Structural Estimation of Intertemporal Externalities with Application in ICU Admissions

Abstract

Problem definition: In many service systems, the system manager needs to balance between addressing the needs of current customers and ensuring the system’s ability to serve future customers. Such balancing behavior is particularly important in capacity-constrained systems with heterogeneous service levels, in which the manager needs to decide which level of service to provide to the current customer, taking into account the intertemporal externalities of their decisions.
Methodology/results: We develop a dynamic discrete choice model to describe the decision-making process in a gatekeeper system with multiple classes of servers and customers. The discount factor in the model captures how much the decision-maker internalizes the intertemporal externalities of their customer routing decisions. In contrast to most empirical studies in the literature which use a pre-specified discount factor, we establish joint identification of the discount factor and the utility parameters from data. We then apply the model to empirically study the Intensive Care Unit (ICU) admission decisions for Emergency Department (ED) patients. Using a large hospitalization data set, we find that there is large heterogeneity in the estimated discount factors across hospitals. Via counterfactual simulations, we show that correctly estimating the discount factor is crucial for hospitals to evaluate the ICU congestion levels and the impact of system changes.
Managerial implications: Our results suggest that it is important to understand how the decision-maker internalizes the intertemporal externalities from data. In addition, the balancing behavior regarding current customers and future available capacity provides a potential channel for improving system performance.

Keywords: structural estimation, dynamic discrete choice model, empirical operations management, healthcare, intensive care unit