agent i is then :

[31] V(Y0 -550 * V(Y0 -x) + (1 -*i) V(Y0)
Then -only the potential agents j (j E J ; J C I) who have high risk level : Jtj > jt will contract insurance policy.

-the balance budget constraint ot the insurance is no more completed :

[32] I * j > I 5t

_______ i Q -i£J___________________________________________________________________ ____
might improve the situation of each potential trader" (M. Mougeot, 1989, p 297) ; on the other side, a loss for insurance. In order to find a remedy for his loss, insurance has to elaborate discriminating contracts so that agents are incited to reveal their characteristics by themselves.

Moral hazard and adverse selection may coexist in the same agency relationship, as will be clarified in the second part devoted to the analysis of ambulatory care market.

Specifying agency relationship on the ambulatory care market.

After identifying the different actors of ambulatory care market, we will focus on two agency relationships : on one side, the relationships between insurance-principal and patient-agent, on the other side, the relationship between patient-principal and physician-agent.

Actors.

The demand for medical services on ambulatory care market is a demand divided up into three poles : the patient solicits health care ; the physician reveals the patient's needs and decides on treatments and prescriptions ; the insurance finances.

In addition to these three actors : the patient, the physician and the insurance, it is advisable to distinguish a fourth actor: public authorities. In any liberal functioning system of health care market and of medical insurance market, the public authorities' intervention is legitimated by the existence of external features (contagion, prevention of disease) which the market does not take into account. It is also legitimated by the existence of a social utility function that differs from the individual utilities' agregation (Medicare and Medicaid programmes guarantee minimum medical protection for the poorest and for the oldest independently from their solvency. In any socialized financing of health care expenditures, as in France, insurance and public authorities are merged into a unique entity "the public sponsor".

Nevertheless we can consider that two separate target functions are underlying : in the context of private financing of health care expenditures,the insurance target is profit maximization ; in the context of socialized financing, it becomes the research of budget equilibrium under constraints, didacted by public authorities, of minimal quality and minimal health care access equity. The public authorities target is symetrically the maximization of supplied services quality and of health care access under budget equilibrium constraint.

2.2

The relationship between insurance-principal an d insured-agent on the medical insurance market.

The medical insurance market is based, like each insurance market, on the existence of uncertainty : disease is an event. At the same time, the patient can influence disease occurence by medical prevention. We can say, in agency terms, that the insurance-principal delegates to the insured-agent (who is also the patient) the medical prevention's effort supposed to reduce the disease event, financially covered by the insurance.

An agency relationship with adverse selection.

More precisely, it is the relationship between one principal (insurance) and a few agents (insured people). The individual probabilities of disease occurence are not observed by the insurance. As a general rule, whenever public authorities differ from insurance, the information asymmetry, in favour of the patient -potentially insured -holder of the information relative to his characteristics, causes adverse selection.

On the contrary, whenever insurance and public authorities are merged, that is whenever insurance policies are compulsory and whenever the financing of health care expenditures by the insured is independent from his disease event risk, adverse selection diseappears ; it can exist only on the market of complementary medical insurance. Some authors justify rationally the existence of "French social security" because it allows to avoid adverse selection, in better account according to the collectivity than private insurance would, setting up discriminant contracts.

An agency relationship with moral hazard.

On another hand, in the insured -insurance relationship, in which the insurance-principal lets the insured-agent choose his medical self prevention level, this level is not observed by the insurance that observed only the ex-post health care expenses. This information asymmetry in favour of the insured patient is also relative to his preventive behaviour. "Moral hazard conveys the idea that one can doubt about the effort the insured agents will produce in order to reduce the probability of the insured event occurence" (M. Mougeot 1989 p 298).

A) It has been proved (cf diagram n°4 from JJ. Laffont 1987) that moral hazard can be diminished, in other words that a second best optimum risk-sharing can be achieved if the patient, who is supposed to be risk-adverse, is not completely insured : co-insurance incites the patient to produce preventive effort.

B) The Arrow-Pauly controversy. M.V. [START_REF] Pauly | The Economics of Moral Hazard : Comment[END_REF] postulates, contrary to K.J. [START_REF] Arrow | Uncertainty and the Welfare Economics of Medical Care[END_REF]1968) that the influence of medical insurance on health care expenses does not only depend on the strength of preventive effort. He considers that "the quantity of medical care an individual will demand depends on his income and tastes, how ill he is, and the price charged for it" (M.V. Pauly 1968 p 532). As insurance diminishes the price of health care for the patient, the phenomenon called moral hazard "is a result not of moral perfidy but of rational economic behaviour" (p 535) as it is a response to a price decrease.

