Reimbursement and Investment: Prospective Payment and For-Profit Hospitals’ Market Share

Abstract

This paper studies how the change from retrospective cost-based reimbursement to a prospective payment system shifted hospital investment strategies from quality-enhancing technologies to cost-saving technologies. A consequence of this change was the opportunity for for-profit hospitals to capture a larger share of the market. When all of a patient’s treatment costs are paid under a retrospective average cost-based program, not-for-profit hospitals invest only in the quality-enhancing technology. For-profit hospitals have no incentive to invest in either technology. As a result, most patients select not-for-profit hospitals and for-profit hospitals attract only those few patients who have extreme time preference. When hospitals are reimbursed prospectively, however, not-for-profit hospitals invest in both quality-improving and the cost-saving technologies, as do for-profit hospitals, although at lesser amounts. Quality and market shares are more equal under prospective payment, helping to explain the increasing market share of for-profit hospitals as prospective payment has become the norm.

Appendix: Demand, waiting time and investment in quality

As discussed in the text and shown in Fig. 1, quality is a concave function of investment in quality. The minimum quality required for licensing is q _min. Investment in quality increases the quality of output up to an investment level of t _1opt , after which further investment, because of crowding or other inefficiency, lowers quality – for investment beyond t _1opt the marginal product of the investment is negative. Hospitals will never invest more than t _1opt and the highest possible quality is q _max so the range of quality for each hospital is $\left[ {{q_{{\min }}},{q_{{\max }}}} \right]$. The difference in hospital quality is q _f  − q _n which has a range of $\left[ {{q_{{\min }}} - {q_{{max}}},{q_{{\max }}} - {q_{{\min }}}} \right]$ where the lower end is realized if the for-profit hospital chooses t _1f  = 0 and the not-for-profit hospital chooses t _1n  = t _1opt and the upper end is realized if the choices are opposite. We note that if both hospitals choose the same level of quality investment, whatever level is chosen, then the hospital quality difference is 0.

Patients choose which hospital to go to by relative quality and waiting time. Waiting time, T _k, at hospital k is a function of the number of patients choosing that hospital. For convenience, we assume waiting time is proportionate to the share of patients choosing each hospital. Individual consumers are attracted to a hospital if its differential quality is positive but repelled if its differential waiting time is positive. As is normal in congestion externalities, all patients ignore their own contribution to congestion, taking Q _k , hence T _k , as fixed, k = f, n.

Individual tolerances regarding waiting time are heterogeneous. The following characterization provides an example of how patients choose between relative quality and waiting time. Patient i chooses hospital y over hospital x if q _y  − q _x  > γ _i where ${\gamma_i} \in \left[ {0,{q_{{\max }}} - {q_{{\min }}} + \varepsilon } \right]$ measures her personal dislike for waiting time—it represents the heterogeneity of preferences about waiting time and relative quality—and ε is a small positive constant. Patients with γ _i  = 0 have a high tolerance for waiting time and will always choose a hospital with higher quality. Those with γ _i near its upper boundary have little tolerance for waiting time and, knowing a quality difference will attract patients to hospital y thus increasing the waiting time at that hospital, will go there only if the quality difference is very large. In fact, such is the disdain for waiting among some patients that they choose the lower quality hospital even if the quality difference is at its extreme value.

Given this behavior, the quality difference provides a metric of the share of patients using each hospital. At the lower end point where ${q_f} - {q_n} = {q_{{\min }}} - {q_{{\max }}}$ almost all patients choose the not-for-profit hospital and only those patients with an extreme dislike of waiting (where γ _i approaches its maximum value) use the for-profit hospital. At the other extreme where ${q_f} - {q_n} = {q_{{\max }}} - {q_{{\min }}}$ most patients choose the for-profit hospital. Only those few patients who truly disdain waiting will go to the not-for-profit hospital—these are the same patients who would choose the for-profit hospital when it had the much lower quality.