Estimating technology characteristics of the U.S. hospital industry using directional distance functions with optimal directions

• Published in: Omega (Oxford) 2022-12, Vol.113, p.102716, Article 102716
• Main Authors: Vardanyan, Michael, Valdmanis, Vivian G., Leleu, Hervé, Ferrier, Gary D.
• Format: Article
• Language: English
• Subjects: Directional distance function; Hospitals; Nonlinear programming
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2022.102716

•Directional distance function with endogenously determined directions and shape restrictions is used to approximate hospital technology.•The nonlinear programming methodology is illustrated using data on eight different categories of U.S. hospitals.•Technology characteristics are compared across hospital categories to pinpoint differences among hospital groups.•Marginal rate of transformation between the inpatient and outpatient activities is relatively similar across different hospital categories.•Marginal rates of substitution between inputs and marginal productivities vary across hospital groups. The use of the directional distance function (DDF) in empirical studies has steadily increased over the past decade due to its general representation of a production technology. The DDF is particularly useful in health economics as a tool for modeling the hospital technology. Choosing the direction when modeling technology with the DDF is a crucial, albeit not fully resolved, issue that has important ramifications. We first address the choice of direction by using a recently proposed approach for endogenizing the DDF’s direction vector and then extend it by imposing regularity conditions on the technology. We apply this framework to a sample of U.S. hospitals and obtain their technology characteristics after grouping them into several distinct categories. We find that publicly owned non-teaching hospitals face substantial opportunity costs of inpatient care – hundreds of outpatient visits must be forgone for each additional admission. This information can help these hospitals forecast the adjustment in outpatient capacity needed to achieve a desired level of inpatient activity. We also find that while urban-area teaching hospitals can substitute approximately two nurses per bed at the frontier of technology, the rate of substitution is less than one nurse per bed at public non-teaching hospitals as well as at all rural-area hospitals. Information on the technological trade off between beds and nurses is helpful to hospital administrators and policy makers as nursing shortages intensify and staffing requirements continue to be debated. In addition, we demonstrate that rural public hospitals, which heavily rely on licensed practical nurses (LPNs) to staff their beds, are the only hospitals that can meaningfully substitute LPNs for the other inputs, replacing each bed and each registered nurse with medians of 17 and 23 LPNs, respectively.