We can say, on a synthetic point of view, that the insurance-principal and insured-agent relationship is an agency relationship where, neither the preventive effort level of the agent, nor his behaviour relative to health care use are observed. Moral hazard is theoretically measured by the consumption of health care over what would be consumed without insurance ; moral hazard is caused, ex ante, by the preventive effort decline and, ex post, by demand reacting to price decline.

Diagram n°4 : Moral hazard and co-insurance on the medical insurance market (From J.J. Laffont 1987).

* Notations and assumptions

Consider the problem set out in the secong diagram and adjust it to the medical insurance market, x : loss in case of illness ; x > 0 e : insured's prevention level not observed by insurance F(x ; e) and f(x ; e) respectively the cumulative probability function and the probability distribution of x, influenced by e [33J Jf(x ; e)dx = 1 -f(0 ; e) : probability of illness. The function f(x ; e) is discontinuous when x = 0 -The insured-agent is supposed to diminish his illness probability by his preventive behaviour :

[34] M L i £ ) > o de
-He is also supposed to diminish his probability of undergoing a loss equal to x :

|3 5 | 3f(x ; e) < 0 de -The insurance's utility (supposed to be risk neutral: U" = 0) is a negative function of the insured loss x and a positive function of premiums t(x) :

[36] U(-x + t(x)) U' < 0 ; U" = 0 -The insured-agent's utility is function of his initial wealth Yo, of the premium he pays to the insurance and of his preventive behaviour, his utility function is supposed to be separable :

[37] V (Y0 -t(x) ; e) = v(Y0 -t(x)) -w(e) v' < 0 ; v" < 0 ; w' > 0 ; w" > 0 The left side is continuous in t(.) but the right side is discontinuous in x = 0 ; t(x) has then to be discontinuous in x = 0 :

*

[39] t(x) = z if x = 0 = z + h(x) if x > 0
Where z is the insurance premium and h(x) is the co-insurance, increasing with x (cf diagram n°2 : putting (-x) in the place of y, we obtain t'(x) > 0 and t(x) > t(0) then h'(x) > 0). The agent's utility is then : -in the event of illness (x > 0) : V(Yo -z -h(x) ; e) -in the absence of illness (x = 0) : V(Yo -z ; e) _____ The insurance's utility is U(z) if x = 0 and U(-x + z + h(x)) if x > 0.

On the private insurance market, the individual over consumption is eventually transformed into insurance premium adjustment ; whether the individual goes out of the market because his individual rationality constraint is not satisfied, whether he restrains his further consumption while reflecting the insurance premium increase on the apparent price of medical services.

In public financing of health care expenditures where insurance policy suscribing is compulsory, one cannot escape from premium increase while going out of the market. But, as insurance premium does not depend on his risk level (and the premium is such as insurance could adjust it observing any overconsumption), that is more precisely as over-cost is shared by all insured people, the restriction of his further consumption will be above the one of the previous situation, even if it is assumed that price elasticity of demand is positive (in absolute value). Moreover we can say that insured people can adopt free rider behaviour towards this collective good : social insurance.

Any individual being both insured and health care demander, expects to bear only a little part of the cost additional care he used ; at the same time the individual behaviour agrégation can induce the whole health care cost to grow so that the individual premium's increase will be above the expected one (P. Naveau 1983). That is why A. Branciard and P. Huard (1989 p 134) define moral hazard as being "a paradox which discovers the limits of individualistic logic".

2.3

The relationship between patient-principal and physicianagent on the medical services market.

The patient delegates his power decision to an expert : the physician. This expert is not a "perfect agent" who acts in favour of the patient-principal, using his technical knowledge, depending only on the principal's preferences. Beyond medical knowledge, the physician holds on the information relative to the quality of the services he supplies, that is relative to their fitting to the patient's needs as he, the physician, apprehends these needs. The information asymmetry in favour of the physician can induce adverse selection, even if the existence of graduation guarantees a minimum of quality : at the price defined by the market, if it is assumed that it is the market price, the quality would be below what it should be.

On another hand -and particularly -the hidden information is relative to the physician's behaviour in prescribing and in diagnosis. Is this agency relationship with moral hazard improvable ?

