Raphael Thomadsen

Structural Applications of the Discrete Choice Model

A growing body of empirical literature uses structurally-derived economic models to study the nature of competition and to measure explicitly the economic impact of strategic policies. While several approaches have been proposed, the discrete choice demand system has experienced wide usage. The heterogeneous, or “mixed”, logit in particular has been widely applied due to its parsimonious structure and its ability to capture flexibly substitution patterns for a large number of differentiated products.We outline the derivation of the heterogeneous logit demand system. We then present a number of applications of such models to various data sources. Finally, we conclude with a discussion of directions for future research in this area.

Vertical Differentiation with Variety-Seeking Consumers

We analyze price and quality competition in a vertically differentiated duopoly in which consumers have a preference for variety. The preference for variety is a consequence of diminishing marginal utility for repeated experiences with the same product. We find consumer variety seeking can either soften or intensify price competition, depending on the difference in firm qualities and the strength of consumer preference for variety. When the qualities are similar or the consumer preference for variety is strong, prices and profits are higher than would be obtained in the absence of variety seeking. On the other hand, if qualities differ enough or the preference for variety is weak, stronger preferences for variety are associated with more intense price competition and lower profits. When firms set their qualities before competing on price and the range of feasible qualities is restricted such that variety seeking softens competition, competing firms choose to minimally differentiate themselves from each other. The preference for variety can drive the firms to offer multiunit discounts, and the greater price flexibility from these discounts does not necessarily reduce profits relative to simple unit pricing. This paper was accepted by J. Miguel Villas-Boas, marketing.

Profit-Increasing Consumer Exit

This paper examines the phenomenon of profit-increasing consumer exit and the related phenomenon of profit-decreasing consumer entry. We demonstrate that firms can be better off in shrinking markets and worse off in growing markets, even in the absence of competitive entry or exit. Specifically, firms may benefit if a segment of consumers who are relatively indifferent about consuming any product in the category leave the market. Profits can increase for all firms even if the exiting consumers have strong preferences for only one of the products in the market. In shrinking markets, it is reasonable to assume that the people who are likely to exit the market first are people who are “least committed” to the category. In particular, people who are the least satisfied with the existing offers are the most likely to change their behavior by finding an alternative or adopting a new technology. Similarly, in growing markets, consumers who enter the market late are generally the least committed to the category. Such exiting can relax the competitive pressure between firms and lead to increased profitability. Our findings provide an explanation for profit growth that has been observed in product industries exhibiting slow and predictable declines over time, including vacuum tubes, cigarettes, and soft drinks.

Behavior-Based Pricing in Vertically Differentiated Industries

We study behavior-based pricing BBP in a vertically differentiated model. Vertical differentiation is innately asymmetric because all customers prefer the higher-quality product when prices are equal. This asymmetry causes BBP to have different properties than symmetric horizontally differentiated models. We highlight two dimensions that affect the analysis: the role of quality-adjusted cost differences between the firms and the role of consumer discounting relative to firm discounting. In the second period, consistent with the prior literature, we find that there are conditions based on market shares and quality-adjusted costs under which either the low-quality firm or the high-quality firm-but not both-will reward its current customers with lower prices than it charges to new customers. We then consider whether these conditions can arise in a two-period equilibrium. We find that if consumers sufficiently discount the future periods, then firms at enough of a competitive disadvantage will reward their customers: i.e., the low-quality firm will reward its current customers if the quality-adjusted cost differential between the two firms is small, while the high-quality firm will reward its current customers if this cost differential is large. Conversely, we find that if consumers do not discount the future very much, then the firm at a competitive disadvantage i.e., a low-quality firm competing against a low-cost high-quality firm, or a high-quality firm that has very high costs can earn greater profits with BBP than without BBP, although there are cases where both firms may benefit from BBP. This paper was accepted by J. Miguel Villas-Boas, marketing.

How Point-of-Sale Marketing Mix Impacts National-Brand Purchase Shares

Purchase shares of major national brands in consumer packaged-goods industries vary substantially across stores, both between geographic markets and across stores within markets. We measure the relationship between the variation in national-brand purchase shares and five store-specific marketing mix factors: prices, assortment shares, features, displays, and promotion intensity. We do this by first demonstrating the extent to which purchase shares of the top two national brands across six different categories vary across markets, accounts (defined as chain–market interactions) and stores: market-level variation accounts for approximately 30% of the weekly purchase share variation across stores, whereas account-level and store-level variation explain an additional 13% and 5% of the variation, respectively. We then measure the extent to which assortment, pricing, feature, display, and promotion activities affect the purchase shares of the top national brands. We find that price and assortment share are the ...

