Scalable Models Of Consumer Demand With Large Choice Sets

This dissertation consists of three essays related to the analysis of heterogeneity in consumer preferences based on individual level data on historical choices. In particular, they are connected by their application of modern Bayesian approaches to model consumers who differ both in their preferences for observed characteristics as well as their preferences for characteristics that are unobserved by the econometrician, but can instead be inferred from the correlations in choice behavior across different subsets of the population of consumers. The three chapters of this dissertation are also connected by their focus on scalability (both in computation and statistical efficiency) to large choice sets. Large choice sets are all around us, and the rise of E-commerce is leading to even larger sets of products that consumers can choose between. The average grocery store has tens of thousands of unique SKUs. The South Bay region around Stanford University has thousands of restaurants to choose between when you decide to go out for lunch. Large web retailers like Amazon sell hundreds of millions of distinct items. Individual level data on choices in situations like these present both opportunities and challenges. While these data sources are often large and rich in information, it is almost always the case that the number of choice occasions that we observe for any single individual is very small relative to the number of possible items they could have chosen between. Some types of products are easily described as a bundle of characteristics that consumers have preferences over, for example cars (horsepower, number of doors, leather seats) or digital cameras (resolution, zoom, flash), however for many other product categories it is more difficult to find a ''feature representation'' of products that accurately captures the heterogeneity in preferences across consumers. What are the characteristics that differ between Coke and Pepsi that lead to such strong disagreements over which is best. My work builds on recently developed approaches from machine learning for estimating models with large numbers of latent variables. This allows us to infer latent ''characteristics'' of products that are not directly observed by the econometrician, but can be inferred based on similarities in choice patterns across a large set of consumers. This allows us to model consumer preferences with heterogeneity in preferences for both observed and unobserved product characteristics. The first chapter of this dissertation is a paper written together with Susan Athey, David Blei, Francisco Ruiz, and Tobias Schmidt which analyzes consumer choices over lunchtime restaurants using data from a sample of several thousand anonymous mobile phone users in the San Francisco Bay Area. The data is used to identify users' approximate typical morning location, as well as their choices of lunchtime restaurants. We build a model where restaurants have latent characteristics (whose distribution may depend on restaurant observables, such as star ratings, food category, and price range), each user has preferences for these latent characteristics, and these preferences are heterogeneous across users. Similarly, each restaurant has latent characteristics that describe users' willingness to travel to the restaurant, and each user has individual-specific preferences for those latent characteristics. Thus, both users' willingness to travel and their base utility for each restaurant vary across user-restaurant pairs. We use a Bayesian approach to estimation. To make the estimation computationally feasible, we rely on variational inference to approximate the posterior distribution, as well as stochastic gradient descent as a computational approach. Our model performs better than more standard competing models such as multinomial logit and nested logit models, in part due to the personalization of the estimates. We analyze how consumers re-allocate their demand after a restaurant opens or closes and compare our predictions to the actual realized outcomes. Finally, we show how the model can be used to analyze counterfactual questions such as what type of restaurant would attract the most consumers in a given location. The second chapter is a paper written together with Susan Athey, David Blei, and Francisco Ruiz applies a similar approach in the context of supermarket scanner data. This paper demonstrates a method for estimating consumer preferences among discrete choices, where the consumer makes choices from many different categories. The consumer's utility is additive in the different categories, and her preferences about product attributes as well as her price sensitivity vary across products. Her preferences are correlated across products. We build on techniques from the machine learning literature on probabilistic models of matrix factorization, extending the methods to account for time-varying product attributes, a more realistic functional form for price sensitivity, and products going out of stock. We incorporate the information about the product hierarchy, so that consumers are assumed to select at most one alternative within a category. We evaluate the performance of the model using held-out data from weeks with price changes. We show that our model improves over traditional modeling approaches that consider each category in isolation, when we evaluate the ability of the model to predict responsiveness to price changes (using held-out data from a large number of price changes that occurred in our sample). We show that one source of the improvement is the ability of the model to accurately estimate heterogeneity in preferences (by pooling information across categories); another source of improvement is its ability to estimate the preferences of consumers who have rarely or never made a purchase in a given category in the training data. We consider counterfactuals such as personally targeted price discounts, showing that using a richer model such as the one we propose substantially increases the benefits of personalization in discounts. The third chapter of this dissertation proposes a novel estimator for learning heterogeneous consumer preferences based on both browsing and purchase data from online retailers with large product assortments. This work was done in collaboration with Ilya Morozov. Despite increasing availability data on the product pages consumers browse prior to making a purchase, the existing marketing literature provides little guidance on how retailers can use it to make better marketing decisions. In this paper, we propose an empirical framework that allows to efficiently extract information from consumers' search histories and use it to design personalized product recommendations. Our framework is based on the standard consideration set model from the marketing literature. To extract information from the unstructured search data, we augment the model with rich consumer heterogeneity and include several unobserved product characteristics. We then propose a way to estimate this model's parameters using a latent factorization approach from the computer science literature. The proposed framework can be seen as combining a structural approach to modeling consumer consideration from marketing with nonparametric estimation methods commonly used in the computer science. We are in discussion with a large online retailer to gain access to data and to run an AB test to experimentally validate the effects of improved rankings and recommendations of products.