Can the patient get the information back ? In case of chronic diseases, the patient, because he is often in the same clinical situation, learns to recognize his unhealthy symptoms and to use the appropriate treatment. But, as a general rule, especially in emergency cases, the costs of information research are prohibitive and even infinite. The patient's difficulty to appreciate the opportunity of the medical intervention exceeds the inherent difficulty of each power delegation by a layman-principal to an expert-agent: the improvement of health condition expected as a result of the medical operation might not be objectively appreciated by a layman because of inherent difficulties in health measurement. When psychical and social dimensions are taken into account, health measurement becomes not only complex but also subjective ; on another hand, medicine is not an exact science, relationships between symptoms, diagnosis, treatments and results are basically only possible ; finally, whenever insurance and public authorities are merged as in France or whenever private financing brings in incentive schemes in order to restrain the medical suppliers' workload (HMO for instance in the USA), the conditions of implicit contract between the physician and the patient are widely predetermined by the rules of the game settled by insurance.

Consequently the patient's ignorance facing the practitioner is greater than that of a layman facing an expert (S. Darbon and A. Letourmy 1983). This agency relationship with moral hazard and adverse selection extends to supplier induced demand hypothesis. The discretionary power would let physicians create demand, either to cancel the effects of the expected decline of both their workload and their income in the event of increasing competition, according to the monopolistic competition model extended to the inducement hypothesis (Cf diagram n°5 from R.G. Evans 1974), or to adjust their real income to their desired one, according to the target income hypothesis (R.G. Evans 1974). There is consequently an effect of overproduction symetrically to the effect of overconsumption inherent to moral hazard in the agency relationship between insurance-principal and insured-patient-agent.

For instance if we look at the French context of fee-for-service, it is characterized by the juxtaposition of two sectors : -in sector l 1, fees are 1 Since 1980, there are two kinds of professional agreements in France between "social security" and private physicians : in both cases, practitioners are paid on a fee-for-service basis. In "sectorl", fees are fixed on the agreement basis and are paid by the patient. In "sector 2", physicians can choose free pricing, in counterpart, they pay a higher social insurance administratively fixed on an agreement basis, the use of discretionary power lets physicians induce quantities, that is completed services -in sector 2, fees The model predicts that, whenever competition (R) increases on the market, the market adjusts itself by quantities. On the contrary, whenever net prices diminish exogeneously (for instance whenever the financing of health care expenses is socialized), the market adjusts itself by quantities.____________ contribution, but the patient is refunded on the basis of sector 1 fixed fees. Consequently he has to pay the co-insurance part himself (as a patient of a sector 1 physician) and the difference between free and fixed prices, i.e. over pricing. Since December 1989, the second agreement has been forbidden to be chosen by the new practitioners. are freely fixed, the use of discretionary power lets them increase fees as well as induce quantities.

It is often assumed that the inducement hypothesis presupposes that price elasticity of demand is, in absolute value, below 1 ; without this assumption, a rise in fees would be replaced by a decline in consumed quantities and it would not allow physicians to increase their income. But is this assumption necessary ? -either we consider that the characteristics of health needs make medical services a "first necessary good" for which no substituable good exists (that is especially rational in emergency cases), price elasticity of demand for medical services is then, in absolute value, below 1, if not equal to zero. The physician's "strategy" of inducement by fee rising cannot be held in check by the patient.

-or, on the contrary, we do not assume anything about the nature of "medical good" but we assume that the persuasion power of the physician lets him modify, if needed, the patient's price sensitivity, that is to persuade the patient of his justified intervention. From the point of view of the theory of human capital where demand for medical services is a demand for health investment (M. Grossman 1972 and C. Le Pen 1988), A.J. Culyer (1990 p 5) writes that the discretionary power lets the physician "induce patients to believe either that the value of health is higher than it truly is or that the productivity of investment in health by consuming health care is higher than it truly is". Any assumption about price elasticity is then useless.

Testing the agency relationship between patient-principal and phvsician-agent.

A specified relationship is a hypothesis that has to be corroborated. We will focus on the methodological limits of this venture before presenting and estimating an original, even simple, econometric model of the agency relationship between patient-principal and physician-agent.

Methodological limits.

They come from the collection of individual data, unexistent or subjected to medical secret and, at the same time, essential to test the individual behaviours hypothesis.

They also come from the intrinsic limits of an econometric model specification which, without being ad hoc, allows to separate the different effects that coexist in the same relationship.

Both practical ways of inducement, by quantity inducement or by fees increasing, imply that empirical studies, established from agregated data, test two correlations : -the correlation between physician density and fees level tests the hypothesis according to which an increasing competition (estimating by medical density) incites physicians to increase fees in order to keep their income level.