Cooperation in Games with Forgetfulness

Companies and managers are apt to forget information, yet classic game theory analysis assumes that all players have perfect recall. This paper expands the literature by examining how introducing forgetfulness into a multiplayer game-theoretic framework can help or hinder cooperative behavior. We find that forgetfulness impacts the ability of firms to cooperate in countervailing directions. On one hand, forgetfulness can diminish the ability to punish deviators, making cooperation more difficult. On the other hand, under some conditions forgetfulness can make meting out severe punishments---even below-(stage) minimax punishments---credible and decrease the ability for players to effectively deviate, facilitating cooperation even in circumstances where cooperation cannot be sustained under perfect recall. We apply our model to a number of strategic games that commonly appear in the literature. This paper was accepted by Preyas Desai, marketing.

The Impact of Switching Stores on State Dependence in Brand Choice

This paper demonstrates that brand-level state dependence is affected by the store at which a consumer shops. The classic structural state dependence literature models inertia in brand choice by assuming that consumers experience an extra boost in utility from consuming the products they last purchased. We demonstrate that the level of inertia depends on the context in which the purchase was made, which suggests that a richer decision process is driving the state dependence. Specifically, we find that consumers exhibit more state dependence if they shop at the same store that they previously patronized as compared to if they switch to a different store. This result replicates across 14 diverse consumer packaged goods (CPG) supermarket categories, and on-average across categories, the level of state dependence when the customer switches stores is about two-thirds of the level of state dependence when the customer patronizes the same store. This difference in same vs. different store state dependence translates into an additional willingness-to-pay for a product equal to 8% of the product’s price. When consumers switch back to a store they previously visited, both the brand purchased on the last shopping occasion (at the different store) and the brand purchased the last time the consumer was at the store they are currently patronizing influence the consumer’s decisions, but the consumer is more influenced by the last purchase they made at the particular store they are currently patronizing. We conclude by discussing possible theories behind the results.

Foreword---Revisiting the Workshop on Quantitative Marketing and Structural Econometrics

This foreword and the subsequent four invited articles were commissioned by Eric T. Bradlow while Editor-in-Chief of Marketing Science. The foreword was written in four parts; each part covers a different aspect of the Workshop on Quantitative Marketing and Structural Econometrics. The workshop was cosponsored by Columbia Business School, Duke University, the University of California at Los Angeles, and the INFORMS Society for Marketing Science and was held at the Fuqua School of Business at Duke University in August 2010. The introductory section, written by Bradlow, covers why he commissioned these articles in the first place. In his section, Jean-Pierre Dube discusses “going from good to great” in the structural econometrics area as applied to marketing problems. A section jointly written by Brett R. Gordon and Raphael Thomadsen (both co-organizers of the workshop) discusses the workshop itself and some important thoughts for those people doing “structural econometrics in the trenches.” Finally, co-workshop organizer Richard Staelins section provides some perspective on both the workshop and structural econometrics as they relate to analytical models and empirical work for quantitative marketing researchers.

Optimal Minimum Wage in the Classic Labor Supply-and-Demand Paradigm

ABSTRACT This article demonstrates that minimum wage laws need not induce unemployment even under the classic labor supply-and-demand paradigm. As a result, minimum wage laws can be welfare-enhancing under the basic labor supply and demand model, suggesting the presence of an optimal minimum wage. We discuss conditions under which the optimal minimum wage level is the subsistence wage level. As a consequence, minimum wages should vary across states or countries with the local subsistence levels.

A Salesforce-Driven Model of Consumer Choice

We develop a salesforce-driven consumer choice model to study how performance-based commissions incentivize a salesperson’s service effort toward heterogeneous, substitutable products carried by the firm. We use a structural approach to back out the effort that is unobserved from data, and conduct counterfactual experiments that help provide important managerial insights. The model quantifies the impact of commissions on salespeople’s service effort toward differentiated products, and the impact of such effort on the demand and the substitution pattern between products. In our empirical application, we calculate the own- and cross-elasticities of demand with respect to the change in commissions. We further demonstrate how to use these results to compare the effectiveness of various performance-based incentive policies.