9 Agency and Different Payment Models
In the prior chapter, we introduced a simple model of physician agency and financial incentives, showing how it could predict “excess” care—that is, situations where physicians provide more care than patients would have chosen for themselves. But payment systems go well beyond the simple fee-for-service setup we considered there. In reality, physicians and health systems face a variety of reimbursement models that shape their incentives in important ways, particularly when we think about different payment systems around the world. In this chapter, we extend the model to examine two of the most prominent approaches—fee-for-service (FFS) and capitation—and show how these payment structures generate systematically different predictions for physician behavior.
9.1 FFS and Capitated Payments
9.1.1 Definitions
For our purposes, FFS payments simply consist of separate payments for each service, creating a system where more care leads to more revenue. This is how we envisioned payments in the model in the prior chapter. And with some slight adjustments, this is also how traditional Medicare pays for health care among its beneficiaries.
In contrast, capitated payments provide a fixed amount intended to cover all expenses for a specific person or group, presenting a financial risk for healthcare providers. If actual expenses exceed the allocated amount, providers experience potential losses, while keeping costs below the capitated payment leads to profitability. The Kaiser system is probably the best example of a totally capitated payment system in the U.S. It’s a private health insurance plan with an associated network of providers. Only people enrolled in the Kaiser insurance plan have access to the Kaiser providers, so it’s a closed system of insurance and providers. Accountable Care Organizations are also similar to a fully capitated model, although not exactly since ACOs are voluntary.
9.1.2 Incentives
The differences between FFS and capitated payments create distinct incentives for healthcare providers. Under fee-for-service arrangements, revenue increases with the number of services provided, creating a natural incentive to deliver more care—even if some of that care is only marginally beneficial. By contrast, under capitation, providers receive a fixed payment per patient regardless of the amount of care delivered. This structure rewards cost containment but also introduces the risk of undertreatment, since each additional service raises costs without increasing revenue.
The key takeaway is that payment systems pull physician behavior in opposite directions: fee-for-service tends toward overprovision, while capitation tends toward underprovision. Most real-world systems lie somewhere in between, but these extremes provide a useful benchmark for understanding how incentives operate.
9.2 Physician Agency with FFS vs Capitation
To see this more formally, let’s set up a new version of our agency model. Physicians receive a fixed amount per patient, denoted \(R\), along with a price per unit of service, \(p_{s}\). Given the choice of quantity of care, \(x\), (assumed to be the same for each patient) physicians receive \(R + (p_{s} - c)x\) for each patient. Finally, the number of patients for each physician is expressed as a positive function of the net benefit offered, \(n(NB)\), where \(NB=B(x) - p_{d}x\). Here, we’re also allowing separate prices paid by the patient versus prices received by the provider, where the patient pays \(p_{d}\) and the physician receives \(p_{s}\). We also assume that the physician has no control over prices. They can only affect the amount of care, \(x\).
Physician’s again aim to maximize profits by optimizing the profit function, \(\pi=n(NB)\left[R+(p_{s}-c)x\right]\). This maximization problems yields the following first order condition:
\[n'(NB)(B'(x) - p_{d}) \left[R + (p_{s} - c)x \right] + n(NB)(p_{s}-c) = 0.\]
Rearranging terms and multiplying both sides by \(\frac{1}{NB}\), we get: \[\frac{B'(x) - p_{d}}{NB} \frac{R + (p_{s} - c)x}{p_{s}-c} = - \frac{1}{\varepsilon_{n,NB}}. \tag{9.1}\]
Even without any specific assumptions on the benefit function, we can begin to say something about the physician’s selection of \(x\) relative to the patient’s own optimal \(x\) under different payment scenarios. For example, assume that \(R=0\) and \(p_{s}>c\), so that there is no capitated payment and the physician is reimbursed entirely on a FFS basis. In that case, the second term on the left hand side of Equation 9.1 must be positive. Since we know the product on the left hand side must be negative (to match the sign of the right hand side), then it follows that \(B'(x) - p_{d}<0\). Since we also know that the patient would optimally set \(B'(x)=p_{d}\), then the case of \(R=0\) and \(p_{s}>c\) must be such that the physician overtreats relative to the patient’s optimal. That’s the only way for \(B'(x)<p_{d}\).