-the correlation between physician density and health care use tests the hypothesis according to which the same cause brings physicians to induce service quantities in order to keep their workload level.

Inducement by fee rising : hypothesis facing two competitive hypotheses.

A positive correlation between medical staff increase and fee rising can be explained, beyond the inducement hypothesis, by two competitive hypotheses : -The hypothesis of monopolistic competition with differenciated tarifying : J.P. Newhouse (1970), following R.A. Kessel (1958), considers the market of medical services as a monopolistic competition market where price discrimination satisfies the profit maximization target of the monopolist whenever newcomers arrive on the market, the monopolist physician gradually increases fees according to his patient's income, in order to cancel workload decrease expected from increasing competition. We can then observe a positive statistical correlation between physician density and fees level.

-The hypothesis of increasing monopoly : established by M.V. Pauly and M.A. [START_REF]The Pricing of Primary Care Physician Services[END_REF], this model constitutes a second alternative option to explain this statistical correlation. The physician produces medical services that can be called "reputation good" (M.A. Satterthwaite 1979) in so far as the market research by patients is not direct : it precisely goes through the physician's "reputation". On this monopolistic competitive market, whenever medical density increases, the quality of information patients have concerning the physicians' relative qualifications and prices declines. If the number of physicians within a community is small, then the patient can get detailed information from relatives and family ; if the number of physician within a community is larger, then each physician's reputation is less defined. This makes the patient's search less efficient and the patient becomes less price sensitive and this causes the physicians' equilibrium fees to rise.

31.2

The hypothesis of quantity inducement : a practical test under some assumptions.

So, a positive correlation between a rise in medical supply and a rise in per capita health care utilization can be explained by two competitive hypotheses of the inducement one :

-the competitive model assumes that supply and demand are independent and demand is function of both access costs and income. Access costs are monetary costs (the price of medical services) and also time costs (travel and waiting time) that we can rationally assume to decline if the physicians' density rises. Then demand reacts upon access costs'decline in rising and one can observe a rise of both supply and demand.

-the hypothesis of differenciated output explains the geographical differences in health care use by the quality differences that variations exist accross high medical density area and low medical density area. In the high medical density areas where competition is strong, physicians would adopt strategies of output différenciation : they would produce high quality services to consumers that react in demanding more health care.

In order to decide betwen the inducement hypothesis and these two ones, each empirical study of quantity inducement has to try to keep time costs and quality constant. One faces, then, difficult measurement problems. F.H. Sloan and J.H. Lorant (1977) found that there was a positive relationship between physicians per capita and length of visit or waiting time but that the elasticity is quite small. Consequently, the assumption of uniform average quality across market areas is acceptable and it would allow to give preference to the inducement hypothesis.

A simplified quantity inducement model.

32.1 Assumptions.

The model gives preference to quantity inducement for two reasons :

first of all because it is tested on the French system where sector 2, though rising, is still smaller than sector 1 ; on another hand because empirical study of the correlation between medical density and health care use is relevant to decide between induced demand model and others (L. Rochaix 1991, S. Bejean 1989).

In the health care sector one cannot work with individual data : the medical secret prevents the connection between data concerning the physician and data concerning his patients. Therefore empirical studies are set out according to data agregated by geographical areas. The choice of departments (main administrative divisions in France) as geographical areas allows to eliminate bordercrossing linked with the physician's reputation.

Choosing the sector of general practitioners (GPs) to test the induced demand hypothesis is justified by the fact that services provided are more homogeneous for GPs than for specialists.

It is assumed that average quality across market areas is uniform (F.A. Sloan and J.H. Lorant 1977 opus cited).

Finally we limit the model to the demand function since the object of this study is not to test a complete demand-supply model but to test the influence of supply on utilization rates.

The equality between utilization rates and demand assumes that the market is balanced : Whenever there is excess supply, quantity has to be equal to demand if there is no inducement: then a is equal to zero. On the contrary, if there is supply induced demand a is positive.

D =
Therefore, it is convenient to divide up the sample according to a significant variable of the excess (or not) of supply. The sample of ninety-five cross section data points has been divided into two samples. In sample one, the level of the physicians' workload (i.e. the number of acts per GP) is less than the average workload. In sample two , the level of physicians workload is above the average. The division into both samples would allow us to distinguish revealed demand from induced demand : -whenever there is excess demand on the market, the physicians' workload is expected to be high. Then a positive correlation between health care utilization and GPs density can be defined by revealed demand ; -whenever there is excess supply on the market, the physicians' workload is expected to be low. Then, the same positive correlation between health care utilization and GPs density can be defined by induced demand (and not revealed demand).

