Profit Luenberger and Malmquist-Luenberger indexes for multi-activity decision-making units: The case of the star-rated hotel industry in China

Due to the vigorous economic development of the tourism industry in China, the number of star-rated hotels has rapidly increased. As a result, techniques to evaluate the performances of star-rated hotels have gained in popularity. In this paper, we develop two indexes for dynamic settings: the profit Luenberger and Malmquist-Luenberger indexes. The distinguishing features of our indexes are three-fold. One, we adopt an economic perspective by considering that hotels are profit maximizers. Two, we model hotels as multi-activity decision-making units by considering that they provide multiple services. Three, our indexes are nonparametric, and work when prices are partially observed. We apply our technique to 30 provinces during 2005-2015. We find that star-rated hotels present better performances over time, but not for every activity. Next, we highlight particular patterns for the provinces. These results are useful for managers to better target their investments, and also for policy makers.