Integrating quality into the nonparametric analysis of efficiency: a simulation comparison of popular methods

Measuring efficiency in service-producing industries is challenging, because output quality may have to be considered in addition to output quantity. Previous studies have relied on different nonparametric methods to model the relationship between efficiency and quality; however, limited work has been done so far to compare and integrate these methods. Our literature search identified the following popular methods: a one-stage approach, a congestion analysis, and a two-stage approach. The first two methods treat quality as an additional output (or input) of the production process, whereas the two-stage approach first estimates efficiency without considering quality and then regresses the efficiency estimates on quality in the second stage. In this study, we compare the performance of these three conventional methods to a fairly novel method, the so-called conditional approach, that can also be used to incorporate quality into the analysis of efficiency. We simulate data using eight data generating processes that reflect potential relationships between efficiency and quality in empirical settings. Our simulation exercise illustrates the dominance of the conditional approach over the conventional methods in terms of both predicting the true efficiency scores and capturing the original relationship between efficiency and quality. The conditional approach represents a powerful and flexible tool that can be used when the theoretical link between efficiency and quality is unclear.