Bargaining and the Provision of Health Services

We model and compare the bargaining process between a purchaser of health services, such as a health authority, and a provider (the hospital) in three plausible scenarios: a) the purchaser sets the price, and activity is bargained between the purchaser and the provider: activity bargaining; b) the price is bargained between the purchaser and the provider, but activity is chosen unilaterally by the provider: price bargaining; c) price and activity are simultaneously bargained between the purchaser and the provider: efficient bargaining. We show that: 1) if the bargaining power of the purchaser is high (low), efficient bargaining leads to higher (lower) activity and purchaser's utility, and lower (higher) prices and provider's utility compared to price bargaining. 2) In activity bargaining, prices are lowest, the purchaser's utility is highest and the provider's utility is lowest; activity is generally lowest, but higher than in price bargaining for high bargaining power of the purchaser. 3) If the purchaser has higher bargaining power, this reduces prices and activity in price bargaining, it reduces prices but increases activity in activity bargaining, and it reduces prices but has no effect on activity in efficient bargaining.bargaining. negotiation. purchasing.

Third degree waiting time discrimination: optimal allocation of a public sector health care treatment under rationing by waiting

In many public health care systems treatment is rationed by waiting time. We examine the optimal allocation of a .xed supply of a treatment between di¤erent groups of patients. Even in the absence of any distributional aims welfare is increased by third degree waiting time discrimination. Because waiting time imposes dead weight losses on patients, lower waiting times should be o¤ered to groups with higher marginal waiting time costs and with less elastic demand for the treatment.Waiting times, prioritisation, rationing

Optimal Waits and Charges in Health Insurance

Waiting times are commonly used in the health sector to ration demand. We show that when money charges (coinsurance rates) are optimally set and there are no redistributional considerations, it is never optimal to have a positive waiting time if the marginal cost of waiting is higher for patients with greater benefits from health care. Although waiting time provides an additional instrument to control demand it does not mitigate the conflict between efficient risk bearing and efficient consumption of health care.Waiting times, rationing, optimal pricing, insurance

Is Waiting-time Prioritisation Welfare Improving?

Rationing by waiting time is commonly used in health care systems with zero or low money prices. Some systems prioritise particular types of patient and offer them lower waiting times. We investigate whether prioritisation is welfare improving when the benefit from treatment is the sum of two components, one of which is not observed by providers. We show that positive prioritisation (shorter waits for patients with higher observable benefit) is welfare improving if the mean observable benefit of the patients who are indifferent about receiving the treat- ment is larger than the mean observable benefit of the patients who receive the treatment. This is true (a) if the distribution of the un- observable benefit is uniform for any distribution of the observable benefit; or (b) if the distribution of the observable benefit is uniform and the distribution of the unobservable benefit is log-concave. We also show that prioritisation is never welfare increasing if and only if the distribution of unobservable benefit is negative exponential.Waiting times, prioritisation, rationing

Multitasking, Quality and Pay for Performance

We present a model of optimal contracting between a purchaser and a provider of health services when quality has two dimensions. We assume that one dimension of quality is veri?able (dimension 1) and one dimension is not verifiable (dimension 2). We show that the power of the incentive scheme for the verifiable dimension depends critically on the extent to which quality 1 increases or decreases the provider's marginal disutility and the patients' marginal benefit from quality 2 (i.e. substitutability or complementarity). Our main result is that under some circumstances a high-powered incentive scheme can be optimal even when the two quality dimensions are substitutes.quality; altruism; pay for performance.