Demand for home visits and for consultations at the GPs' surgery are estimated according to the hypothesis which implies that home visits are patient initiated and, on the contrary, consultations are physician induced.

The empirical relationships to be estimated and tested is a linear function which explains the utilization of health care per capita in terms of explanatory variables (that are presented in diagram n°6 Among other things we can establish : -that overpricing elasticity of demand is very low (-0,075 for 1988). This result confirms a low patient sensitivity to health care prices according to the assumption that the discretionary power is all the more used by physicians since price elasticity of demand is close to zero.

-The estimated parameter of GPS' density is positive and it corroborates the supplier induced demand hypothesis. An increasing competition brings practitioners to induce quantities : whenever GPs' density rises by 10%, the consumption of GPs services rises by 4,4%.

-The positive influence of supply on demand for home visits is lower (or not significant) than the one on demand for consultations and it corroborates the hypothesis that home visits are patient initiated and consultations are supplier induced.

-The results of the regression on sample one (where the physicians' workload is low so that it can be assumed that there is no excess demand on the market) also corroborate the induced demand hypothesis as they allow to distinguish induced demand from revealed demand. The quality of the statistical results is even better when there is excess supply and the influence of socio-demographic factors diminishes. The sign and the size of the DENG parameter are confirmed.

As a conclusion we can say that the theoretical analysis of relationships between actors in ambulatory care gives coherent framework that explains the non-optimal resource allocation often denounced in the health care sector. The existence of information asymmetries induces strategical behaviours that cause moral hazard and adverse selection. Then, for instance, moral hazard in the agency relationship between insurance-principal and insured-patient-agent can cause health care overconsumption while moral hazard in the agency relationship between patient-principal and physician-agent can cause medical services overproduction. The latter, called inducement, would be difficult to get round in so far as the subjective characteristic of health need would confer a discretionary power to physicians. But it is also difficult to test because of methodological limits. However stakes in empirical studies are not negligible (U.E. Reinhardt 1985) :

From a theoretical point of view, challenging the assumption of the independence of supply and demand is assaulting "one of the crucial pillars of the neoclassical framework" (U.E. Reinhardt 1985 p 188), with no surprise, the guardians of that framework are reacting with vigor.

The choices concerning the health policy rely on the previous issue : the state control over the medical staff and more generally government imposed limitations on the supply of medical manpower may be legitimated whenever the induced demand hypothesis is corroborated by empirical findings.

As to the political ideology, the individual economists' point of view about the state intervention conditions "their more or less important reluctance towards econometric studies" (E. Levy 1989 p 472).

We can carefully suggest some rules of the game susceptible to be applied to French ambulatory care in order to counter the dysfunctioning inherent to information asymmetries, in a context where economic growth decline endangers the achievement of the three targets that make the originality of the French system : the guarantee of care access equity by making demand financially solvent, the keeping of the principles of liberal practice supposed to be guarantors of freedom of patient's and physician's mutual choice, and the health care containment. About the relationships studied in this paper : -We can say that moral hazard in the agency relationship between insurance and insured people can be countered on the private insurance market by coinsurance implying risk-sharing between insurance and insured people. But if we consider moral hazard defined by Pauly, price elasticity of demand for health care has to be assumed above zero (in absolute value). On the contrary, co-insurance is surely not efficient in a social insurance system because of the free rider behaviour of insured people.

-We can also say that, on the medical services market, each attempt from the patient to get information back, either directly by medical education, or indirectly by public authorities intervention, can limit the discretionary power use inherent to the induced demand hypothesis. For instance, in France, the agreement that fixes administrative prices in sector 1 allows to control inducement by fee rising (which, on the contrary, can freely develop in sector 2). The system of TSAP (statistical indicator of practitioner workload and practice) that defines workload standards for each speciality, constitutes regulation instrument of quantity inducement (the TSAP standards are questionable in practice because of their technical imperfection and because of the way they are institutionally applied, but that is another problem...).

