Price to Compete ... with Many: How to Identify Price Competition in High-Dimensional Space

We study price competition in markets with a large number (in the magnitude of hundreds or thousands) of potential competitors. We address two methodological challenges: simultaneity bias and high dimensionality. Simultaneity bias arises from joint determination of prices in competitive markets. We propose a new instrumental variable approach to address simultaneity bias in high dimensions. The novelty of the idea is to exploit online search and clickstream data to uncover customer preferences at a granular level, with sufficient variations both over time and across competitors in order to obtain valid instruments at a large scale. We then develop a methodology to identify relevant competitors in high dimensions combining the instrumental variable approach with high-dimensional l - 1 norm regularization. We apply this data-driven approach to study the patterns of hotel price competition in the New York City market. We also show that the competitive responses identified through our method can help hoteliers proactively manage their prices and promotions.