Multitasking, quality and pay for performance

We present a model of optimal contracting between a purchaser and a provider of health services when quality has two dimensions. We assume that one dimension of quality is contractible (dimension 1) and one dimension is not contractible (dimension 2). We show that the optimal incentive scheme for the contractible dimension depends critically on the extent to which quality 1 increases or decreases the marginal cost and marginal bene?t of quality 2 (i.e. substitutability or complementarity). If the two quality dimensions are substitutes, three possible solutions arise: a) the optimal incentive scheme is high powered: the incentive is equal to the marginal bene?t of quality dimension 1 and the optimal quality in dimension 2 is zero; b) the optimal incentive scheme is low powered: both quality dimensions are positive; the incentive is below the marginal bene?t of quality dimension 1; c) it is not optimal to introduce pay for performance as the gain of welfare from an increase in quality dimension 1 is lower than the loss of welfare from an increase in quality dimension 2. If the two quality dimensions are complements the incentive scheme is always high powered: the incentive is above the marginal bene?t of dimension 1 and both quality dimensions are positive.quality, altruism, incentives

DRG prospective payment system: refine or not refine?

We present a model of contracting between a purchaser of health services and a provider (a hospital). We assume that hospitals provide two alternative treatments for a given diagnosis: a less intensive one (for example a medical treatment) and a more intensive one (surgical treatment). We assume that prices are set equal to the average cost reported by the providers, as observed in many OECD countries (yardstick competition). The purchaser has two options: 1) to set one tariff based on the diagnosis only; 2) to differentiate the tariff between the surgical and the medical treatment (i.e.to refine the tariff). We show that when tariffs are refined, the provider has always an incentive to overprovide the surgical treatment. If the tariff is not refined, the hospital underprovides the surgical treatment (and overprovides the medical treatment) if the degree of altruism is sufficiently low compared the opportunity cost of public funds. Our main result is that price refinement might not be optimal.Hospitals; Refinement; Diagnosis-Related-Groups.

Do waiting times reduce hospital costs?

Using a sample of 137 hospitals over the period 1998-2002 in the English National Health Service, we estimate the elasticity of hospital costs with respect to waiting times. Our cross-sectional and panel-data results suggest that at the sample mean (103 days), waiting times have no significant effect on hospital, costs or, at most, a positive one. If significant, the elasticity of cost with respect to waiting time from our cross-sectional estimates is in the range 0.4-1. The elasticity is still positive but lower in our fixed-effects specifications (0.2-0.4). In all specifications, the effect of waiting time on cost is non-linear, suggesting a U-shaped relationship between hospital costs and waiting times: the level of waiting time which minimises total costs is always below ten days.

Price Adjustment in the Hospital Sector

Prospective payment systems are currently used in many OECD countries, where hospitals are paid a fixed price for each patient treated. We develop a theoretical model to analyse the properties of the optimal fixed prices to be paid to hospitals when no lump-sum transfers are allowed and when the price can differ across providers to reflect observable exogenous differences in costs (for example land, building and staff costs). We find that: a) when the marginal benefit from treatment is decreasing and the cost function is the (commonly used) power function, the optimal price adjustment for hospitals with higher costs is positive but partial; if the marginal benefit from treatment is constant, then the price is identical across providers; b) if the cost function is exponential, then the price adjustment is positive even when the marginal benefit from treatment is constant; c) the optimal price is lower when lump-sum transfers are not allowed, compared to when they are allowed; d) higher inequality aversion of the purchaser is associated with an increase in the price for the high-cost providers and a reduction in the price of the low-cost providers.Price adjustment, Hospitals, DRGs.

Quality competition with motivated providers and sluggish demand

We study incentives for quality provision in markets where providers are motivated (semi-altruistic); prices are regulated and firms are funded by a combination of block grants and unit prices; competition is based on quality, and demand adjusts sluggishly. Health or education are sectors in which the mentioned features are the rule. We show that the presence of motivated providers makes dynamic competition tougher, resulting in higher steady-state levels of quality in the closed-loop solutions than in the benchmark open-loop solution, if the price is sufficiently high. However, this result is reversed if the price is sufficiently low (and below unit costs). Sufficiently low prices also imply that a reduction in demand sluggishness will lead to lower steady-state quality. Prices below unit costs will nevertheless be welfare optimal if the providers are sufficiently motivated.Quality competition; Differential games;Motivated agents