1. Tor Iversen 03.05.2005 6. Health service provision Economic incentives and organization of the hospital sector I

2. 2 Problems to be addressed In general: Do revenue systems and organization in specialist care (particularly hospitals) influence providers effort and the number and types of patients and the quality of the treatment? In particular: Economic incentives related to a GPs referral decision (this point could also have been included under the previous topic about physicians) How to encourage low cost and high quality when cost-reducing effort and quality are not verifiable (Chalkley and Malcomson) The effect of activity based financing on hospital efficiency (Biørn et al.) The effect of activity based financing on the composition of treatments and admitted patients Trade-offs involved in the of making of optimal payment- and revenue-systems.

3. 3 The relationship between rate of referrals and payment system for GPs The referral rate among general practitioners (GPs) varies considerable Is the payment system for GPs likely to have an impact on the proportion of patients who is referred to second-level providers. Question asked: Does a switch from a practice allowance/fee for service system in general practice to a capitation/fee for service system have an impact on GP's referral rates? Two types of referrals: supplementary and alternative Supplementary referrals: supplement to the services general practitioners are expected to deliver Alternative referrals: services provided by a specialist that could be equally well handled by the GP himself Two alternative payment systems for GPs are considered: –A fee-per-item of health services (fee-for-service) according to a fixed fee schedule combined with a practice allowance –A fee-per-item of health services according to a fixed fee schedule combined with a capitation payment depending on the number of patients on the GPs list

4. 4 We may distinguish between factors related to the payment system and factors related to the organization of general practice. Introduction of a patient list system as an organization: The role as a personal spokesman for the patient tends to encourage the GP to refer (+) The continuity in medical care implies that the GP gets to know the patient better and hence will have less need for a referral (-) That everyone is registered with a GP, may imply that individuals with no previous contacts in the health care system will start using the service (-?) Previously, it may have been difficult to make an appointment with a GP, and the patient went directly to a privately practising specialist (-) Hence, some of the changes in the organization point to a higher referral rate and other changes point to the opposite.

5. 5 What about the change in payment system? Assume that in general there is a is a time input related to the preparation and the follow- up of a referral. There is no fee for this kind of work. Under practice allowance / fee-for-service: An increase in the referral rate takes time that is not compensated in monetary terms. Hence, the number of alternative referrals is expected to be equal to zero. Under capitation / fee-for-service: An increase in the rate of referrals takes time that is not directly compensated in monetary terms. But since the workload connected to each patient may decline, there is scope for increasing the list of patients if the time cost related to a referral is small relative to the capitation fee. For a small level of effort related to a referral we would expect the referral rate to be higher under capitation/fee-for-service than under practice allowance/fee-for-service. Then, we predict that the change in the payment system unambiguously tends to increase rate of referrals. A study of the Norwegian list patient system (Iversen, T. and Lurås, H., 2000, The effect of capitation on GPs referral decisions, Health Economics 9, 199-210) points in that direction; in particular with regard to referrals to private specialists

6. 6 An overview of problems involved in constructing an optimal revenue/financing system for hospitals Central reference: Chalkley and Malcomson Problem: Quality and cost-reducing effort are unverifiable, although they may be observable Full cost-reimbursement: high quality and low level of cost-reducing efforts Fixed price independent of actual costs (prospective payment): High level of cost-reducing effort and low level of quality Two agents: Purchaser and provider (supplier)

7. 7 Suppliers objective function: u=P-F-c(x,q,e)-v(x,q,e) X is number of treated patients q is quality of treatment e is cost-reducing efforts F is fixed cost c(.) is variable cost, c x (.)>0, c q (.)>0, c e (.)<0 P is the payment from the purchaser v(.) is non-monetary cost, v x (.) and v q (.) may well be negative, v e (.)>0 hospitals are often non-profit institutions Assume that c(.)+v(.) is strictly convex for all (x,q,e) ¯u is the minimum utility for which the supplier provides the service

8. 8 The purchasers objective function: b(x,q) + u – (1+α)P b(.) is the benefit from treatment – concave and increasing in both arguments α is the cost of public funds – distortion caused by taxation

9. 9 Substitution of P from providers objective function, enables the purchasers objective to be written Max b(x,q)-(1+α)[F+c(x,q,e)+v(x,q,e)]- αu x,q,e,u subject to feasibility constraint on the number of patients who demand treatment and The solution is the first best outcome (x*,q*,e*) always involving The first order conditions: b x (x*,q*)-(1+α)[c x (x*,q*,e*)+ v x (x*,q*,e*)]=0 b q (x*,q*)-(1+α)[c q (x*,q*,e*)+ v q (x*,q*,e*)]=0 c e (x*,q*,e*)+ v e (x*,q*,e*)=0

10. 10 Concern for quality and effort: Assume: c q (x*,q*,e*)+ v q (x*,q*,e*)>0 q and e are not verifiable Always positive marginal cost to quality The providers first order conditions: P x - [c x (x ~,q ~,e~)+ v x (x ~,q ~,e ~ )]=0 -c q (x ~,q ~,e ~ ) - v q (x ~,q ~,e ~ ) = 0 -c e (x ~,q ~,e ~ ) - v e (x ~,q ~,e ~ )=0 Since c q (x*,q*,e*)+ v q (x*,q*,e*)>0, q ~ <q * Underprovision of quality if no compensation of quality to the provider at the margin What if v q (.)=0? If v q (.)<0: Reimburse a proportion of the providers cost Set an appropriate γ (the share of costs compensated). Then provider sets (1-γ)c q (.)=-v q (.). Why does that help? Requires organizations that care for providing quality health care Again: Supply side cost-sharing

11. 11 Problem: Adverse effects on effort decision if v e (.)>0, since the provider sets (1-γ)c e (.)=-v e (.) Trade off between quality and incentives to provide cost-reducing efforts A proportion of cost-sharing may nevertheless be preferable.

12. 12 The promise of the fixed price contract when quality influences demand Then by an appropriate choice of price the purchaser can influence the level of quality We now have the number of patients: n=n(q) with n(q)>0 for all q. B(q)=b[n(q),q] C(q,e)=F+c[n(q),q,e]+v[n(q),q,e] Assume B(q) concave and C(.) strictly convex Purchasers objective function:

13. 13 The purchaser pays the supplier a lump sum a and a fixed payment p per patient treated. The supplier chooses q and e to max a+pn(q)-C(q,e) q,e First order conditions: (**) pn(q) - C q (q,e)=0 C e (q,e)=0 From (*) and (**) we find the optimal price: What kind of factors determine the magnitude if p?

14. 14 Challenges Do patients correctly perceive the quality? OK if perceptions are positively correlated with actual quality This may not be the case. The provider may concentrate too much on unimportant quality characteristics with regard to the treatment result because they are appreciated by the patient – examples? What about rationing of patients? What would we expect (w.r.t. q and e) from the introduction of a fixed payment per treatment if there is an excess demand for treatments? Some patients may be more responsive to q than others Some patients may be more attractive than others: determining optimal provider prices with heterogeneous patients Uncertainty about costs combined with a risk averse provider implies that the provider is interested in partial reimbursement of actual costs. Introduces trade off between insurance and incentives to cost reducing efforts.