Alternatively, let’s consider the case of \(R>0\) with \(p_{s}<c\), so that the physician now earns a set amount of money per patient but loses money on each unit of care. In a purely capitated model, we would set \(p_{s}=0<c\). Imposing these constraints onto Equation 9.1, note that the second half of the left hand side is now negative since \(p_{s}-c<0\) (assuming \(R-(p_{s} -c)x>0\), which is necessary in order for the physician to stay in the market anyway). This means that the first part of the left hand side must be positive (i.e., \(B'(x)>p_{d}\)), so that physicians now undertreat relative to the patient’s optimal.
9.3 Beyond FFS vs Capitation
Although fee-for-service and capitation are often presented as opposite ends of the spectrum, most modern payment systems blend features of both. Policymakers have sought to address the shortcomings of these two models by layering in additional incentives that tie reimbursement to quality or efficiency.
One prominent example is Pay-for-Performance (P4P), in which providers face bonuses or penalties based on measurable outcomes such as hospital readmission rates, patient satisfaction, or adherence to clinical guidelines. Medicare’s Hospital Readmission Reduction Program and Value-Based Purchasing initiative both operate on this principle, rewarding hospitals that deliver high-quality care at lower cost.
Private insurers have pursued similar strategies, often under the umbrella of value-based contracts. Large commercial payers such as UnitedHealthcare, Aetna, and Blue Cross Blue Shield have developed arrangements that tie provider reimbursement to cost and quality benchmarks. These contracts sometimes resemble shared savings programs, with physicians or health systems receiving a portion of the savings they generate, and in other cases they function as performance-based bonuses layered on top of fee-for-service payments.
Another approach is the rise of Accountable Care Organizations (ACOs), which move beyond simple capitation by incorporating shared savings or losses. ACOs give providers a financial stake in the overall spending and quality of a patient population, encouraging coordination across settings and reducing unnecessary utilization.
A further hybrid is bundled payments, where providers receive a fixed payment for an entire episode of care, such as a joint replacement or maternity stay. Bundled payments create incentives to coordinate across providers and reduce unnecessary services within the episode, while still avoiding the blunt incentives of pure capitation. Both Medicare and commercial insurers have experimented with these models, often with promising results in terms of cost savings and efficiency.
These hybrid arrangements highlight an important theme: real-world payment models are rarely “pure.” Instead, they reflect attempts to balance the incentives of volume, cost containment, and quality—three dimensions that lie at the heart of physician agency.
9.4 Agency IRL
More generally, physicians choose some care, \(x\), incorporating their own profit, the benefit to the patient, and some disutility of work \[u(x) = V(\pi) -e(x) + \alpha B(x),\] where \(x\) need not be “quantity of care” and could instead capture which type of treatment a physician chooses rather than “how much” care to provide. The important point here is simply that, in real life, physicians are often choosing between different treatment options rather than some easily measured “quantity.” In this sense, the empirical literature has consistently found significant and meaningful physician responses to financial incentives, including effects on treatment patterns (Clemens and Gottlieb (2014)), discharge patterns (Einav, Finkelstein, and Mahoney (2023), Einav, Finkelstein, and Mahoney (2018), and Eliason et al. (2018)), the types of patients seen (Cabral, Carey, and Son (2023)), as well as location of care (Munnich et al. (2021) and Baker, Bundorf, and Kessler (2016)). Financial incentives also spillover across insurance types, where changes in payments from one insurer can influence how other types of patients are treated (Barnett, Olenski, and Sacarny (2023)). The takeaway from all this is that, on the margin, financial incentives do affect treatment decisions. Thankfully, there is less evidence that such responses decrease quality of care.