-The establishment of RSC (French Coordinated Care Networks inspired from American Health Maintenance Organizations ; P. Giraud and R.J. Launois 1985 ; R.J. Launois and D. Truchet 1986) would allow to counter simultaneously inducement and adverse selection, on the medical services market and moral hazard on the insurance market: practitioners, paid for their services with lump sum and financially interested in the network's profit (difference between resources, that are per capita annual lump sum coming from medical insurance, and expenses, function of provided services), are not incited to use their discretionary power to induce demand ; competition across networks would bring physicians to provide good quality services with low prices and that would counter adverse selection ; finally, the system of the physician's payment is favourable to rising medical prevention and, therefore, to moral hazard control (from Arrow's point of view). On the contrary, the system can induce adverse selection in the respect of insurance ; in order to escape from the adverse selection consequences, the network would be incited to "risk-creaming" except if the annual lump sum given by insurance is precisely function of the patient's individual risk (that of premium is independent from this very risk). In France, the managers of social medical insurance have put foward an outline of "health agreement" : the physician is still paid on a fee-for-service basis but in the context of contractual relationship with the patient. This contract is established annually and the physician gets complementary lump sum corresponding to his prevention and evaluation practice. In counterpart of this faithfullness from his practice, he undertakes to keep the patient's record up to date, which constitutes an instrument for public authorities to get information back and to control the physician's discretionary power. The revalorized prevention practice of the physician is propitious to reduce moral hazard on the medical insurance market (that is to reduce overconsumption) but one should stress the fact that a direct payment of the physician by insurance consented to the patient in order to incite him to suscribe such a contract, can diminish the expected result.

In a complex situation combining moral hazard and adverse selection, one might also inherently fear for incentive strategies to be widely inoperative. Only the trust between the different actors would allow to solve the problem. "A rule is made to be infringed", one says, except if it is itself submitted to another rule (the rule of the rule, the meta-rule) which is precisely the nontransgression, that is the trust. Does this mean that the solution would consist, beyond the services and information markets, in creating "vertical trust networks" (A. Breton 1991) ? One may agree that the "trust output", independently of any moral interpretation that would make it similar to some kind of manipulation, is a concern of a particular sterile paradoxal injunction. One would then recognize the justification for a medical deontology focusing on a categorical legitimacy of the particular relationship between practitioner and patient, that is of the compassion protocole.

  JU(y -t(y)) fe(y ; e)dy + \i [Jv(t(y)) fee(y ; e)dy -w"(e)] = 0 The agent's optimization programme is concave in e -and then the first order condition [20] characterizes the optimum -only under the following assumptions (J. Mirrlees 1975) : -F(y ; e) convex in e. fe(y ; e) .

Diagram n°5 :

 n°5 The monopolistic competition model extended to the inducement hypothesis (from R.G. Evans 1974). The physician's utility is function of his income Y, of his workload W and of the psychological cost inherent to the use of his discretionary power D.D can also be interpreted as being a preference to quantity adjustment rather thanThe demand for medical care is function of health care net price (which depends of the financing system of this health care) and of the discretionary power

). Ninety-five crossection data points (there are 95 departments in France) have been collected for each variable for 1988. Equations have been estimated by OLS. The regression results are presented in diagram n°7 (first part of the table). The second part of diagram n°7 presents the regression results estimated on the sample where it is assumed that there is excess supply, the only relevant case in this respect. The variable HOMM is eliminated because its parameter is never significant. Data points come from CNAMTS (social medical insurance) and from INSEE (statistical national institute). They have been collected thanks to F. Tonnellier and H. Faure from CREDES (institute of health economic research). Dependent variables : -Demand : D : average number of per capita GP's acts C : average number of per capita surgery consultations V : average number of per capita home visits Explanatory variables : -Demographic : PI5 : ratio of under fifteen year old population P65 : ratio of over sixty-five year old population PW : ratio of over fifteen and under sixty-five year old women -Socio-economic :Y : average income -Fees : OP : average overpricing per act P : average fees without overpricing per act -Distance : DIS : average distance to reach the physician's surgery FARM : % of farms -Supply : DENSG : GP's density ___________ _____ DENSP : density of specialists.__________________________ Explanatory variables

		Dependent variables 95 data points -1988 hypothesis of balanced market	42 data points -1988 hypothesis of excess suply
		D	C	V	D	C	V
	Constant	-13,33	-4,55	-5,81	-7,04	-0,559	0,06
	DENG	0,02	0,01	0,003	0,02	0,015	0,009
	DENSP			-0,003
	OP	-0,056 -0,015	-0,04	-0,06	-0,01	-0,032
	Y	0,00002 0,0001
	RW	25,44	9,96	13,2	18,8
	P15	11,17	5,8			7,67
	P65	11,81		10,23			5,75
	FARM	-1,97		-1,97		2,65
	DIS	0,31	0,21
	R2	0,7	0,44	0,52	0,82	0,68	0,66

NB : The variables which of their parameters were not significant at the level of 5% have been eliminated.